From 7834ac894a844418681ab436ab64b1caca5cb0a1 Mon Sep 17 00:00:00 2001
From: tian jiax <446100073@qq.com>
Date: Wed, 3 Jan 2024 16:21:31 +0800
Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E5=8F=B6=E9=9D=A2=E7=A7=AF?=
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 =?UTF-8?q?=E8=83=BD?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
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---
 tool/LAI/LAIProcess.cp38-win_amd64.pyd        |   Bin 0 -> 101888 bytes
 tool/LAI/LAIProcess.pyx                       |   166 +
 tool/LAI/build/LAIProcess.c                   | 11637 ++++++++++++++++
 .../build/LAIProcess.cp38-win_amd64.exp       |   Bin 0 -> 763 bytes
 .../build/LAIProcess.cp38-win_amd64.lib       |   Bin 0 -> 2052 bytes
 .../Release/build/LAIProcess.obj              |   Bin 0 -> 600245 bytes
 tool/LAI/setup.py                             |    45 +
 .../transforml1a/build/SAR_geo/SAR_GEO.c      |  9744 +++++++++++++
 .../build/SAR_geo/SAR_GEO.cp38-win_amd64.exp  |   Bin 0 -> 769 bytes
 .../build/SAR_geo/SAR_GEO.cp38-win_amd64.lib  |   Bin 0 -> 2000 bytes
 .../Release/build/SAR_geo/SAR_GEO.obj         |   Bin 0 -> 484497 bytes
 tool/algorithm/xml/AnalysisXml.py             |   135 +
 12 files changed, 21727 insertions(+)
 create mode 100644 tool/LAI/LAIProcess.cp38-win_amd64.pyd
 create mode 100644 tool/LAI/LAIProcess.pyx
 create mode 100644 tool/LAI/build/LAIProcess.c
 create mode 100644 tool/LAI/build/temp.win-amd64-3.8/Release/build/LAIProcess.cp38-win_amd64.exp
 create mode 100644 tool/LAI/build/temp.win-amd64-3.8/Release/build/LAIProcess.cp38-win_amd64.lib
 create mode 100644 tool/LAI/build/temp.win-amd64-3.8/Release/build/LAIProcess.obj
 create mode 100644 tool/LAI/setup.py
 create mode 100644 tool/algorithm/transforml1a/build/SAR_geo/SAR_GEO.c
 create mode 100644 tool/algorithm/transforml1a/build/temp.win-amd64-3.8/Release/build/SAR_geo/SAR_GEO.cp38-win_amd64.exp
 create mode 100644 tool/algorithm/transforml1a/build/temp.win-amd64-3.8/Release/build/SAR_geo/SAR_GEO.cp38-win_amd64.lib
 create mode 100644 tool/algorithm/transforml1a/build/temp.win-amd64-3.8/Release/build/SAR_geo/SAR_GEO.obj
 create mode 100644 tool/algorithm/xml/AnalysisXml.py

diff --git a/tool/LAI/LAIProcess.cp38-win_amd64.pyd b/tool/LAI/LAIProcess.cp38-win_amd64.pyd
new file mode 100644
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diff --git a/tool/LAI/LAIProcess.pyx b/tool/LAI/LAIProcess.pyx
new file mode 100644
index 00000000..a445ffd1
--- /dev/null
+++ b/tool/LAI/LAIProcess.pyx
@@ -0,0 +1,166 @@
+#
+# 模型计算的库
+# 
+import cython
+cimport cython # 必须导入
+import numpy as np
+cimport numpy as np
+from libc.math cimport pi
+from scipy.optimize import leastsq
+import random
+import logging
+logger = logging.getLogger("mylog")
+
+
+def WMCModel(param_arr,sample_lai,sample_soil,sample_inc,sample_sigma):
+    """ WMC模型 增加 归一化植被指数
+
+    Args:
+        param_arr (np.ndarray): 参数数组
+        sample_lai (double): 叶面积指数
+        sample_soil (double): 土壤含水量
+        sample_inc (double): 入射角（弧度值）
+        sample_sigma (double): 后向散射系数（线性值）
+
+    Returns:
+        double: 方程值
+    """
+    # 映射参数，方便修改模型
+    A,B,C,D,M,N=param_arr  # 在这里修改模型
+    V_lai=sample_lai
+    #V_lai=E*sample_lai+F
+    exp_gamma=np.exp(-2*B*((V_lai*D+C))*(1/np.cos(sample_inc)))
+    sigma_soil=M*sample_soil+N
+    sigma_veg=A*((V_lai))*np.cos(sample_inc)
+    f_veg=1
+    result=sigma_veg*(1-exp_gamma)+sigma_soil*exp_gamma-sample_sigma
+    return result
+
+
+
+
+def train_WMCmodel(lai_water_inc_sigma_list,params_X0,train_err_image_path,draw_flag=True):
+    """ 训练模型参数
+
+    Args:
+        lai_waiter_inc_sigma_list (list): 训练模型使用的样本呢
+    """
+    def f(X):
+        eqs=[]
+        for lai_water_inc_sigma_item in lai_water_inc_sigma_list:
+            sample_lai=lai_water_inc_sigma_item[4]
+            sample_sigma=lai_water_inc_sigma_item[5] # 5: csv_sigma, 8:tiff_sigma
+            sample_soil=lai_water_inc_sigma_item[6]
+            sample_inc=lai_water_inc_sigma_item[7]
+            FVC=lai_water_inc_sigma_item[8]
+            eqs.append(WMCModel(X,sample_lai,sample_soil,sample_inc,sample_sigma))
+        return eqs
+    
+    X0 = params_X0 # 初始值
+    # logger.info(str(X0))
+    h = leastsq(f, X0)
+    # logger.info(h[0],h[1])
+    err_f=f(h[0])
+    x_arr=[lai_waiter_inc_sigma_item[4] for lai_waiter_inc_sigma_item in lai_water_inc_sigma_list]
+    # 根据误差大小进行排序
+    # logger.info("训练集：\n根据误差输出点序\n数量：{}\n点序\t误差值\t 样点信息".format(str(np.array(err_f).shape)))
+    # for i in np.argsort(np.array(err_f)):
+    #     logger.info('{}\t{}\t{}'.format(i,err_f[i],str(lai_water_inc_sigma_list[i])))
+    # logger.info("\n误差点序输出结束\n")
+
+    if draw_flag:
+        # logger.info(err_f)
+        # logger.info(np.where(np.abs(err_f)<10))
+        from matplotlib import pyplot as plt
+        plt.scatter(x_arr,err_f)
+        plt.title("equation-err")
+        plt.savefig(train_err_image_path,dpi=600)
+        plt.show()
+        
+    return h[0]
+
+def test_WMCModel(lai_waiter_inc_sigma_list,param_arr,lai_X0,test_err_image_path,draw_flag=True):
+    """ 测试模型训练结果
+
+    Args:
+        lai_waiter_inc_sigma_list (list): 测试使用的样本集
+        A (_type_): 参数A
+        B (_type_): 参数B
+        C (_type_): 参数C
+        D (_type_): 参数D
+        M (_type_): 参数M
+        N (_type_): 参数N
+        lai_X0 (_type_): 初始值
+
+    Returns:
+        list: 误差列表 [sample_lai,err,predict]
+    """
+    err=[]
+    err_f=[]
+    x_arr=[]
+    err_lai=[]
+    for lai_waiter_inc_sigma_item in lai_waiter_inc_sigma_list:
+        sample_time,sample_code,sample_lon,sample_lat,sample_lai,csv_sigma,sample_soil,sample_inc,sample_sigma=lai_waiter_inc_sigma_item
+        def f(X):
+            lai=X[0]
+            eqs=[WMCModel(param_arr,lai,sample_soil,sample_inc,csv_sigma)]
+            return eqs
+        X0=lai_X0
+        h = leastsq(f, X0)
+        temp_err=h[0]-sample_lai
+        err_lai.append(temp_err[0]) # lai预测的插值
+        err.append([sample_lai,temp_err[0],h[0][0],sample_code])
+        err_f.append(f(h[0])[0]) # 方程差
+        x_arr.append(sample_lai)
+    
+    # 根据误差大小进行排序
+    # logger.info("测试集：\n根据误差输出点序\n数量：{}\n点序\t误差值\t 方程差\t样点信息".format(str(np.array(err_lai).shape)))
+    # for i in np.argsort(np.array(err_lai)):
+    #     logger.info('{}\t{}\t{}\t{}'.format(i,err_lai[i],err_f[i],str(lai_waiter_inc_sigma_list[i])))
+    # logger.info("\n误差点序输出结束\n")
+
+    if draw_flag:
+        from matplotlib import pyplot as plt
+        plt.scatter(x_arr,err_lai)
+        plt.title("equation-err")
+        plt.savefig(test_err_image_path,dpi=600)
+        plt.show() 
+    return err
+
+def processs_WMCModel(param_arr,lai_X0,sigma,inc_angle,soil_water):
+    
+    if(sigma<0 ):
+        return np.nan
+    def f(X):
+        lai=X[0]
+        eqs=[WMCModel(param_arr,lai,soil_water,inc_angle,sigma )]
+        return eqs
+    h = leastsq(f, [lai_X0])
+
+    return h[0][0]
+
+# Cython 的扩展地址
+cpdef np.ndarray[double,ndim=2] process_tiff(np.ndarray[double,ndim=2] sigma_tiff,
+                                             np.ndarray[double,ndim=2] inc_tiff,
+                                             np.ndarray[double,ndim=2] soil_water_tiff,
+                                             np.ndarray[double,ndim=1] param_arr,
+                                             double lai_X0):
+    
+    cdef np.ndarray[double,ndim=2] result=sigma_tiff
+    cdef int param_arr_length=param_arr.shape[0]
+    cdef int height=sigma_tiff.shape[0]
+    cdef int width=sigma_tiff.shape[1]
+    cdef int i=0
+    cdef int j=0
+    cdef double temp=0
+
+    while i<height:
+        j=0
+        while j<width:
+            temp = processs_WMCModel(param_arr,lai_X0,sigma_tiff[i,j],inc_tiff[i,j],soil_water_tiff[i,j])
+            temp=temp if temp<10 and temp>=0 else np.nan
+            result[i,j]=temp
+            j=j+1
+        i=i+1
+    return result
+    
\ No newline at end of file
diff --git a/tool/LAI/build/LAIProcess.c b/tool/LAI/build/LAIProcess.c
new file mode 100644
index 00000000..eb1f1439
--- /dev/null
+++ b/tool/LAI/build/LAIProcess.c
@@ -0,0 +1,11637 @@
+/* Generated by Cython 0.29.24 */
+
+/* BEGIN: Cython Metadata
+{
+    "distutils": {
+        "depends": [],
+        "name": "LAIProcess",
+        "sources": [
+            "./LAIProcess.pyx"
+        ]
+    },
+    "module_name": "LAIProcess"
+}
+END: Cython Metadata */
+
+#ifndef PY_SSIZE_T_CLEAN
+#define PY_SSIZE_T_CLEAN
+#endif /* PY_SSIZE_T_CLEAN */
+#include "Python.h"
+#ifndef Py_PYTHON_H
+    #error Python headers needed to compile C extensions, please install development version of Python.
+#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000)
+    #error Cython requires Python 2.6+ or Python 3.3+.
+#else
+#define CYTHON_ABI "0_29_24"
+#define CYTHON_HEX_VERSION 0x001D18F0
+#define CYTHON_FUTURE_DIVISION 0
+#include <stddef.h>
+#ifndef offsetof
+  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
+#endif
+#if !defined(WIN32) && !defined(MS_WINDOWS)
+  #ifndef __stdcall
+    #define __stdcall
+  #endif
+  #ifndef __cdecl
+    #define __cdecl
+  #endif
+  #ifndef __fastcall
+    #define __fastcall
+  #endif
+#endif
+#ifndef DL_IMPORT
+  #define DL_IMPORT(t) t
+#endif
+#ifndef DL_EXPORT
+  #define DL_EXPORT(t) t
+#endif
+#define __PYX_COMMA ,
+#ifndef HAVE_LONG_LONG
+  #if PY_VERSION_HEX >= 0x02070000
+    #define HAVE_LONG_LONG
+  #endif
+#endif
+#ifndef PY_LONG_LONG
+  #define PY_LONG_LONG LONG_LONG
+#endif
+#ifndef Py_HUGE_VAL
+  #define Py_HUGE_VAL HUGE_VAL
+#endif
+#ifdef PYPY_VERSION
+  #define CYTHON_COMPILING_IN_PYPY 1
+  #define CYTHON_COMPILING_IN_PYSTON 0
+  #define CYTHON_COMPILING_IN_CPYTHON 0
+  #undef CYTHON_USE_TYPE_SLOTS
+  #define CYTHON_USE_TYPE_SLOTS 0
+  #undef CYTHON_USE_PYTYPE_LOOKUP
+  #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #if PY_VERSION_HEX < 0x03050000
+    #undef CYTHON_USE_ASYNC_SLOTS
+    #define CYTHON_USE_ASYNC_SLOTS 0
+  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
+    #define CYTHON_USE_ASYNC_SLOTS 1
+  #endif
+  #undef CYTHON_USE_PYLIST_INTERNALS
+  #define CYTHON_USE_PYLIST_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_INTERNALS
+  #define CYTHON_USE_UNICODE_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_WRITER
+  #define CYTHON_USE_UNICODE_WRITER 0
+  #undef CYTHON_USE_PYLONG_INTERNALS
+  #define CYTHON_USE_PYLONG_INTERNALS 0
+  #undef CYTHON_AVOID_BORROWED_REFS
+  #define CYTHON_AVOID_BORROWED_REFS 1
+  #undef CYTHON_ASSUME_SAFE_MACROS
+  #define CYTHON_ASSUME_SAFE_MACROS 0
+  #undef CYTHON_UNPACK_METHODS
+  #define CYTHON_UNPACK_METHODS 0
+  #undef CYTHON_FAST_THREAD_STATE
+  #define CYTHON_FAST_THREAD_STATE 0
+  #undef CYTHON_FAST_PYCALL
+  #define CYTHON_FAST_PYCALL 0
+  #undef CYTHON_PEP489_MULTI_PHASE_INIT
+  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
+  #undef CYTHON_USE_TP_FINALIZE
+  #define CYTHON_USE_TP_FINALIZE 0
+  #undef CYTHON_USE_DICT_VERSIONS
+  #define CYTHON_USE_DICT_VERSIONS 0
+  #undef CYTHON_USE_EXC_INFO_STACK
+  #define CYTHON_USE_EXC_INFO_STACK 0
+#elif defined(PYSTON_VERSION)
+  #define CYTHON_COMPILING_IN_PYPY 0
+  #define CYTHON_COMPILING_IN_PYSTON 1
+  #define CYTHON_COMPILING_IN_CPYTHON 0
+  #ifndef CYTHON_USE_TYPE_SLOTS
+    #define CYTHON_USE_TYPE_SLOTS 1
+  #endif
+  #undef CYTHON_USE_PYTYPE_LOOKUP
+  #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #undef CYTHON_USE_ASYNC_SLOTS
+  #define CYTHON_USE_ASYNC_SLOTS 0
+  #undef CYTHON_USE_PYLIST_INTERNALS
+  #define CYTHON_USE_PYLIST_INTERNALS 0
+  #ifndef CYTHON_USE_UNICODE_INTERNALS
+    #define CYTHON_USE_UNICODE_INTERNALS 1
+  #endif
+  #undef CYTHON_USE_UNICODE_WRITER
+  #define CYTHON_USE_UNICODE_WRITER 0
+  #undef CYTHON_USE_PYLONG_INTERNALS
+  #define CYTHON_USE_PYLONG_INTERNALS 0
+  #ifndef CYTHON_AVOID_BORROWED_REFS
+    #define CYTHON_AVOID_BORROWED_REFS 0
+  #endif
+  #ifndef CYTHON_ASSUME_SAFE_MACROS
+    #define CYTHON_ASSUME_SAFE_MACROS 1
+  #endif
+  #ifndef CYTHON_UNPACK_METHODS
+    #define CYTHON_UNPACK_METHODS 1
+  #endif
+  #undef CYTHON_FAST_THREAD_STATE
+  #define CYTHON_FAST_THREAD_STATE 0
+  #undef CYTHON_FAST_PYCALL
+  #define CYTHON_FAST_PYCALL 0
+  #undef CYTHON_PEP489_MULTI_PHASE_INIT
+  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
+  #undef CYTHON_USE_TP_FINALIZE
+  #define CYTHON_USE_TP_FINALIZE 0
+  #undef CYTHON_USE_DICT_VERSIONS
+  #define CYTHON_USE_DICT_VERSIONS 0
+  #undef CYTHON_USE_EXC_INFO_STACK
+  #define CYTHON_USE_EXC_INFO_STACK 0
+#else
+  #define CYTHON_COMPILING_IN_PYPY 0
+  #define CYTHON_COMPILING_IN_PYSTON 0
+  #define CYTHON_COMPILING_IN_CPYTHON 1
+  #ifndef CYTHON_USE_TYPE_SLOTS
+    #define CYTHON_USE_TYPE_SLOTS 1
+  #endif
+  #if PY_VERSION_HEX < 0x02070000
+    #undef CYTHON_USE_PYTYPE_LOOKUP
+    #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #elif !defined(CYTHON_USE_PYTYPE_LOOKUP)
+    #define CYTHON_USE_PYTYPE_LOOKUP 1
+  #endif
+  #if PY_MAJOR_VERSION < 3
+    #undef CYTHON_USE_ASYNC_SLOTS
+    #define CYTHON_USE_ASYNC_SLOTS 0
+  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
+    #define CYTHON_USE_ASYNC_SLOTS 1
+  #endif
+  #if PY_VERSION_HEX < 0x02070000
+    #undef CYTHON_USE_PYLONG_INTERNALS
+    #define CYTHON_USE_PYLONG_INTERNALS 0
+  #elif !defined(CYTHON_USE_PYLONG_INTERNALS)
+    #define CYTHON_USE_PYLONG_INTERNALS 1
+  #endif
+  #ifndef CYTHON_USE_PYLIST_INTERNALS
+    #define CYTHON_USE_PYLIST_INTERNALS 1
+  #endif
+  #ifndef CYTHON_USE_UNICODE_INTERNALS
+    #define CYTHON_USE_UNICODE_INTERNALS 1
+  #endif
+  #if PY_VERSION_HEX < 0x030300F0
+    #undef CYTHON_USE_UNICODE_WRITER
+    #define CYTHON_USE_UNICODE_WRITER 0
+  #elif !defined(CYTHON_USE_UNICODE_WRITER)
+    #define CYTHON_USE_UNICODE_WRITER 1
+  #endif
+  #ifndef CYTHON_AVOID_BORROWED_REFS
+    #define CYTHON_AVOID_BORROWED_REFS 0
+  #endif
+  #ifndef CYTHON_ASSUME_SAFE_MACROS
+    #define CYTHON_ASSUME_SAFE_MACROS 1
+  #endif
+  #ifndef CYTHON_UNPACK_METHODS
+    #define CYTHON_UNPACK_METHODS 1
+  #endif
+  #ifndef CYTHON_FAST_THREAD_STATE
+    #define CYTHON_FAST_THREAD_STATE 1
+  #endif
+  #ifndef CYTHON_FAST_PYCALL
+    #define CYTHON_FAST_PYCALL 1
+  #endif
+  #ifndef CYTHON_PEP489_MULTI_PHASE_INIT
+    #define CYTHON_PEP489_MULTI_PHASE_INIT (PY_VERSION_HEX >= 0x03050000)
+  #endif
+  #ifndef CYTHON_USE_TP_FINALIZE
+    #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1)
+  #endif
+  #ifndef CYTHON_USE_DICT_VERSIONS
+    #define CYTHON_USE_DICT_VERSIONS (PY_VERSION_HEX >= 0x030600B1)
+  #endif
+  #ifndef CYTHON_USE_EXC_INFO_STACK
+    #define CYTHON_USE_EXC_INFO_STACK (PY_VERSION_HEX >= 0x030700A3)
+  #endif
+#endif
+#if !defined(CYTHON_FAST_PYCCALL)
+#define CYTHON_FAST_PYCCALL  (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1)
+#endif
+#if CYTHON_USE_PYLONG_INTERNALS
+  #include "longintrepr.h"
+  #undef SHIFT
+  #undef BASE
+  #undef MASK
+  #ifdef SIZEOF_VOID_P
+    enum { __pyx_check_sizeof_voidp = 1 / (int)(SIZEOF_VOID_P == sizeof(void*)) };
+  #endif
+#endif
+#ifndef __has_attribute
+  #define __has_attribute(x) 0
+#endif
+#ifndef __has_cpp_attribute
+  #define __has_cpp_attribute(x) 0
+#endif
+#ifndef CYTHON_RESTRICT
+  #if defined(__GNUC__)
+    #define CYTHON_RESTRICT __restrict__
+  #elif defined(_MSC_VER) && _MSC_VER >= 1400
+    #define CYTHON_RESTRICT __restrict
+  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define CYTHON_RESTRICT restrict
+  #else
+    #define CYTHON_RESTRICT
+  #endif
+#endif
+#ifndef CYTHON_UNUSED
+# if defined(__GNUC__)
+#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
+#     define CYTHON_UNUSED __attribute__ ((__unused__))
+#   else
+#     define CYTHON_UNUSED
+#   endif
+# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
+#   define CYTHON_UNUSED __attribute__ ((__unused__))
+# else
+#   define CYTHON_UNUSED
+# endif
+#endif
+#ifndef CYTHON_MAYBE_UNUSED_VAR
+#  if defined(__cplusplus)
+     template<class T> void CYTHON_MAYBE_UNUSED_VAR( const T& ) { }
+#  else
+#    define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x)
+#  endif
+#endif
+#ifndef CYTHON_NCP_UNUSED
+# if CYTHON_COMPILING_IN_CPYTHON
+#  define CYTHON_NCP_UNUSED
+# else
+#  define CYTHON_NCP_UNUSED CYTHON_UNUSED
+# endif
+#endif
+#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
+#ifdef _MSC_VER
+    #ifndef _MSC_STDINT_H_
+        #if _MSC_VER < 1300
+           typedef unsigned char     uint8_t;
+           typedef unsigned int      uint32_t;
+        #else
+           typedef unsigned __int8   uint8_t;
+           typedef unsigned __int32  uint32_t;
+        #endif
+    #endif
+#else
+   #include <stdint.h>
+#endif
+#ifndef CYTHON_FALLTHROUGH
+  #if defined(__cplusplus) && __cplusplus >= 201103L
+    #if __has_cpp_attribute(fallthrough)
+      #define CYTHON_FALLTHROUGH [[fallthrough]]
+    #elif __has_cpp_attribute(clang::fallthrough)
+      #define CYTHON_FALLTHROUGH [[clang::fallthrough]]
+    #elif __has_cpp_attribute(gnu::fallthrough)
+      #define CYTHON_FALLTHROUGH [[gnu::fallthrough]]
+    #endif
+  #endif
+  #ifndef CYTHON_FALLTHROUGH
+    #if __has_attribute(fallthrough)
+      #define CYTHON_FALLTHROUGH __attribute__((fallthrough))
+    #else
+      #define CYTHON_FALLTHROUGH
+    #endif
+  #endif
+  #if defined(__clang__ ) && defined(__apple_build_version__)
+    #if __apple_build_version__ < 7000000
+      #undef  CYTHON_FALLTHROUGH
+      #define CYTHON_FALLTHROUGH
+    #endif
+  #endif
+#endif
+
+#ifndef CYTHON_INLINE
+  #if defined(__clang__)
+    #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))
+  #elif defined(__GNUC__)
+    #define CYTHON_INLINE __inline__
+  #elif defined(_MSC_VER)
+    #define CYTHON_INLINE __inline
+  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define CYTHON_INLINE inline
+  #else
+    #define CYTHON_INLINE
+  #endif
+#endif
+
+#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)
+  #define Py_OptimizeFlag 0
+#endif
+#define __PYX_BUILD_PY_SSIZE_T "n"
+#define CYTHON_FORMAT_SSIZE_T "z"
+#if PY_MAJOR_VERSION < 3
+  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
+  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+  #define __Pyx_DefaultClassType PyClass_Type
+#else
+  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
+#if PY_VERSION_HEX >= 0x030800A4 && PY_VERSION_HEX < 0x030800B2
+  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_New(a, 0, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+#else
+  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+#endif
+  #define __Pyx_DefaultClassType PyType_Type
+#endif
+#ifndef Py_TPFLAGS_CHECKTYPES
+  #define Py_TPFLAGS_CHECKTYPES 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_INDEX
+  #define Py_TPFLAGS_HAVE_INDEX 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_NEWBUFFER
+  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_FINALIZE
+  #define Py_TPFLAGS_HAVE_FINALIZE 0
+#endif
+#ifndef METH_STACKLESS
+  #define METH_STACKLESS 0
+#endif
+#if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL)
+  #ifndef METH_FASTCALL
+     #define METH_FASTCALL 0x80
+  #endif
+  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs);
+  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
+                                                          Py_ssize_t nargs, PyObject *kwnames);
+#else
+  #define __Pyx_PyCFunctionFast _PyCFunctionFast
+  #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
+#endif
+#if CYTHON_FAST_PYCCALL
+#define __Pyx_PyFastCFunction_Check(func)\
+    ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)))))
+#else
+#define __Pyx_PyFastCFunction_Check(func) 0
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
+  #define PyObject_Malloc(s)   PyMem_Malloc(s)
+  #define PyObject_Free(p)     PyMem_Free(p)
+  #define PyObject_Realloc(p)  PyMem_Realloc(p)
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030400A1
+  #define PyMem_RawMalloc(n)           PyMem_Malloc(n)
+  #define PyMem_RawRealloc(p, n)       PyMem_Realloc(p, n)
+  #define PyMem_RawFree(p)             PyMem_Free(p)
+#endif
+#if CYTHON_COMPILING_IN_PYSTON
+  #define __Pyx_PyCode_HasFreeVars(co)  PyCode_HasFreeVars(co)
+  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno)
+#else
+  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
+  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)  (frame)->f_lineno = (lineno)
+#endif
+#if !CYTHON_FAST_THREAD_STATE || PY_VERSION_HEX < 0x02070000
+  #define __Pyx_PyThreadState_Current PyThreadState_GET()
+#elif PY_VERSION_HEX >= 0x03060000
+  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
+#elif PY_VERSION_HEX >= 0x03000000
+  #define __Pyx_PyThreadState_Current PyThreadState_GET()
+#else
+  #define __Pyx_PyThreadState_Current _PyThreadState_Current
+#endif
+#if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT)
+#include "pythread.h"
+#define Py_tss_NEEDS_INIT 0
+typedef int Py_tss_t;
+static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) {
+  *key = PyThread_create_key();
+  return 0;
+}
+static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) {
+  Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t));
+  *key = Py_tss_NEEDS_INIT;
+  return key;
+}
+static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) {
+  PyObject_Free(key);
+}
+static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) {
+  return *key != Py_tss_NEEDS_INIT;
+}
+static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) {
+  PyThread_delete_key(*key);
+  *key = Py_tss_NEEDS_INIT;
+}
+static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) {
+  return PyThread_set_key_value(*key, value);
+}
+static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) {
+  return PyThread_get_key_value(*key);
+}
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized)
+#define __Pyx_PyDict_NewPresized(n)  ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
+#else
+#define __Pyx_PyDict_NewPresized(n)  PyDict_New()
+#endif
+#if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION
+  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
+  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
+#else
+  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
+  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && CYTHON_USE_UNICODE_INTERNALS
+#define __Pyx_PyDict_GetItemStr(dict, name)  _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
+#else
+#define __Pyx_PyDict_GetItemStr(dict, name)  PyDict_GetItem(dict, name)
+#endif
+#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
+  #define CYTHON_PEP393_ENABLED 1
+  #if defined(PyUnicode_IS_READY)
+  #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\
+                                              0 : _PyUnicode_Ready((PyObject *)(op)))
+  #else
+  #define __Pyx_PyUnicode_READY(op)       (0)
+  #endif
+  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_LENGTH(u)
+  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
+  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   PyUnicode_MAX_CHAR_VALUE(u)
+  #define __Pyx_PyUnicode_KIND(u)         PyUnicode_KIND(u)
+  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)
+  #define __Pyx_PyUnicode_READ(k, d, i)   PyUnicode_READ(k, d, i)
+  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  PyUnicode_WRITE(k, d, i, ch)
+  #if defined(PyUnicode_IS_READY) && defined(PyUnicode_GET_SIZE)
+  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03090000
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : ((PyCompactUnicodeObject *)(u))->wstr_length))
+  #else
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
+  #endif
+  #else
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_LENGTH(u))
+  #endif
+#else
+  #define CYTHON_PEP393_ENABLED 0
+  #define PyUnicode_1BYTE_KIND  1
+  #define PyUnicode_2BYTE_KIND  2
+  #define PyUnicode_4BYTE_KIND  4
+  #define __Pyx_PyUnicode_READY(op)       (0)
+  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_SIZE(u)
+  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
+  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111)
+  #define __Pyx_PyUnicode_KIND(u)         (sizeof(Py_UNICODE))
+  #define __Pyx_PyUnicode_DATA(u)         ((void*)PyUnicode_AS_UNICODE(u))
+  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
+  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  (((void)(k)), ((Py_UNICODE*)d)[i] = ch)
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_SIZE(u))
+#endif
+#if CYTHON_COMPILING_IN_PYPY
+  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
+  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
+#else
+  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
+  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
+      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
+  #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check)
+  #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
+  #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
+#endif
+#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None || (PyString_Check(b) && !PyString_CheckExact(b)))) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
+#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
+#else
+  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
+#endif
+#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
+  #define PyObject_ASCII(o)            PyObject_Repr(o)
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyBaseString_Type            PyUnicode_Type
+  #define PyStringObject               PyUnicodeObject
+  #define PyString_Type                PyUnicode_Type
+  #define PyString_Check               PyUnicode_Check
+  #define PyString_CheckExact          PyUnicode_CheckExact
+#ifndef PyObject_Unicode
+  #define PyObject_Unicode             PyObject_Str
+#endif
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
+  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
+#else
+  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
+  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
+#endif
+#ifndef PySet_CheckExact
+  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)
+#endif
+#if PY_VERSION_HEX >= 0x030900A4
+  #define __Pyx_SET_REFCNT(obj, refcnt) Py_SET_REFCNT(obj, refcnt)
+  #define __Pyx_SET_SIZE(obj, size) Py_SET_SIZE(obj, size)
+#else
+  #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt)
+  #define __Pyx_SET_SIZE(obj, size) Py_SIZE(obj) = (size)
+#endif
+#if CYTHON_ASSUME_SAFE_MACROS
+  #define __Pyx_PySequence_SIZE(seq)  Py_SIZE(seq)
+#else
+  #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyIntObject                  PyLongObject
+  #define PyInt_Type                   PyLong_Type
+  #define PyInt_Check(op)              PyLong_Check(op)
+  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
+  #define PyInt_FromString             PyLong_FromString
+  #define PyInt_FromUnicode            PyLong_FromUnicode
+  #define PyInt_FromLong               PyLong_FromLong
+  #define PyInt_FromSize_t             PyLong_FromSize_t
+  #define PyInt_FromSsize_t            PyLong_FromSsize_t
+  #define PyInt_AsLong                 PyLong_AsLong
+  #define PyInt_AS_LONG                PyLong_AS_LONG
+  #define PyInt_AsSsize_t              PyLong_AsSsize_t
+  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
+  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
+  #define PyNumber_Int                 PyNumber_Long
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyBoolObject                 PyLongObject
+#endif
+#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
+  #ifndef PyUnicode_InternFromString
+    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
+  #endif
+#endif
+#if PY_VERSION_HEX < 0x030200A4
+  typedef long Py_hash_t;
+  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
+  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
+#else
+  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
+  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? ((void)(klass), PyMethod_New(func, self)) : __Pyx_NewRef(func))
+#else
+  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
+#endif
+#if CYTHON_USE_ASYNC_SLOTS
+  #if PY_VERSION_HEX >= 0x030500B1
+    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
+    #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
+  #else
+    #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
+  #endif
+#else
+  #define __Pyx_PyType_AsAsync(obj) NULL
+#endif
+#ifndef __Pyx_PyAsyncMethodsStruct
+    typedef struct {
+        unaryfunc am_await;
+        unaryfunc am_aiter;
+        unaryfunc am_anext;
+    } __Pyx_PyAsyncMethodsStruct;
+#endif
+
+#if defined(WIN32) || defined(MS_WINDOWS)
+  #define _USE_MATH_DEFINES
+#endif
+#include <math.h>
+#ifdef NAN
+#define __PYX_NAN() ((float) NAN)
+#else
+static CYTHON_INLINE float __PYX_NAN() {
+  float value;
+  memset(&value, 0xFF, sizeof(value));
+  return value;
+}
+#endif
+#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
+#define __Pyx_truncl trunc
+#else
+#define __Pyx_truncl truncl
+#endif
+
+#define __PYX_MARK_ERR_POS(f_index, lineno) \
+    { __pyx_filename = __pyx_f[f_index]; (void)__pyx_filename; __pyx_lineno = lineno; (void)__pyx_lineno; __pyx_clineno = __LINE__; (void)__pyx_clineno; }
+#define __PYX_ERR(f_index, lineno, Ln_error) \
+    { __PYX_MARK_ERR_POS(f_index, lineno) goto Ln_error; }
+
+#ifndef __PYX_EXTERN_C
+  #ifdef __cplusplus
+    #define __PYX_EXTERN_C extern "C"
+  #else
+    #define __PYX_EXTERN_C extern
+  #endif
+#endif
+
+#define __PYX_HAVE__LAIProcess
+#define __PYX_HAVE_API__LAIProcess
+/* Early includes */
+#include <string.h>
+#include <stdio.h>
+#include "numpy/arrayobject.h"
+#include "numpy/ndarrayobject.h"
+#include "numpy/ndarraytypes.h"
+#include "numpy/arrayscalars.h"
+#include "numpy/ufuncobject.h"
+
+    /* NumPy API declarations from "numpy/__init__.pxd" */
+    
+#include <math.h>
+#ifdef _OPENMP
+#include <omp.h>
+#endif /* _OPENMP */
+
+#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
+#define CYTHON_WITHOUT_ASSERTIONS
+#endif
+
+typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
+                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
+
+#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
+#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
+#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)
+#define __PYX_DEFAULT_STRING_ENCODING ""
+#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
+#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
+#define __Pyx_uchar_cast(c) ((unsigned char)c)
+#define __Pyx_long_cast(x) ((long)x)
+#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
+    (sizeof(type) < sizeof(Py_ssize_t))  ||\
+    (sizeof(type) > sizeof(Py_ssize_t) &&\
+          likely(v < (type)PY_SSIZE_T_MAX ||\
+                 v == (type)PY_SSIZE_T_MAX)  &&\
+          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
+                                v == (type)PY_SSIZE_T_MIN)))  ||\
+    (sizeof(type) == sizeof(Py_ssize_t) &&\
+          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
+                               v == (type)PY_SSIZE_T_MAX)))  )
+static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
+    return (size_t) i < (size_t) limit;
+}
+#if defined (__cplusplus) && __cplusplus >= 201103L
+    #include <cstdlib>
+    #define __Pyx_sst_abs(value) std::abs(value)
+#elif SIZEOF_INT >= SIZEOF_SIZE_T
+    #define __Pyx_sst_abs(value) abs(value)
+#elif SIZEOF_LONG >= SIZEOF_SIZE_T
+    #define __Pyx_sst_abs(value) labs(value)
+#elif defined (_MSC_VER)
+    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
+#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define __Pyx_sst_abs(value) llabs(value)
+#elif defined (__GNUC__)
+    #define __Pyx_sst_abs(value) __builtin_llabs(value)
+#else
+    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
+#endif
+static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
+static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
+#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
+#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
+#define __Pyx_PyBytes_FromString        PyBytes_FromString
+#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
+static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
+#if PY_MAJOR_VERSION < 3
+    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
+    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
+#else
+    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
+    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
+#endif
+#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyObject_AsWritableString(s)    ((char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
+#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
+#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
+#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
+#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
+static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
+    const Py_UNICODE *u_end = u;
+    while (*u_end++) ;
+    return (size_t)(u_end - u - 1);
+}
+#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
+#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
+#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
+#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
+#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
+static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
+static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
+#define __Pyx_PySequence_Tuple(obj)\
+    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
+#if CYTHON_ASSUME_SAFE_MACROS
+#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
+#else
+#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
+#endif
+#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
+#if PY_MAJOR_VERSION >= 3
+#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
+#else
+#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
+#endif
+#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
+#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+static int __Pyx_sys_getdefaultencoding_not_ascii;
+static int __Pyx_init_sys_getdefaultencoding_params(void) {
+    PyObject* sys;
+    PyObject* default_encoding = NULL;
+    PyObject* ascii_chars_u = NULL;
+    PyObject* ascii_chars_b = NULL;
+    const char* default_encoding_c;
+    sys = PyImport_ImportModule("sys");
+    if (!sys) goto bad;
+    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
+    Py_DECREF(sys);
+    if (!default_encoding) goto bad;
+    default_encoding_c = PyBytes_AsString(default_encoding);
+    if (!default_encoding_c) goto bad;
+    if (strcmp(default_encoding_c, "ascii") == 0) {
+        __Pyx_sys_getdefaultencoding_not_ascii = 0;
+    } else {
+        char ascii_chars[128];
+        int c;
+        for (c = 0; c < 128; c++) {
+            ascii_chars[c] = c;
+        }
+        __Pyx_sys_getdefaultencoding_not_ascii = 1;
+        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
+        if (!ascii_chars_u) goto bad;
+        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
+        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
+            PyErr_Format(
+                PyExc_ValueError,
+                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
+                default_encoding_c);
+            goto bad;
+        }
+        Py_DECREF(ascii_chars_u);
+        Py_DECREF(ascii_chars_b);
+    }
+    Py_DECREF(default_encoding);
+    return 0;
+bad:
+    Py_XDECREF(default_encoding);
+    Py_XDECREF(ascii_chars_u);
+    Py_XDECREF(ascii_chars_b);
+    return -1;
+}
+#endif
+#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
+#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
+#else
+#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
+#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+static char* __PYX_DEFAULT_STRING_ENCODING;
+static int __Pyx_init_sys_getdefaultencoding_params(void) {
+    PyObject* sys;
+    PyObject* default_encoding = NULL;
+    char* default_encoding_c;
+    sys = PyImport_ImportModule("sys");
+    if (!sys) goto bad;
+    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
+    Py_DECREF(sys);
+    if (!default_encoding) goto bad;
+    default_encoding_c = PyBytes_AsString(default_encoding);
+    if (!default_encoding_c) goto bad;
+    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);
+    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
+    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
+    Py_DECREF(default_encoding);
+    return 0;
+bad:
+    Py_XDECREF(default_encoding);
+    return -1;
+}
+#endif
+#endif
+
+
+/* Test for GCC > 2.95 */
+#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
+  #define likely(x)   __builtin_expect(!!(x), 1)
+  #define unlikely(x) __builtin_expect(!!(x), 0)
+#else /* !__GNUC__ or GCC < 2.95 */
+  #define likely(x)   (x)
+  #define unlikely(x) (x)
+#endif /* __GNUC__ */
+static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
+
+static PyObject *__pyx_m = NULL;
+static PyObject *__pyx_d;
+static PyObject *__pyx_b;
+static PyObject *__pyx_cython_runtime = NULL;
+static PyObject *__pyx_empty_tuple;
+static PyObject *__pyx_empty_bytes;
+static PyObject *__pyx_empty_unicode;
+static int __pyx_lineno;
+static int __pyx_clineno = 0;
+static const char * __pyx_cfilenm= __FILE__;
+static const char *__pyx_filename;
+
+/* Header.proto */
+#if !defined(CYTHON_CCOMPLEX)
+  #if defined(__cplusplus)
+    #define CYTHON_CCOMPLEX 1
+  #elif defined(_Complex_I)
+    #define CYTHON_CCOMPLEX 1
+  #else
+    #define CYTHON_CCOMPLEX 0
+  #endif
+#endif
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    #include <complex>
+  #else
+    #include <complex.h>
+  #endif
+#endif
+#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
+  #undef _Complex_I
+  #define _Complex_I 1.0fj
+#endif
+
+
+static const char *__pyx_f[] = {
+  "LAIProcess.pyx",
+  "__init__.pxd",
+  "type.pxd",
+};
+/* BufferFormatStructs.proto */
+#define IS_UNSIGNED(type) (((type) -1) > 0)
+struct __Pyx_StructField_;
+#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
+typedef struct {
+  const char* name;
+  struct __Pyx_StructField_* fields;
+  size_t size;
+  size_t arraysize[8];
+  int ndim;
+  char typegroup;
+  char is_unsigned;
+  int flags;
+} __Pyx_TypeInfo;
+typedef struct __Pyx_StructField_ {
+  __Pyx_TypeInfo* type;
+  const char* name;
+  size_t offset;
+} __Pyx_StructField;
+typedef struct {
+  __Pyx_StructField* field;
+  size_t parent_offset;
+} __Pyx_BufFmt_StackElem;
+typedef struct {
+  __Pyx_StructField root;
+  __Pyx_BufFmt_StackElem* head;
+  size_t fmt_offset;
+  size_t new_count, enc_count;
+  size_t struct_alignment;
+  int is_complex;
+  char enc_type;
+  char new_packmode;
+  char enc_packmode;
+  char is_valid_array;
+} __Pyx_BufFmt_Context;
+
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":690
+ * # in Cython to enable them only on the right systems.
+ * 
+ * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t
+ */
+typedef npy_int8 __pyx_t_5numpy_int8_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":691
+ * 
+ * ctypedef npy_int8       int8_t
+ * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int32      int32_t
+ * ctypedef npy_int64      int64_t
+ */
+typedef npy_int16 __pyx_t_5numpy_int16_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":692
+ * ctypedef npy_int8       int8_t
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int64      int64_t
+ * #ctypedef npy_int96      int96_t
+ */
+typedef npy_int32 __pyx_t_5numpy_int32_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":693
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t
+ * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_int96      int96_t
+ * #ctypedef npy_int128     int128_t
+ */
+typedef npy_int64 __pyx_t_5numpy_int64_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":697
+ * #ctypedef npy_int128     int128_t
+ * 
+ * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t
+ */
+typedef npy_uint8 __pyx_t_5numpy_uint8_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":698
+ * 
+ * ctypedef npy_uint8      uint8_t
+ * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint32     uint32_t
+ * ctypedef npy_uint64     uint64_t
+ */
+typedef npy_uint16 __pyx_t_5numpy_uint16_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":699
+ * ctypedef npy_uint8      uint8_t
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint64     uint64_t
+ * #ctypedef npy_uint96     uint96_t
+ */
+typedef npy_uint32 __pyx_t_5numpy_uint32_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":700
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t
+ * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_uint96     uint96_t
+ * #ctypedef npy_uint128    uint128_t
+ */
+typedef npy_uint64 __pyx_t_5numpy_uint64_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":704
+ * #ctypedef npy_uint128    uint128_t
+ * 
+ * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_float64    float64_t
+ * #ctypedef npy_float80    float80_t
+ */
+typedef npy_float32 __pyx_t_5numpy_float32_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":705
+ * 
+ * ctypedef npy_float32    float32_t
+ * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_float80    float80_t
+ * #ctypedef npy_float128   float128_t
+ */
+typedef npy_float64 __pyx_t_5numpy_float64_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":714
+ * # The int types are mapped a bit surprising --
+ * # numpy.int corresponds to 'l' and numpy.long to 'q'
+ * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longlong   long_t
+ * ctypedef npy_longlong   longlong_t
+ */
+typedef npy_long __pyx_t_5numpy_int_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":715
+ * # numpy.int corresponds to 'l' and numpy.long to 'q'
+ * ctypedef npy_long       int_t
+ * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longlong   longlong_t
+ * 
+ */
+typedef npy_longlong __pyx_t_5numpy_long_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":716
+ * ctypedef npy_long       int_t
+ * ctypedef npy_longlong   long_t
+ * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_ulong      uint_t
+ */
+typedef npy_longlong __pyx_t_5numpy_longlong_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":718
+ * ctypedef npy_longlong   longlong_t
+ * 
+ * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_ulonglong  ulong_t
+ * ctypedef npy_ulonglong  ulonglong_t
+ */
+typedef npy_ulong __pyx_t_5numpy_uint_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":719
+ * 
+ * ctypedef npy_ulong      uint_t
+ * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_ulonglong  ulonglong_t
+ * 
+ */
+typedef npy_ulonglong __pyx_t_5numpy_ulong_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":720
+ * ctypedef npy_ulong      uint_t
+ * ctypedef npy_ulonglong  ulong_t
+ * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_intp       intp_t
+ */
+typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":722
+ * ctypedef npy_ulonglong  ulonglong_t
+ * 
+ * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uintp      uintp_t
+ * 
+ */
+typedef npy_intp __pyx_t_5numpy_intp_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":723
+ * 
+ * ctypedef npy_intp       intp_t
+ * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_double     float_t
+ */
+typedef npy_uintp __pyx_t_5numpy_uintp_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":725
+ * ctypedef npy_uintp      uintp_t
+ * 
+ * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_double     double_t
+ * ctypedef npy_longdouble longdouble_t
+ */
+typedef npy_double __pyx_t_5numpy_float_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":726
+ * 
+ * ctypedef npy_double     float_t
+ * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longdouble longdouble_t
+ * 
+ */
+typedef npy_double __pyx_t_5numpy_double_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":727
+ * ctypedef npy_double     float_t
+ * ctypedef npy_double     double_t
+ * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_cfloat      cfloat_t
+ */
+typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
+/* Declarations.proto */
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    typedef ::std::complex< float > __pyx_t_float_complex;
+  #else
+    typedef float _Complex __pyx_t_float_complex;
+  #endif
+#else
+    typedef struct { float real, imag; } __pyx_t_float_complex;
+#endif
+static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);
+
+/* Declarations.proto */
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    typedef ::std::complex< double > __pyx_t_double_complex;
+  #else
+    typedef double _Complex __pyx_t_double_complex;
+  #endif
+#else
+    typedef struct { double real, imag; } __pyx_t_double_complex;
+#endif
+static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);
+
+
+/*--- Type declarations ---*/
+struct __pyx_obj_10LAIProcess___pyx_scope_struct__train_WMCmodel;
+struct __pyx_obj_10LAIProcess___pyx_scope_struct_1_test_WMCModel;
+struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":729
+ * ctypedef npy_longdouble longdouble_t
+ * 
+ * ctypedef npy_cfloat      cfloat_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_cdouble     cdouble_t
+ * ctypedef npy_clongdouble clongdouble_t
+ */
+typedef npy_cfloat __pyx_t_5numpy_cfloat_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":730
+ * 
+ * ctypedef npy_cfloat      cfloat_t
+ * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_clongdouble clongdouble_t
+ * 
+ */
+typedef npy_cdouble __pyx_t_5numpy_cdouble_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":731
+ * ctypedef npy_cfloat      cfloat_t
+ * ctypedef npy_cdouble     cdouble_t
+ * ctypedef npy_clongdouble clongdouble_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_cdouble     complex_t
+ */
+typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;
+
+/* "../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":733
+ * ctypedef npy_clongdouble clongdouble_t
+ * 
+ * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
+ * 
+ * cdef inline object PyArray_MultiIterNew1(a):
+ */
+typedef npy_cdouble __pyx_t_5numpy_complex_t;
+
+/* "LAIProcess.pyx":42
+ * 
+ * 
+ * def train_WMCmodel(lai_water_inc_sigma_list,params_X0,train_err_image_path,draw_flag=True):             # <<<<<<<<<<<<<<
+ *     """
+ * 
+ */
+struct __pyx_obj_10LAIProcess___pyx_scope_struct__train_WMCmodel {
+  PyObject_HEAD
+  PyObject *__pyx_v_lai_water_inc_sigma_list;
+};
+
+
+/* "LAIProcess.pyx":82
+ *     return h[0]
+ * 
+ * def test_WMCModel(lai_waiter_inc_sigma_list,param_arr,lai_X0,test_err_image_path,draw_flag=True):             # <<<<<<<<<<<<<<
+ *     """
+ * 
+ */
+struct __pyx_obj_10LAIProcess___pyx_scope_struct_1_test_WMCModel {
+  PyObject_HEAD
+  PyObject *__pyx_v_csv_sigma;
+  PyObject *__pyx_v_param_arr;
+  PyObject *__pyx_v_sample_inc;
+  PyObject *__pyx_v_sample_soil;
+};
+
+
+/* "LAIProcess.pyx":130
+ *     return err
+ * 
+ * def processs_WMCModel(param_arr,lai_X0,sigma,inc_angle,soil_water):             # <<<<<<<<<<<<<<
+ * 
+ *     if(sigma<0 ):
+ */
+struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel {
+  PyObject_HEAD
+  PyObject *__pyx_v_inc_angle;
+  PyObject *__pyx_v_param_arr;
+  PyObject *__pyx_v_sigma;
+  PyObject *__pyx_v_soil_water;
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+
+
+/* --- Runtime support code (head) --- */
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+  #define __Pyx_DECREF(r)  __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
+  #define __Pyx_GOTREF(r)  __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
+  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
+  #define __Pyx_XINCREF(r)  do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0)
+  #define __Pyx_XDECREF(r)  do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)
+  #define __Pyx_XGOTREF(r)  do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)
+  #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0)
+#else
+  #define __Pyx_RefNannyDeclarations
+  #define __Pyx_RefNannySetupContext(name, acquire_gil)
+  #define __Pyx_RefNannyFinishContext()
+  #define __Pyx_INCREF(r) Py_INCREF(r)
+  #define __Pyx_DECREF(r) Py_DECREF(r)
+  #define __Pyx_GOTREF(r)
+  #define __Pyx_GIVEREF(r)
+  #define __Pyx_XINCREF(r) Py_XINCREF(r)
+  #define __Pyx_XDECREF(r) Py_XDECREF(r)
+  #define __Pyx_XGOTREF(r)
+  #define __Pyx_XGIVEREF(r)
+#endif
+#define __Pyx_XDECREF_SET(r, v) do {\
+        PyObject *tmp = (PyObject *) r;\
+        r = v; __Pyx_XDECREF(tmp);\
+    } while (0)
+#define __Pyx_DECREF_SET(r, v) do {\
+        PyObject *tmp = (PyObject *) r;\
+        r = v; __Pyx_DECREF(tmp);\
+    } while (0)
+#define __Pyx_CLEAR(r)    do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
+#define __Pyx_XCLEAR(r)   do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)
+
+/* RaiseArgTupleInvalid.proto */
+static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
+    Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
+
+/* RaiseDoubleKeywords.proto */
+static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
+
+/* ParseKeywords.proto */
+static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
+    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
+    const char* function_name);
+
+/* RaiseTooManyValuesToUnpack.proto */
+static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);
+
+/* RaiseNeedMoreValuesToUnpack.proto */
+static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);
+
+/* IterFinish.proto */
+static CYTHON_INLINE int __Pyx_IterFinish(void);
+
+/* UnpackItemEndCheck.proto */
+static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected);
+
+/* PyObjectGetAttrStr.proto */
+#if CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name);
+#else
+#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
+#endif
+
+/* GetBuiltinName.proto */
+static PyObject *__Pyx_GetBuiltinName(PyObject *name);
+
+/* PyDictVersioning.proto */
+#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
+#define __PYX_DICT_VERSION_INIT  ((PY_UINT64_T) -1)
+#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
+#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
+    (version_var) = __PYX_GET_DICT_VERSION(dict);\
+    (cache_var) = (value);
+#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
+    static PY_UINT64_T __pyx_dict_version = 0;\
+    static PyObject *__pyx_dict_cached_value = NULL;\
+    if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
+        (VAR) = __pyx_dict_cached_value;\
+    } else {\
+        (VAR) = __pyx_dict_cached_value = (LOOKUP);\
+        __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
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+}
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
+static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
+#else
+#define __PYX_GET_DICT_VERSION(dict)  (0)
+#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
+#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
+#endif
+
+/* GetModuleGlobalName.proto */
+#if CYTHON_USE_DICT_VERSIONS
+#define __Pyx_GetModuleGlobalName(var, name)  {\
+    static PY_UINT64_T __pyx_dict_version = 0;\
+    static PyObject *__pyx_dict_cached_value = NULL;\
+    (var) = (likely(__pyx_dict_version == __PYX_GET_DICT_VERSION(__pyx_d))) ?\
+        (likely(__pyx_dict_cached_value) ? __Pyx_NewRef(__pyx_dict_cached_value) : __Pyx_GetBuiltinName(name)) :\
+        __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
+}
+#define __Pyx_GetModuleGlobalNameUncached(var, name)  {\
+    PY_UINT64_T __pyx_dict_version;\
+    PyObject *__pyx_dict_cached_value;\
+    (var) = __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
+}
+static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value);
+#else
+#define __Pyx_GetModuleGlobalName(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
+#define __Pyx_GetModuleGlobalNameUncached(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
+static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name);
+#endif
+
+/* PyCFunctionFastCall.proto */
+#if CYTHON_FAST_PYCCALL
+static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
+#else
+#define __Pyx_PyCFunction_FastCall(func, args, nargs)  (assert(0), NULL)
+#endif
+
+/* PyFunctionFastCall.proto */
+#if CYTHON_FAST_PYCALL
+#define __Pyx_PyFunction_FastCall(func, args, nargs)\
+    __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
+#if 1 || PY_VERSION_HEX < 0x030600B1
+static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs);
+#else
+#define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
+#endif
+#define __Pyx_BUILD_ASSERT_EXPR(cond)\
+    (sizeof(char [1 - 2*!(cond)]) - 1)
+#ifndef Py_MEMBER_SIZE
+#define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member)
+#endif
+  static size_t __pyx_pyframe_localsplus_offset = 0;
+  #include "frameobject.h"
+  #define __Pxy_PyFrame_Initialize_Offsets()\
+    ((void)__Pyx_BUILD_ASSERT_EXPR(sizeof(PyFrameObject) == offsetof(PyFrameObject, f_localsplus) + Py_MEMBER_SIZE(PyFrameObject, f_localsplus)),\
+     (void)(__pyx_pyframe_localsplus_offset = ((size_t)PyFrame_Type.tp_basicsize) - Py_MEMBER_SIZE(PyFrameObject, f_localsplus)))
+  #define __Pyx_PyFrame_GetLocalsplus(frame)\
+    (assert(__pyx_pyframe_localsplus_offset), (PyObject **)(((char *)(frame)) + __pyx_pyframe_localsplus_offset))
+#endif
+
+/* PyObjectCall.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
+#else
+#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
+#endif
+
+/* PyObjectCall2Args.proto */
+static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2);
+
+/* PyObjectCallMethO.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
+#endif
+
+/* PyObjectCallOneArg.proto */
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
+
+/* PyIntBinop.proto */
+#if !CYTHON_COMPILING_IN_PYPY
+static PyObject* __Pyx_PyInt_SubtractCObj(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
+#else
+#define __Pyx_PyInt_SubtractCObj(op1, op2, intval, inplace, zerodivision_check)\
+    (inplace ? PyNumber_InPlaceSubtract(op1, op2) : PyNumber_Subtract(op1, op2))
+#endif
+
+/* None.proto */
+static CYTHON_INLINE void __Pyx_RaiseClosureNameError(const char *varname);
+
+/* GetItemInt.proto */
+#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
+    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
+    __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\
+    (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\
+               __Pyx_GetItemInt_Generic(o, to_py_func(i))))
+#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
+    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
+    __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
+    (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
+                                                              int wraparound, int boundscheck);
+#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
+    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
+    __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
+    (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL))
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
+                                                              int wraparound, int boundscheck);
+static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
+                                                     int is_list, int wraparound, int boundscheck);
+
+/* ListAppend.proto */
+#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
+static CYTHON_INLINE int __Pyx_PyList_Append(PyObject* list, PyObject* x) {
+    PyListObject* L = (PyListObject*) list;
+    Py_ssize_t len = Py_SIZE(list);
+    if (likely(L->allocated > len) & likely(len > (L->allocated >> 1))) {
+        Py_INCREF(x);
+        PyList_SET_ITEM(list, len, x);
+        __Pyx_SET_SIZE(list, len + 1);
+        return 0;
+    }
+    return PyList_Append(list, x);
+}
+#else
+#define __Pyx_PyList_Append(L,x) PyList_Append(L,x)
+#endif
+
+/* FetchCommonType.proto */
+static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type);
+
+/* CythonFunctionShared.proto */
+#define __Pyx_CyFunction_USED 1
+#define __Pyx_CYFUNCTION_STATICMETHOD  0x01
+#define __Pyx_CYFUNCTION_CLASSMETHOD   0x02
+#define __Pyx_CYFUNCTION_CCLASS        0x04
+#define __Pyx_CyFunction_GetClosure(f)\
+    (((__pyx_CyFunctionObject *) (f))->func_closure)
+#define __Pyx_CyFunction_GetClassObj(f)\
+    (((__pyx_CyFunctionObject *) (f))->func_classobj)
+#define __Pyx_CyFunction_Defaults(type, f)\
+    ((type *)(((__pyx_CyFunctionObject *) (f))->defaults))
+#define __Pyx_CyFunction_SetDefaultsGetter(f, g)\
+    ((__pyx_CyFunctionObject *) (f))->defaults_getter = (g)
+typedef struct {
+    PyCFunctionObject func;
+#if PY_VERSION_HEX < 0x030500A0
+    PyObject *func_weakreflist;
+#endif
+    PyObject *func_dict;
+    PyObject *func_name;
+    PyObject *func_qualname;
+    PyObject *func_doc;
+    PyObject *func_globals;
+    PyObject *func_code;
+    PyObject *func_closure;
+    PyObject *func_classobj;
+    void *defaults;
+    int defaults_pyobjects;
+    size_t defaults_size;  // used by FusedFunction for copying defaults
+    int flags;
+    PyObject *defaults_tuple;
+    PyObject *defaults_kwdict;
+    PyObject *(*defaults_getter)(PyObject *);
+    PyObject *func_annotations;
+} __pyx_CyFunctionObject;
+static PyTypeObject *__pyx_CyFunctionType = 0;
+#define __Pyx_CyFunction_Check(obj)  (__Pyx_TypeCheck(obj, __pyx_CyFunctionType))
+static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject* op, PyMethodDef *ml,
+                                      int flags, PyObject* qualname,
+                                      PyObject *self,
+                                      PyObject *module, PyObject *globals,
+                                      PyObject* code);
+static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *m,
+                                                         size_t size,
+                                                         int pyobjects);
+static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *m,
+                                                            PyObject *tuple);
+static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *m,
+                                                             PyObject *dict);
+static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *m,
+                                                              PyObject *dict);
+static int __pyx_CyFunction_init(void);
+
+/* CythonFunction.proto */
+static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml,
+                                      int flags, PyObject* qualname,
+                                      PyObject *closure,
+                                      PyObject *module, PyObject *globals,
+                                      PyObject* code);
+
+/* ListCompAppend.proto */
+#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
+static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) {
+    PyListObject* L = (PyListObject*) list;
+    Py_ssize_t len = Py_SIZE(list);
+    if (likely(L->allocated > len)) {
+        Py_INCREF(x);
+        PyList_SET_ITEM(list, len, x);
+        __Pyx_SET_SIZE(list, len + 1);
+        return 0;
+    }
+    return PyList_Append(list, x);
+}
+#else
+#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x)
+#endif
+
+/* Import.proto */
+static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
+
+/* ImportFrom.proto */
+static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name);
+
+/* PyObjectCallNoArg.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
+#else
+#define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
+#endif
+
+/* IsLittleEndian.proto */
+static CYTHON_INLINE int __Pyx_Is_Little_Endian(void);
+
+/* BufferFormatCheck.proto */
+static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts);
+static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
+                              __Pyx_BufFmt_StackElem* stack,
+                              __Pyx_TypeInfo* type);
+
+/* BufferGetAndValidate.proto */
+#define __Pyx_GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)\
+    ((obj == Py_None || obj == NULL) ?\
+    (__Pyx_ZeroBuffer(buf), 0) :\
+    __Pyx__GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack))
+static int  __Pyx__GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
+    __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack);
+static void __Pyx_ZeroBuffer(Py_buffer* buf);
+static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);
+static Py_ssize_t __Pyx_minusones[] = { -1, -1, -1, -1, -1, -1, -1, -1 };
+static Py_ssize_t __Pyx_zeros[] = { 0, 0, 0, 0, 0, 0, 0, 0 };
+
+/* BufferIndexError.proto */
+static void __Pyx_RaiseBufferIndexError(int axis);
+
+#define __Pyx_BufPtrStrided2d(type, buf, i0, s0, i1, s1) (type)((char*)buf + i0 * s0 + i1 * s1)
+/* PyThreadStateGet.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_PyThreadState_declare  PyThreadState *__pyx_tstate;
+#define __Pyx_PyThreadState_assign  __pyx_tstate = __Pyx_PyThreadState_Current;
+#define __Pyx_PyErr_Occurred()  __pyx_tstate->curexc_type
+#else
+#define __Pyx_PyThreadState_declare
+#define __Pyx_PyThreadState_assign
+#define __Pyx_PyErr_Occurred()  PyErr_Occurred()
+#endif
+
+/* PyErrFetchRestore.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
+#define __Pyx_ErrRestoreWithState(type, value, tb)  __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
+#define __Pyx_ErrFetchWithState(type, value, tb)    __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
+#define __Pyx_ErrRestore(type, value, tb)  __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
+#define __Pyx_ErrFetch(type, value, tb)    __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
+static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
+static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
+#if CYTHON_COMPILING_IN_CPYTHON
+#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
+#else
+#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
+#endif
+#else
+#define __Pyx_PyErr_Clear() PyErr_Clear()
+#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
+#define __Pyx_ErrRestoreWithState(type, value, tb)  PyErr_Restore(type, value, tb)
+#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
+#define __Pyx_ErrRestoreInState(tstate, type, value, tb)  PyErr_Restore(type, value, tb)
+#define __Pyx_ErrFetchInState(tstate, type, value, tb)  PyErr_Fetch(type, value, tb)
+#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
+#define __Pyx_ErrFetch(type, value, tb)  PyErr_Fetch(type, value, tb)
+#endif
+
+/* ArgTypeTest.proto */
+#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
+    ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
+        __Pyx__ArgTypeTest(obj, type, name, exact))
+static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);
+
+/* GetTopmostException.proto */
+#if CYTHON_USE_EXC_INFO_STACK
+static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
+#endif
+
+/* SaveResetException.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
+static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
+#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
+static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
+#else
+#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
+#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
+#endif
+
+/* PyErrExceptionMatches.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
+static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
+#else
+#define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)
+#endif
+
+/* GetException.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
+static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
+#else
+static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
+#endif
+
+/* RaiseException.proto */
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
+
+/* IncludeStringH.proto */
+#include <string.h>
+
+/* PyObject_GenericGetAttrNoDict.proto */
+#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name);
+#else
+#define __Pyx_PyObject_GenericGetAttrNoDict PyObject_GenericGetAttr
+#endif
+
+/* TypeImport.proto */
+#ifndef __PYX_HAVE_RT_ImportType_proto
+#define __PYX_HAVE_RT_ImportType_proto
+enum __Pyx_ImportType_CheckSize {
+   __Pyx_ImportType_CheckSize_Error = 0,
+   __Pyx_ImportType_CheckSize_Warn = 1,
+   __Pyx_ImportType_CheckSize_Ignore = 2
+};
+static PyTypeObject *__Pyx_ImportType(PyObject* module, const char *module_name, const char *class_name, size_t size, enum __Pyx_ImportType_CheckSize check_size);
+#endif
+
+/* CLineInTraceback.proto */
+#ifdef CYTHON_CLINE_IN_TRACEBACK
+#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
+#else
+static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
+#endif
+
+/* CodeObjectCache.proto */
+typedef struct {
+    PyCodeObject* code_object;
+    int code_line;
+} __Pyx_CodeObjectCacheEntry;
+struct __Pyx_CodeObjectCache {
+    int count;
+    int max_count;
+    __Pyx_CodeObjectCacheEntry* entries;
+};
+static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
+static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
+static PyCodeObject *__pyx_find_code_object(int code_line);
+static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
+
+/* AddTraceback.proto */
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename);
+
+/* BufferStructDeclare.proto */
+typedef struct {
+  Py_ssize_t shape, strides, suboffsets;
+} __Pyx_Buf_DimInfo;
+typedef struct {
+  size_t refcount;
+  Py_buffer pybuffer;
+} __Pyx_Buffer;
+typedef struct {
+  __Pyx_Buffer *rcbuffer;
+  char *data;
+  __Pyx_Buf_DimInfo diminfo[8];
+} __Pyx_LocalBuf_ND;
+
+#if PY_MAJOR_VERSION < 3
+    static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
+    static void __Pyx_ReleaseBuffer(Py_buffer *view);
+#else
+    #define __Pyx_GetBuffer PyObject_GetBuffer
+    #define __Pyx_ReleaseBuffer PyBuffer_Release
+#endif
+
+
+/* GCCDiagnostics.proto */
+#if defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
+#define __Pyx_HAS_GCC_DIAGNOSTIC
+#endif
+
+/* RealImag.proto */
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    #define __Pyx_CREAL(z) ((z).real())
+    #define __Pyx_CIMAG(z) ((z).imag())
+  #else
+    #define __Pyx_CREAL(z) (__real__(z))
+    #define __Pyx_CIMAG(z) (__imag__(z))
+  #endif
+#else
+    #define __Pyx_CREAL(z) ((z).real)
+    #define __Pyx_CIMAG(z) ((z).imag)
+#endif
+#if defined(__cplusplus) && CYTHON_CCOMPLEX\
+        && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
+    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
+    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
+#else
+    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
+    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
+#endif
+
+/* Arithmetic.proto */
+#if CYTHON_CCOMPLEX
+    #define __Pyx_c_eq_float(a, b)   ((a)==(b))
+    #define __Pyx_c_sum_float(a, b)  ((a)+(b))
+    #define __Pyx_c_diff_float(a, b) ((a)-(b))
+    #define __Pyx_c_prod_float(a, b) ((a)*(b))
+    #define __Pyx_c_quot_float(a, b) ((a)/(b))
+    #define __Pyx_c_neg_float(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zero_float(z) ((z)==(float)0)
+    #define __Pyx_c_conj_float(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_abs_float(z)     (::std::abs(z))
+        #define __Pyx_c_pow_float(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zero_float(z) ((z)==0)
+    #define __Pyx_c_conj_float(z)    (conjf(z))
+    #if 1
+        #define __Pyx_c_abs_float(z)     (cabsf(z))
+        #define __Pyx_c_pow_float(a, b)  (cpowf(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex);
+    #if 1
+        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex);
+        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    #endif
+#endif
+
+/* Arithmetic.proto */
+#if CYTHON_CCOMPLEX
+    #define __Pyx_c_eq_double(a, b)   ((a)==(b))
+    #define __Pyx_c_sum_double(a, b)  ((a)+(b))
+    #define __Pyx_c_diff_double(a, b) ((a)-(b))
+    #define __Pyx_c_prod_double(a, b) ((a)*(b))
+    #define __Pyx_c_quot_double(a, b) ((a)/(b))
+    #define __Pyx_c_neg_double(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
+    #define __Pyx_c_conj_double(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_abs_double(z)     (::std::abs(z))
+        #define __Pyx_c_pow_double(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zero_double(z) ((z)==0)
+    #define __Pyx_c_conj_double(z)    (conj(z))
+    #if 1
+        #define __Pyx_c_abs_double(z)     (cabs(z))
+        #define __Pyx_c_pow_double(a, b)  (cpow(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);
+    #if 1
+        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);
+        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    #endif
+#endif
+
+/* CIntToPy.proto */
+static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
+
+/* CIntFromPy.proto */
+static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
+
+/* CIntFromPy.proto */
+static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
+
+/* FastTypeChecks.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
+static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
+#else
+#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
+#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
+#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
+#endif
+#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
+
+/* CheckBinaryVersion.proto */
+static int __Pyx_check_binary_version(void);
+
+/* InitStrings.proto */
+static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
+
+
+/* Module declarations from 'cython' */
+
+/* Module declarations from 'cpython.buffer' */
+
+/* Module declarations from 'libc.string' */
+
+/* Module declarations from 'libc.stdio' */
+
+/* Module declarations from '__builtin__' */
+
+/* Module declarations from 'cpython.type' */
+static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;
+
+/* Module declarations from 'cpython' */
+
+/* Module declarations from 'cpython.object' */
+
+/* Module declarations from 'cpython.ref' */
+
+/* Module declarations from 'cpython.mem' */
+
+/* Module declarations from 'numpy' */
+
+/* Module declarations from 'numpy' */
+static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;
+static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
+static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
+static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;
+static PyTypeObject *__pyx_ptype_5numpy_generic = 0;
+static PyTypeObject *__pyx_ptype_5numpy_number = 0;
+static PyTypeObject *__pyx_ptype_5numpy_integer = 0;
+static PyTypeObject *__pyx_ptype_5numpy_signedinteger = 0;
+static PyTypeObject *__pyx_ptype_5numpy_unsignedinteger = 0;
+static PyTypeObject *__pyx_ptype_5numpy_inexact = 0;
+static PyTypeObject *__pyx_ptype_5numpy_floating = 0;
+static PyTypeObject *__pyx_ptype_5numpy_complexfloating = 0;
+static PyTypeObject *__pyx_ptype_5numpy_flexible = 0;
+static PyTypeObject *__pyx_ptype_5numpy_character = 0;
+static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
+
+/* Module declarations from 'libc.math' */
+
+/* Module declarations from 'LAIProcess' */
+static PyTypeObject *__pyx_ptype_10LAIProcess___pyx_scope_struct__train_WMCmodel = 0;
+static PyTypeObject *__pyx_ptype_10LAIProcess___pyx_scope_struct_1_test_WMCModel = 0;
+static PyTypeObject *__pyx_ptype_10LAIProcess___pyx_scope_struct_2_processs_WMCModel = 0;
+static PyArrayObject *__pyx_f_10LAIProcess_process_tiff(PyArrayObject *, PyArrayObject *, PyArrayObject *, PyArrayObject *, double, int __pyx_skip_dispatch); /*proto*/
+static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 };
+#define __Pyx_MODULE_NAME "LAIProcess"
+extern int __pyx_module_is_main_LAIProcess;
+int __pyx_module_is_main_LAIProcess = 0;
+
+/* Implementation of 'LAIProcess' */
+static PyObject *__pyx_builtin_ImportError;
+static const char __pyx_k_A[] = "A";
+static const char __pyx_k_B[] = "B";
+static const char __pyx_k_C[] = "C";
+static const char __pyx_k_D[] = "D";
+static const char __pyx_k_M[] = "M";
+static const char __pyx_k_N[] = "N";
+static const char __pyx_k_X[] = "X";
+static const char __pyx_k_f[] = "f";
+static const char __pyx_k_h[] = "h";
+static const char __pyx_k_X0[] = "X0";
+static const char __pyx_k_np[] = "np";
+static const char __pyx_k_FVC[] = "FVC";
+static const char __pyx_k_cos[] = "cos";
+static const char __pyx_k_dpi[] = "dpi";
+static const char __pyx_k_eqs[] = "eqs";
+static const char __pyx_k_err[] = "err";
+static const char __pyx_k_exp[] = "exp";
+static const char __pyx_k_lai[] = "lai";
+static const char __pyx_k_nan[] = "nan";
+static const char __pyx_k_plt[] = "plt";
+static const char __pyx_k_main[] = "__main__";
+static const char __pyx_k_name[] = "__name__";
+static const char __pyx_k_show[] = "show";
+static const char __pyx_k_test[] = "__test__";
+static const char __pyx_k_V_lai[] = "V_lai";
+static const char __pyx_k_err_f[] = "err_f";
+static const char __pyx_k_f_veg[] = "f_veg";
+static const char __pyx_k_mylog[] = "mylog";
+static const char __pyx_k_numpy[] = "numpy";
+static const char __pyx_k_sigma[] = "sigma";
+static const char __pyx_k_title[] = "title";
+static const char __pyx_k_x_arr[] = "x_arr";
+static const char __pyx_k_import[] = "__import__";
+static const char __pyx_k_lai_X0[] = "lai_X0";
+static const char __pyx_k_logger[] = "logger";
+static const char __pyx_k_pyplot[] = "pyplot";
+static const char __pyx_k_random[] = "random";
+static const char __pyx_k_result[] = "result";
+static const char __pyx_k_err_lai[] = "err_lai";
+static const char __pyx_k_leastsq[] = "leastsq";
+static const char __pyx_k_logging[] = "logging";
+static const char __pyx_k_savefig[] = "savefig";
+static const char __pyx_k_scatter[] = "scatter";
+static const char __pyx_k_WMCModel[] = "WMCModel";
+static const char __pyx_k_inc_tiff[] = "inc_tiff";
+static const char __pyx_k_temp_err[] = "temp_err";
+static const char __pyx_k_csv_sigma[] = "csv_sigma";
+static const char __pyx_k_draw_flag[] = "draw_flag";
+static const char __pyx_k_exp_gamma[] = "exp_gamma";
+static const char __pyx_k_getLogger[] = "getLogger";
+static const char __pyx_k_inc_angle[] = "inc_angle";
+static const char __pyx_k_param_arr[] = "param_arr";
+static const char __pyx_k_params_X0[] = "params_X0";
+static const char __pyx_k_sigma_veg[] = "sigma_veg";
+static const char __pyx_k_LAIProcess[] = "LAIProcess";
+static const char __pyx_k_matplotlib[] = "matplotlib";
+static const char __pyx_k_sample_inc[] = "sample_inc";
+static const char __pyx_k_sample_lai[] = "sample_lai";
+static const char __pyx_k_sample_lat[] = "sample_lat";
+static const char __pyx_k_sample_lon[] = "sample_lon";
+static const char __pyx_k_sigma_soil[] = "sigma_soil";
+static const char __pyx_k_sigma_tiff[] = "sigma_tiff";
+static const char __pyx_k_soil_water[] = "soil_water";
+static const char __pyx_k_ImportError[] = "ImportError";
+static const char __pyx_k_sample_code[] = "sample_code";
+static const char __pyx_k_sample_soil[] = "sample_soil";
+static const char __pyx_k_sample_time[] = "sample_time";
+static const char __pyx_k_equation_err[] = "equation-err";
+static const char __pyx_k_sample_sigma[] = "sample_sigma";
+static const char __pyx_k_test_WMCModel[] = "test_WMCModel";
+static const char __pyx_k_LAIProcess_pyx[] = "LAIProcess.pyx";
+static const char __pyx_k_scipy_optimize[] = "scipy.optimize";
+static const char __pyx_k_train_WMCmodel[] = "train_WMCmodel";
+static const char __pyx_k_soil_water_tiff[] = "soil_water_tiff";
+static const char __pyx_k_processs_WMCModel[] = "processs_WMCModel";
+static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
+static const char __pyx_k_test_err_image_path[] = "test_err_image_path";
+static const char __pyx_k_train_err_image_path[] = "train_err_image_path";
+static const char __pyx_k_test_WMCModel_locals_f[] = "test_WMCModel.<locals>.f";
+static const char __pyx_k_train_WMCmodel_locals_f[] = "train_WMCmodel.<locals>.f";
+static const char __pyx_k_lai_water_inc_sigma_item[] = "lai_water_inc_sigma_item";
+static const char __pyx_k_lai_water_inc_sigma_list[] = "lai_water_inc_sigma_list";
+static const char __pyx_k_lai_waiter_inc_sigma_item[] = "lai_waiter_inc_sigma_item";
+static const char __pyx_k_lai_waiter_inc_sigma_list[] = "lai_waiter_inc_sigma_list";
+static const char __pyx_k_processs_WMCModel_locals_f[] = "processs_WMCModel.<locals>.f";
+static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import";
+static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import";
+static PyObject *__pyx_n_s_A;
+static PyObject *__pyx_n_s_B;
+static PyObject *__pyx_n_s_C;
+static PyObject *__pyx_n_s_D;
+static PyObject *__pyx_n_s_FVC;
+static PyObject *__pyx_n_s_ImportError;
+static PyObject *__pyx_n_s_LAIProcess;
+static PyObject *__pyx_kp_s_LAIProcess_pyx;
+static PyObject *__pyx_n_s_M;
+static PyObject *__pyx_n_s_N;
+static PyObject *__pyx_n_s_V_lai;
+static PyObject *__pyx_n_s_WMCModel;
+static PyObject *__pyx_n_s_X;
+static PyObject *__pyx_n_s_X0;
+static PyObject *__pyx_n_s_cline_in_traceback;
+static PyObject *__pyx_n_s_cos;
+static PyObject *__pyx_n_s_csv_sigma;
+static PyObject *__pyx_n_s_dpi;
+static PyObject *__pyx_n_s_draw_flag;
+static PyObject *__pyx_n_s_eqs;
+static PyObject *__pyx_kp_s_equation_err;
+static PyObject *__pyx_n_s_err;
+static PyObject *__pyx_n_s_err_f;
+static PyObject *__pyx_n_s_err_lai;
+static PyObject *__pyx_n_s_exp;
+static PyObject *__pyx_n_s_exp_gamma;
+static PyObject *__pyx_n_s_f;
+static PyObject *__pyx_n_s_f_veg;
+static PyObject *__pyx_n_s_getLogger;
+static PyObject *__pyx_n_s_h;
+static PyObject *__pyx_n_s_import;
+static PyObject *__pyx_n_s_inc_angle;
+static PyObject *__pyx_n_s_inc_tiff;
+static PyObject *__pyx_n_s_lai;
+static PyObject *__pyx_n_s_lai_X0;
+static PyObject *__pyx_n_s_lai_waiter_inc_sigma_item;
+static PyObject *__pyx_n_s_lai_waiter_inc_sigma_list;
+static PyObject *__pyx_n_s_lai_water_inc_sigma_item;
+static PyObject *__pyx_n_s_lai_water_inc_sigma_list;
+static PyObject *__pyx_n_s_leastsq;
+static PyObject *__pyx_n_s_logger;
+static PyObject *__pyx_n_s_logging;
+static PyObject *__pyx_n_s_main;
+static PyObject *__pyx_n_s_matplotlib;
+static PyObject *__pyx_n_s_mylog;
+static PyObject *__pyx_n_s_name;
+static PyObject *__pyx_n_s_nan;
+static PyObject *__pyx_n_s_np;
+static PyObject *__pyx_n_s_numpy;
+static PyObject *__pyx_kp_s_numpy_core_multiarray_failed_to;
+static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor;
+static PyObject *__pyx_n_s_param_arr;
+static PyObject *__pyx_n_s_params_X0;
+static PyObject *__pyx_n_s_plt;
+static PyObject *__pyx_n_s_processs_WMCModel;
+static PyObject *__pyx_n_s_processs_WMCModel_locals_f;
+static PyObject *__pyx_n_s_pyplot;
+static PyObject *__pyx_n_s_random;
+static PyObject *__pyx_n_s_result;
+static PyObject *__pyx_n_s_sample_code;
+static PyObject *__pyx_n_s_sample_inc;
+static PyObject *__pyx_n_s_sample_lai;
+static PyObject *__pyx_n_s_sample_lat;
+static PyObject *__pyx_n_s_sample_lon;
+static PyObject *__pyx_n_s_sample_sigma;
+static PyObject *__pyx_n_s_sample_soil;
+static PyObject *__pyx_n_s_sample_time;
+static PyObject *__pyx_n_s_savefig;
+static PyObject *__pyx_n_s_scatter;
+static PyObject *__pyx_n_s_scipy_optimize;
+static PyObject *__pyx_n_s_show;
+static PyObject *__pyx_n_s_sigma;
+static PyObject *__pyx_n_s_sigma_soil;
+static PyObject *__pyx_n_s_sigma_tiff;
+static PyObject *__pyx_n_s_sigma_veg;
+static PyObject *__pyx_n_s_soil_water;
+static PyObject *__pyx_n_s_soil_water_tiff;
+static PyObject *__pyx_n_s_temp_err;
+static PyObject *__pyx_n_s_test;
+static PyObject *__pyx_n_s_test_WMCModel;
+static PyObject *__pyx_n_s_test_WMCModel_locals_f;
+static PyObject *__pyx_n_s_test_err_image_path;
+static PyObject *__pyx_n_s_title;
+static PyObject *__pyx_n_s_train_WMCmodel;
+static PyObject *__pyx_n_s_train_WMCmodel_locals_f;
+static PyObject *__pyx_n_s_train_err_image_path;
+static PyObject *__pyx_n_s_x_arr;
+static PyObject *__pyx_pf_10LAIProcess_WMCModel(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_param_arr, PyObject *__pyx_v_sample_lai, PyObject *__pyx_v_sample_soil, PyObject *__pyx_v_sample_inc, PyObject *__pyx_v_sample_sigma); /* proto */
+static PyObject *__pyx_pf_10LAIProcess_14train_WMCmodel_f(PyObject *__pyx_self, PyObject *__pyx_v_X); /* proto */
+static PyObject *__pyx_pf_10LAIProcess_2train_WMCmodel(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_lai_water_inc_sigma_list, PyObject *__pyx_v_params_X0, PyObject *__pyx_v_train_err_image_path, PyObject *__pyx_v_draw_flag); /* proto */
+static PyObject *__pyx_pf_10LAIProcess_13test_WMCModel_f(PyObject *__pyx_self, PyObject *__pyx_v_X); /* proto */
+static PyObject *__pyx_pf_10LAIProcess_4test_WMCModel(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_lai_waiter_inc_sigma_list, PyObject *__pyx_v_param_arr, PyObject *__pyx_v_lai_X0, PyObject *__pyx_v_test_err_image_path, PyObject *__pyx_v_draw_flag); /* proto */
+static PyObject *__pyx_pf_10LAIProcess_17processs_WMCModel_f(PyObject *__pyx_self, PyObject *__pyx_v_X); /* proto */
+static PyObject *__pyx_pf_10LAIProcess_6processs_WMCModel(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_param_arr, PyObject *__pyx_v_lai_X0, PyObject *__pyx_v_sigma, PyObject *__pyx_v_inc_angle, PyObject *__pyx_v_soil_water); /* proto */
+static PyObject *__pyx_pf_10LAIProcess_8process_tiff(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_sigma_tiff, PyArrayObject *__pyx_v_inc_tiff, PyArrayObject *__pyx_v_soil_water_tiff, PyArrayObject *__pyx_v_param_arr, double __pyx_v_lai_X0); /* proto */
+static PyObject *__pyx_tp_new_10LAIProcess___pyx_scope_struct__train_WMCmodel(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
+static PyObject *__pyx_tp_new_10LAIProcess___pyx_scope_struct_1_test_WMCModel(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
+static PyObject *__pyx_tp_new_10LAIProcess___pyx_scope_struct_2_processs_WMCModel(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
+static PyObject *__pyx_int_0;
+static PyObject *__pyx_int_1;
+static PyObject *__pyx_int_600;
+static PyObject *__pyx_int_neg_2;
+static PyObject *__pyx_tuple_;
+static PyObject *__pyx_tuple__3;
+static PyObject *__pyx_tuple__5;
+static PyObject *__pyx_tuple__7;
+static PyObject *__pyx_tuple__8;
+static PyObject *__pyx_tuple__9;
+static PyObject *__pyx_tuple__10;
+static PyObject *__pyx_tuple__12;
+static PyObject *__pyx_tuple__14;
+static PyObject *__pyx_tuple__16;
+static PyObject *__pyx_codeobj__2;
+static PyObject *__pyx_codeobj__4;
+static PyObject *__pyx_codeobj__6;
+static PyObject *__pyx_codeobj__11;
+static PyObject *__pyx_codeobj__13;
+static PyObject *__pyx_codeobj__15;
+static PyObject *__pyx_codeobj__17;
+/* Late includes */
+
+/* "LAIProcess.pyx":15
+ * 
+ * 
+ * def WMCModel(param_arr,sample_lai,sample_soil,sample_inc,sample_sigma):             # <<<<<<<<<<<<<<
+ *     """ WMC
+ * 
+ */
+
+/* Python wrapper */
+static PyObject *__pyx_pw_10LAIProcess_1WMCModel(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
+static char __pyx_doc_10LAIProcess_WMCModel[] = " WMC\346\250\241\345\236\213 \345\242\236\345\212\240 \345\275\222\344\270\200\345\214\226\346\244\215\350\242\253\346\214\207\346\225\260\n\n    Args:\n        param_arr (np.ndarray): \345\217\202\346\225\260\346\225\260\347\273\204\n        sample_lai (double): \345\217\266\351\235\242\347\247\257\346\214\207\346\225\260\n        sample_soil (double): \345\234\237\345\243\244\345\220\253\346\260\264\351\207\217\n        sample_inc (double): \345\205\245\345\260\204\350\247\222\357\274\210\345\274\247\345\272\246\345\200\274\357\274\211\n        sample_sigma (double): \345\220\216\345\220\221\346\225\243\345\260\204\347\263\273\346\225\260\357\274\210\347\272\277\346\200\247\345\200\274\357\274\211\n\n    Returns:\n        double: \346\226\271\347\250\213\345\200\274\n    ";
+static PyMethodDef __pyx_mdef_10LAIProcess_1WMCModel = {"WMCModel", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_10LAIProcess_1WMCModel, METH_VARARGS|METH_KEYWORDS, __pyx_doc_10LAIProcess_WMCModel};
+static PyObject *__pyx_pw_10LAIProcess_1WMCModel(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
+  PyObject *__pyx_v_param_arr = 0;
+  PyObject *__pyx_v_sample_lai = 0;
+  PyObject *__pyx_v_sample_soil = 0;
+  PyObject *__pyx_v_sample_inc = 0;
+  PyObject *__pyx_v_sample_sigma = 0;
+  int __pyx_lineno = 0;
+  const char *__pyx_filename = NULL;
+  int __pyx_clineno = 0;
+  PyObject *__pyx_r = 0;
+  __Pyx_RefNannyDeclarations
+  __Pyx_RefNannySetupContext("WMCModel (wrapper)", 0);
+  {
+    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_param_arr,&__pyx_n_s_sample_lai,&__pyx_n_s_sample_soil,&__pyx_n_s_sample_inc,&__pyx_n_s_sample_sigma,0};
+    PyObject* values[5] = {0,0,0,0,0};
+    if (unlikely(__pyx_kwds)) {
+      Py_ssize_t kw_args;
+      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
+      switch (pos_args) {
+        case  5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
+        CYTHON_FALLTHROUGH;
+        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
+        CYTHON_FALLTHROUGH;
+        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
+        CYTHON_FALLTHROUGH;
+        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
+        CYTHON_FALLTHROUGH;
+        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
+        CYTHON_FALLTHROUGH;
+        case  0: break;
+        default: goto __pyx_L5_argtuple_error;
+      }
+      kw_args = PyDict_Size(__pyx_kwds);
+      switch (pos_args) {
+        case  0:
+        if (likely((values[0] = __Pyx_PyDict_GetItemStr(__pyx_kwds, __pyx_n_s_param_arr)) != 0)) kw_args--;
+        else goto __pyx_L5_argtuple_error;
+        CYTHON_FALLTHROUGH;
+        case  1:
+        if (likely((values[1] = __Pyx_PyDict_GetItemStr(__pyx_kwds, __pyx_n_s_sample_lai)) != 0)) kw_args--;
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+        CYTHON_FALLTHROUGH;
+        case  2:
+        if (likely((values[2] = __Pyx_PyDict_GetItemStr(__pyx_kwds, __pyx_n_s_sample_soil)) != 0)) kw_args--;
+        else {
+          __Pyx_RaiseArgtupleInvalid("WMCModel", 1, 5, 5, 2); __PYX_ERR(0, 15, __pyx_L3_error)
+        }
+        CYTHON_FALLTHROUGH;
+        case  3:
+        if (likely((values[3] = __Pyx_PyDict_GetItemStr(__pyx_kwds, __pyx_n_s_sample_inc)) != 0)) kw_args--;
+        else {
+          __Pyx_RaiseArgtupleInvalid("WMCModel", 1, 5, 5, 3); __PYX_ERR(0, 15, __pyx_L3_error)
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+        CYTHON_FALLTHROUGH;
+        case  4:
+        if (likely((values[4] = __Pyx_PyDict_GetItemStr(__pyx_kwds, __pyx_n_s_sample_sigma)) != 0)) kw_args--;
+        else {
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+        }
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+      if (unlikely(kw_args > 0)) {
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+      goto __pyx_L5_argtuple_error;
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+      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
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+      values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
+      values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
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+    __pyx_v_param_arr = values[0];
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+    __pyx_v_sample_soil = values[2];
+    __pyx_v_sample_inc = values[3];
+    __pyx_v_sample_sigma = values[4];
+  }
+  goto __pyx_L4_argument_unpacking_done;
+  __pyx_L5_argtuple_error:;
+  __Pyx_RaiseArgtupleInvalid("WMCModel", 1, 5, 5, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 15, __pyx_L3_error)
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+  __Pyx_AddTraceback("LAIProcess.WMCModel", __pyx_clineno, __pyx_lineno, __pyx_filename);
+  __Pyx_RefNannyFinishContext();
+  return NULL;
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+
+  /* function exit code */
+  __Pyx_RefNannyFinishContext();
+  return __pyx_r;
+}
+
+static PyObject *__pyx_pf_10LAIProcess_WMCModel(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_param_arr, PyObject *__pyx_v_sample_lai, PyObject *__pyx_v_sample_soil, PyObject *__pyx_v_sample_inc, PyObject *__pyx_v_sample_sigma) {
+  PyObject *__pyx_v_A = NULL;
+  PyObject *__pyx_v_B = NULL;
+  PyObject *__pyx_v_C = NULL;
+  PyObject *__pyx_v_D = NULL;
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+  0, /*tp_version_tag*/
+  #if PY_VERSION_HEX >= 0x030400a1
+  0, /*tp_finalize*/
+  #endif
+  #if PY_VERSION_HEX >= 0x030800b1
+  0, /*tp_vectorcall*/
+  #endif
+  #if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
+  0, /*tp_print*/
+  #endif
+};
+
+static struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel *__pyx_freelist_10LAIProcess___pyx_scope_struct_2_processs_WMCModel[8];
+static int __pyx_freecount_10LAIProcess___pyx_scope_struct_2_processs_WMCModel = 0;
+
+static PyObject *__pyx_tp_new_10LAIProcess___pyx_scope_struct_2_processs_WMCModel(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
+  PyObject *o;
+  if (CYTHON_COMPILING_IN_CPYTHON && likely((__pyx_freecount_10LAIProcess___pyx_scope_struct_2_processs_WMCModel > 0) & (t->tp_basicsize == sizeof(struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel)))) {
+    o = (PyObject*)__pyx_freelist_10LAIProcess___pyx_scope_struct_2_processs_WMCModel[--__pyx_freecount_10LAIProcess___pyx_scope_struct_2_processs_WMCModel];
+    memset(o, 0, sizeof(struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel));
+    (void) PyObject_INIT(o, t);
+    PyObject_GC_Track(o);
+  } else {
+    o = (*t->tp_alloc)(t, 0);
+    if (unlikely(!o)) return 0;
+  }
+  return o;
+}
+
+static void __pyx_tp_dealloc_10LAIProcess___pyx_scope_struct_2_processs_WMCModel(PyObject *o) {
+  struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel *p = (struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel *)o;
+  PyObject_GC_UnTrack(o);
+  Py_CLEAR(p->__pyx_v_inc_angle);
+  Py_CLEAR(p->__pyx_v_param_arr);
+  Py_CLEAR(p->__pyx_v_sigma);
+  Py_CLEAR(p->__pyx_v_soil_water);
+  if (CYTHON_COMPILING_IN_CPYTHON && ((__pyx_freecount_10LAIProcess___pyx_scope_struct_2_processs_WMCModel < 8) & (Py_TYPE(o)->tp_basicsize == sizeof(struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel)))) {
+    __pyx_freelist_10LAIProcess___pyx_scope_struct_2_processs_WMCModel[__pyx_freecount_10LAIProcess___pyx_scope_struct_2_processs_WMCModel++] = ((struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel *)o);
+  } else {
+    (*Py_TYPE(o)->tp_free)(o);
+  }
+}
+
+static int __pyx_tp_traverse_10LAIProcess___pyx_scope_struct_2_processs_WMCModel(PyObject *o, visitproc v, void *a) {
+  int e;
+  struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel *p = (struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel *)o;
+  if (p->__pyx_v_inc_angle) {
+    e = (*v)(p->__pyx_v_inc_angle, a); if (e) return e;
+  }
+  if (p->__pyx_v_param_arr) {
+    e = (*v)(p->__pyx_v_param_arr, a); if (e) return e;
+  }
+  if (p->__pyx_v_sigma) {
+    e = (*v)(p->__pyx_v_sigma, a); if (e) return e;
+  }
+  if (p->__pyx_v_soil_water) {
+    e = (*v)(p->__pyx_v_soil_water, a); if (e) return e;
+  }
+  return 0;
+}
+
+static int __pyx_tp_clear_10LAIProcess___pyx_scope_struct_2_processs_WMCModel(PyObject *o) {
+  PyObject* tmp;
+  struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel *p = (struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel *)o;
+  tmp = ((PyObject*)p->__pyx_v_inc_angle);
+  p->__pyx_v_inc_angle = Py_None; Py_INCREF(Py_None);
+  Py_XDECREF(tmp);
+  tmp = ((PyObject*)p->__pyx_v_param_arr);
+  p->__pyx_v_param_arr = Py_None; Py_INCREF(Py_None);
+  Py_XDECREF(tmp);
+  tmp = ((PyObject*)p->__pyx_v_sigma);
+  p->__pyx_v_sigma = Py_None; Py_INCREF(Py_None);
+  Py_XDECREF(tmp);
+  tmp = ((PyObject*)p->__pyx_v_soil_water);
+  p->__pyx_v_soil_water = Py_None; Py_INCREF(Py_None);
+  Py_XDECREF(tmp);
+  return 0;
+}
+
+static PyTypeObject __pyx_type_10LAIProcess___pyx_scope_struct_2_processs_WMCModel = {
+  PyVarObject_HEAD_INIT(0, 0)
+  "LAIProcess.__pyx_scope_struct_2_processs_WMCModel", /*tp_name*/
+  sizeof(struct __pyx_obj_10LAIProcess___pyx_scope_struct_2_processs_WMCModel), /*tp_basicsize*/
+  0, /*tp_itemsize*/
+  __pyx_tp_dealloc_10LAIProcess___pyx_scope_struct_2_processs_WMCModel, /*tp_dealloc*/
+  #if PY_VERSION_HEX < 0x030800b4
+  0, /*tp_print*/
+  #endif
+  #if PY_VERSION_HEX >= 0x030800b4
+  0, /*tp_vectorcall_offset*/
+  #endif
+  0, /*tp_getattr*/
+  0, /*tp_setattr*/
+  #if PY_MAJOR_VERSION < 3
+  0, /*tp_compare*/
+  #endif
+  #if PY_MAJOR_VERSION >= 3
+  0, /*tp_as_async*/
+  #endif
+  0, /*tp_repr*/
+  0, /*tp_as_number*/
+  0, /*tp_as_sequence*/
+  0, /*tp_as_mapping*/
+  0, /*tp_hash*/
+  0, /*tp_call*/
+  0, /*tp_str*/
+  0, /*tp_getattro*/
+  0, /*tp_setattro*/
+  0, /*tp_as_buffer*/
+  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
+  0, /*tp_doc*/
+  __pyx_tp_traverse_10LAIProcess___pyx_scope_struct_2_processs_WMCModel, /*tp_traverse*/
+  __pyx_tp_clear_10LAIProcess___pyx_scope_struct_2_processs_WMCModel, /*tp_clear*/
+  0, /*tp_richcompare*/
+  0, /*tp_weaklistoffset*/
+  0, /*tp_iter*/
+  0, /*tp_iternext*/
+  0, /*tp_methods*/
+  0, /*tp_members*/
+  0, /*tp_getset*/
+  0, /*tp_base*/
+  0, /*tp_dict*/
+  0, /*tp_descr_get*/
+  0, /*tp_descr_set*/
+  0, /*tp_dictoffset*/
+  0, /*tp_init*/
+  0, /*tp_alloc*/
+  __pyx_tp_new_10LAIProcess___pyx_scope_struct_2_processs_WMCModel, /*tp_new*/
+  0, /*tp_free*/
+  0, /*tp_is_gc*/
+  0, /*tp_bases*/
+  0, /*tp_mro*/
+  0, /*tp_cache*/
+  0, /*tp_subclasses*/
+  0, /*tp_weaklist*/
+  0, /*tp_del*/
+  0, /*tp_version_tag*/
+  #if PY_VERSION_HEX >= 0x030400a1
+  0, /*tp_finalize*/
+  #endif
+  #if PY_VERSION_HEX >= 0x030800b1
+  0, /*tp_vectorcall*/
+  #endif
+  #if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
+  0, /*tp_print*/
+  #endif
+};
+
+static PyMethodDef __pyx_methods[] = {
+  {"process_tiff", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_10LAIProcess_9process_tiff, METH_VARARGS|METH_KEYWORDS, 0},
+  {0, 0, 0, 0}
+};
+
+#if PY_MAJOR_VERSION >= 3
+#if CYTHON_PEP489_MULTI_PHASE_INIT
+static PyObject* __pyx_pymod_create(PyObject *spec, PyModuleDef *def); /*proto*/
+static int __pyx_pymod_exec_LAIProcess(PyObject* module); /*proto*/
+static PyModuleDef_Slot __pyx_moduledef_slots[] = {
+  {Py_mod_create, (void*)__pyx_pymod_create},
+  {Py_mod_exec, (void*)__pyx_pymod_exec_LAIProcess},
+  {0, NULL}
+};
+#endif
+
+static struct PyModuleDef __pyx_moduledef = {
+    PyModuleDef_HEAD_INIT,
+    "LAIProcess",
+    0, /* m_doc */
+  #if CYTHON_PEP489_MULTI_PHASE_INIT
+    0, /* m_size */
+  #else
+    -1, /* m_size */
+  #endif
+    __pyx_methods /* m_methods */,
+  #if CYTHON_PEP489_MULTI_PHASE_INIT
+    __pyx_moduledef_slots, /* m_slots */
+  #else
+    NULL, /* m_reload */
+  #endif
+    NULL, /* m_traverse */
+    NULL, /* m_clear */
+    NULL /* m_free */
+};
+#endif
+#ifndef CYTHON_SMALL_CODE
+#if defined(__clang__)
+    #define CYTHON_SMALL_CODE
+#elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3))
+    #define CYTHON_SMALL_CODE __attribute__((cold))
+#else
+    #define CYTHON_SMALL_CODE
+#endif
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+  {&__pyx_kp_s_equation_err, __pyx_k_equation_err, sizeof(__pyx_k_equation_err), 0, 0, 1, 0},
+  {&__pyx_n_s_err, __pyx_k_err, sizeof(__pyx_k_err), 0, 0, 1, 1},
+  {&__pyx_n_s_err_f, __pyx_k_err_f, sizeof(__pyx_k_err_f), 0, 0, 1, 1},
+  {&__pyx_n_s_err_lai, __pyx_k_err_lai, sizeof(__pyx_k_err_lai), 0, 0, 1, 1},
+  {&__pyx_n_s_exp, __pyx_k_exp, sizeof(__pyx_k_exp), 0, 0, 1, 1},
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+  {&__pyx_n_s_logging, __pyx_k_logging, sizeof(__pyx_k_logging), 0, 0, 1, 1},
+  {&__pyx_n_s_main, __pyx_k_main, sizeof(__pyx_k_main), 0, 0, 1, 1},
+  {&__pyx_n_s_matplotlib, __pyx_k_matplotlib, sizeof(__pyx_k_matplotlib), 0, 0, 1, 1},
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+  {&__pyx_n_s_name, __pyx_k_name, sizeof(__pyx_k_name), 0, 0, 1, 1},
+  {&__pyx_n_s_nan, __pyx_k_nan, sizeof(__pyx_k_nan), 0, 0, 1, 1},
+  {&__pyx_n_s_np, __pyx_k_np, sizeof(__pyx_k_np), 0, 0, 1, 1},
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+  {&__pyx_n_s_plt, __pyx_k_plt, sizeof(__pyx_k_plt), 0, 0, 1, 1},
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+  {&__pyx_n_s_pyplot, __pyx_k_pyplot, sizeof(__pyx_k_pyplot), 0, 0, 1, 1},
+  {&__pyx_n_s_random, __pyx_k_random, sizeof(__pyx_k_random), 0, 0, 1, 1},
+  {&__pyx_n_s_result, __pyx_k_result, sizeof(__pyx_k_result), 0, 0, 1, 1},
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+  {&__pyx_n_s_sample_sigma, __pyx_k_sample_sigma, sizeof(__pyx_k_sample_sigma), 0, 0, 1, 1},
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+  {&__pyx_n_s_scipy_optimize, __pyx_k_scipy_optimize, sizeof(__pyx_k_scipy_optimize), 0, 0, 1, 1},
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+  {&__pyx_n_s_sigma_veg, __pyx_k_sigma_veg, sizeof(__pyx_k_sigma_veg), 0, 0, 1, 1},
+  {&__pyx_n_s_soil_water, __pyx_k_soil_water, sizeof(__pyx_k_soil_water), 0, 0, 1, 1},
+  {&__pyx_n_s_soil_water_tiff, __pyx_k_soil_water_tiff, sizeof(__pyx_k_soil_water_tiff), 0, 0, 1, 1},
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+  {&__pyx_n_s_test, __pyx_k_test, sizeof(__pyx_k_test), 0, 0, 1, 1},
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+  return 0;
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+  return -1;
+}
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+static CYTHON_SMALL_CODE int __Pyx_InitCachedConstants(void) {
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+  /* "LAIProcess.pyx":48
+ *         lai_waiter_inc_sigma_list (list):
+ *     """
+ *     def f(X):             # <<<<<<<<<<<<<<
+ *         eqs=[]
+ *         for lai_water_inc_sigma_item in lai_water_inc_sigma_list:
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+#ifdef __cplusplus
+#define __Pyx_PyMODINIT_FUNC extern "C" void
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+#define __Pyx_PyMODINIT_FUNC void
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+#ifdef __cplusplus
+#define __Pyx_PyMODINIT_FUNC extern "C" PyObject *
+#else
+#define __Pyx_PyMODINIT_FUNC PyObject *
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+static CYTHON_SMALL_CODE PyObject* __pyx_pymod_create(PyObject *spec, CYTHON_UNUSED PyModuleDef *def) {
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+    if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "origin", "__file__", 1) < 0)) goto bad;
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+  #if CYTHON_PEP489_MULTI_PHASE_INIT
+  __pyx_m = __pyx_pyinit_module;
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+ * cimport numpy as np
+ * from libc.math cimport pi
+ */
+  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numpy, 0, -1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 6, __pyx_L1_error)
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+ * from scipy.optimize import leastsq             # <<<<<<<<<<<<<<
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+ * import logging
+ */
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+static int __Pyx_ParseOptionalKeywords(
+    PyObject *kwds,
+    PyObject **argnames[],
+    PyObject *kwds2,
+    PyObject *values[],
+    Py_ssize_t num_pos_args,
+    const char* function_name)
+{
+    PyObject *key = 0, *value = 0;
+    Py_ssize_t pos = 0;
+    PyObject*** name;
+    PyObject*** first_kw_arg = argnames + num_pos_args;
+    while (PyDict_Next(kwds, &pos, &key, &value)) {
+        name = first_kw_arg;
+        while (*name && (**name != key)) name++;
+        if (*name) {
+            values[name-argnames] = value;
+            continue;
+        }
+        name = first_kw_arg;
+        #if PY_MAJOR_VERSION < 3
+        if (likely(PyString_Check(key))) {
+            while (*name) {
+                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
+                        && _PyString_Eq(**name, key)) {
+                    values[name-argnames] = value;
+                    break;
+                }
+                name++;
+            }
+            if (*name) continue;
+            else {
+                PyObject*** argname = argnames;
+                while (argname != first_kw_arg) {
+                    if ((**argname == key) || (
+                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
+                             && _PyString_Eq(**argname, key))) {
+                        goto arg_passed_twice;
+                    }
+                    argname++;
+                }
+            }
+        } else
+        #endif
+        if (likely(PyUnicode_Check(key))) {
+            while (*name) {
+                int cmp = (**name == key) ? 0 :
+                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
+                    (__Pyx_PyUnicode_GET_LENGTH(**name) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
+                #endif
+                    PyUnicode_Compare(**name, key);
+                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
+                if (cmp == 0) {
+                    values[name-argnames] = value;
+                    break;
+                }
+                name++;
+            }
+            if (*name) continue;
+            else {
+                PyObject*** argname = argnames;
+                while (argname != first_kw_arg) {
+                    int cmp = (**argname == key) ? 0 :
+                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
+                        (__Pyx_PyUnicode_GET_LENGTH(**argname) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
+                    #endif
+                        PyUnicode_Compare(**argname, key);
+                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
+                    if (cmp == 0) goto arg_passed_twice;
+                    argname++;
+                }
+            }
+        } else
+            goto invalid_keyword_type;
+        if (kwds2) {
+            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
+        } else {
+            goto invalid_keyword;
+        }
+    }
+    return 0;
+arg_passed_twice:
+    __Pyx_RaiseDoubleKeywordsError(function_name, key);
+    goto bad;
+invalid_keyword_type:
+    PyErr_Format(PyExc_TypeError,
+        "%.200s() keywords must be strings", function_name);
+    goto bad;
+invalid_keyword:
+    PyErr_Format(PyExc_TypeError,
+    #if PY_MAJOR_VERSION < 3
+        "%.200s() got an unexpected keyword argument '%.200s'",
+        function_name, PyString_AsString(key));
+    #else
+        "%s() got an unexpected keyword argument '%U'",
+        function_name, key);
+    #endif
+bad:
+    return -1;
+}
+
+/* RaiseTooManyValuesToUnpack */
+static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
+    PyErr_Format(PyExc_ValueError,
+                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
+}
+
+/* RaiseNeedMoreValuesToUnpack */
+static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
+    PyErr_Format(PyExc_ValueError,
+                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
+                 index, (index == 1) ? "" : "s");
+}
+
+/* IterFinish */
+static CYTHON_INLINE int __Pyx_IterFinish(void) {
+#if CYTHON_FAST_THREAD_STATE
+    PyThreadState *tstate = __Pyx_PyThreadState_Current;
+    PyObject* exc_type = tstate->curexc_type;
+    if (unlikely(exc_type)) {
+        if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) {
+            PyObject *exc_value, *exc_tb;
+            exc_value = tstate->curexc_value;
+            exc_tb = tstate->curexc_traceback;
+            tstate->curexc_type = 0;
+            tstate->curexc_value = 0;
+            tstate->curexc_traceback = 0;
+            Py_DECREF(exc_type);
+            Py_XDECREF(exc_value);
+            Py_XDECREF(exc_tb);
+            return 0;
+        } else {
+            return -1;
+        }
+    }
+    return 0;
+#else
+    if (unlikely(PyErr_Occurred())) {
+        if (likely(PyErr_ExceptionMatches(PyExc_StopIteration))) {
+            PyErr_Clear();
+            return 0;
+        } else {
+            return -1;
+        }
+    }
+    return 0;
+#endif
+}
+
+/* UnpackItemEndCheck */
+static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) {
+    if (unlikely(retval)) {
+        Py_DECREF(retval);
+        __Pyx_RaiseTooManyValuesError(expected);
+        return -1;
+    } else {
+        return __Pyx_IterFinish();
+    }
+    return 0;
+}
+
+/* PyObjectGetAttrStr */
+#if CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
+    PyTypeObject* tp = Py_TYPE(obj);
+    if (likely(tp->tp_getattro))
+        return tp->tp_getattro(obj, attr_name);
+#if PY_MAJOR_VERSION < 3
+    if (likely(tp->tp_getattr))
+        return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
+#endif
+    return PyObject_GetAttr(obj, attr_name);
+}
+#endif
+
+/* GetBuiltinName */
+static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
+    PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
+    if (unlikely(!result)) {
+        PyErr_Format(PyExc_NameError,
+#if PY_MAJOR_VERSION >= 3
+            "name '%U' is not defined", name);
+#else
+            "name '%.200s' is not defined", PyString_AS_STRING(name));
+#endif
+    }
+    return result;
+}
+
+/* PyDictVersioning */
+#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
+    PyObject *dict = Py_TYPE(obj)->tp_dict;
+    return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
+}
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
+    PyObject **dictptr = NULL;
+    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
+    if (offset) {
+#if CYTHON_COMPILING_IN_CPYTHON
+        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
+#else
+        dictptr = _PyObject_GetDictPtr(obj);
+#endif
+    }
+    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
+}
+static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
+    PyObject *dict = Py_TYPE(obj)->tp_dict;
+    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
+        return 0;
+    return obj_dict_version == __Pyx_get_object_dict_version(obj);
+}
+#endif
+
+/* GetModuleGlobalName */
+#if CYTHON_USE_DICT_VERSIONS
+static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)
+#else
+static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)
+#endif
+{
+    PyObject *result;
+#if !CYTHON_AVOID_BORROWED_REFS
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
+    result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
+    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
+    if (likely(result)) {
+        return __Pyx_NewRef(result);
+    } else if (unlikely(PyErr_Occurred())) {
+        return NULL;
+    }
+#else
+    result = PyDict_GetItem(__pyx_d, name);
+    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
+    if (likely(result)) {
+        return __Pyx_NewRef(result);
+    }
+#endif
+#else
+    result = PyObject_GetItem(__pyx_d, name);
+    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
+    if (likely(result)) {
+        return __Pyx_NewRef(result);
+    }
+    PyErr_Clear();
+#endif
+    return __Pyx_GetBuiltinName(name);
+}
+
+/* PyCFunctionFastCall */
+#if CYTHON_FAST_PYCCALL
+static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
+    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
+    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
+    PyObject *self = PyCFunction_GET_SELF(func);
+    int flags = PyCFunction_GET_FLAGS(func);
+    assert(PyCFunction_Check(func));
+    assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)));
+    assert(nargs >= 0);
+    assert(nargs == 0 || args != NULL);
+    /* _PyCFunction_FastCallDict() must not be called with an exception set,
+       because it may clear it (directly or indirectly) and so the
+       caller loses its exception */
+    assert(!PyErr_Occurred());
+    if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
+        return (*((__Pyx_PyCFunctionFastWithKeywords)(void*)meth)) (self, args, nargs, NULL);
+    } else {
+        return (*((__Pyx_PyCFunctionFast)(void*)meth)) (self, args, nargs);
+    }
+}
+#endif
+
+/* PyFunctionFastCall */
+#if CYTHON_FAST_PYCALL
+static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
+                                               PyObject *globals) {
+    PyFrameObject *f;
+    PyThreadState *tstate = __Pyx_PyThreadState_Current;
+    PyObject **fastlocals;
+    Py_ssize_t i;
+    PyObject *result;
+    assert(globals != NULL);
+    /* XXX Perhaps we should create a specialized
+       PyFrame_New() that doesn't take locals, but does
+       take builtins without sanity checking them.
+       */
+    assert(tstate != NULL);
+    f = PyFrame_New(tstate, co, globals, NULL);
+    if (f == NULL) {
+        return NULL;
+    }
+    fastlocals = __Pyx_PyFrame_GetLocalsplus(f);
+    for (i = 0; i < na; i++) {
+        Py_INCREF(*args);
+        fastlocals[i] = *args++;
+    }
+    result = PyEval_EvalFrameEx(f,0);
+    ++tstate->recursion_depth;
+    Py_DECREF(f);
+    --tstate->recursion_depth;
+    return result;
+}
+#if 1 || PY_VERSION_HEX < 0x030600B1
+static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs) {
+    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
+    PyObject *globals = PyFunction_GET_GLOBALS(func);
+    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
+    PyObject *closure;
+#if PY_MAJOR_VERSION >= 3
+    PyObject *kwdefs;
+#endif
+    PyObject *kwtuple, **k;
+    PyObject **d;
+    Py_ssize_t nd;
+    Py_ssize_t nk;
+    PyObject *result;
+    assert(kwargs == NULL || PyDict_Check(kwargs));
+    nk = kwargs ? PyDict_Size(kwargs) : 0;
+    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
+        return NULL;
+    }
+    if (
+#if PY_MAJOR_VERSION >= 3
+            co->co_kwonlyargcount == 0 &&
+#endif
+            likely(kwargs == NULL || nk == 0) &&
+            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
+        if (argdefs == NULL && co->co_argcount == nargs) {
+            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
+            goto done;
+        }
+        else if (nargs == 0 && argdefs != NULL
+                 && co->co_argcount == Py_SIZE(argdefs)) {
+            /* function called with no arguments, but all parameters have
+               a default value: use default values as arguments .*/
+            args = &PyTuple_GET_ITEM(argdefs, 0);
+            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
+            goto done;
+        }
+    }
+    if (kwargs != NULL) {
+        Py_ssize_t pos, i;
+        kwtuple = PyTuple_New(2 * nk);
+        if (kwtuple == NULL) {
+            result = NULL;
+            goto done;
+        }
+        k = &PyTuple_GET_ITEM(kwtuple, 0);
+        pos = i = 0;
+        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
+            Py_INCREF(k[i]);
+            Py_INCREF(k[i+1]);
+            i += 2;
+        }
+        nk = i / 2;
+    }
+    else {
+        kwtuple = NULL;
+        k = NULL;
+    }
+    closure = PyFunction_GET_CLOSURE(func);
+#if PY_MAJOR_VERSION >= 3
+    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
+#endif
+    if (argdefs != NULL) {
+        d = &PyTuple_GET_ITEM(argdefs, 0);
+        nd = Py_SIZE(argdefs);
+    }
+    else {
+        d = NULL;
+        nd = 0;
+    }
+#if PY_MAJOR_VERSION >= 3
+    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
+                               args, (int)nargs,
+                               k, (int)nk,
+                               d, (int)nd, kwdefs, closure);
+#else
+    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
+                               args, (int)nargs,
+                               k, (int)nk,
+                               d, (int)nd, closure);
+#endif
+    Py_XDECREF(kwtuple);
+done:
+    Py_LeaveRecursiveCall();
+    return result;
+}
+#endif
+#endif
+
+/* PyObjectCall */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
+    PyObject *result;
+    ternaryfunc call = Py_TYPE(func)->tp_call;
+    if (unlikely(!call))
+        return PyObject_Call(func, arg, kw);
+    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
+        return NULL;
+    result = (*call)(func, arg, kw);
+    Py_LeaveRecursiveCall();
+    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
+        PyErr_SetString(
+            PyExc_SystemError,
+            "NULL result without error in PyObject_Call");
+    }
+    return result;
+}
+#endif
+
+/* PyObjectCall2Args */
+static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) {
+    PyObject *args, *result = NULL;
+    #if CYTHON_FAST_PYCALL
+    if (PyFunction_Check(function)) {
+        PyObject *args[2] = {arg1, arg2};
+        return __Pyx_PyFunction_FastCall(function, args, 2);
+    }
+    #endif
+    #if CYTHON_FAST_PYCCALL
+    if (__Pyx_PyFastCFunction_Check(function)) {
+        PyObject *args[2] = {arg1, arg2};
+        return __Pyx_PyCFunction_FastCall(function, args, 2);
+    }
+    #endif
+    args = PyTuple_New(2);
+    if (unlikely(!args)) goto done;
+    Py_INCREF(arg1);
+    PyTuple_SET_ITEM(args, 0, arg1);
+    Py_INCREF(arg2);
+    PyTuple_SET_ITEM(args, 1, arg2);
+    Py_INCREF(function);
+    result = __Pyx_PyObject_Call(function, args, NULL);
+    Py_DECREF(args);
+    Py_DECREF(function);
+done:
+    return result;
+}
+
+/* PyObjectCallMethO */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
+    PyObject *self, *result;
+    PyCFunction cfunc;
+    cfunc = PyCFunction_GET_FUNCTION(func);
+    self = PyCFunction_GET_SELF(func);
+    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
+        return NULL;
+    result = cfunc(self, arg);
+    Py_LeaveRecursiveCall();
+    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
+        PyErr_SetString(
+            PyExc_SystemError,
+            "NULL result without error in PyObject_Call");
+    }
+    return result;
+}
+#endif
+
+/* PyObjectCallOneArg */
+#if CYTHON_COMPILING_IN_CPYTHON
+static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+    PyObject *result;
+    PyObject *args = PyTuple_New(1);
+    if (unlikely(!args)) return NULL;
+    Py_INCREF(arg);
+    PyTuple_SET_ITEM(args, 0, arg);
+    result = __Pyx_PyObject_Call(func, args, NULL);
+    Py_DECREF(args);
+    return result;
+}
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+#if CYTHON_FAST_PYCALL
+    if (PyFunction_Check(func)) {
+        return __Pyx_PyFunction_FastCall(func, &arg, 1);
+    }
+#endif
+    if (likely(PyCFunction_Check(func))) {
+        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
+            return __Pyx_PyObject_CallMethO(func, arg);
+#if CYTHON_FAST_PYCCALL
+        } else if (__Pyx_PyFastCFunction_Check(func)) {
+            return __Pyx_PyCFunction_FastCall(func, &arg, 1);
+#endif
+        }
+    }
+    return __Pyx__PyObject_CallOneArg(func, arg);
+}
+#else
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+    PyObject *result;
+    PyObject *args = PyTuple_Pack(1, arg);
+    if (unlikely(!args)) return NULL;
+    result = __Pyx_PyObject_Call(func, args, NULL);
+    Py_DECREF(args);
+    return result;
+}
+#endif
+
+/* PyIntBinop */
+#if !CYTHON_COMPILING_IN_PYPY
+static PyObject* __Pyx_PyInt_SubtractCObj(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, int inplace, int zerodivision_check) {
+    (void)inplace;
+    (void)zerodivision_check;
+    #if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_CheckExact(op2))) {
+        const long a = intval;
+        long x;
+        long b = PyInt_AS_LONG(op2);
+            x = (long)((unsigned long)a - b);
+            if (likely((x^a) >= 0 || (x^~b) >= 0))
+                return PyInt_FromLong(x);
+            return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
+    }
+    #endif
+    #if CYTHON_USE_PYLONG_INTERNALS
+    if (likely(PyLong_CheckExact(op2))) {
+        const long a = intval;
+        long b, x;
+#ifdef HAVE_LONG_LONG
+        const PY_LONG_LONG lla = intval;
+        PY_LONG_LONG llb, llx;
+#endif
+        const digit* digits = ((PyLongObject*)op2)->ob_digit;
+        const Py_ssize_t size = Py_SIZE(op2);
+        if (likely(__Pyx_sst_abs(size) <= 1)) {
+            b = likely(size) ? digits[0] : 0;
+            if (size == -1) b = -b;
+        } else {
+            switch (size) {
+                case -2:
+                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                        b = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
+                        llb = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case 2:
+                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                        b = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
+                        llb = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case -3:
+                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                        b = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
+                        llb = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case 3:
+                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                        b = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
+                        llb = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case -4:
+                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
+                        b = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
+                        llb = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                case 4:
+                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
+                        b = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
+                        break;
+#ifdef HAVE_LONG_LONG
+                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
+                        llb = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
+                        goto long_long;
+#endif
+                    }
+                    CYTHON_FALLTHROUGH;
+                default: return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
+            }
+        }
+                x = a - b;
+            return PyLong_FromLong(x);
+#ifdef HAVE_LONG_LONG
+        long_long:
+                llx = lla - llb;
+            return PyLong_FromLongLong(llx);
+#endif
+        
+        
+    }
+    #endif
+    if (PyFloat_CheckExact(op2)) {
+        const long a = intval;
+        double b = PyFloat_AS_DOUBLE(op2);
+            double result;
+            PyFPE_START_PROTECT("subtract", return NULL)
+            result = ((double)a) - (double)b;
+            PyFPE_END_PROTECT(result)
+            return PyFloat_FromDouble(result);
+    }
+    return (inplace ? PyNumber_InPlaceSubtract : PyNumber_Subtract)(op1, op2);
+}
+#endif
+
+/* None */
+static CYTHON_INLINE void __Pyx_RaiseClosureNameError(const char *varname) {
+    PyErr_Format(PyExc_NameError, "free variable '%s' referenced before assignment in enclosing scope", varname);
+}
+
+/* GetItemInt */
+static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
+    PyObject *r;
+    if (!j) return NULL;
+    r = PyObject_GetItem(o, j);
+    Py_DECREF(j);
+    return r;
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
+                                                              CYTHON_NCP_UNUSED int wraparound,
+                                                              CYTHON_NCP_UNUSED int boundscheck) {
+#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+    Py_ssize_t wrapped_i = i;
+    if (wraparound & unlikely(i < 0)) {
+        wrapped_i += PyList_GET_SIZE(o);
+    }
+    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyList_GET_SIZE(o)))) {
+        PyObject *r = PyList_GET_ITEM(o, wrapped_i);
+        Py_INCREF(r);
+        return r;
+    }
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+#else
+    return PySequence_GetItem(o, i);
+#endif
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
+                                                              CYTHON_NCP_UNUSED int wraparound,
+                                                              CYTHON_NCP_UNUSED int boundscheck) {
+#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+    Py_ssize_t wrapped_i = i;
+    if (wraparound & unlikely(i < 0)) {
+        wrapped_i += PyTuple_GET_SIZE(o);
+    }
+    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyTuple_GET_SIZE(o)))) {
+        PyObject *r = PyTuple_GET_ITEM(o, wrapped_i);
+        Py_INCREF(r);
+        return r;
+    }
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+#else
+    return PySequence_GetItem(o, i);
+#endif
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
+                                                     CYTHON_NCP_UNUSED int wraparound,
+                                                     CYTHON_NCP_UNUSED int boundscheck) {
+#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
+    if (is_list || PyList_CheckExact(o)) {
+        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
+        if ((!boundscheck) || (likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o))))) {
+            PyObject *r = PyList_GET_ITEM(o, n);
+            Py_INCREF(r);
+            return r;
+        }
+    }
+    else if (PyTuple_CheckExact(o)) {
+        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
+        if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyTuple_GET_SIZE(o)))) {
+            PyObject *r = PyTuple_GET_ITEM(o, n);
+            Py_INCREF(r);
+            return r;
+        }
+    } else {
+        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
+        if (likely(m && m->sq_item)) {
+            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
+                Py_ssize_t l = m->sq_length(o);
+                if (likely(l >= 0)) {
+                    i += l;
+                } else {
+                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
+                        return NULL;
+                    PyErr_Clear();
+                }
+            }
+            return m->sq_item(o, i);
+        }
+    }
+#else
+    if (is_list || PySequence_Check(o)) {
+        return PySequence_GetItem(o, i);
+    }
+#endif
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+}
+
+/* FetchCommonType */
+static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
+    PyObject* fake_module;
+    PyTypeObject* cached_type = NULL;
+    fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
+    if (!fake_module) return NULL;
+    Py_INCREF(fake_module);
+    cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
+    if (cached_type) {
+        if (!PyType_Check((PyObject*)cached_type)) {
+            PyErr_Format(PyExc_TypeError,
+                "Shared Cython type %.200s is not a type object",
+                type->tp_name);
+            goto bad;
+        }
+        if (cached_type->tp_basicsize != type->tp_basicsize) {
+            PyErr_Format(PyExc_TypeError,
+                "Shared Cython type %.200s has the wrong size, try recompiling",
+                type->tp_name);
+            goto bad;
+        }
+    } else {
+        if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
+        PyErr_Clear();
+        if (PyType_Ready(type) < 0) goto bad;
+        if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
+            goto bad;
+        Py_INCREF(type);
+        cached_type = type;
+    }
+done:
+    Py_DECREF(fake_module);
+    return cached_type;
+bad:
+    Py_XDECREF(cached_type);
+    cached_type = NULL;
+    goto done;
+}
+
+/* CythonFunctionShared */
+#include <structmember.h>
+static PyObject *
+__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *closure)
+{
+    if (unlikely(op->func_doc == NULL)) {
+        if (op->func.m_ml->ml_doc) {
+#if PY_MAJOR_VERSION >= 3
+            op->func_doc = PyUnicode_FromString(op->func.m_ml->ml_doc);
+#else
+            op->func_doc = PyString_FromString(op->func.m_ml->ml_doc);
+#endif
+            if (unlikely(op->func_doc == NULL))
+                return NULL;
+        } else {
+            Py_INCREF(Py_None);
+            return Py_None;
+        }
+    }
+    Py_INCREF(op->func_doc);
+    return op->func_doc;
+}
+static int
+__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value, CYTHON_UNUSED void *context)
+{
+    PyObject *tmp = op->func_doc;
+    if (value == NULL) {
+        value = Py_None;
+    }
+    Py_INCREF(value);
+    op->func_doc = value;
+    Py_XDECREF(tmp);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *context)
+{
+    if (unlikely(op->func_name == NULL)) {
+#if PY_MAJOR_VERSION >= 3
+        op->func_name = PyUnicode_InternFromString(op->func.m_ml->ml_name);
+#else
+        op->func_name = PyString_InternFromString(op->func.m_ml->ml_name);
+#endif
+        if (unlikely(op->func_name == NULL))
+            return NULL;
+    }
+    Py_INCREF(op->func_name);
+    return op->func_name;
+}
+static int
+__Pyx_CyFunction_set_name(__pyx_CyFunctionObject *op, PyObject *value, CYTHON_UNUSED void *context)
+{
+    PyObject *tmp;
+#if PY_MAJOR_VERSION >= 3
+    if (unlikely(value == NULL || !PyUnicode_Check(value)))
+#else
+    if (unlikely(value == NULL || !PyString_Check(value)))
+#endif
+    {
+        PyErr_SetString(PyExc_TypeError,
+                        "__name__ must be set to a string object");
+        return -1;
+    }
+    tmp = op->func_name;
+    Py_INCREF(value);
+    op->func_name = value;
+    Py_XDECREF(tmp);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_qualname(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *context)
+{
+    Py_INCREF(op->func_qualname);
+    return op->func_qualname;
+}
+static int
+__Pyx_CyFunction_set_qualname(__pyx_CyFunctionObject *op, PyObject *value, CYTHON_UNUSED void *context)
+{
+    PyObject *tmp;
+#if PY_MAJOR_VERSION >= 3
+    if (unlikely(value == NULL || !PyUnicode_Check(value)))
+#else
+    if (unlikely(value == NULL || !PyString_Check(value)))
+#endif
+    {
+        PyErr_SetString(PyExc_TypeError,
+                        "__qualname__ must be set to a string object");
+        return -1;
+    }
+    tmp = op->func_qualname;
+    Py_INCREF(value);
+    op->func_qualname = value;
+    Py_XDECREF(tmp);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_self(__pyx_CyFunctionObject *m, CYTHON_UNUSED void *closure)
+{
+    PyObject *self;
+    self = m->func_closure;
+    if (self == NULL)
+        self = Py_None;
+    Py_INCREF(self);
+    return self;
+}
+static PyObject *
+__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *context)
+{
+    if (unlikely(op->func_dict == NULL)) {
+        op->func_dict = PyDict_New();
+        if (unlikely(op->func_dict == NULL))
+            return NULL;
+    }
+    Py_INCREF(op->func_dict);
+    return op->func_dict;
+}
+static int
+__Pyx_CyFunction_set_dict(__pyx_CyFunctionObject *op, PyObject *value, CYTHON_UNUSED void *context)
+{
+    PyObject *tmp;
+    if (unlikely(value == NULL)) {
+        PyErr_SetString(PyExc_TypeError,
+               "function's dictionary may not be deleted");
+        return -1;
+    }
+    if (unlikely(!PyDict_Check(value))) {
+        PyErr_SetString(PyExc_TypeError,
+               "setting function's dictionary to a non-dict");
+        return -1;
+    }
+    tmp = op->func_dict;
+    Py_INCREF(value);
+    op->func_dict = value;
+    Py_XDECREF(tmp);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_globals(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *context)
+{
+    Py_INCREF(op->func_globals);
+    return op->func_globals;
+}
+static PyObject *
+__Pyx_CyFunction_get_closure(CYTHON_UNUSED __pyx_CyFunctionObject *op, CYTHON_UNUSED void *context)
+{
+    Py_INCREF(Py_None);
+    return Py_None;
+}
+static PyObject *
+__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *context)
+{
+    PyObject* result = (op->func_code) ? op->func_code : Py_None;
+    Py_INCREF(result);
+    return result;
+}
+static int
+__Pyx_CyFunction_init_defaults(__pyx_CyFunctionObject *op) {
+    int result = 0;
+    PyObject *res = op->defaults_getter((PyObject *) op);
+    if (unlikely(!res))
+        return -1;
+    #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+    op->defaults_tuple = PyTuple_GET_ITEM(res, 0);
+    Py_INCREF(op->defaults_tuple);
+    op->defaults_kwdict = PyTuple_GET_ITEM(res, 1);
+    Py_INCREF(op->defaults_kwdict);
+    #else
+    op->defaults_tuple = PySequence_ITEM(res, 0);
+    if (unlikely(!op->defaults_tuple)) result = -1;
+    else {
+        op->defaults_kwdict = PySequence_ITEM(res, 1);
+        if (unlikely(!op->defaults_kwdict)) result = -1;
+    }
+    #endif
+    Py_DECREF(res);
+    return result;
+}
+static int
+__Pyx_CyFunction_set_defaults(__pyx_CyFunctionObject *op, PyObject* value, CYTHON_UNUSED void *context) {
+    PyObject* tmp;
+    if (!value) {
+        value = Py_None;
+    } else if (value != Py_None && !PyTuple_Check(value)) {
+        PyErr_SetString(PyExc_TypeError,
+                        "__defaults__ must be set to a tuple object");
+        return -1;
+    }
+    Py_INCREF(value);
+    tmp = op->defaults_tuple;
+    op->defaults_tuple = value;
+    Py_XDECREF(tmp);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *context) {
+    PyObject* result = op->defaults_tuple;
+    if (unlikely(!result)) {
+        if (op->defaults_getter) {
+            if (__Pyx_CyFunction_init_defaults(op) < 0) return NULL;
+            result = op->defaults_tuple;
+        } else {
+            result = Py_None;
+        }
+    }
+    Py_INCREF(result);
+    return result;
+}
+static int
+__Pyx_CyFunction_set_kwdefaults(__pyx_CyFunctionObject *op, PyObject* value, CYTHON_UNUSED void *context) {
+    PyObject* tmp;
+    if (!value) {
+        value = Py_None;
+    } else if (value != Py_None && !PyDict_Check(value)) {
+        PyErr_SetString(PyExc_TypeError,
+                        "__kwdefaults__ must be set to a dict object");
+        return -1;
+    }
+    Py_INCREF(value);
+    tmp = op->defaults_kwdict;
+    op->defaults_kwdict = value;
+    Py_XDECREF(tmp);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_kwdefaults(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *context) {
+    PyObject* result = op->defaults_kwdict;
+    if (unlikely(!result)) {
+        if (op->defaults_getter) {
+            if (__Pyx_CyFunction_init_defaults(op) < 0) return NULL;
+            result = op->defaults_kwdict;
+        } else {
+            result = Py_None;
+        }
+    }
+    Py_INCREF(result);
+    return result;
+}
+static int
+__Pyx_CyFunction_set_annotations(__pyx_CyFunctionObject *op, PyObject* value, CYTHON_UNUSED void *context) {
+    PyObject* tmp;
+    if (!value || value == Py_None) {
+        value = NULL;
+    } else if (!PyDict_Check(value)) {
+        PyErr_SetString(PyExc_TypeError,
+                        "__annotations__ must be set to a dict object");
+        return -1;
+    }
+    Py_XINCREF(value);
+    tmp = op->func_annotations;
+    op->func_annotations = value;
+    Py_XDECREF(tmp);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_annotations(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *context) {
+    PyObject* result = op->func_annotations;
+    if (unlikely(!result)) {
+        result = PyDict_New();
+        if (unlikely(!result)) return NULL;
+        op->func_annotations = result;
+    }
+    Py_INCREF(result);
+    return result;
+}
+static PyGetSetDef __pyx_CyFunction_getsets[] = {
+    {(char *) "func_doc", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
+    {(char *) "__doc__",  (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
+    {(char *) "func_name", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
+    {(char *) "__name__", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
+    {(char *) "__qualname__", (getter)__Pyx_CyFunction_get_qualname, (setter)__Pyx_CyFunction_set_qualname, 0, 0},
+    {(char *) "__self__", (getter)__Pyx_CyFunction_get_self, 0, 0, 0},
+    {(char *) "func_dict", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
+    {(char *) "__dict__", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
+    {(char *) "func_globals", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
+    {(char *) "__globals__", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
+    {(char *) "func_closure", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
+    {(char *) "__closure__", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
+    {(char *) "func_code", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
+    {(char *) "__code__", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
+    {(char *) "func_defaults", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
+    {(char *) "__defaults__", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
+    {(char *) "__kwdefaults__", (getter)__Pyx_CyFunction_get_kwdefaults, (setter)__Pyx_CyFunction_set_kwdefaults, 0, 0},
+    {(char *) "__annotations__", (getter)__Pyx_CyFunction_get_annotations, (setter)__Pyx_CyFunction_set_annotations, 0, 0},
+    {0, 0, 0, 0, 0}
+};
+static PyMemberDef __pyx_CyFunction_members[] = {
+    {(char *) "__module__", T_OBJECT, offsetof(PyCFunctionObject, m_module), PY_WRITE_RESTRICTED, 0},
+    {0, 0, 0,  0, 0}
+};
+static PyObject *
+__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, CYTHON_UNUSED PyObject *args)
+{
+#if PY_MAJOR_VERSION >= 3
+    Py_INCREF(m->func_qualname);
+    return m->func_qualname;
+#else
+    return PyString_FromString(m->func.m_ml->ml_name);
+#endif
+}
+static PyMethodDef __pyx_CyFunction_methods[] = {
+    {"__reduce__", (PyCFunction)__Pyx_CyFunction_reduce, METH_VARARGS, 0},
+    {0, 0, 0, 0}
+};
+#if PY_VERSION_HEX < 0x030500A0
+#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func_weakreflist)
+#else
+#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func.m_weakreflist)
+#endif
+static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject *op, PyMethodDef *ml, int flags, PyObject* qualname,
+                                       PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
+    if (unlikely(op == NULL))
+        return NULL;
+    op->flags = flags;
+    __Pyx_CyFunction_weakreflist(op) = NULL;
+    op->func.m_ml = ml;
+    op->func.m_self = (PyObject *) op;
+    Py_XINCREF(closure);
+    op->func_closure = closure;
+    Py_XINCREF(module);
+    op->func.m_module = module;
+    op->func_dict = NULL;
+    op->func_name = NULL;
+    Py_INCREF(qualname);
+    op->func_qualname = qualname;
+    op->func_doc = NULL;
+    op->func_classobj = NULL;
+    op->func_globals = globals;
+    Py_INCREF(op->func_globals);
+    Py_XINCREF(code);
+    op->func_code = code;
+    op->defaults_pyobjects = 0;
+    op->defaults_size = 0;
+    op->defaults = NULL;
+    op->defaults_tuple = NULL;
+    op->defaults_kwdict = NULL;
+    op->defaults_getter = NULL;
+    op->func_annotations = NULL;
+    return (PyObject *) op;
+}
+static int
+__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m)
+{
+    Py_CLEAR(m->func_closure);
+    Py_CLEAR(m->func.m_module);
+    Py_CLEAR(m->func_dict);
+    Py_CLEAR(m->func_name);
+    Py_CLEAR(m->func_qualname);
+    Py_CLEAR(m->func_doc);
+    Py_CLEAR(m->func_globals);
+    Py_CLEAR(m->func_code);
+    Py_CLEAR(m->func_classobj);
+    Py_CLEAR(m->defaults_tuple);
+    Py_CLEAR(m->defaults_kwdict);
+    Py_CLEAR(m->func_annotations);
+    if (m->defaults) {
+        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
+        int i;
+        for (i = 0; i < m->defaults_pyobjects; i++)
+            Py_XDECREF(pydefaults[i]);
+        PyObject_Free(m->defaults);
+        m->defaults = NULL;
+    }
+    return 0;
+}
+static void __Pyx__CyFunction_dealloc(__pyx_CyFunctionObject *m)
+{
+    if (__Pyx_CyFunction_weakreflist(m) != NULL)
+        PyObject_ClearWeakRefs((PyObject *) m);
+    __Pyx_CyFunction_clear(m);
+    PyObject_GC_Del(m);
+}
+static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m)
+{
+    PyObject_GC_UnTrack(m);
+    __Pyx__CyFunction_dealloc(m);
+}
+static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg)
+{
+    Py_VISIT(m->func_closure);
+    Py_VISIT(m->func.m_module);
+    Py_VISIT(m->func_dict);
+    Py_VISIT(m->func_name);
+    Py_VISIT(m->func_qualname);
+    Py_VISIT(m->func_doc);
+    Py_VISIT(m->func_globals);
+    Py_VISIT(m->func_code);
+    Py_VISIT(m->func_classobj);
+    Py_VISIT(m->defaults_tuple);
+    Py_VISIT(m->defaults_kwdict);
+    if (m->defaults) {
+        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
+        int i;
+        for (i = 0; i < m->defaults_pyobjects; i++)
+            Py_VISIT(pydefaults[i]);
+    }
+    return 0;
+}
+static PyObject *__Pyx_CyFunction_descr_get(PyObject *func, PyObject *obj, PyObject *type)
+{
+#if PY_MAJOR_VERSION < 3
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    if (m->flags & __Pyx_CYFUNCTION_STATICMETHOD) {
+        Py_INCREF(func);
+        return func;
+    }
+    if (m->flags & __Pyx_CYFUNCTION_CLASSMETHOD) {
+        if (type == NULL)
+            type = (PyObject *)(Py_TYPE(obj));
+        return __Pyx_PyMethod_New(func, type, (PyObject *)(Py_TYPE(type)));
+    }
+    if (obj == Py_None)
+        obj = NULL;
+#endif
+    return __Pyx_PyMethod_New(func, obj, type);
+}
+static PyObject*
+__Pyx_CyFunction_repr(__pyx_CyFunctionObject *op)
+{
+#if PY_MAJOR_VERSION >= 3
+    return PyUnicode_FromFormat("<cyfunction %U at %p>",
+                                op->func_qualname, (void *)op);
+#else
+    return PyString_FromFormat("<cyfunction %s at %p>",
+                               PyString_AsString(op->func_qualname), (void *)op);
+#endif
+}
+static PyObject * __Pyx_CyFunction_CallMethod(PyObject *func, PyObject *self, PyObject *arg, PyObject *kw) {
+    PyCFunctionObject* f = (PyCFunctionObject*)func;
+    PyCFunction meth = f->m_ml->ml_meth;
+    Py_ssize_t size;
+    switch (f->m_ml->ml_flags & (METH_VARARGS | METH_KEYWORDS | METH_NOARGS | METH_O)) {
+    case METH_VARARGS:
+        if (likely(kw == NULL || PyDict_Size(kw) == 0))
+            return (*meth)(self, arg);
+        break;
+    case METH_VARARGS | METH_KEYWORDS:
+        return (*(PyCFunctionWithKeywords)(void*)meth)(self, arg, kw);
+    case METH_NOARGS:
+        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
+            size = PyTuple_GET_SIZE(arg);
+            if (likely(size == 0))
+                return (*meth)(self, NULL);
+            PyErr_Format(PyExc_TypeError,
+                "%.200s() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                f->m_ml->ml_name, size);
+            return NULL;
+        }
+        break;
+    case METH_O:
+        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
+            size = PyTuple_GET_SIZE(arg);
+            if (likely(size == 1)) {
+                PyObject *result, *arg0;
+                #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+                arg0 = PyTuple_GET_ITEM(arg, 0);
+                #else
+                arg0 = PySequence_ITEM(arg, 0); if (unlikely(!arg0)) return NULL;
+                #endif
+                result = (*meth)(self, arg0);
+                #if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
+                Py_DECREF(arg0);
+                #endif
+                return result;
+            }
+            PyErr_Format(PyExc_TypeError,
+                "%.200s() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                f->m_ml->ml_name, size);
+            return NULL;
+        }
+        break;
+    default:
+        PyErr_SetString(PyExc_SystemError, "Bad call flags in "
+                        "__Pyx_CyFunction_Call. METH_OLDARGS is no "
+                        "longer supported!");
+        return NULL;
+    }
+    PyErr_Format(PyExc_TypeError, "%.200s() takes no keyword arguments",
+                 f->m_ml->ml_name);
+    return NULL;
+}
+static CYTHON_INLINE PyObject *__Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) {
+    return __Pyx_CyFunction_CallMethod(func, ((PyCFunctionObject*)func)->m_self, arg, kw);
+}
+static PyObject *__Pyx_CyFunction_CallAsMethod(PyObject *func, PyObject *args, PyObject *kw) {
+    PyObject *result;
+    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *) func;
+    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
+        Py_ssize_t argc;
+        PyObject *new_args;
+        PyObject *self;
+        argc = PyTuple_GET_SIZE(args);
+        new_args = PyTuple_GetSlice(args, 1, argc);
+        if (unlikely(!new_args))
+            return NULL;
+        self = PyTuple_GetItem(args, 0);
+        if (unlikely(!self)) {
+            Py_DECREF(new_args);
+            return NULL;
+        }
+        result = __Pyx_CyFunction_CallMethod(func, self, new_args, kw);
+        Py_DECREF(new_args);
+    } else {
+        result = __Pyx_CyFunction_Call(func, args, kw);
+    }
+    return result;
+}
+static PyTypeObject __pyx_CyFunctionType_type = {
+    PyVarObject_HEAD_INIT(0, 0)
+    "cython_function_or_method",
+    sizeof(__pyx_CyFunctionObject),
+    0,
+    (destructor) __Pyx_CyFunction_dealloc,
+    0,
+    0,
+    0,
+#if PY_MAJOR_VERSION < 3
+    0,
+#else
+    0,
+#endif
+    (reprfunc) __Pyx_CyFunction_repr,
+    0,
+    0,
+    0,
+    0,
+    __Pyx_CyFunction_CallAsMethod,
+    0,
+    0,
+    0,
+    0,
+    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,
+    0,
+    (traverseproc) __Pyx_CyFunction_traverse,
+    (inquiry) __Pyx_CyFunction_clear,
+    0,
+#if PY_VERSION_HEX < 0x030500A0
+    offsetof(__pyx_CyFunctionObject, func_weakreflist),
+#else
+    offsetof(PyCFunctionObject, m_weakreflist),
+#endif
+    0,
+    0,
+    __pyx_CyFunction_methods,
+    __pyx_CyFunction_members,
+    __pyx_CyFunction_getsets,
+    0,
+    0,
+    __Pyx_CyFunction_descr_get,
+    0,
+    offsetof(__pyx_CyFunctionObject, func_dict),
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+#if PY_VERSION_HEX >= 0x030400a1
+    0,
+#endif
+#if PY_VERSION_HEX >= 0x030800b1
+    0,
+#endif
+#if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
+    0,
+#endif
+};
+static int __pyx_CyFunction_init(void) {
+    __pyx_CyFunctionType = __Pyx_FetchCommonType(&__pyx_CyFunctionType_type);
+    if (unlikely(__pyx_CyFunctionType == NULL)) {
+        return -1;
+    }
+    return 0;
+}
+static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *func, size_t size, int pyobjects) {
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    m->defaults = PyObject_Malloc(size);
+    if (unlikely(!m->defaults))
+        return PyErr_NoMemory();
+    memset(m->defaults, 0, size);
+    m->defaults_pyobjects = pyobjects;
+    m->defaults_size = size;
+    return m->defaults;
+}
+static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *func, PyObject *tuple) {
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    m->defaults_tuple = tuple;
+    Py_INCREF(tuple);
+}
+static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *func, PyObject *dict) {
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    m->defaults_kwdict = dict;
+    Py_INCREF(dict);
+}
+static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *func, PyObject *dict) {
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    m->func_annotations = dict;
+    Py_INCREF(dict);
+}
+
+/* CythonFunction */
+static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml, int flags, PyObject* qualname,
+                                      PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
+    PyObject *op = __Pyx_CyFunction_Init(
+        PyObject_GC_New(__pyx_CyFunctionObject, __pyx_CyFunctionType),
+        ml, flags, qualname, closure, module, globals, code
+    );
+    if (likely(op)) {
+        PyObject_GC_Track(op);
+    }
+    return op;
+}
+
+/* Import */
+static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
+    PyObject *empty_list = 0;
+    PyObject *module = 0;
+    PyObject *global_dict = 0;
+    PyObject *empty_dict = 0;
+    PyObject *list;
+    #if PY_MAJOR_VERSION < 3
+    PyObject *py_import;
+    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
+    if (!py_import)
+        goto bad;
+    #endif
+    if (from_list)
+        list = from_list;
+    else {
+        empty_list = PyList_New(0);
+        if (!empty_list)
+            goto bad;
+        list = empty_list;
+    }
+    global_dict = PyModule_GetDict(__pyx_m);
+    if (!global_dict)
+        goto bad;
+    empty_dict = PyDict_New();
+    if (!empty_dict)
+        goto bad;
+    {
+        #if PY_MAJOR_VERSION >= 3
+        if (level == -1) {
+            if ((1) && (strchr(__Pyx_MODULE_NAME, '.'))) {
+                module = PyImport_ImportModuleLevelObject(
+                    name, global_dict, empty_dict, list, 1);
+                if (!module) {
+                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
+                        goto bad;
+                    PyErr_Clear();
+                }
+            }
+            level = 0;
+        }
+        #endif
+        if (!module) {
+            #if PY_MAJOR_VERSION < 3
+            PyObject *py_level = PyInt_FromLong(level);
+            if (!py_level)
+                goto bad;
+            module = PyObject_CallFunctionObjArgs(py_import,
+                name, global_dict, empty_dict, list, py_level, (PyObject *)NULL);
+            Py_DECREF(py_level);
+            #else
+            module = PyImport_ImportModuleLevelObject(
+                name, global_dict, empty_dict, list, level);
+            #endif
+        }
+    }
+bad:
+    #if PY_MAJOR_VERSION < 3
+    Py_XDECREF(py_import);
+    #endif
+    Py_XDECREF(empty_list);
+    Py_XDECREF(empty_dict);
+    return module;
+}
+
+/* ImportFrom */
+static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
+    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
+    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
+        PyErr_Format(PyExc_ImportError,
+        #if PY_MAJOR_VERSION < 3
+            "cannot import name %.230s", PyString_AS_STRING(name));
+        #else
+            "cannot import name %S", name);
+        #endif
+    }
+    return value;
+}
+
+/* PyObjectCallNoArg */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
+#if CYTHON_FAST_PYCALL
+    if (PyFunction_Check(func)) {
+        return __Pyx_PyFunction_FastCall(func, NULL, 0);
+    }
+#endif
+#ifdef __Pyx_CyFunction_USED
+    if (likely(PyCFunction_Check(func) || __Pyx_CyFunction_Check(func)))
+#else
+    if (likely(PyCFunction_Check(func)))
+#endif
+    {
+        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
+            return __Pyx_PyObject_CallMethO(func, NULL);
+        }
+    }
+    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
+}
+#endif
+
+/* IsLittleEndian */
+static CYTHON_INLINE int __Pyx_Is_Little_Endian(void)
+{
+  union {
+    uint32_t u32;
+    uint8_t u8[4];
+  } S;
+  S.u32 = 0x01020304;
+  return S.u8[0] == 4;
+}
+
+/* BufferFormatCheck */
+static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
+                              __Pyx_BufFmt_StackElem* stack,
+                              __Pyx_TypeInfo* type) {
+  stack[0].field = &ctx->root;
+  stack[0].parent_offset = 0;
+  ctx->root.type = type;
+  ctx->root.name = "buffer dtype";
+  ctx->root.offset = 0;
+  ctx->head = stack;
+  ctx->head->field = &ctx->root;
+  ctx->fmt_offset = 0;
+  ctx->head->parent_offset = 0;
+  ctx->new_packmode = '@';
+  ctx->enc_packmode = '@';
+  ctx->new_count = 1;
+  ctx->enc_count = 0;
+  ctx->enc_type = 0;
+  ctx->is_complex = 0;
+  ctx->is_valid_array = 0;
+  ctx->struct_alignment = 0;
+  while (type->typegroup == 'S') {
+    ++ctx->head;
+    ctx->head->field = type->fields;
+    ctx->head->parent_offset = 0;
+    type = type->fields->type;
+  }
+}
+static int __Pyx_BufFmt_ParseNumber(const char** ts) {
+    int count;
+    const char* t = *ts;
+    if (*t < '0' || *t > '9') {
+      return -1;
+    } else {
+        count = *t++ - '0';
+        while (*t >= '0' && *t <= '9') {
+            count *= 10;
+            count += *t++ - '0';
+        }
+    }
+    *ts = t;
+    return count;
+}
+static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
+    int number = __Pyx_BufFmt_ParseNumber(ts);
+    if (number == -1)
+        PyErr_Format(PyExc_ValueError,\
+                     "Does not understand character buffer dtype format string ('%c')", **ts);
+    return number;
+}
+static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
+  PyErr_Format(PyExc_ValueError,
+               "Unexpected format string character: '%c'", ch);
+}
+static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
+  switch (ch) {
+    case '?': return "'bool'";
+    case 'c': return "'char'";
+    case 'b': return "'signed char'";
+    case 'B': return "'unsigned char'";
+    case 'h': return "'short'";
+    case 'H': return "'unsigned short'";
+    case 'i': return "'int'";
+    case 'I': return "'unsigned int'";
+    case 'l': return "'long'";
+    case 'L': return "'unsigned long'";
+    case 'q': return "'long long'";
+    case 'Q': return "'unsigned long long'";
+    case 'f': return (is_complex ? "'complex float'" : "'float'");
+    case 'd': return (is_complex ? "'complex double'" : "'double'");
+    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
+    case 'T': return "a struct";
+    case 'O': return "Python object";
+    case 'P': return "a pointer";
+    case 's': case 'p': return "a string";
+    case 0: return "end";
+    default: return "unparseable format string";
+  }
+}
+static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return 2;
+    case 'i': case 'I': case 'l': case 'L': return 4;
+    case 'q': case 'Q': return 8;
+    case 'f': return (is_complex ? 8 : 4);
+    case 'd': return (is_complex ? 16 : 8);
+    case 'g': {
+      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
+      return 0;
+    }
+    case 'O': case 'P': return sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(short);
+    case 'i': case 'I': return sizeof(int);
+    case 'l': case 'L': return sizeof(long);
+    #ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
+    #endif
+    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
+    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
+    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
+    case 'O': case 'P': return sizeof(void*);
+    default: {
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+  }
+}
+typedef struct { char c; short x; } __Pyx_st_short;
+typedef struct { char c; int x; } __Pyx_st_int;
+typedef struct { char c; long x; } __Pyx_st_long;
+typedef struct { char c; float x; } __Pyx_st_float;
+typedef struct { char c; double x; } __Pyx_st_double;
+typedef struct { char c; long double x; } __Pyx_st_longdouble;
+typedef struct { char c; void *x; } __Pyx_st_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
+#endif
+static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
+    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
+    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
+#endif
+    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
+    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
+    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
+    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+/* These are for computing the padding at the end of the struct to align
+   on the first member of the struct. This will probably the same as above,
+   but we don't have any guarantees.
+ */
+typedef struct { short x; char c; } __Pyx_pad_short;
+typedef struct { int x; char c; } __Pyx_pad_int;
+typedef struct { long x; char c; } __Pyx_pad_long;
+typedef struct { float x; char c; } __Pyx_pad_float;
+typedef struct { double x; char c; } __Pyx_pad_double;
+typedef struct { long double x; char c; } __Pyx_pad_longdouble;
+typedef struct { void *x; char c; } __Pyx_pad_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
+#endif
+static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
+    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
+    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
+#endif
+    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
+    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
+    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
+    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
+  switch (ch) {
+    case 'c':
+        return 'H';
+    case 'b': case 'h': case 'i':
+    case 'l': case 'q': case 's': case 'p':
+        return 'I';
+    case '?': case 'B': case 'H': case 'I': case 'L': case 'Q':
+        return 'U';
+    case 'f': case 'd': case 'g':
+        return (is_complex ? 'C' : 'R');
+    case 'O':
+        return 'O';
+    case 'P':
+        return 'P';
+    default: {
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+  }
+}
+static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
+  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
+    const char* expected;
+    const char* quote;
+    if (ctx->head == NULL) {
+      expected = "end";
+      quote = "";
+    } else {
+      expected = ctx->head->field->type->name;
+      quote = "'";
+    }
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer dtype mismatch, expected %s%s%s but got %s",
+                 quote, expected, quote,
+                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
+  } else {
+    __Pyx_StructField* field = ctx->head->field;
+    __Pyx_StructField* parent = (ctx->head - 1)->field;
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
+                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
+                 parent->type->name, field->name);
+  }
+}
+static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
+  char group;
+  size_t size, offset, arraysize = 1;
+  if (ctx->enc_type == 0) return 0;
+  if (ctx->head->field->type->arraysize[0]) {
+    int i, ndim = 0;
+    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
+        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
+        ndim = 1;
+        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
+            PyErr_Format(PyExc_ValueError,
+                         "Expected a dimension of size %zu, got %zu",
+                         ctx->head->field->type->arraysize[0], ctx->enc_count);
+            return -1;
+        }
+    }
+    if (!ctx->is_valid_array) {
+      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
+                   ctx->head->field->type->ndim, ndim);
+      return -1;
+    }
+    for (i = 0; i < ctx->head->field->type->ndim; i++) {
+      arraysize *= ctx->head->field->type->arraysize[i];
+    }
+    ctx->is_valid_array = 0;
+    ctx->enc_count = 1;
+  }
+  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
+  do {
+    __Pyx_StructField* field = ctx->head->field;
+    __Pyx_TypeInfo* type = field->type;
+    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
+      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
+    } else {
+      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
+    }
+    if (ctx->enc_packmode == '@') {
+      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
+      size_t align_mod_offset;
+      if (align_at == 0) return -1;
+      align_mod_offset = ctx->fmt_offset % align_at;
+      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
+      if (ctx->struct_alignment == 0)
+          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
+                                                                 ctx->is_complex);
+    }
+    if (type->size != size || type->typegroup != group) {
+      if (type->typegroup == 'C' && type->fields != NULL) {
+        size_t parent_offset = ctx->head->parent_offset + field->offset;
+        ++ctx->head;
+        ctx->head->field = type->fields;
+        ctx->head->parent_offset = parent_offset;
+        continue;
+      }
+      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
+      } else {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return -1;
+      }
+    }
+    offset = ctx->head->parent_offset + field->offset;
+    if (ctx->fmt_offset != offset) {
+      PyErr_Format(PyExc_ValueError,
+                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
+                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
+      return -1;
+    }
+    ctx->fmt_offset += size;
+    if (arraysize)
+      ctx->fmt_offset += (arraysize - 1) * size;
+    --ctx->enc_count;
+    while (1) {
+      if (field == &ctx->root) {
+        ctx->head = NULL;
+        if (ctx->enc_count != 0) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return -1;
+        }
+        break;
+      }
+      ctx->head->field = ++field;
+      if (field->type == NULL) {
+        --ctx->head;
+        field = ctx->head->field;
+        continue;
+      } else if (field->type->typegroup == 'S') {
+        size_t parent_offset = ctx->head->parent_offset + field->offset;
+        if (field->type->fields->type == NULL) continue;
+        field = field->type->fields;
+        ++ctx->head;
+        ctx->head->field = field;
+        ctx->head->parent_offset = parent_offset;
+        break;
+      } else {
+        break;
+      }
+    }
+  } while (ctx->enc_count);
+  ctx->enc_type = 0;
+  ctx->is_complex = 0;
+  return 0;
+}
+static PyObject *
+__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
+{
+    const char *ts = *tsp;
+    int i = 0, number, ndim;
+    ++ts;
+    if (ctx->new_count != 1) {
+        PyErr_SetString(PyExc_ValueError,
+                        "Cannot handle repeated arrays in format string");
+        return NULL;
+    }
+    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+    ndim = ctx->head->field->type->ndim;
+    while (*ts && *ts != ')') {
+        switch (*ts) {
+            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
+            default:  break;
+        }
+        number = __Pyx_BufFmt_ExpectNumber(&ts);
+        if (number == -1) return NULL;
+        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
+            return PyErr_Format(PyExc_ValueError,
+                        "Expected a dimension of size %zu, got %d",
+                        ctx->head->field->type->arraysize[i], number);
+        if (*ts != ',' && *ts != ')')
+            return PyErr_Format(PyExc_ValueError,
+                                "Expected a comma in format string, got '%c'", *ts);
+        if (*ts == ',') ts++;
+        i++;
+    }
+    if (i != ndim)
+        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
+                            ctx->head->field->type->ndim, i);
+    if (!*ts) {
+        PyErr_SetString(PyExc_ValueError,
+                        "Unexpected end of format string, expected ')'");
+        return NULL;
+    }
+    ctx->is_valid_array = 1;
+    ctx->new_count = 1;
+    *tsp = ++ts;
+    return Py_None;
+}
+static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
+  int got_Z = 0;
+  while (1) {
+    switch(*ts) {
+      case 0:
+        if (ctx->enc_type != 0 && ctx->head == NULL) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return NULL;
+        }
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        if (ctx->head != NULL) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return NULL;
+        }
+        return ts;
+      case ' ':
+      case '\r':
+      case '\n':
+        ++ts;
+        break;
+      case '<':
+        if (!__Pyx_Is_Little_Endian()) {
+          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
+          return NULL;
+        }
+        ctx->new_packmode = '=';
+        ++ts;
+        break;
+      case '>':
+      case '!':
+        if (__Pyx_Is_Little_Endian()) {
+          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
+          return NULL;
+        }
+        ctx->new_packmode = '=';
+        ++ts;
+        break;
+      case '=':
+      case '@':
+      case '^':
+        ctx->new_packmode = *ts++;
+        break;
+      case 'T':
+        {
+          const char* ts_after_sub;
+          size_t i, struct_count = ctx->new_count;
+          size_t struct_alignment = ctx->struct_alignment;
+          ctx->new_count = 1;
+          ++ts;
+          if (*ts != '{') {
+            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
+            return NULL;
+          }
+          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+          ctx->enc_type = 0;
+          ctx->enc_count = 0;
+          ctx->struct_alignment = 0;
+          ++ts;
+          ts_after_sub = ts;
+          for (i = 0; i != struct_count; ++i) {
+            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
+            if (!ts_after_sub) return NULL;
+          }
+          ts = ts_after_sub;
+          if (struct_alignment) ctx->struct_alignment = struct_alignment;
+        }
+        break;
+      case '}':
+        {
+          size_t alignment = ctx->struct_alignment;
+          ++ts;
+          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+          ctx->enc_type = 0;
+          if (alignment && ctx->fmt_offset % alignment) {
+            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
+          }
+        }
+        return ts;
+      case 'x':
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        ctx->fmt_offset += ctx->new_count;
+        ctx->new_count = 1;
+        ctx->enc_count = 0;
+        ctx->enc_type = 0;
+        ctx->enc_packmode = ctx->new_packmode;
+        ++ts;
+        break;
+      case 'Z':
+        got_Z = 1;
+        ++ts;
+        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
+          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
+          return NULL;
+        }
+        CYTHON_FALLTHROUGH;
+      case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
+      case 'l': case 'L': case 'q': case 'Q':
+      case 'f': case 'd': case 'g':
+      case 'O': case 'p':
+        if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) &&
+            (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) {
+          ctx->enc_count += ctx->new_count;
+          ctx->new_count = 1;
+          got_Z = 0;
+          ++ts;
+          break;
+        }
+        CYTHON_FALLTHROUGH;
+      case 's':
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        ctx->enc_count = ctx->new_count;
+        ctx->enc_packmode = ctx->new_packmode;
+        ctx->enc_type = *ts;
+        ctx->is_complex = got_Z;
+        ++ts;
+        ctx->new_count = 1;
+        got_Z = 0;
+        break;
+      case ':':
+        ++ts;
+        while(*ts != ':') ++ts;
+        ++ts;
+        break;
+      case '(':
+        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
+        break;
+      default:
+        {
+          int number = __Pyx_BufFmt_ExpectNumber(&ts);
+          if (number == -1) return NULL;
+          ctx->new_count = (size_t)number;
+        }
+    }
+  }
+}
+
+/* BufferGetAndValidate */
+  static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
+  if (unlikely(info->buf == NULL)) return;
+  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
+  __Pyx_ReleaseBuffer(info);
+}
+static void __Pyx_ZeroBuffer(Py_buffer* buf) {
+  buf->buf = NULL;
+  buf->obj = NULL;
+  buf->strides = __Pyx_zeros;
+  buf->shape = __Pyx_zeros;
+  buf->suboffsets = __Pyx_minusones;
+}
+static int __Pyx__GetBufferAndValidate(
+        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
+        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
+{
+  buf->buf = NULL;
+  if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) {
+    __Pyx_ZeroBuffer(buf);
+    return -1;
+  }
+  if (unlikely(buf->ndim != nd)) {
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer has wrong number of dimensions (expected %d, got %d)",
+                 nd, buf->ndim);
+    goto fail;
+  }
+  if (!cast) {
+    __Pyx_BufFmt_Context ctx;
+    __Pyx_BufFmt_Init(&ctx, stack, dtype);
+    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
+  }
+  if (unlikely((size_t)buf->itemsize != dtype->size)) {
+    PyErr_Format(PyExc_ValueError,
+      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
+      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
+      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
+    goto fail;
+  }
+  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
+  return 0;
+fail:;
+  __Pyx_SafeReleaseBuffer(buf);
+  return -1;
+}
+
+/* BufferIndexError */
+  static void __Pyx_RaiseBufferIndexError(int axis) {
+  PyErr_Format(PyExc_IndexError,
+     "Out of bounds on buffer access (axis %d)", axis);
+}
+
+/* PyErrFetchRestore */
+  #if CYTHON_FAST_THREAD_STATE
+static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    tmp_type = tstate->curexc_type;
+    tmp_value = tstate->curexc_value;
+    tmp_tb = tstate->curexc_traceback;
+    tstate->curexc_type = type;
+    tstate->curexc_value = value;
+    tstate->curexc_traceback = tb;
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+}
+static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
+    *type = tstate->curexc_type;
+    *value = tstate->curexc_value;
+    *tb = tstate->curexc_traceback;
+    tstate->curexc_type = 0;
+    tstate->curexc_value = 0;
+    tstate->curexc_traceback = 0;
+}
+#endif
+
+/* ArgTypeTest */
+  static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
+{
+    if (unlikely(!type)) {
+        PyErr_SetString(PyExc_SystemError, "Missing type object");
+        return 0;
+    }
+    else if (exact) {
+        #if PY_MAJOR_VERSION == 2
+        if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
+        #endif
+    }
+    else {
+        if (likely(__Pyx_TypeCheck(obj, type))) return 1;
+    }
+    PyErr_Format(PyExc_TypeError,
+        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
+        name, type->tp_name, Py_TYPE(obj)->tp_name);
+    return 0;
+}
+
+/* GetTopmostException */
+  #if CYTHON_USE_EXC_INFO_STACK
+static _PyErr_StackItem *
+__Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
+{
+    _PyErr_StackItem *exc_info = tstate->exc_info;
+    while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) &&
+           exc_info->previous_item != NULL)
+    {
+        exc_info = exc_info->previous_item;
+    }
+    return exc_info;
+}
+#endif
+
+/* SaveResetException */
+  #if CYTHON_FAST_THREAD_STATE
+static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
+    #if CYTHON_USE_EXC_INFO_STACK
+    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
+    *type = exc_info->exc_type;
+    *value = exc_info->exc_value;
+    *tb = exc_info->exc_traceback;
+    #else
+    *type = tstate->exc_type;
+    *value = tstate->exc_value;
+    *tb = tstate->exc_traceback;
+    #endif
+    Py_XINCREF(*type);
+    Py_XINCREF(*value);
+    Py_XINCREF(*tb);
+}
+static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    #if CYTHON_USE_EXC_INFO_STACK
+    _PyErr_StackItem *exc_info = tstate->exc_info;
+    tmp_type = exc_info->exc_type;
+    tmp_value = exc_info->exc_value;
+    tmp_tb = exc_info->exc_traceback;
+    exc_info->exc_type = type;
+    exc_info->exc_value = value;
+    exc_info->exc_traceback = tb;
+    #else
+    tmp_type = tstate->exc_type;
+    tmp_value = tstate->exc_value;
+    tmp_tb = tstate->exc_traceback;
+    tstate->exc_type = type;
+    tstate->exc_value = value;
+    tstate->exc_traceback = tb;
+    #endif
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+}
+#endif
+
+/* PyErrExceptionMatches */
+  #if CYTHON_FAST_THREAD_STATE
+static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
+    Py_ssize_t i, n;
+    n = PyTuple_GET_SIZE(tuple);
+#if PY_MAJOR_VERSION >= 3
+    for (i=0; i<n; i++) {
+        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
+    }
+#endif
+    for (i=0; i<n; i++) {
+        if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
+    }
+    return 0;
+}
+static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
+    PyObject *exc_type = tstate->curexc_type;
+    if (exc_type == err) return 1;
+    if (unlikely(!exc_type)) return 0;
+    if (unlikely(PyTuple_Check(err)))
+        return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
+    return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
+}
+#endif
+
+/* GetException */
+  #if CYTHON_FAST_THREAD_STATE
+static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)
+#else
+static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)
+#endif
+{
+    PyObject *local_type, *local_value, *local_tb;
+#if CYTHON_FAST_THREAD_STATE
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    local_type = tstate->curexc_type;
+    local_value = tstate->curexc_value;
+    local_tb = tstate->curexc_traceback;
+    tstate->curexc_type = 0;
+    tstate->curexc_value = 0;
+    tstate->curexc_traceback = 0;
+#else
+    PyErr_Fetch(&local_type, &local_value, &local_tb);
+#endif
+    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
+#if CYTHON_FAST_THREAD_STATE
+    if (unlikely(tstate->curexc_type))
+#else
+    if (unlikely(PyErr_Occurred()))
+#endif
+        goto bad;
+    #if PY_MAJOR_VERSION >= 3
+    if (local_tb) {
+        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
+            goto bad;
+    }
+    #endif
+    Py_XINCREF(local_tb);
+    Py_XINCREF(local_type);
+    Py_XINCREF(local_value);
+    *type = local_type;
+    *value = local_value;
+    *tb = local_tb;
+#if CYTHON_FAST_THREAD_STATE
+    #if CYTHON_USE_EXC_INFO_STACK
+    {
+        _PyErr_StackItem *exc_info = tstate->exc_info;
+        tmp_type = exc_info->exc_type;
+        tmp_value = exc_info->exc_value;
+        tmp_tb = exc_info->exc_traceback;
+        exc_info->exc_type = local_type;
+        exc_info->exc_value = local_value;
+        exc_info->exc_traceback = local_tb;
+    }
+    #else
+    tmp_type = tstate->exc_type;
+    tmp_value = tstate->exc_value;
+    tmp_tb = tstate->exc_traceback;
+    tstate->exc_type = local_type;
+    tstate->exc_value = local_value;
+    tstate->exc_traceback = local_tb;
+    #endif
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+#else
+    PyErr_SetExcInfo(local_type, local_value, local_tb);
+#endif
+    return 0;
+bad:
+    *type = 0;
+    *value = 0;
+    *tb = 0;
+    Py_XDECREF(local_type);
+    Py_XDECREF(local_value);
+    Py_XDECREF(local_tb);
+    return -1;
+}
+
+/* RaiseException */
+  #if PY_MAJOR_VERSION < 3
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
+                        CYTHON_UNUSED PyObject *cause) {
+    __Pyx_PyThreadState_declare
+    Py_XINCREF(type);
+    if (!value || value == Py_None)
+        value = NULL;
+    else
+        Py_INCREF(value);
+    if (!tb || tb == Py_None)
+        tb = NULL;
+    else {
+        Py_INCREF(tb);
+        if (!PyTraceBack_Check(tb)) {
+            PyErr_SetString(PyExc_TypeError,
+                "raise: arg 3 must be a traceback or None");
+            goto raise_error;
+        }
+    }
+    if (PyType_Check(type)) {
+#if CYTHON_COMPILING_IN_PYPY
+        if (!value) {
+            Py_INCREF(Py_None);
+            value = Py_None;
+        }
+#endif
+        PyErr_NormalizeException(&type, &value, &tb);
+    } else {
+        if (value) {
+            PyErr_SetString(PyExc_TypeError,
+                "instance exception may not have a separate value");
+            goto raise_error;
+        }
+        value = type;
+        type = (PyObject*) Py_TYPE(type);
+        Py_INCREF(type);
+        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
+            PyErr_SetString(PyExc_TypeError,
+                "raise: exception class must be a subclass of BaseException");
+            goto raise_error;
+        }
+    }
+    __Pyx_PyThreadState_assign
+    __Pyx_ErrRestore(type, value, tb);
+    return;
+raise_error:
+    Py_XDECREF(value);
+    Py_XDECREF(type);
+    Py_XDECREF(tb);
+    return;
+}
+#else
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
+    PyObject* owned_instance = NULL;
+    if (tb == Py_None) {
+        tb = 0;
+    } else if (tb && !PyTraceBack_Check(tb)) {
+        PyErr_SetString(PyExc_TypeError,
+            "raise: arg 3 must be a traceback or None");
+        goto bad;
+    }
+    if (value == Py_None)
+        value = 0;
+    if (PyExceptionInstance_Check(type)) {
+        if (value) {
+            PyErr_SetString(PyExc_TypeError,
+                "instance exception may not have a separate value");
+            goto bad;
+        }
+        value = type;
+        type = (PyObject*) Py_TYPE(value);
+    } else if (PyExceptionClass_Check(type)) {
+        PyObject *instance_class = NULL;
+        if (value && PyExceptionInstance_Check(value)) {
+            instance_class = (PyObject*) Py_TYPE(value);
+            if (instance_class != type) {
+                int is_subclass = PyObject_IsSubclass(instance_class, type);
+                if (!is_subclass) {
+                    instance_class = NULL;
+                } else if (unlikely(is_subclass == -1)) {
+                    goto bad;
+                } else {
+                    type = instance_class;
+                }
+            }
+        }
+        if (!instance_class) {
+            PyObject *args;
+            if (!value)
+                args = PyTuple_New(0);
+            else if (PyTuple_Check(value)) {
+                Py_INCREF(value);
+                args = value;
+            } else
+                args = PyTuple_Pack(1, value);
+            if (!args)
+                goto bad;
+            owned_instance = PyObject_Call(type, args, NULL);
+            Py_DECREF(args);
+            if (!owned_instance)
+                goto bad;
+            value = owned_instance;
+            if (!PyExceptionInstance_Check(value)) {
+                PyErr_Format(PyExc_TypeError,
+                             "calling %R should have returned an instance of "
+                             "BaseException, not %R",
+                             type, Py_TYPE(value));
+                goto bad;
+            }
+        }
+    } else {
+        PyErr_SetString(PyExc_TypeError,
+            "raise: exception class must be a subclass of BaseException");
+        goto bad;
+    }
+    if (cause) {
+        PyObject *fixed_cause;
+        if (cause == Py_None) {
+            fixed_cause = NULL;
+        } else if (PyExceptionClass_Check(cause)) {
+            fixed_cause = PyObject_CallObject(cause, NULL);
+            if (fixed_cause == NULL)
+                goto bad;
+        } else if (PyExceptionInstance_Check(cause)) {
+            fixed_cause = cause;
+            Py_INCREF(fixed_cause);
+        } else {
+            PyErr_SetString(PyExc_TypeError,
+                            "exception causes must derive from "
+                            "BaseException");
+            goto bad;
+        }
+        PyException_SetCause(value, fixed_cause);
+    }
+    PyErr_SetObject(type, value);
+    if (tb) {
+#if CYTHON_COMPILING_IN_PYPY
+        PyObject *tmp_type, *tmp_value, *tmp_tb;
+        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
+        Py_INCREF(tb);
+        PyErr_Restore(tmp_type, tmp_value, tb);
+        Py_XDECREF(tmp_tb);
+#else
+        PyThreadState *tstate = __Pyx_PyThreadState_Current;
+        PyObject* tmp_tb = tstate->curexc_traceback;
+        if (tb != tmp_tb) {
+            Py_INCREF(tb);
+            tstate->curexc_traceback = tb;
+            Py_XDECREF(tmp_tb);
+        }
+#endif
+    }
+bad:
+    Py_XDECREF(owned_instance);
+    return;
+}
+#endif
+
+/* PyObject_GenericGetAttrNoDict */
+  #if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
+static PyObject *__Pyx_RaiseGenericGetAttributeError(PyTypeObject *tp, PyObject *attr_name) {
+    PyErr_Format(PyExc_AttributeError,
+#if PY_MAJOR_VERSION >= 3
+                 "'%.50s' object has no attribute '%U'",
+                 tp->tp_name, attr_name);
+#else
+                 "'%.50s' object has no attribute '%.400s'",
+                 tp->tp_name, PyString_AS_STRING(attr_name));
+#endif
+    return NULL;
+}
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name) {
+    PyObject *descr;
+    PyTypeObject *tp = Py_TYPE(obj);
+    if (unlikely(!PyString_Check(attr_name))) {
+        return PyObject_GenericGetAttr(obj, attr_name);
+    }
+    assert(!tp->tp_dictoffset);
+    descr = _PyType_Lookup(tp, attr_name);
+    if (unlikely(!descr)) {
+        return __Pyx_RaiseGenericGetAttributeError(tp, attr_name);
+    }
+    Py_INCREF(descr);
+    #if PY_MAJOR_VERSION < 3
+    if (likely(PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_HAVE_CLASS)))
+    #endif
+    {
+        descrgetfunc f = Py_TYPE(descr)->tp_descr_get;
+        if (unlikely(f)) {
+            PyObject *res = f(descr, obj, (PyObject *)tp);
+            Py_DECREF(descr);
+            return res;
+        }
+    }
+    return descr;
+}
+#endif
+
+/* TypeImport */
+  #ifndef __PYX_HAVE_RT_ImportType
+#define __PYX_HAVE_RT_ImportType
+static PyTypeObject *__Pyx_ImportType(PyObject *module, const char *module_name, const char *class_name,
+    size_t size, enum __Pyx_ImportType_CheckSize check_size)
+{
+    PyObject *result = 0;
+    char warning[200];
+    Py_ssize_t basicsize;
+#ifdef Py_LIMITED_API
+    PyObject *py_basicsize;
+#endif
+    result = PyObject_GetAttrString(module, class_name);
+    if (!result)
+        goto bad;
+    if (!PyType_Check(result)) {
+        PyErr_Format(PyExc_TypeError,
+            "%.200s.%.200s is not a type object",
+            module_name, class_name);
+        goto bad;
+    }
+#ifndef Py_LIMITED_API
+    basicsize = ((PyTypeObject *)result)->tp_basicsize;
+#else
+    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
+    if (!py_basicsize)
+        goto bad;
+    basicsize = PyLong_AsSsize_t(py_basicsize);
+    Py_DECREF(py_basicsize);
+    py_basicsize = 0;
+    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
+        goto bad;
+#endif
+    if ((size_t)basicsize < size) {
+        PyErr_Format(PyExc_ValueError,
+            "%.200s.%.200s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd from PyObject",
+            module_name, class_name, size, basicsize);
+        goto bad;
+    }
+    if (check_size == __Pyx_ImportType_CheckSize_Error && (size_t)basicsize != size) {
+        PyErr_Format(PyExc_ValueError,
+            "%.200s.%.200s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd from PyObject",
+            module_name, class_name, size, basicsize);
+        goto bad;
+    }
+    else if (check_size == __Pyx_ImportType_CheckSize_Warn && (size_t)basicsize > size) {
+        PyOS_snprintf(warning, sizeof(warning),
+            "%s.%s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd from PyObject",
+            module_name, class_name, size, basicsize);
+        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
+    }
+    return (PyTypeObject *)result;
+bad:
+    Py_XDECREF(result);
+    return NULL;
+}
+#endif
+
+/* CLineInTraceback */
+  #ifndef CYTHON_CLINE_IN_TRACEBACK
+static int __Pyx_CLineForTraceback(CYTHON_NCP_UNUSED PyThreadState *tstate, int c_line) {
+    PyObject *use_cline;
+    PyObject *ptype, *pvalue, *ptraceback;
+#if CYTHON_COMPILING_IN_CPYTHON
+    PyObject **cython_runtime_dict;
+#endif
+    if (unlikely(!__pyx_cython_runtime)) {
+        return c_line;
+    }
+    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
+#if CYTHON_COMPILING_IN_CPYTHON
+    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
+    if (likely(cython_runtime_dict)) {
+        __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
+            use_cline, *cython_runtime_dict,
+            __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback))
+    } else
+#endif
+    {
+      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
+      if (use_cline_obj) {
+        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
+        Py_DECREF(use_cline_obj);
+      } else {
+        PyErr_Clear();
+        use_cline = NULL;
+      }
+    }
+    if (!use_cline) {
+        c_line = 0;
+        PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
+    }
+    else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
+        c_line = 0;
+    }
+    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
+    return c_line;
+}
+#endif
+
+/* CodeObjectCache */
+  static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
+    int start = 0, mid = 0, end = count - 1;
+    if (end >= 0 && code_line > entries[end].code_line) {
+        return count;
+    }
+    while (start < end) {
+        mid = start + (end - start) / 2;
+        if (code_line < entries[mid].code_line) {
+            end = mid;
+        } else if (code_line > entries[mid].code_line) {
+             start = mid + 1;
+        } else {
+            return mid;
+        }
+    }
+    if (code_line <= entries[mid].code_line) {
+        return mid;
+    } else {
+        return mid + 1;
+    }
+}
+static PyCodeObject *__pyx_find_code_object(int code_line) {
+    PyCodeObject* code_object;
+    int pos;
+    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
+        return NULL;
+    }
+    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
+    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
+        return NULL;
+    }
+    code_object = __pyx_code_cache.entries[pos].code_object;
+    Py_INCREF(code_object);
+    return code_object;
+}
+static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
+    int pos, i;
+    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
+    if (unlikely(!code_line)) {
+        return;
+    }
+    if (unlikely(!entries)) {
+        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
+        if (likely(entries)) {
+            __pyx_code_cache.entries = entries;
+            __pyx_code_cache.max_count = 64;
+            __pyx_code_cache.count = 1;
+            entries[0].code_line = code_line;
+            entries[0].code_object = code_object;
+            Py_INCREF(code_object);
+        }
+        return;
+    }
+    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
+    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
+        PyCodeObject* tmp = entries[pos].code_object;
+        entries[pos].code_object = code_object;
+        Py_DECREF(tmp);
+        return;
+    }
+    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
+        int new_max = __pyx_code_cache.max_count + 64;
+        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
+            __pyx_code_cache.entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry));
+        if (unlikely(!entries)) {
+            return;
+        }
+        __pyx_code_cache.entries = entries;
+        __pyx_code_cache.max_count = new_max;
+    }
+    for (i=__pyx_code_cache.count; i>pos; i--) {
+        entries[i] = entries[i-1];
+    }
+    entries[pos].code_line = code_line;
+    entries[pos].code_object = code_object;
+    __pyx_code_cache.count++;
+    Py_INCREF(code_object);
+}
+
+/* AddTraceback */
+  #include "compile.h"
+#include "frameobject.h"
+#include "traceback.h"
+static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
+            const char *funcname, int c_line,
+            int py_line, const char *filename) {
+    PyCodeObject *py_code = 0;
+    PyObject *py_srcfile = 0;
+    PyObject *py_funcname = 0;
+    #if PY_MAJOR_VERSION < 3
+    py_srcfile = PyString_FromString(filename);
+    #else
+    py_srcfile = PyUnicode_FromString(filename);
+    #endif
+    if (!py_srcfile) goto bad;
+    if (c_line) {
+        #if PY_MAJOR_VERSION < 3
+        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
+        #else
+        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
+        #endif
+    }
+    else {
+        #if PY_MAJOR_VERSION < 3
+        py_funcname = PyString_FromString(funcname);
+        #else
+        py_funcname = PyUnicode_FromString(funcname);
+        #endif
+    }
+    if (!py_funcname) goto bad;
+    py_code = __Pyx_PyCode_New(
+        0,
+        0,
+        0,
+        0,
+        0,
+        __pyx_empty_bytes, /*PyObject *code,*/
+        __pyx_empty_tuple, /*PyObject *consts,*/
+        __pyx_empty_tuple, /*PyObject *names,*/
+        __pyx_empty_tuple, /*PyObject *varnames,*/
+        __pyx_empty_tuple, /*PyObject *freevars,*/
+        __pyx_empty_tuple, /*PyObject *cellvars,*/
+        py_srcfile,   /*PyObject *filename,*/
+        py_funcname,  /*PyObject *name,*/
+        py_line,
+        __pyx_empty_bytes  /*PyObject *lnotab*/
+    );
+    Py_DECREF(py_srcfile);
+    Py_DECREF(py_funcname);
+    return py_code;
+bad:
+    Py_XDECREF(py_srcfile);
+    Py_XDECREF(py_funcname);
+    return NULL;
+}
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename) {
+    PyCodeObject *py_code = 0;
+    PyFrameObject *py_frame = 0;
+    PyThreadState *tstate = __Pyx_PyThreadState_Current;
+    if (c_line) {
+        c_line = __Pyx_CLineForTraceback(tstate, c_line);
+    }
+    py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
+    if (!py_code) {
+        py_code = __Pyx_CreateCodeObjectForTraceback(
+            funcname, c_line, py_line, filename);
+        if (!py_code) goto bad;
+        __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
+    }
+    py_frame = PyFrame_New(
+        tstate,            /*PyThreadState *tstate,*/
+        py_code,           /*PyCodeObject *code,*/
+        __pyx_d,    /*PyObject *globals,*/
+        0                  /*PyObject *locals*/
+    );
+    if (!py_frame) goto bad;
+    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
+    PyTraceBack_Here(py_frame);
+bad:
+    Py_XDECREF(py_code);
+    Py_XDECREF(py_frame);
+}
+
+#if PY_MAJOR_VERSION < 3
+static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
+    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
+    PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
+    return -1;
+}
+static void __Pyx_ReleaseBuffer(Py_buffer *view) {
+    PyObject *obj = view->obj;
+    if (!obj) return;
+    if (PyObject_CheckBuffer(obj)) {
+        PyBuffer_Release(view);
+        return;
+    }
+    if ((0)) {}
+    view->obj = NULL;
+    Py_DECREF(obj);
+}
+#endif
+
+
+  /* Declarations */
+  #if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      return ::std::complex< float >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      return x + y*(__pyx_t_float_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      __pyx_t_float_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+/* Arithmetic */
+  #if CYTHON_CCOMPLEX
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    #if 1
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else if (fabsf(b.real) >= fabsf(b.imag)) {
+            if (b.real == 0 && b.imag == 0) {
+                return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);
+            } else {
+                float r = b.imag / b.real;
+                float s = (float)(1.0) / (b.real + b.imag * r);
+                return __pyx_t_float_complex_from_parts(
+                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
+            }
+        } else {
+            float r = b.real / b.imag;
+            float s = (float)(1.0) / (b.imag + b.real * r);
+            return __pyx_t_float_complex_from_parts(
+                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
+        }
+    }
+    #else
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else {
+            float denom = b.real * b.real + b.imag * b.imag;
+            return __pyx_t_float_complex_from_parts(
+                (a.real * b.real + a.imag * b.imag) / denom,
+                (a.imag * b.real - a.real * b.imag) / denom);
+        }
+    }
+    #endif
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) {
+        __pyx_t_float_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) {
+        __pyx_t_float_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrtf(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypotf(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+            __pyx_t_float_complex z;
+            float r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    float denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        return __Pyx_c_prod_float(a, a);
+                    case 3:
+                        z = __Pyx_c_prod_float(a, a);
+                        return __Pyx_c_prod_float(z, a);
+                    case 4:
+                        z = __Pyx_c_prod_float(a, a);
+                        return __Pyx_c_prod_float(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                } else if (b.imag == 0) {
+                    z.real = powf(a.real, b.real);
+                    z.imag = 0;
+                    return z;
+                } else if (a.real > 0) {
+                    r = a.real;
+                    theta = 0;
+                } else {
+                    r = -a.real;
+                    theta = atan2f(0.0, -1.0);
+                }
+            } else {
+                r = __Pyx_c_abs_float(a);
+                theta = atan2f(a.imag, a.real);
+            }
+            lnr = logf(r);
+            z_r = expf(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cosf(z_theta);
+            z.imag = z_r * sinf(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+/* Declarations */
+  #if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      return ::std::complex< double >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      return x + y*(__pyx_t_double_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      __pyx_t_double_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+/* Arithmetic */
+  #if CYTHON_CCOMPLEX
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    #if 1
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else if (fabs(b.real) >= fabs(b.imag)) {
+            if (b.real == 0 && b.imag == 0) {
+                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
+            } else {
+                double r = b.imag / b.real;
+                double s = (double)(1.0) / (b.real + b.imag * r);
+                return __pyx_t_double_complex_from_parts(
+                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
+            }
+        } else {
+            double r = b.real / b.imag;
+            double s = (double)(1.0) / (b.imag + b.real * r);
+            return __pyx_t_double_complex_from_parts(
+                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
+        }
+    }
+    #else
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else {
+            double denom = b.real * b.real + b.imag * b.imag;
+            return __pyx_t_double_complex_from_parts(
+                (a.real * b.real + a.imag * b.imag) / denom,
+                (a.imag * b.real - a.real * b.imag) / denom);
+        }
+    }
+    #endif
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) {
+        __pyx_t_double_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) {
+        __pyx_t_double_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrt(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypot(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+            __pyx_t_double_complex z;
+            double r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    double denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        return __Pyx_c_prod_double(a, a);
+                    case 3:
+                        z = __Pyx_c_prod_double(a, a);
+                        return __Pyx_c_prod_double(z, a);
+                    case 4:
+                        z = __Pyx_c_prod_double(a, a);
+                        return __Pyx_c_prod_double(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                } else if (b.imag == 0) {
+                    z.real = pow(a.real, b.real);
+                    z.imag = 0;
+                    return z;
+                } else if (a.real > 0) {
+                    r = a.real;
+                    theta = 0;
+                } else {
+                    r = -a.real;
+                    theta = atan2(0.0, -1.0);
+                }
+            } else {
+                r = __Pyx_c_abs_double(a);
+                theta = atan2(a.imag, a.real);
+            }
+            lnr = log(r);
+            z_r = exp(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cos(z_theta);
+            z.imag = z_r * sin(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+/* CIntToPy */
+  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const long neg_one = (long) -1, const_zero = (long) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+    if (is_unsigned) {
+        if (sizeof(long) < sizeof(long)) {
+            return PyInt_FromLong((long) value);
+        } else if (sizeof(long) <= sizeof(unsigned long)) {
+            return PyLong_FromUnsignedLong((unsigned long) value);
+#ifdef HAVE_LONG_LONG
+        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
+            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
+#endif
+        }
+    } else {
+        if (sizeof(long) <= sizeof(long)) {
+            return PyInt_FromLong((long) value);
+#ifdef HAVE_LONG_LONG
+        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
+            return PyLong_FromLongLong((PY_LONG_LONG) value);
+#endif
+        }
+    }
+    {
+        int one = 1; int little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&value;
+        return _PyLong_FromByteArray(bytes, sizeof(long),
+                                     little, !is_unsigned);
+    }
+}
+
+/* CIntFromPyVerify */
+  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
+    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
+#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
+    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
+#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
+    {\
+        func_type value = func_value;\
+        if (sizeof(target_type) < sizeof(func_type)) {\
+            if (unlikely(value != (func_type) (target_type) value)) {\
+                func_type zero = 0;\
+                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
+                    return (target_type) -1;\
+                if (is_unsigned && unlikely(value < zero))\
+                    goto raise_neg_overflow;\
+                else\
+                    goto raise_overflow;\
+            }\
+        }\
+        return (target_type) value;\
+    }
+
+/* CIntFromPy */
+  static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const long neg_one = (long) -1, const_zero = (long) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if (sizeof(long) < sizeof(long)) {
+            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (long) val;
+        }
+    } else
+#endif
+    if (likely(PyLong_Check(x))) {
+        if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (long) 0;
+                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
+                case 2:
+                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
+                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
+                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
+                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+            }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON
+            if (unlikely(Py_SIZE(x) < 0)) {
+                goto raise_neg_overflow;
+            }
+#else
+            {
+                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+                if (unlikely(result < 0))
+                    return (long) -1;
+                if (unlikely(result == 1))
+                    goto raise_neg_overflow;
+            }
+#endif
+            if (sizeof(long) <= sizeof(unsigned long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+            }
+        } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (long) 0;
+                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
+                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
+                case -2:
+                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
+                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
+                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+            }
+#endif
+            if (sizeof(long) <= sizeof(long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+            }
+        }
+        {
+#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
+            PyErr_SetString(PyExc_RuntimeError,
+                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
+#else
+            long val;
+            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
+ #if PY_MAJOR_VERSION < 3
+            if (likely(v) && !PyLong_Check(v)) {
+                PyObject *tmp = v;
+                v = PyNumber_Long(tmp);
+                Py_DECREF(tmp);
+            }
+ #endif
+            if (likely(v)) {
+                int one = 1; int is_little = (int)*(unsigned char *)&one;
+                unsigned char *bytes = (unsigned char *)&val;
+                int ret = _PyLong_AsByteArray((PyLongObject *)v,
+                                              bytes, sizeof(val),
+                                              is_little, !is_unsigned);
+                Py_DECREF(v);
+                if (likely(!ret))
+                    return val;
+            }
+#endif
+            return (long) -1;
+        }
+    } else {
+        long val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (long) -1;
+        val = __Pyx_PyInt_As_long(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to long");
+    return (long) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to long");
+    return (long) -1;
+}
+
+/* CIntFromPy */
+  static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const int neg_one = (int) -1, const_zero = (int) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if (sizeof(int) < sizeof(long)) {
+            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (int) val;
+        }
+    } else
+#endif
+    if (likely(PyLong_Check(x))) {
+        if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (int) 0;
+                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
+                case 2:
+                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
+                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
+                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
+                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+            }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON
+            if (unlikely(Py_SIZE(x) < 0)) {
+                goto raise_neg_overflow;
+            }
+#else
+            {
+                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+                if (unlikely(result < 0))
+                    return (int) -1;
+                if (unlikely(result == 1))
+                    goto raise_neg_overflow;
+            }
+#endif
+            if (sizeof(int) <= sizeof(unsigned long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+            }
+        } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (int) 0;
+                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
+                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
+                case -2:
+                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
+                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
+                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
+                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
+                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
+                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
+                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+            }
+#endif
+            if (sizeof(int) <= sizeof(long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+            }
+        }
+        {
+#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
+            PyErr_SetString(PyExc_RuntimeError,
+                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
+#else
+            int val;
+            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
+ #if PY_MAJOR_VERSION < 3
+            if (likely(v) && !PyLong_Check(v)) {
+                PyObject *tmp = v;
+                v = PyNumber_Long(tmp);
+                Py_DECREF(tmp);
+            }
+ #endif
+            if (likely(v)) {
+                int one = 1; int is_little = (int)*(unsigned char *)&one;
+                unsigned char *bytes = (unsigned char *)&val;
+                int ret = _PyLong_AsByteArray((PyLongObject *)v,
+                                              bytes, sizeof(val),
+                                              is_little, !is_unsigned);
+                Py_DECREF(v);
+                if (likely(!ret))
+                    return val;
+            }
+#endif
+            return (int) -1;
+        }
+    } else {
+        int val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (int) -1;
+        val = __Pyx_PyInt_As_int(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to int");
+    return (int) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to int");
+    return (int) -1;
+}
+
+/* FastTypeChecks */
+  #if CYTHON_COMPILING_IN_CPYTHON
+static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
+    while (a) {
+        a = a->tp_base;
+        if (a == b)
+            return 1;
+    }
+    return b == &PyBaseObject_Type;
+}
+static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
+    PyObject *mro;
+    if (a == b) return 1;
+    mro = a->tp_mro;
+    if (likely(mro)) {
+        Py_ssize_t i, n;
+        n = PyTuple_GET_SIZE(mro);
+        for (i = 0; i < n; i++) {
+            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
+                return 1;
+        }
+        return 0;
+    }
+    return __Pyx_InBases(a, b);
+}
+#if PY_MAJOR_VERSION == 2
+static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
+    PyObject *exception, *value, *tb;
+    int res;
+    __Pyx_PyThreadState_declare
+    __Pyx_PyThreadState_assign
+    __Pyx_ErrFetch(&exception, &value, &tb);
+    res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
+    if (unlikely(res == -1)) {
+        PyErr_WriteUnraisable(err);
+        res = 0;
+    }
+    if (!res) {
+        res = PyObject_IsSubclass(err, exc_type2);
+        if (unlikely(res == -1)) {
+            PyErr_WriteUnraisable(err);
+            res = 0;
+        }
+    }
+    __Pyx_ErrRestore(exception, value, tb);
+    return res;
+}
+#else
+static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
+    int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
+    if (!res) {
+        res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
+    }
+    return res;
+}
+#endif
+static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
+    Py_ssize_t i, n;
+    assert(PyExceptionClass_Check(exc_type));
+    n = PyTuple_GET_SIZE(tuple);
+#if PY_MAJOR_VERSION >= 3
+    for (i=0; i<n; i++) {
+        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
+    }
+#endif
+    for (i=0; i<n; i++) {
+        PyObject *t = PyTuple_GET_ITEM(tuple, i);
+        #if PY_MAJOR_VERSION < 3
+        if (likely(exc_type == t)) return 1;
+        #endif
+        if (likely(PyExceptionClass_Check(t))) {
+            if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
+        } else {
+        }
+    }
+    return 0;
+}
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
+    if (likely(err == exc_type)) return 1;
+    if (likely(PyExceptionClass_Check(err))) {
+        if (likely(PyExceptionClass_Check(exc_type))) {
+            return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
+        } else if (likely(PyTuple_Check(exc_type))) {
+            return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
+        } else {
+        }
+    }
+    return PyErr_GivenExceptionMatches(err, exc_type);
+}
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
+    assert(PyExceptionClass_Check(exc_type1));
+    assert(PyExceptionClass_Check(exc_type2));
+    if (likely(err == exc_type1 || err == exc_type2)) return 1;
+    if (likely(PyExceptionClass_Check(err))) {
+        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
+    }
+    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
+}
+#endif
+
+/* CheckBinaryVersion */
+  static int __Pyx_check_binary_version(void) {
+    char ctversion[4], rtversion[4];
+    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
+    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
+    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
+        char message[200];
+        PyOS_snprintf(message, sizeof(message),
+                      "compiletime version %s of module '%.100s' "
+                      "does not match runtime version %s",
+                      ctversion, __Pyx_MODULE_NAME, rtversion);
+        return PyErr_WarnEx(NULL, message, 1);
+    }
+    return 0;
+}
+
+/* InitStrings */
+  static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
+    while (t->p) {
+        #if PY_MAJOR_VERSION < 3
+        if (t->is_unicode) {
+            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
+        } else if (t->intern) {
+            *t->p = PyString_InternFromString(t->s);
+        } else {
+            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
+        }
+        #else
+        if (t->is_unicode | t->is_str) {
+            if (t->intern) {
+                *t->p = PyUnicode_InternFromString(t->s);
+            } else if (t->encoding) {
+                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
+            } else {
+                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
+            }
+        } else {
+            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
+        }
+        #endif
+        if (!*t->p)
+            return -1;
+        if (PyObject_Hash(*t->p) == -1)
+            return -1;
+        ++t;
+    }
+    return 0;
+}
+
+static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
+    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
+}
+static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
+    Py_ssize_t ignore;
+    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
+}
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+#if !CYTHON_PEP393_ENABLED
+static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+    char* defenc_c;
+    PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
+    if (!defenc) return NULL;
+    defenc_c = PyBytes_AS_STRING(defenc);
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+    {
+        char* end = defenc_c + PyBytes_GET_SIZE(defenc);
+        char* c;
+        for (c = defenc_c; c < end; c++) {
+            if ((unsigned char) (*c) >= 128) {
+                PyUnicode_AsASCIIString(o);
+                return NULL;
+            }
+        }
+    }
+#endif
+    *length = PyBytes_GET_SIZE(defenc);
+    return defenc_c;
+}
+#else
+static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+    if (likely(PyUnicode_IS_ASCII(o))) {
+        *length = PyUnicode_GET_LENGTH(o);
+        return PyUnicode_AsUTF8(o);
+    } else {
+        PyUnicode_AsASCIIString(o);
+        return NULL;
+    }
+#else
+    return PyUnicode_AsUTF8AndSize(o, length);
+#endif
+}
+#endif
+#endif
+static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+    if (
+#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+            __Pyx_sys_getdefaultencoding_not_ascii &&
+#endif
+            PyUnicode_Check(o)) {
+        return __Pyx_PyUnicode_AsStringAndSize(o, length);
+    } else
+#endif
+#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
+    if (PyByteArray_Check(o)) {
+        *length = PyByteArray_GET_SIZE(o);
+        return PyByteArray_AS_STRING(o);
+    } else
+#endif
+    {
+        char* result;
+        int r = PyBytes_AsStringAndSize(o, &result, length);
+        if (unlikely(r < 0)) {
+            return NULL;
+        } else {
+            return result;
+        }
+    }
+}
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
+   int is_true = x == Py_True;
+   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
+   else return PyObject_IsTrue(x);
+}
+static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
+    int retval;
+    if (unlikely(!x)) return -1;
+    retval = __Pyx_PyObject_IsTrue(x);
+    Py_DECREF(x);
+    return retval;
+}
+static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
+#if PY_MAJOR_VERSION >= 3
+    if (PyLong_Check(result)) {
+        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
+                "__int__ returned non-int (type %.200s).  "
+                "The ability to return an instance of a strict subclass of int "
+                "is deprecated, and may be removed in a future version of Python.",
+                Py_TYPE(result)->tp_name)) {
+            Py_DECREF(result);
+            return NULL;
+        }
+        return result;
+    }
+#endif
+    PyErr_Format(PyExc_TypeError,
+                 "__%.4s__ returned non-%.4s (type %.200s)",
+                 type_name, type_name, Py_TYPE(result)->tp_name);
+    Py_DECREF(result);
+    return NULL;
+}
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
+#if CYTHON_USE_TYPE_SLOTS
+  PyNumberMethods *m;
+#endif
+  const char *name = NULL;
+  PyObject *res = NULL;
+#if PY_MAJOR_VERSION < 3
+  if (likely(PyInt_Check(x) || PyLong_Check(x)))
+#else
+  if (likely(PyLong_Check(x)))
+#endif
+    return __Pyx_NewRef(x);
+#if CYTHON_USE_TYPE_SLOTS
+  m = Py_TYPE(x)->tp_as_number;
+  #if PY_MAJOR_VERSION < 3
+  if (m && m->nb_int) {
+    name = "int";
+    res = m->nb_int(x);
+  }
+  else if (m && m->nb_long) {
+    name = "long";
+    res = m->nb_long(x);
+  }
+  #else
+  if (likely(m && m->nb_int)) {
+    name = "int";
+    res = m->nb_int(x);
+  }
+  #endif
+#else
+  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
+    res = PyNumber_Int(x);
+  }
+#endif
+  if (likely(res)) {
+#if PY_MAJOR_VERSION < 3
+    if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
+#else
+    if (unlikely(!PyLong_CheckExact(res))) {
+#endif
+        return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
+    }
+  }
+  else if (!PyErr_Occurred()) {
+    PyErr_SetString(PyExc_TypeError,
+                    "an integer is required");
+  }
+  return res;
+}
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
+  Py_ssize_t ival;
+  PyObject *x;
+#if PY_MAJOR_VERSION < 3
+  if (likely(PyInt_CheckExact(b))) {
+    if (sizeof(Py_ssize_t) >= sizeof(long))
+        return PyInt_AS_LONG(b);
+    else
+        return PyInt_AsSsize_t(b);
+  }
+#endif
+  if (likely(PyLong_CheckExact(b))) {
+    #if CYTHON_USE_PYLONG_INTERNALS
+    const digit* digits = ((PyLongObject*)b)->ob_digit;
+    const Py_ssize_t size = Py_SIZE(b);
+    if (likely(__Pyx_sst_abs(size) <= 1)) {
+        ival = likely(size) ? digits[0] : 0;
+        if (size == -1) ival = -ival;
+        return ival;
+    } else {
+      switch (size) {
+         case 2:
+           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -2:
+           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case 3:
+           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -3:
+           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case 4:
+           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -4:
+           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+      }
+    }
+    #endif
+    return PyLong_AsSsize_t(b);
+  }
+  x = PyNumber_Index(b);
+  if (!x) return -1;
+  ival = PyInt_AsSsize_t(x);
+  Py_DECREF(x);
+  return ival;
+}
+static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
+  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
+}
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
+    return PyInt_FromSize_t(ival);
+}
+
+
+#endif /* Py_PYTHON_H */
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diff --git a/tool/LAI/setup.py b/tool/LAI/setup.py
new file mode 100644
index 00000000..67c737a4
--- /dev/null
+++ b/tool/LAI/setup.py
@@ -0,0 +1,45 @@
+from setuptools import setup
+from setuptools.extension import Extension
+from Cython.Distutils import build_ext
+from Cython.Build import cythonize
+import numpy
+from pathlib import Path
+import shutil
+
+
+class MyBuildExt(build_ext):
+    def run(self):
+        build_ext.run(self)
+
+        build_dir = Path(self.build_lib)
+        root_dir = Path(__file__).parent
+        target_dir = build_dir if not self.inplace else root_dir
+
+        self.copy_file(Path('./LAIProcess') / '__init__.py', root_dir, target_dir)
+        #self.copy_file(Path('./pkg2') / '__init__.py', root_dir, target_dir)
+        self.copy_file(Path('.') / '__init__.py', root_dir, target_dir)
+    def copy_file(self, path, source_dir, destination_dir):
+        if not (source_dir / path).exists():
+            return
+        shutil.copyfile(str(source_dir / path), str(destination_dir / path))
+
+setup(
+    name="MyModule",
+    ext_modules=cythonize(
+        [
+           #Extension("pkg1.*", ["root/pkg1/*.py"]),
+           Extension("pkg2.*", ["./LAIProcess.pyx"]),
+           #Extension("1.*", ["root/*.py"])
+        ],
+        build_dir="build",
+        compiler_directives=dict(
+        always_allow_keywords=True
+        )),
+    cmdclass=dict(
+        build_ext=MyBuildExt
+    ),
+    packages=[],
+    include_dirs=[numpy.get_include()],
+)
+
+# 指令： python setup.py build_ext --inplace
diff --git a/tool/algorithm/transforml1a/build/SAR_geo/SAR_GEO.c b/tool/algorithm/transforml1a/build/SAR_geo/SAR_GEO.c
new file mode 100644
index 00000000..626b2eda
--- /dev/null
+++ b/tool/algorithm/transforml1a/build/SAR_geo/SAR_GEO.c
@@ -0,0 +1,9744 @@
+/* Generated by Cython 0.29.24 */
+
+/* BEGIN: Cython Metadata
+{
+    "distutils": {
+        "depends": [],
+        "name": "SAR_GEO",
+        "sources": [
+            "./SAR_geo/SAR_GEO.pyx"
+        ]
+    },
+    "module_name": "SAR_GEO"
+}
+END: Cython Metadata */
+
+#ifndef PY_SSIZE_T_CLEAN
+#define PY_SSIZE_T_CLEAN
+#endif /* PY_SSIZE_T_CLEAN */
+#include "Python.h"
+#ifndef Py_PYTHON_H
+    #error Python headers needed to compile C extensions, please install development version of Python.
+#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000)
+    #error Cython requires Python 2.6+ or Python 3.3+.
+#else
+#define CYTHON_ABI "0_29_24"
+#define CYTHON_HEX_VERSION 0x001D18F0
+#define CYTHON_FUTURE_DIVISION 0
+#include <stddef.h>
+#ifndef offsetof
+  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
+#endif
+#if !defined(WIN32) && !defined(MS_WINDOWS)
+  #ifndef __stdcall
+    #define __stdcall
+  #endif
+  #ifndef __cdecl
+    #define __cdecl
+  #endif
+  #ifndef __fastcall
+    #define __fastcall
+  #endif
+#endif
+#ifndef DL_IMPORT
+  #define DL_IMPORT(t) t
+#endif
+#ifndef DL_EXPORT
+  #define DL_EXPORT(t) t
+#endif
+#define __PYX_COMMA ,
+#ifndef HAVE_LONG_LONG
+  #if PY_VERSION_HEX >= 0x02070000
+    #define HAVE_LONG_LONG
+  #endif
+#endif
+#ifndef PY_LONG_LONG
+  #define PY_LONG_LONG LONG_LONG
+#endif
+#ifndef Py_HUGE_VAL
+  #define Py_HUGE_VAL HUGE_VAL
+#endif
+#ifdef PYPY_VERSION
+  #define CYTHON_COMPILING_IN_PYPY 1
+  #define CYTHON_COMPILING_IN_PYSTON 0
+  #define CYTHON_COMPILING_IN_CPYTHON 0
+  #undef CYTHON_USE_TYPE_SLOTS
+  #define CYTHON_USE_TYPE_SLOTS 0
+  #undef CYTHON_USE_PYTYPE_LOOKUP
+  #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #if PY_VERSION_HEX < 0x03050000
+    #undef CYTHON_USE_ASYNC_SLOTS
+    #define CYTHON_USE_ASYNC_SLOTS 0
+  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
+    #define CYTHON_USE_ASYNC_SLOTS 1
+  #endif
+  #undef CYTHON_USE_PYLIST_INTERNALS
+  #define CYTHON_USE_PYLIST_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_INTERNALS
+  #define CYTHON_USE_UNICODE_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_WRITER
+  #define CYTHON_USE_UNICODE_WRITER 0
+  #undef CYTHON_USE_PYLONG_INTERNALS
+  #define CYTHON_USE_PYLONG_INTERNALS 0
+  #undef CYTHON_AVOID_BORROWED_REFS
+  #define CYTHON_AVOID_BORROWED_REFS 1
+  #undef CYTHON_ASSUME_SAFE_MACROS
+  #define CYTHON_ASSUME_SAFE_MACROS 0
+  #undef CYTHON_UNPACK_METHODS
+  #define CYTHON_UNPACK_METHODS 0
+  #undef CYTHON_FAST_THREAD_STATE
+  #define CYTHON_FAST_THREAD_STATE 0
+  #undef CYTHON_FAST_PYCALL
+  #define CYTHON_FAST_PYCALL 0
+  #undef CYTHON_PEP489_MULTI_PHASE_INIT
+  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
+  #undef CYTHON_USE_TP_FINALIZE
+  #define CYTHON_USE_TP_FINALIZE 0
+  #undef CYTHON_USE_DICT_VERSIONS
+  #define CYTHON_USE_DICT_VERSIONS 0
+  #undef CYTHON_USE_EXC_INFO_STACK
+  #define CYTHON_USE_EXC_INFO_STACK 0
+#elif defined(PYSTON_VERSION)
+  #define CYTHON_COMPILING_IN_PYPY 0
+  #define CYTHON_COMPILING_IN_PYSTON 1
+  #define CYTHON_COMPILING_IN_CPYTHON 0
+  #ifndef CYTHON_USE_TYPE_SLOTS
+    #define CYTHON_USE_TYPE_SLOTS 1
+  #endif
+  #undef CYTHON_USE_PYTYPE_LOOKUP
+  #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #undef CYTHON_USE_ASYNC_SLOTS
+  #define CYTHON_USE_ASYNC_SLOTS 0
+  #undef CYTHON_USE_PYLIST_INTERNALS
+  #define CYTHON_USE_PYLIST_INTERNALS 0
+  #ifndef CYTHON_USE_UNICODE_INTERNALS
+    #define CYTHON_USE_UNICODE_INTERNALS 1
+  #endif
+  #undef CYTHON_USE_UNICODE_WRITER
+  #define CYTHON_USE_UNICODE_WRITER 0
+  #undef CYTHON_USE_PYLONG_INTERNALS
+  #define CYTHON_USE_PYLONG_INTERNALS 0
+  #ifndef CYTHON_AVOID_BORROWED_REFS
+    #define CYTHON_AVOID_BORROWED_REFS 0
+  #endif
+  #ifndef CYTHON_ASSUME_SAFE_MACROS
+    #define CYTHON_ASSUME_SAFE_MACROS 1
+  #endif
+  #ifndef CYTHON_UNPACK_METHODS
+    #define CYTHON_UNPACK_METHODS 1
+  #endif
+  #undef CYTHON_FAST_THREAD_STATE
+  #define CYTHON_FAST_THREAD_STATE 0
+  #undef CYTHON_FAST_PYCALL
+  #define CYTHON_FAST_PYCALL 0
+  #undef CYTHON_PEP489_MULTI_PHASE_INIT
+  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
+  #undef CYTHON_USE_TP_FINALIZE
+  #define CYTHON_USE_TP_FINALIZE 0
+  #undef CYTHON_USE_DICT_VERSIONS
+  #define CYTHON_USE_DICT_VERSIONS 0
+  #undef CYTHON_USE_EXC_INFO_STACK
+  #define CYTHON_USE_EXC_INFO_STACK 0
+#else
+  #define CYTHON_COMPILING_IN_PYPY 0
+  #define CYTHON_COMPILING_IN_PYSTON 0
+  #define CYTHON_COMPILING_IN_CPYTHON 1
+  #ifndef CYTHON_USE_TYPE_SLOTS
+    #define CYTHON_USE_TYPE_SLOTS 1
+  #endif
+  #if PY_VERSION_HEX < 0x02070000
+    #undef CYTHON_USE_PYTYPE_LOOKUP
+    #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #elif !defined(CYTHON_USE_PYTYPE_LOOKUP)
+    #define CYTHON_USE_PYTYPE_LOOKUP 1
+  #endif
+  #if PY_MAJOR_VERSION < 3
+    #undef CYTHON_USE_ASYNC_SLOTS
+    #define CYTHON_USE_ASYNC_SLOTS 0
+  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
+    #define CYTHON_USE_ASYNC_SLOTS 1
+  #endif
+  #if PY_VERSION_HEX < 0x02070000
+    #undef CYTHON_USE_PYLONG_INTERNALS
+    #define CYTHON_USE_PYLONG_INTERNALS 0
+  #elif !defined(CYTHON_USE_PYLONG_INTERNALS)
+    #define CYTHON_USE_PYLONG_INTERNALS 1
+  #endif
+  #ifndef CYTHON_USE_PYLIST_INTERNALS
+    #define CYTHON_USE_PYLIST_INTERNALS 1
+  #endif
+  #ifndef CYTHON_USE_UNICODE_INTERNALS
+    #define CYTHON_USE_UNICODE_INTERNALS 1
+  #endif
+  #if PY_VERSION_HEX < 0x030300F0
+    #undef CYTHON_USE_UNICODE_WRITER
+    #define CYTHON_USE_UNICODE_WRITER 0
+  #elif !defined(CYTHON_USE_UNICODE_WRITER)
+    #define CYTHON_USE_UNICODE_WRITER 1
+  #endif
+  #ifndef CYTHON_AVOID_BORROWED_REFS
+    #define CYTHON_AVOID_BORROWED_REFS 0
+  #endif
+  #ifndef CYTHON_ASSUME_SAFE_MACROS
+    #define CYTHON_ASSUME_SAFE_MACROS 1
+  #endif
+  #ifndef CYTHON_UNPACK_METHODS
+    #define CYTHON_UNPACK_METHODS 1
+  #endif
+  #ifndef CYTHON_FAST_THREAD_STATE
+    #define CYTHON_FAST_THREAD_STATE 1
+  #endif
+  #ifndef CYTHON_FAST_PYCALL
+    #define CYTHON_FAST_PYCALL 1
+  #endif
+  #ifndef CYTHON_PEP489_MULTI_PHASE_INIT
+    #define CYTHON_PEP489_MULTI_PHASE_INIT (PY_VERSION_HEX >= 0x03050000)
+  #endif
+  #ifndef CYTHON_USE_TP_FINALIZE
+    #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1)
+  #endif
+  #ifndef CYTHON_USE_DICT_VERSIONS
+    #define CYTHON_USE_DICT_VERSIONS (PY_VERSION_HEX >= 0x030600B1)
+  #endif
+  #ifndef CYTHON_USE_EXC_INFO_STACK
+    #define CYTHON_USE_EXC_INFO_STACK (PY_VERSION_HEX >= 0x030700A3)
+  #endif
+#endif
+#if !defined(CYTHON_FAST_PYCCALL)
+#define CYTHON_FAST_PYCCALL  (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1)
+#endif
+#if CYTHON_USE_PYLONG_INTERNALS
+  #include "longintrepr.h"
+  #undef SHIFT
+  #undef BASE
+  #undef MASK
+  #ifdef SIZEOF_VOID_P
+    enum { __pyx_check_sizeof_voidp = 1 / (int)(SIZEOF_VOID_P == sizeof(void*)) };
+  #endif
+#endif
+#ifndef __has_attribute
+  #define __has_attribute(x) 0
+#endif
+#ifndef __has_cpp_attribute
+  #define __has_cpp_attribute(x) 0
+#endif
+#ifndef CYTHON_RESTRICT
+  #if defined(__GNUC__)
+    #define CYTHON_RESTRICT __restrict__
+  #elif defined(_MSC_VER) && _MSC_VER >= 1400
+    #define CYTHON_RESTRICT __restrict
+  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define CYTHON_RESTRICT restrict
+  #else
+    #define CYTHON_RESTRICT
+  #endif
+#endif
+#ifndef CYTHON_UNUSED
+# if defined(__GNUC__)
+#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
+#     define CYTHON_UNUSED __attribute__ ((__unused__))
+#   else
+#     define CYTHON_UNUSED
+#   endif
+# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
+#   define CYTHON_UNUSED __attribute__ ((__unused__))
+# else
+#   define CYTHON_UNUSED
+# endif
+#endif
+#ifndef CYTHON_MAYBE_UNUSED_VAR
+#  if defined(__cplusplus)
+     template<class T> void CYTHON_MAYBE_UNUSED_VAR( const T& ) { }
+#  else
+#    define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x)
+#  endif
+#endif
+#ifndef CYTHON_NCP_UNUSED
+# if CYTHON_COMPILING_IN_CPYTHON
+#  define CYTHON_NCP_UNUSED
+# else
+#  define CYTHON_NCP_UNUSED CYTHON_UNUSED
+# endif
+#endif
+#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
+#ifdef _MSC_VER
+    #ifndef _MSC_STDINT_H_
+        #if _MSC_VER < 1300
+           typedef unsigned char     uint8_t;
+           typedef unsigned int      uint32_t;
+        #else
+           typedef unsigned __int8   uint8_t;
+           typedef unsigned __int32  uint32_t;
+        #endif
+    #endif
+#else
+   #include <stdint.h>
+#endif
+#ifndef CYTHON_FALLTHROUGH
+  #if defined(__cplusplus) && __cplusplus >= 201103L
+    #if __has_cpp_attribute(fallthrough)
+      #define CYTHON_FALLTHROUGH [[fallthrough]]
+    #elif __has_cpp_attribute(clang::fallthrough)
+      #define CYTHON_FALLTHROUGH [[clang::fallthrough]]
+    #elif __has_cpp_attribute(gnu::fallthrough)
+      #define CYTHON_FALLTHROUGH [[gnu::fallthrough]]
+    #endif
+  #endif
+  #ifndef CYTHON_FALLTHROUGH
+    #if __has_attribute(fallthrough)
+      #define CYTHON_FALLTHROUGH __attribute__((fallthrough))
+    #else
+      #define CYTHON_FALLTHROUGH
+    #endif
+  #endif
+  #if defined(__clang__ ) && defined(__apple_build_version__)
+    #if __apple_build_version__ < 7000000
+      #undef  CYTHON_FALLTHROUGH
+      #define CYTHON_FALLTHROUGH
+    #endif
+  #endif
+#endif
+
+#ifndef CYTHON_INLINE
+  #if defined(__clang__)
+    #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))
+  #elif defined(__GNUC__)
+    #define CYTHON_INLINE __inline__
+  #elif defined(_MSC_VER)
+    #define CYTHON_INLINE __inline
+  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define CYTHON_INLINE inline
+  #else
+    #define CYTHON_INLINE
+  #endif
+#endif
+
+#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)
+  #define Py_OptimizeFlag 0
+#endif
+#define __PYX_BUILD_PY_SSIZE_T "n"
+#define CYTHON_FORMAT_SSIZE_T "z"
+#if PY_MAJOR_VERSION < 3
+  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
+  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+  #define __Pyx_DefaultClassType PyClass_Type
+#else
+  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
+#if PY_VERSION_HEX >= 0x030800A4 && PY_VERSION_HEX < 0x030800B2
+  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_New(a, 0, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+#else
+  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+#endif
+  #define __Pyx_DefaultClassType PyType_Type
+#endif
+#ifndef Py_TPFLAGS_CHECKTYPES
+  #define Py_TPFLAGS_CHECKTYPES 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_INDEX
+  #define Py_TPFLAGS_HAVE_INDEX 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_NEWBUFFER
+  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_FINALIZE
+  #define Py_TPFLAGS_HAVE_FINALIZE 0
+#endif
+#ifndef METH_STACKLESS
+  #define METH_STACKLESS 0
+#endif
+#if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL)
+  #ifndef METH_FASTCALL
+     #define METH_FASTCALL 0x80
+  #endif
+  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs);
+  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
+                                                          Py_ssize_t nargs, PyObject *kwnames);
+#else
+  #define __Pyx_PyCFunctionFast _PyCFunctionFast
+  #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
+#endif
+#if CYTHON_FAST_PYCCALL
+#define __Pyx_PyFastCFunction_Check(func)\
+    ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)))))
+#else
+#define __Pyx_PyFastCFunction_Check(func) 0
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
+  #define PyObject_Malloc(s)   PyMem_Malloc(s)
+  #define PyObject_Free(p)     PyMem_Free(p)
+  #define PyObject_Realloc(p)  PyMem_Realloc(p)
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030400A1
+  #define PyMem_RawMalloc(n)           PyMem_Malloc(n)
+  #define PyMem_RawRealloc(p, n)       PyMem_Realloc(p, n)
+  #define PyMem_RawFree(p)             PyMem_Free(p)
+#endif
+#if CYTHON_COMPILING_IN_PYSTON
+  #define __Pyx_PyCode_HasFreeVars(co)  PyCode_HasFreeVars(co)
+  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno)
+#else
+  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
+  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)  (frame)->f_lineno = (lineno)
+#endif
+#if !CYTHON_FAST_THREAD_STATE || PY_VERSION_HEX < 0x02070000
+  #define __Pyx_PyThreadState_Current PyThreadState_GET()
+#elif PY_VERSION_HEX >= 0x03060000
+  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
+#elif PY_VERSION_HEX >= 0x03000000
+  #define __Pyx_PyThreadState_Current PyThreadState_GET()
+#else
+  #define __Pyx_PyThreadState_Current _PyThreadState_Current
+#endif
+#if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT)
+#include "pythread.h"
+#define Py_tss_NEEDS_INIT 0
+typedef int Py_tss_t;
+static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) {
+  *key = PyThread_create_key();
+  return 0;
+}
+static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) {
+  Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t));
+  *key = Py_tss_NEEDS_INIT;
+  return key;
+}
+static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) {
+  PyObject_Free(key);
+}
+static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) {
+  return *key != Py_tss_NEEDS_INIT;
+}
+static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) {
+  PyThread_delete_key(*key);
+  *key = Py_tss_NEEDS_INIT;
+}
+static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) {
+  return PyThread_set_key_value(*key, value);
+}
+static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) {
+  return PyThread_get_key_value(*key);
+}
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized)
+#define __Pyx_PyDict_NewPresized(n)  ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
+#else
+#define __Pyx_PyDict_NewPresized(n)  PyDict_New()
+#endif
+#if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION
+  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
+  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
+#else
+  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
+  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && CYTHON_USE_UNICODE_INTERNALS
+#define __Pyx_PyDict_GetItemStr(dict, name)  _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
+#else
+#define __Pyx_PyDict_GetItemStr(dict, name)  PyDict_GetItem(dict, name)
+#endif
+#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
+  #define CYTHON_PEP393_ENABLED 1
+  #if defined(PyUnicode_IS_READY)
+  #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\
+                                              0 : _PyUnicode_Ready((PyObject *)(op)))
+  #else
+  #define __Pyx_PyUnicode_READY(op)       (0)
+  #endif
+  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_LENGTH(u)
+  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
+  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   PyUnicode_MAX_CHAR_VALUE(u)
+  #define __Pyx_PyUnicode_KIND(u)         PyUnicode_KIND(u)
+  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)
+  #define __Pyx_PyUnicode_READ(k, d, i)   PyUnicode_READ(k, d, i)
+  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  PyUnicode_WRITE(k, d, i, ch)
+  #if defined(PyUnicode_IS_READY) && defined(PyUnicode_GET_SIZE)
+  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03090000
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : ((PyCompactUnicodeObject *)(u))->wstr_length))
+  #else
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
+  #endif
+  #else
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_LENGTH(u))
+  #endif
+#else
+  #define CYTHON_PEP393_ENABLED 0
+  #define PyUnicode_1BYTE_KIND  1
+  #define PyUnicode_2BYTE_KIND  2
+  #define PyUnicode_4BYTE_KIND  4
+  #define __Pyx_PyUnicode_READY(op)       (0)
+  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_SIZE(u)
+  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
+  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111)
+  #define __Pyx_PyUnicode_KIND(u)         (sizeof(Py_UNICODE))
+  #define __Pyx_PyUnicode_DATA(u)         ((void*)PyUnicode_AS_UNICODE(u))
+  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
+  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  (((void)(k)), ((Py_UNICODE*)d)[i] = ch)
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_SIZE(u))
+#endif
+#if CYTHON_COMPILING_IN_PYPY
+  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
+  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
+#else
+  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
+  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
+      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
+  #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check)
+  #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
+  #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
+#endif
+#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None || (PyString_Check(b) && !PyString_CheckExact(b)))) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
+#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
+#else
+  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
+#endif
+#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
+  #define PyObject_ASCII(o)            PyObject_Repr(o)
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyBaseString_Type            PyUnicode_Type
+  #define PyStringObject               PyUnicodeObject
+  #define PyString_Type                PyUnicode_Type
+  #define PyString_Check               PyUnicode_Check
+  #define PyString_CheckExact          PyUnicode_CheckExact
+#ifndef PyObject_Unicode
+  #define PyObject_Unicode             PyObject_Str
+#endif
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
+  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
+#else
+  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
+  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
+#endif
+#ifndef PySet_CheckExact
+  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)
+#endif
+#if PY_VERSION_HEX >= 0x030900A4
+  #define __Pyx_SET_REFCNT(obj, refcnt) Py_SET_REFCNT(obj, refcnt)
+  #define __Pyx_SET_SIZE(obj, size) Py_SET_SIZE(obj, size)
+#else
+  #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt)
+  #define __Pyx_SET_SIZE(obj, size) Py_SIZE(obj) = (size)
+#endif
+#if CYTHON_ASSUME_SAFE_MACROS
+  #define __Pyx_PySequence_SIZE(seq)  Py_SIZE(seq)
+#else
+  #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyIntObject                  PyLongObject
+  #define PyInt_Type                   PyLong_Type
+  #define PyInt_Check(op)              PyLong_Check(op)
+  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
+  #define PyInt_FromString             PyLong_FromString
+  #define PyInt_FromUnicode            PyLong_FromUnicode
+  #define PyInt_FromLong               PyLong_FromLong
+  #define PyInt_FromSize_t             PyLong_FromSize_t
+  #define PyInt_FromSsize_t            PyLong_FromSsize_t
+  #define PyInt_AsLong                 PyLong_AsLong
+  #define PyInt_AS_LONG                PyLong_AS_LONG
+  #define PyInt_AsSsize_t              PyLong_AsSsize_t
+  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
+  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
+  #define PyNumber_Int                 PyNumber_Long
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyBoolObject                 PyLongObject
+#endif
+#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
+  #ifndef PyUnicode_InternFromString
+    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
+  #endif
+#endif
+#if PY_VERSION_HEX < 0x030200A4
+  typedef long Py_hash_t;
+  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
+  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
+#else
+  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
+  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? ((void)(klass), PyMethod_New(func, self)) : __Pyx_NewRef(func))
+#else
+  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
+#endif
+#if CYTHON_USE_ASYNC_SLOTS
+  #if PY_VERSION_HEX >= 0x030500B1
+    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
+    #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
+  #else
+    #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
+  #endif
+#else
+  #define __Pyx_PyType_AsAsync(obj) NULL
+#endif
+#ifndef __Pyx_PyAsyncMethodsStruct
+    typedef struct {
+        unaryfunc am_await;
+        unaryfunc am_aiter;
+        unaryfunc am_anext;
+    } __Pyx_PyAsyncMethodsStruct;
+#endif
+
+#if defined(WIN32) || defined(MS_WINDOWS)
+  #define _USE_MATH_DEFINES
+#endif
+#include <math.h>
+#ifdef NAN
+#define __PYX_NAN() ((float) NAN)
+#else
+static CYTHON_INLINE float __PYX_NAN() {
+  float value;
+  memset(&value, 0xFF, sizeof(value));
+  return value;
+}
+#endif
+#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
+#define __Pyx_truncl trunc
+#else
+#define __Pyx_truncl truncl
+#endif
+
+#define __PYX_MARK_ERR_POS(f_index, lineno) \
+    { __pyx_filename = __pyx_f[f_index]; (void)__pyx_filename; __pyx_lineno = lineno; (void)__pyx_lineno; __pyx_clineno = __LINE__; (void)__pyx_clineno; }
+#define __PYX_ERR(f_index, lineno, Ln_error) \
+    { __PYX_MARK_ERR_POS(f_index, lineno) goto Ln_error; }
+
+#ifndef __PYX_EXTERN_C
+  #ifdef __cplusplus
+    #define __PYX_EXTERN_C extern "C"
+  #else
+    #define __PYX_EXTERN_C extern
+  #endif
+#endif
+
+#define __PYX_HAVE__SAR_GEO
+#define __PYX_HAVE_API__SAR_GEO
+/* Early includes */
+#include <string.h>
+#include <stdio.h>
+#include "numpy/arrayobject.h"
+#include "numpy/ndarrayobject.h"
+#include "numpy/ndarraytypes.h"
+#include "numpy/arrayscalars.h"
+#include "numpy/ufuncobject.h"
+
+    /* NumPy API declarations from "numpy/__init__.pxd" */
+    
+#include <math.h>
+#ifdef _OPENMP
+#include <omp.h>
+#endif /* _OPENMP */
+
+#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
+#define CYTHON_WITHOUT_ASSERTIONS
+#endif
+
+typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
+                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
+
+#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
+#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
+#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)
+#define __PYX_DEFAULT_STRING_ENCODING ""
+#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
+#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
+#define __Pyx_uchar_cast(c) ((unsigned char)c)
+#define __Pyx_long_cast(x) ((long)x)
+#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
+    (sizeof(type) < sizeof(Py_ssize_t))  ||\
+    (sizeof(type) > sizeof(Py_ssize_t) &&\
+          likely(v < (type)PY_SSIZE_T_MAX ||\
+                 v == (type)PY_SSIZE_T_MAX)  &&\
+          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
+                                v == (type)PY_SSIZE_T_MIN)))  ||\
+    (sizeof(type) == sizeof(Py_ssize_t) &&\
+          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
+                               v == (type)PY_SSIZE_T_MAX)))  )
+static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
+    return (size_t) i < (size_t) limit;
+}
+#if defined (__cplusplus) && __cplusplus >= 201103L
+    #include <cstdlib>
+    #define __Pyx_sst_abs(value) std::abs(value)
+#elif SIZEOF_INT >= SIZEOF_SIZE_T
+    #define __Pyx_sst_abs(value) abs(value)
+#elif SIZEOF_LONG >= SIZEOF_SIZE_T
+    #define __Pyx_sst_abs(value) labs(value)
+#elif defined (_MSC_VER)
+    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
+#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define __Pyx_sst_abs(value) llabs(value)
+#elif defined (__GNUC__)
+    #define __Pyx_sst_abs(value) __builtin_llabs(value)
+#else
+    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
+#endif
+static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
+static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
+#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
+#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
+#define __Pyx_PyBytes_FromString        PyBytes_FromString
+#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
+static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
+#if PY_MAJOR_VERSION < 3
+    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
+    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
+#else
+    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
+    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
+#endif
+#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyObject_AsWritableString(s)    ((char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
+#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
+#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
+#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
+#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
+static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
+    const Py_UNICODE *u_end = u;
+    while (*u_end++) ;
+    return (size_t)(u_end - u - 1);
+}
+#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
+#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
+#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
+#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
+#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
+static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
+static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
+#define __Pyx_PySequence_Tuple(obj)\
+    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
+#if CYTHON_ASSUME_SAFE_MACROS
+#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
+#else
+#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
+#endif
+#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
+#if PY_MAJOR_VERSION >= 3
+#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
+#else
+#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
+#endif
+#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
+#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+static int __Pyx_sys_getdefaultencoding_not_ascii;
+static int __Pyx_init_sys_getdefaultencoding_params(void) {
+    PyObject* sys;
+    PyObject* default_encoding = NULL;
+    PyObject* ascii_chars_u = NULL;
+    PyObject* ascii_chars_b = NULL;
+    const char* default_encoding_c;
+    sys = PyImport_ImportModule("sys");
+    if (!sys) goto bad;
+    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
+    Py_DECREF(sys);
+    if (!default_encoding) goto bad;
+    default_encoding_c = PyBytes_AsString(default_encoding);
+    if (!default_encoding_c) goto bad;
+    if (strcmp(default_encoding_c, "ascii") == 0) {
+        __Pyx_sys_getdefaultencoding_not_ascii = 0;
+    } else {
+        char ascii_chars[128];
+        int c;
+        for (c = 0; c < 128; c++) {
+            ascii_chars[c] = c;
+        }
+        __Pyx_sys_getdefaultencoding_not_ascii = 1;
+        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
+        if (!ascii_chars_u) goto bad;
+        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
+        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
+            PyErr_Format(
+                PyExc_ValueError,
+                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
+                default_encoding_c);
+            goto bad;
+        }
+        Py_DECREF(ascii_chars_u);
+        Py_DECREF(ascii_chars_b);
+    }
+    Py_DECREF(default_encoding);
+    return 0;
+bad:
+    Py_XDECREF(default_encoding);
+    Py_XDECREF(ascii_chars_u);
+    Py_XDECREF(ascii_chars_b);
+    return -1;
+}
+#endif
+#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
+#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
+#else
+#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
+#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+static char* __PYX_DEFAULT_STRING_ENCODING;
+static int __Pyx_init_sys_getdefaultencoding_params(void) {
+    PyObject* sys;
+    PyObject* default_encoding = NULL;
+    char* default_encoding_c;
+    sys = PyImport_ImportModule("sys");
+    if (!sys) goto bad;
+    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
+    Py_DECREF(sys);
+    if (!default_encoding) goto bad;
+    default_encoding_c = PyBytes_AsString(default_encoding);
+    if (!default_encoding_c) goto bad;
+    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);
+    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
+    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
+    Py_DECREF(default_encoding);
+    return 0;
+bad:
+    Py_XDECREF(default_encoding);
+    return -1;
+}
+#endif
+#endif
+
+
+/* Test for GCC > 2.95 */
+#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
+  #define likely(x)   __builtin_expect(!!(x), 1)
+  #define unlikely(x) __builtin_expect(!!(x), 0)
+#else /* !__GNUC__ or GCC < 2.95 */
+  #define likely(x)   (x)
+  #define unlikely(x) (x)
+#endif /* __GNUC__ */
+static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
+
+static PyObject *__pyx_m = NULL;
+static PyObject *__pyx_d;
+static PyObject *__pyx_b;
+static PyObject *__pyx_cython_runtime = NULL;
+static PyObject *__pyx_empty_tuple;
+static PyObject *__pyx_empty_bytes;
+static PyObject *__pyx_empty_unicode;
+static int __pyx_lineno;
+static int __pyx_clineno = 0;
+static const char * __pyx_cfilenm= __FILE__;
+static const char *__pyx_filename;
+
+/* Header.proto */
+#if !defined(CYTHON_CCOMPLEX)
+  #if defined(__cplusplus)
+    #define CYTHON_CCOMPLEX 1
+  #elif defined(_Complex_I)
+    #define CYTHON_CCOMPLEX 1
+  #else
+    #define CYTHON_CCOMPLEX 0
+  #endif
+#endif
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    #include <complex>
+  #else
+    #include <complex.h>
+  #endif
+#endif
+#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
+  #undef _Complex_I
+  #define _Complex_I 1.0fj
+#endif
+
+
+static const char *__pyx_f[] = {
+  "SAR_geo\\SAR_GEO.pyx",
+  "__init__.pxd",
+  "type.pxd",
+};
+/* BufferFormatStructs.proto */
+#define IS_UNSIGNED(type) (((type) -1) > 0)
+struct __Pyx_StructField_;
+#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
+typedef struct {
+  const char* name;
+  struct __Pyx_StructField_* fields;
+  size_t size;
+  size_t arraysize[8];
+  int ndim;
+  char typegroup;
+  char is_unsigned;
+  int flags;
+} __Pyx_TypeInfo;
+typedef struct __Pyx_StructField_ {
+  __Pyx_TypeInfo* type;
+  const char* name;
+  size_t offset;
+} __Pyx_StructField;
+typedef struct {
+  __Pyx_StructField* field;
+  size_t parent_offset;
+} __Pyx_BufFmt_StackElem;
+typedef struct {
+  __Pyx_StructField root;
+  __Pyx_BufFmt_StackElem* head;
+  size_t fmt_offset;
+  size_t new_count, enc_count;
+  size_t struct_alignment;
+  int is_complex;
+  char enc_type;
+  char new_packmode;
+  char enc_packmode;
+  char is_valid_array;
+} __Pyx_BufFmt_Context;
+
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":690
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+ * 
+ * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t
+ */
+typedef npy_int8 __pyx_t_5numpy_int8_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":691
+ * 
+ * ctypedef npy_int8       int8_t
+ * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int32      int32_t
+ * ctypedef npy_int64      int64_t
+ */
+typedef npy_int16 __pyx_t_5numpy_int16_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":692
+ * ctypedef npy_int8       int8_t
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int64      int64_t
+ * #ctypedef npy_int96      int96_t
+ */
+typedef npy_int32 __pyx_t_5numpy_int32_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":693
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t
+ * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_int96      int96_t
+ * #ctypedef npy_int128     int128_t
+ */
+typedef npy_int64 __pyx_t_5numpy_int64_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":697
+ * #ctypedef npy_int128     int128_t
+ * 
+ * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t
+ */
+typedef npy_uint8 __pyx_t_5numpy_uint8_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":698
+ * 
+ * ctypedef npy_uint8      uint8_t
+ * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint32     uint32_t
+ * ctypedef npy_uint64     uint64_t
+ */
+typedef npy_uint16 __pyx_t_5numpy_uint16_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":699
+ * ctypedef npy_uint8      uint8_t
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint64     uint64_t
+ * #ctypedef npy_uint96     uint96_t
+ */
+typedef npy_uint32 __pyx_t_5numpy_uint32_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":700
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t
+ * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_uint96     uint96_t
+ * #ctypedef npy_uint128    uint128_t
+ */
+typedef npy_uint64 __pyx_t_5numpy_uint64_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":704
+ * #ctypedef npy_uint128    uint128_t
+ * 
+ * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_float64    float64_t
+ * #ctypedef npy_float80    float80_t
+ */
+typedef npy_float32 __pyx_t_5numpy_float32_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":705
+ * 
+ * ctypedef npy_float32    float32_t
+ * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_float80    float80_t
+ * #ctypedef npy_float128   float128_t
+ */
+typedef npy_float64 __pyx_t_5numpy_float64_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":714
+ * # The int types are mapped a bit surprising --
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+ * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longlong   long_t
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+ */
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+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":715
+ * # numpy.int corresponds to 'l' and numpy.long to 'q'
+ * ctypedef npy_long       int_t
+ * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longlong   longlong_t
+ * 
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+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":716
+ * ctypedef npy_long       int_t
+ * ctypedef npy_longlong   long_t
+ * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_ulong      uint_t
+ */
+typedef npy_longlong __pyx_t_5numpy_longlong_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":718
+ * ctypedef npy_longlong   longlong_t
+ * 
+ * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_ulonglong  ulong_t
+ * ctypedef npy_ulonglong  ulonglong_t
+ */
+typedef npy_ulong __pyx_t_5numpy_uint_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":719
+ * 
+ * ctypedef npy_ulong      uint_t
+ * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_ulonglong  ulonglong_t
+ * 
+ */
+typedef npy_ulonglong __pyx_t_5numpy_ulong_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":720
+ * ctypedef npy_ulong      uint_t
+ * ctypedef npy_ulonglong  ulong_t
+ * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_intp       intp_t
+ */
+typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":722
+ * ctypedef npy_ulonglong  ulonglong_t
+ * 
+ * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uintp      uintp_t
+ * 
+ */
+typedef npy_intp __pyx_t_5numpy_intp_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":723
+ * 
+ * ctypedef npy_intp       intp_t
+ * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_double     float_t
+ */
+typedef npy_uintp __pyx_t_5numpy_uintp_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":725
+ * ctypedef npy_uintp      uintp_t
+ * 
+ * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_double     double_t
+ * ctypedef npy_longdouble longdouble_t
+ */
+typedef npy_double __pyx_t_5numpy_float_t;
+
+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":726
+ * 
+ * ctypedef npy_double     float_t
+ * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longdouble longdouble_t
+ * 
+ */
+typedef npy_double __pyx_t_5numpy_double_t;
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+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":727
+ * ctypedef npy_double     float_t
+ * ctypedef npy_double     double_t
+ * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_cfloat      cfloat_t
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+typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
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+ * ctypedef npy_clongdouble clongdouble_t
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+/* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":730
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+  #define __Pyx_XDECREF(r) Py_XDECREF(r)
+  #define __Pyx_XGOTREF(r)
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+#define __Pyx_BufPtrStrided2d(type, buf, i0, s0, i1, s1) (type)((char*)buf + i0 * s0 + i1 * s1)
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+#define __Pyx_PyErr_Clear() PyErr_Clear()
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+#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
+#define __Pyx_ErrRestoreInState(tstate, type, value, tb)  PyErr_Restore(type, value, tb)
+#define __Pyx_ErrFetchInState(tstate, type, value, tb)  PyErr_Fetch(type, value, tb)
+#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
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+#define __Pyx_BufPtrStrided1d(type, buf, i0, s0) (type)((char*)buf + i0 * s0)
+/* RaiseArgTupleInvalid.proto */
+static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
+    Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
+
+/* RaiseDoubleKeywords.proto */
+static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
+
+/* ParseKeywords.proto */
+static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
+    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
+    const char* function_name);
+
+/* ArgTypeTest.proto */
+#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
+    ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
+        __Pyx__ArgTypeTest(obj, type, name, exact))
+static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);
+
+/* PyObjectGetAttrStr.proto */
+#if CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name);
+#else
+#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
+#endif
+
+/* GetBuiltinName.proto */
+static PyObject *__Pyx_GetBuiltinName(PyObject *name);
+
+/* PyDictVersioning.proto */
+#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
+#define __PYX_DICT_VERSION_INIT  ((PY_UINT64_T) -1)
+#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
+#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
+    (version_var) = __PYX_GET_DICT_VERSION(dict);\
+    (cache_var) = (value);
+#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
+    static PY_UINT64_T __pyx_dict_version = 0;\
+    static PyObject *__pyx_dict_cached_value = NULL;\
+    if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
+        (VAR) = __pyx_dict_cached_value;\
+    } else {\
+        (VAR) = __pyx_dict_cached_value = (LOOKUP);\
+        __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
+    }\
+}
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
+static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
+#else
+#define __PYX_GET_DICT_VERSION(dict)  (0)
+#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
+#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
+#endif
+
+/* GetModuleGlobalName.proto */
+#if CYTHON_USE_DICT_VERSIONS
+#define __Pyx_GetModuleGlobalName(var, name)  {\
+    static PY_UINT64_T __pyx_dict_version = 0;\
+    static PyObject *__pyx_dict_cached_value = NULL;\
+    (var) = (likely(__pyx_dict_version == __PYX_GET_DICT_VERSION(__pyx_d))) ?\
+        (likely(__pyx_dict_cached_value) ? __Pyx_NewRef(__pyx_dict_cached_value) : __Pyx_GetBuiltinName(name)) :\
+        __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
+}
+#define __Pyx_GetModuleGlobalNameUncached(var, name)  {\
+    PY_UINT64_T __pyx_dict_version;\
+    PyObject *__pyx_dict_cached_value;\
+    (var) = __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
+}
+static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value);
+#else
+#define __Pyx_GetModuleGlobalName(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
+#define __Pyx_GetModuleGlobalNameUncached(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
+static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name);
+#endif
+
+/* PyObjectCall.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
+#else
+#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
+#endif
+
+/* ExtTypeTest.proto */
+static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);
+
+#define __Pyx_BufPtrStrided3d(type, buf, i0, s0, i1, s1, i2, s2) (type)((char*)buf + i0 * s0 + i1 * s1 + i2 * s2)
+/* PyCFunctionFastCall.proto */
+#if CYTHON_FAST_PYCCALL
+static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
+#else
+#define __Pyx_PyCFunction_FastCall(func, args, nargs)  (assert(0), NULL)
+#endif
+
+/* PyFunctionFastCall.proto */
+#if CYTHON_FAST_PYCALL
+#define __Pyx_PyFunction_FastCall(func, args, nargs)\
+    __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
+#if 1 || PY_VERSION_HEX < 0x030600B1
+static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs);
+#else
+#define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
+#endif
+#define __Pyx_BUILD_ASSERT_EXPR(cond)\
+    (sizeof(char [1 - 2*!(cond)]) - 1)
+#ifndef Py_MEMBER_SIZE
+#define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member)
+#endif
+  static size_t __pyx_pyframe_localsplus_offset = 0;
+  #include "frameobject.h"
+  #define __Pxy_PyFrame_Initialize_Offsets()\
+    ((void)__Pyx_BUILD_ASSERT_EXPR(sizeof(PyFrameObject) == offsetof(PyFrameObject, f_localsplus) + Py_MEMBER_SIZE(PyFrameObject, f_localsplus)),\
+     (void)(__pyx_pyframe_localsplus_offset = ((size_t)PyFrame_Type.tp_basicsize) - Py_MEMBER_SIZE(PyFrameObject, f_localsplus)))
+  #define __Pyx_PyFrame_GetLocalsplus(frame)\
+    (assert(__pyx_pyframe_localsplus_offset), (PyObject **)(((char *)(frame)) + __pyx_pyframe_localsplus_offset))
+#endif
+
+/* PyObjectCall2Args.proto */
+static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2);
+
+/* PyObjectCallMethO.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
+#endif
+
+/* PyObjectCallOneArg.proto */
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
+
+/* GetItemInt.proto */
+#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
+    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
+    __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\
+    (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\
+               __Pyx_GetItemInt_Generic(o, to_py_func(i))))
+#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
+    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
+    __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
+    (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
+                                                              int wraparound, int boundscheck);
+#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
+    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
+    __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
+    (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL))
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
+                                                              int wraparound, int boundscheck);
+static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
+                                                     int is_list, int wraparound, int boundscheck);
+
+/* ObjectGetItem.proto */
+#if CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key);
+#else
+#define __Pyx_PyObject_GetItem(obj, key)  PyObject_GetItem(obj, key)
+#endif
+
+/* GetTopmostException.proto */
+#if CYTHON_USE_EXC_INFO_STACK
+static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
+#endif
+
+/* SaveResetException.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
+static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
+#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
+static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
+#else
+#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
+#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
+#endif
+
+/* PyErrExceptionMatches.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
+static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
+#else
+#define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)
+#endif
+
+/* GetException.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
+static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
+#else
+static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
+#endif
+
+/* RaiseException.proto */
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
+
+/* TypeImport.proto */
+#ifndef __PYX_HAVE_RT_ImportType_proto
+#define __PYX_HAVE_RT_ImportType_proto
+enum __Pyx_ImportType_CheckSize {
+   __Pyx_ImportType_CheckSize_Error = 0,
+   __Pyx_ImportType_CheckSize_Warn = 1,
+   __Pyx_ImportType_CheckSize_Ignore = 2
+};
+static PyTypeObject *__Pyx_ImportType(PyObject* module, const char *module_name, const char *class_name, size_t size, enum __Pyx_ImportType_CheckSize check_size);
+#endif
+
+/* Import.proto */
+static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
+
+/* ImportFrom.proto */
+static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name);
+
+/* CLineInTraceback.proto */
+#ifdef CYTHON_CLINE_IN_TRACEBACK
+#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
+#else
+static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
+#endif
+
+/* CodeObjectCache.proto */
+typedef struct {
+    PyCodeObject* code_object;
+    int code_line;
+} __Pyx_CodeObjectCacheEntry;
+struct __Pyx_CodeObjectCache {
+    int count;
+    int max_count;
+    __Pyx_CodeObjectCacheEntry* entries;
+};
+static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
+static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
+static PyCodeObject *__pyx_find_code_object(int code_line);
+static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
+
+/* AddTraceback.proto */
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename);
+
+/* BufferStructDeclare.proto */
+typedef struct {
+  Py_ssize_t shape, strides, suboffsets;
+} __Pyx_Buf_DimInfo;
+typedef struct {
+  size_t refcount;
+  Py_buffer pybuffer;
+} __Pyx_Buffer;
+typedef struct {
+  __Pyx_Buffer *rcbuffer;
+  char *data;
+  __Pyx_Buf_DimInfo diminfo[8];
+} __Pyx_LocalBuf_ND;
+
+#if PY_MAJOR_VERSION < 3
+    static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
+    static void __Pyx_ReleaseBuffer(Py_buffer *view);
+#else
+    #define __Pyx_GetBuffer PyObject_GetBuffer
+    #define __Pyx_ReleaseBuffer PyBuffer_Release
+#endif
+
+
+/* GCCDiagnostics.proto */
+#if defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
+#define __Pyx_HAS_GCC_DIAGNOSTIC
+#endif
+
+/* Print.proto */
+static int __Pyx_Print(PyObject*, PyObject *, int);
+#if CYTHON_COMPILING_IN_PYPY || PY_MAJOR_VERSION >= 3
+static PyObject* __pyx_print = 0;
+static PyObject* __pyx_print_kwargs = 0;
+#endif
+
+/* RealImag.proto */
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    #define __Pyx_CREAL(z) ((z).real())
+    #define __Pyx_CIMAG(z) ((z).imag())
+  #else
+    #define __Pyx_CREAL(z) (__real__(z))
+    #define __Pyx_CIMAG(z) (__imag__(z))
+  #endif
+#else
+    #define __Pyx_CREAL(z) ((z).real)
+    #define __Pyx_CIMAG(z) ((z).imag)
+#endif
+#if defined(__cplusplus) && CYTHON_CCOMPLEX\
+        && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
+    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
+    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
+#else
+    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
+    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
+#endif
+
+/* Arithmetic.proto */
+#if CYTHON_CCOMPLEX
+    #define __Pyx_c_eq_float(a, b)   ((a)==(b))
+    #define __Pyx_c_sum_float(a, b)  ((a)+(b))
+    #define __Pyx_c_diff_float(a, b) ((a)-(b))
+    #define __Pyx_c_prod_float(a, b) ((a)*(b))
+    #define __Pyx_c_quot_float(a, b) ((a)/(b))
+    #define __Pyx_c_neg_float(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zero_float(z) ((z)==(float)0)
+    #define __Pyx_c_conj_float(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_abs_float(z)     (::std::abs(z))
+        #define __Pyx_c_pow_float(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zero_float(z) ((z)==0)
+    #define __Pyx_c_conj_float(z)    (conjf(z))
+    #if 1
+        #define __Pyx_c_abs_float(z)     (cabsf(z))
+        #define __Pyx_c_pow_float(a, b)  (cpowf(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex);
+    #if 1
+        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex);
+        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    #endif
+#endif
+
+/* Arithmetic.proto */
+#if CYTHON_CCOMPLEX
+    #define __Pyx_c_eq_double(a, b)   ((a)==(b))
+    #define __Pyx_c_sum_double(a, b)  ((a)+(b))
+    #define __Pyx_c_diff_double(a, b) ((a)-(b))
+    #define __Pyx_c_prod_double(a, b) ((a)*(b))
+    #define __Pyx_c_quot_double(a, b) ((a)/(b))
+    #define __Pyx_c_neg_double(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
+    #define __Pyx_c_conj_double(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_abs_double(z)     (::std::abs(z))
+        #define __Pyx_c_pow_double(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zero_double(z) ((z)==0)
+    #define __Pyx_c_conj_double(z)    (conj(z))
+    #if 1
+        #define __Pyx_c_abs_double(z)     (cabs(z))
+        #define __Pyx_c_pow_double(a, b)  (cpow(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);
+    #if 1
+        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);
+        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    #endif
+#endif
+
+/* CIntToPy.proto */
+static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
+
+/* CIntFromPy.proto */
+static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
+
+/* PrintOne.proto */
+static int __Pyx_PrintOne(PyObject* stream, PyObject *o);
+
+/* CIntToPy.proto */
+static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
+
+/* CIntFromPy.proto */
+static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
+
+/* FastTypeChecks.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
+static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
+#else
+#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
+#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
+#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
+#endif
+#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
+
+/* CheckBinaryVersion.proto */
+static int __Pyx_check_binary_version(void);
+
+/* InitStrings.proto */
+static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
+
+
+/* Module declarations from 'cython' */
+
+/* Module declarations from 'cpython.buffer' */
+
+/* Module declarations from 'libc.string' */
+
+/* Module declarations from 'libc.stdio' */
+
+/* Module declarations from '__builtin__' */
+
+/* Module declarations from 'cpython.type' */
+static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;
+
+/* Module declarations from 'cpython' */
+
+/* Module declarations from 'cpython.object' */
+
+/* Module declarations from 'cpython.ref' */
+
+/* Module declarations from 'cpython.mem' */
+
+/* Module declarations from 'numpy' */
+
+/* Module declarations from 'numpy' */
+static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;
+static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
+static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
+static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;
+static PyTypeObject *__pyx_ptype_5numpy_generic = 0;
+static PyTypeObject *__pyx_ptype_5numpy_number = 0;
+static PyTypeObject *__pyx_ptype_5numpy_integer = 0;
+static PyTypeObject *__pyx_ptype_5numpy_signedinteger = 0;
+static PyTypeObject *__pyx_ptype_5numpy_unsignedinteger = 0;
+static PyTypeObject *__pyx_ptype_5numpy_inexact = 0;
+static PyTypeObject *__pyx_ptype_5numpy_floating = 0;
+static PyTypeObject *__pyx_ptype_5numpy_complexfloating = 0;
+static PyTypeObject *__pyx_ptype_5numpy_flexible = 0;
+static PyTypeObject *__pyx_ptype_5numpy_character = 0;
+static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
+
+/* Module declarations from 'libc.math' */
+
+/* Module declarations from 'SAR_GEO' */
+static int __pyx_f_7SAR_GEO_rayCasting(struct __pyx_t_7SAR_GEO_Point, PyArrayObject *); /*proto*/
+static PyArrayObject *__pyx_f_7SAR_GEO_insert_data(PyArrayObject *, PyArrayObject *, PyArrayObject *, PyArrayObject *, int __pyx_skip_dispatch); /*proto*/
+static PyArrayObject *__pyx_f_7SAR_GEO_cut_L1A_img(PyArrayObject *, PyArrayObject *, int __pyx_skip_dispatch); /*proto*/
+static PyArrayObject *__pyx_f_7SAR_GEO_gereratorMask(PyArrayObject *, PyArrayObject *, PyArrayObject *, int __pyx_skip_dispatch); /*proto*/
+static PyArrayObject *__pyx_f_7SAR_GEO_get_r_c(PyArrayObject *, PyArrayObject *, int __pyx_skip_dispatch); /*proto*/
+static PyArrayObject *__pyx_f_7SAR_GEO_Add(PyArrayObject *, double, int __pyx_skip_dispatch); /*proto*/
+static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 };
+static __Pyx_TypeInfo __Pyx_TypeInfo_int = { "int", NULL, sizeof(int), { 0 }, 0, IS_UNSIGNED(int) ? 'U' : 'I', IS_UNSIGNED(int), 0 };
+#define __Pyx_MODULE_NAME "SAR_GEO"
+extern int __pyx_module_is_main_SAR_GEO;
+int __pyx_module_is_main_SAR_GEO = 0;
+
+/* Implementation of 'SAR_GEO' */
+static PyObject *__pyx_builtin_ImportError;
+static const char __pyx_k_a[] = "a";
+static const char __pyx_k_x[] = "x";
+static const char __pyx_k__4[] = "\350\260\203\347\224\250\346\210\220\345\212\237";
+static const char __pyx_k_np[] = "np";
+static const char __pyx_k_os[] = "os";
+static const char __pyx_k_end[] = "end";
+static const char __pyx_k_max[] = "max";
+static const char __pyx_k_min[] = "min";
+static const char __pyx_k_nan[] = "nan";
+static const char __pyx_k_data[] = "data";
+static const char __pyx_k_file[] = "file";
+static const char __pyx_k_main[] = "__main__";
+static const char __pyx_k_mask[] = "mask";
+static const char __pyx_k_name[] = "__name__";
+static const char __pyx_k_ones[] = "ones";
+static const char __pyx_k_test[] = "__test__";
+static const char __pyx_k_clist[] = "clist";
+static const char __pyx_k_dtype[] = "dtype";
+static const char __pyx_k_numpy[] = "numpy";
+static const char __pyx_k_print[] = "print";
+static const char __pyx_k_rlist[] = "rlist";
+static const char __pyx_k_zeros[] = "zeros";
+static const char __pyx_k_import[] = "__import__";
+static const char __pyx_k_col_ids[] = "col_ids";
+static const char __pyx_k_float64[] = "float64";
+static const char __pyx_k_lon_lat[] = "lon_lat";
+static const char __pyx_k_ori2geo[] = "ori2geo";
+static const char __pyx_k_row_ids[] = "row_ids";
+static const char __pyx_k_griddata[] = "griddata";
+static const char __pyx_k_roi_list[] = "roi_list";
+static const char __pyx_k_ImportError[] = "ImportError";
+static const char __pyx_k_ori2geo_img[] = "ori2geo_img";
+static const char __pyx_k_scipy_interpolate[] = "scipy.interpolate";
+static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
+static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import";
+static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import";
+static PyObject *__pyx_n_s_ImportError;
+static PyObject *__pyx_kp_s__4;
+static PyObject *__pyx_n_s_a;
+static PyObject *__pyx_n_s_cline_in_traceback;
+static PyObject *__pyx_n_s_clist;
+static PyObject *__pyx_n_s_col_ids;
+static PyObject *__pyx_n_s_data;
+static PyObject *__pyx_n_s_dtype;
+static PyObject *__pyx_n_s_end;
+static PyObject *__pyx_n_s_file;
+static PyObject *__pyx_n_s_float64;
+static PyObject *__pyx_n_s_griddata;
+static PyObject *__pyx_n_s_import;
+static PyObject *__pyx_n_s_lon_lat;
+static PyObject *__pyx_n_s_main;
+static PyObject *__pyx_n_s_mask;
+static PyObject *__pyx_n_s_max;
+static PyObject *__pyx_n_s_min;
+static PyObject *__pyx_n_s_name;
+static PyObject *__pyx_n_s_nan;
+static PyObject *__pyx_n_s_np;
+static PyObject *__pyx_n_s_numpy;
+static PyObject *__pyx_kp_s_numpy_core_multiarray_failed_to;
+static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor;
+static PyObject *__pyx_n_s_ones;
+static PyObject *__pyx_n_s_ori2geo;
+static PyObject *__pyx_n_s_ori2geo_img;
+static PyObject *__pyx_n_s_os;
+static PyObject *__pyx_n_s_print;
+static PyObject *__pyx_n_s_rlist;
+static PyObject *__pyx_n_s_roi_list;
+static PyObject *__pyx_n_s_row_ids;
+static PyObject *__pyx_n_s_scipy_interpolate;
+static PyObject *__pyx_n_s_test;
+static PyObject *__pyx_n_s_x;
+static PyObject *__pyx_n_s_zeros;
+static PyObject *__pyx_pf_7SAR_GEO_insert_data(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_ori2geo_img, PyArrayObject *__pyx_v_row_ids, PyArrayObject *__pyx_v_col_ids, PyArrayObject *__pyx_v_data); /* proto */
+static PyObject *__pyx_pf_7SAR_GEO_2cut_L1A_img(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_ori2geo_img, PyArrayObject *__pyx_v_roi_list); /* proto */
+static PyObject *__pyx_pf_7SAR_GEO_4gereratorMask(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_rlist, PyArrayObject *__pyx_v_clist, PyArrayObject *__pyx_v_mask); /* proto */
+static PyObject *__pyx_pf_7SAR_GEO_6get_r_c(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_ori2geo, PyArrayObject *__pyx_v_lon_lat); /* proto */
+static PyObject *__pyx_pf_7SAR_GEO_8Add(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_a, double __pyx_v_x); /* proto */
+static PyObject *__pyx_int_0;
+static PyObject *__pyx_int_1;
+static PyObject *__pyx_int_2;
+static PyObject *__pyx_int_neg_1;
+static PyObject *__pyx_slice_;
+static PyObject *__pyx_tuple__2;
+static PyObject *__pyx_tuple__3;
+static PyObject *__pyx_tuple__5;
+static PyObject *__pyx_tuple__6;
+/* Late includes */
+
+/* "SAR_GEO.pyx":29
+ * #
+ * ######################
+ * cdef int rayCasting(Point p,np.ndarray[double,ndim=2] poly):             # <<<<<<<<<<<<<<
+ *     cdef double  px = p.x,
+ *     cdef double  py = p.y,
+ */
+
+static int __pyx_f_7SAR_GEO_rayCasting(struct __pyx_t_7SAR_GEO_Point __pyx_v_p, PyArrayObject *__pyx_v_poly) {
+  double __pyx_v_px;
+  double __pyx_v_py;
+  int __pyx_v_flag;
+  int __pyx_v_i;
+  int __pyx_v_l;
+  int __pyx_v_j;
+  double __pyx_v_sx;
+  double __pyx_v_sy;
+  double __pyx_v_tx;
+  double __pyx_v_ty;
+  PyObject *__pyx_v_x = 0;
+  __Pyx_LocalBuf_ND __pyx_pybuffernd_poly;
+  __Pyx_Buffer __pyx_pybuffer_poly;
+  int __pyx_r;
+  __Pyx_RefNannyDeclarations
+  double __pyx_t_1;
+  int __pyx_t_2;
+  Py_ssize_t __pyx_t_3;
+  Py_ssize_t __pyx_t_4;
+  int __pyx_t_5;
+  int __pyx_t_6;
+  double __pyx_t_7;
+  PyObject *__pyx_t_8 = NULL;
+  PyObject *__pyx_t_9 = NULL;
+  int __pyx_lineno = 0;
+  const char *__pyx_filename = NULL;
+  int __pyx_clineno = 0;
+  __Pyx_RefNannySetupContext("rayCasting", 0);
+  __pyx_pybuffer_poly.pybuffer.buf = NULL;
+  __pyx_pybuffer_poly.refcount = 0;
+  __pyx_pybuffernd_poly.data = NULL;
+  __pyx_pybuffernd_poly.rcbuffer = &__pyx_pybuffer_poly;
+  {
+    __Pyx_BufFmt_StackElem __pyx_stack[1];
+    if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_poly.rcbuffer->pybuffer, (PyObject*)__pyx_v_poly, &__Pyx_TypeInfo_double, PyBUF_FORMAT| PyBUF_STRIDES, 2, 0, __pyx_stack) == -1)) __PYX_ERR(0, 29, __pyx_L1_error)
+  }
+  __pyx_pybuffernd_poly.diminfo[0].strides = __pyx_pybuffernd_poly.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_poly.diminfo[0].shape = __pyx_pybuffernd_poly.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_poly.diminfo[1].strides = __pyx_pybuffernd_poly.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_poly.diminfo[1].shape = __pyx_pybuffernd_poly.rcbuffer->pybuffer.shape[1];
+
+  /* "SAR_GEO.pyx":30
+ * ######################
+ * cdef int rayCasting(Point p,np.ndarray[double,ndim=2] poly):
+ *     cdef double  px = p.x,             # <<<<<<<<<<<<<<
+ *     cdef double  py = p.y,
+ *     cdef int     flag = 0
+ */
+  __pyx_t_1 = __pyx_v_p.x;
+  __pyx_v_px = __pyx_t_1;
+
+  /* "SAR_GEO.pyx":31
+ * cdef int rayCasting(Point p,np.ndarray[double,ndim=2] poly):
+ *     cdef double  px = p.x,
+ *     cdef double  py = p.y,             # <<<<<<<<<<<<<<
+ *     cdef int     flag = 0
+ * 
+ */
+  __pyx_t_1 = __pyx_v_p.y;
+  __pyx_v_py = __pyx_t_1;
+
+  /* "SAR_GEO.pyx":32
+ *     cdef double  px = p.x,
+ *     cdef double  py = p.y,
+ *     cdef int     flag = 0             # <<<<<<<<<<<<<<
+ * 
+ *     cdef int i=0
+ */
+  __pyx_v_flag = 0;
+
+  /* "SAR_GEO.pyx":34
+ *     cdef int     flag = 0
+ * 
+ *     cdef int i=0             # <<<<<<<<<<<<<<
+ *     cdef int l=poly.shape[0]
+ *     cdef int j=l-1
+ */
+  __pyx_v_i = 0;
+
+  /* "SAR_GEO.pyx":35
+ * 
+ *     cdef int i=0
+ *     cdef int l=poly.shape[0]             # <<<<<<<<<<<<<<
+ *     cdef int j=l-1
+ * 
+ */
+  __pyx_v_l = (__pyx_v_poly->dimensions[0]);
+
+  /* "SAR_GEO.pyx":36
+ *     cdef int i=0
+ *     cdef int l=poly.shape[0]
+ *     cdef int j=l-1             # <<<<<<<<<<<<<<
+ * 
+ *     cdef double sx
+ */
+  __pyx_v_j = (__pyx_v_l - 1);
+
+  /* "SAR_GEO.pyx":42
+ *     cdef double tx
+ *     cdef double ty
+ *     cdef x=0             # <<<<<<<<<<<<<<
+ *     while(i<l):
+ *         sx=poly[i,0]
+ */
+  __Pyx_INCREF(__pyx_int_0);
+  __pyx_v_x = __pyx_int_0;
+
+  /* "SAR_GEO.pyx":43
+ *     cdef double ty
+ *     cdef x=0
+ *     while(i<l):             # <<<<<<<<<<<<<<
+ *         sx=poly[i,0]
+ *         sy=poly[i,1]
+ */
+  while (1) {
+    __pyx_t_2 = ((__pyx_v_i < __pyx_v_l) != 0);
+    if (!__pyx_t_2) break;
+
+    /* "SAR_GEO.pyx":44
+ *     cdef x=0
+ *     while(i<l):
+ *         sx=poly[i,0]             # <<<<<<<<<<<<<<
+ *         sy=poly[i,1]
+ *         tx=poly[j,0]
+ */
+    __pyx_t_3 = __pyx_v_i;
+    __pyx_t_4 = 0;
+    __pyx_t_5 = -1;
+    if (__pyx_t_3 < 0) {
+      __pyx_t_3 += __pyx_pybuffernd_poly.diminfo[0].shape;
+      if (unlikely(__pyx_t_3 < 0)) __pyx_t_5 = 0;
+    } else if (unlikely(__pyx_t_3 >= __pyx_pybuffernd_poly.diminfo[0].shape)) __pyx_t_5 = 0;
+    if (__pyx_t_4 < 0) {
+      __pyx_t_4 += __pyx_pybuffernd_poly.diminfo[1].shape;
+      if (unlikely(__pyx_t_4 < 0)) __pyx_t_5 = 1;
+    } else if (unlikely(__pyx_t_4 >= __pyx_pybuffernd_poly.diminfo[1].shape)) __pyx_t_5 = 1;
+    if (unlikely(__pyx_t_5 != -1)) {
+      __Pyx_RaiseBufferIndexError(__pyx_t_5);
+      __PYX_ERR(0, 44, __pyx_L1_error)
+    }
+    __pyx_v_sx = (*__Pyx_BufPtrStrided2d(double *, __pyx_pybuffernd_poly.rcbuffer->pybuffer.buf, __pyx_t_3, __pyx_pybuffernd_poly.diminfo[0].strides, __pyx_t_4, __pyx_pybuffernd_poly.diminfo[1].strides));
+
+    /* "SAR_GEO.pyx":45
+ *     while(i<l):
+ *         sx=poly[i,0]
+ *         sy=poly[i,1]             # <<<<<<<<<<<<<<
+ *         tx=poly[j,0]
+ *         ty=poly[j,1]
+ */
+    __pyx_t_4 = __pyx_v_i;
+    __pyx_t_3 = 1;
+    __pyx_t_5 = -1;
+    if (__pyx_t_4 < 0) {
+      __pyx_t_4 += __pyx_pybuffernd_poly.diminfo[0].shape;
+      if (unlikely(__pyx_t_4 < 0)) __pyx_t_5 = 0;
+    } else if (unlikely(__pyx_t_4 >= __pyx_pybuffernd_poly.diminfo[0].shape)) __pyx_t_5 = 0;
+    if (__pyx_t_3 < 0) {
+      __pyx_t_3 += __pyx_pybuffernd_poly.diminfo[1].shape;
+      if (unlikely(__pyx_t_3 < 0)) __pyx_t_5 = 1;
+    } else if (unlikely(__pyx_t_3 >= __pyx_pybuffernd_poly.diminfo[1].shape)) __pyx_t_5 = 1;
+    if (unlikely(__pyx_t_5 != -1)) {
+      __Pyx_RaiseBufferIndexError(__pyx_t_5);
+      __PYX_ERR(0, 45, __pyx_L1_error)
+    }
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+
+    /* "SAR_GEO.pyx":46
+ *         sx=poly[i,0]
+ *         sy=poly[i,1]
+ *         tx=poly[j,0]             # <<<<<<<<<<<<<<
+ *         ty=poly[j,1]
+ *         #
+ */
+    __pyx_t_3 = __pyx_v_j;
+    __pyx_t_4 = 0;
+    __pyx_t_5 = -1;
+    if (__pyx_t_3 < 0) {
+      __pyx_t_3 += __pyx_pybuffernd_poly.diminfo[0].shape;
+      if (unlikely(__pyx_t_3 < 0)) __pyx_t_5 = 0;
+    } else if (unlikely(__pyx_t_3 >= __pyx_pybuffernd_poly.diminfo[0].shape)) __pyx_t_5 = 0;
+    if (__pyx_t_4 < 0) {
+      __pyx_t_4 += __pyx_pybuffernd_poly.diminfo[1].shape;
+      if (unlikely(__pyx_t_4 < 0)) __pyx_t_5 = 1;
+    } else if (unlikely(__pyx_t_4 >= __pyx_pybuffernd_poly.diminfo[1].shape)) __pyx_t_5 = 1;
+    if (unlikely(__pyx_t_5 != -1)) {
+      __Pyx_RaiseBufferIndexError(__pyx_t_5);
+      __PYX_ERR(0, 46, __pyx_L1_error)
+    }
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+
+    /* "SAR_GEO.pyx":47
+ *         sy=poly[i,1]
+ *         tx=poly[j,0]
+ *         ty=poly[j,1]             # <<<<<<<<<<<<<<
+ *         #
+ *         if((sx == px and sy == py) or (tx == px and ty == py)):
+ */
+    __pyx_t_4 = __pyx_v_j;
+    __pyx_t_3 = 1;
+    __pyx_t_5 = -1;
+    if (__pyx_t_4 < 0) {
+      __pyx_t_4 += __pyx_pybuffernd_poly.diminfo[0].shape;
+      if (unlikely(__pyx_t_4 < 0)) __pyx_t_5 = 0;
+    } else if (unlikely(__pyx_t_4 >= __pyx_pybuffernd_poly.diminfo[0].shape)) __pyx_t_5 = 0;
+    if (__pyx_t_3 < 0) {
+      __pyx_t_3 += __pyx_pybuffernd_poly.diminfo[1].shape;
+      if (unlikely(__pyx_t_3 < 0)) __pyx_t_5 = 1;
+    } else if (unlikely(__pyx_t_3 >= __pyx_pybuffernd_poly.diminfo[1].shape)) __pyx_t_5 = 1;
+    if (unlikely(__pyx_t_5 != -1)) {
+      __Pyx_RaiseBufferIndexError(__pyx_t_5);
+      __PYX_ERR(0, 47, __pyx_L1_error)
+    }
+    __pyx_v_ty = (*__Pyx_BufPtrStrided2d(double *, __pyx_pybuffernd_poly.rcbuffer->pybuffer.buf, __pyx_t_4, __pyx_pybuffernd_poly.diminfo[0].strides, __pyx_t_3, __pyx_pybuffernd_poly.diminfo[1].strides));
+
+    /* "SAR_GEO.pyx":49
+ *         ty=poly[j,1]
+ *         #
+ *         if((sx == px and sy == py) or (tx == px and ty == py)):             # <<<<<<<<<<<<<<
+ *             return 1
+ *         #//
+ */
+    __pyx_t_6 = ((__pyx_v_sx == __pyx_v_px) != 0);
+    if (!__pyx_t_6) {
+      goto __pyx_L7_next_or;
+    } else {
+    }
+    __pyx_t_6 = ((__pyx_v_sy == __pyx_v_py) != 0);
+    if (!__pyx_t_6) {
+    } else {
+      __pyx_t_2 = __pyx_t_6;
+      goto __pyx_L6_bool_binop_done;
+    }
+    __pyx_L7_next_or:;
+    __pyx_t_6 = ((__pyx_v_tx == __pyx_v_px) != 0);
+    if (__pyx_t_6) {
+    } else {
+      __pyx_t_2 = __pyx_t_6;
+      goto __pyx_L6_bool_binop_done;
+    }
+    __pyx_t_6 = ((__pyx_v_ty == __pyx_v_py) != 0);
+    __pyx_t_2 = __pyx_t_6;
+    __pyx_L6_bool_binop_done:;
+    if (__pyx_t_2) {
+
+      /* "SAR_GEO.pyx":50
+ *         #
+ *         if((sx == px and sy == py) or (tx == px and ty == py)):
+ *             return 1             # <<<<<<<<<<<<<<
+ *         #//
+ *         if((sy < py and ty >= py) or (sy >= py and ty < py)) :
+ */
+      __pyx_r = 1;
+      goto __pyx_L0;
+
+      /* "SAR_GEO.pyx":49
+ *         ty=poly[j,1]
+ *         #
+ *         if((sx == px and sy == py) or (tx == px and ty == py)):             # <<<<<<<<<<<<<<
+ *             return 1
+ *         #//
+ */
+    }
+
+    /* "SAR_GEO.pyx":52
+ *             return 1
+ *         #//
+ *         if((sy < py and ty >= py) or (sy >= py and ty < py)) :             # <<<<<<<<<<<<<<
+ *             #//  Y  X
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+ */
+    __pyx_t_6 = ((__pyx_v_sy < __pyx_v_py) != 0);
+    if (!__pyx_t_6) {
+      goto __pyx_L12_next_or;
+    } else {
+    }
+    __pyx_t_6 = ((__pyx_v_ty >= __pyx_v_py) != 0);
+    if (!__pyx_t_6) {
+    } else {
+      __pyx_t_2 = __pyx_t_6;
+      goto __pyx_L11_bool_binop_done;
+    }
+    __pyx_L12_next_or:;
+    __pyx_t_6 = ((__pyx_v_sy >= __pyx_v_py) != 0);
+    if (__pyx_t_6) {
+    } else {
+      __pyx_t_2 = __pyx_t_6;
+      goto __pyx_L11_bool_binop_done;
+    }
+    __pyx_t_6 = ((__pyx_v_ty < __pyx_v_py) != 0);
+    __pyx_t_2 = __pyx_t_6;
+    __pyx_L11_bool_binop_done:;
+    if (__pyx_t_2) {
+
+      /* "SAR_GEO.pyx":54
+ *         if((sy < py and ty >= py) or (sy >= py and ty < py)) :
+ *             #//  Y  X
+ *             x = sx + (py - sy) * (tx - sx) / (ty - sy)             # <<<<<<<<<<<<<<
+ *             #//
+ *             if(x == px):
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+
+  /* "SAR_GEO.pyx":1
+ * import os             # <<<<<<<<<<<<<<
+ * cimport cython #
+ * import numpy as np##cpythonnp
+ */
+  __pyx_t_2 = __Pyx_PyDict_NewPresized(0); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 1, __pyx_L1_error)
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+
+  /* "../../../../../Anaconda/envs/micro/lib/site-packages/numpy/__init__.pxd":1016
+ * 
+ * 
+ * cdef inline NPY_DATETIMEUNIT get_datetime64_unit(object obj) nogil:             # <<<<<<<<<<<<<<
+ *     """
+ *     returns the unit part of the dtype for a numpy datetime64 object.
+ */
+
+  /*--- Wrapped vars code ---*/
+
+  goto __pyx_L0;
+  __pyx_L1_error:;
+  __Pyx_XDECREF(__pyx_t_1);
+  __Pyx_XDECREF(__pyx_t_2);
+  if (__pyx_m) {
+    if (__pyx_d) {
+      __Pyx_AddTraceback("init SAR_GEO", __pyx_clineno, __pyx_lineno, __pyx_filename);
+    }
+    Py_CLEAR(__pyx_m);
+  } else if (!PyErr_Occurred()) {
+    PyErr_SetString(PyExc_ImportError, "init SAR_GEO");
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+  return (__pyx_m != NULL) ? 0 : -1;
+  #elif PY_MAJOR_VERSION >= 3
+  return __pyx_m;
+  #else
+  return;
+  #endif
+}
+
+/* --- Runtime support code --- */
+/* Refnanny */
+#if CYTHON_REFNANNY
+static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
+    PyObject *m = NULL, *p = NULL;
+    void *r = NULL;
+    m = PyImport_ImportModule(modname);
+    if (!m) goto end;
+    p = PyObject_GetAttrString(m, "RefNannyAPI");
+    if (!p) goto end;
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+    Py_XDECREF(p);
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+/* IsLittleEndian */
+static CYTHON_INLINE int __Pyx_Is_Little_Endian(void)
+{
+  union {
+    uint32_t u32;
+    uint8_t u8[4];
+  } S;
+  S.u32 = 0x01020304;
+  return S.u8[0] == 4;
+}
+
+/* BufferFormatCheck */
+static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
+                              __Pyx_BufFmt_StackElem* stack,
+                              __Pyx_TypeInfo* type) {
+  stack[0].field = &ctx->root;
+  stack[0].parent_offset = 0;
+  ctx->root.type = type;
+  ctx->root.name = "buffer dtype";
+  ctx->root.offset = 0;
+  ctx->head = stack;
+  ctx->head->field = &ctx->root;
+  ctx->fmt_offset = 0;
+  ctx->head->parent_offset = 0;
+  ctx->new_packmode = '@';
+  ctx->enc_packmode = '@';
+  ctx->new_count = 1;
+  ctx->enc_count = 0;
+  ctx->enc_type = 0;
+  ctx->is_complex = 0;
+  ctx->is_valid_array = 0;
+  ctx->struct_alignment = 0;
+  while (type->typegroup == 'S') {
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+    ctx->head->field = type->fields;
+    ctx->head->parent_offset = 0;
+    type = type->fields->type;
+  }
+}
+static int __Pyx_BufFmt_ParseNumber(const char** ts) {
+    int count;
+    const char* t = *ts;
+    if (*t < '0' || *t > '9') {
+      return -1;
+    } else {
+        count = *t++ - '0';
+        while (*t >= '0' && *t <= '9') {
+            count *= 10;
+            count += *t++ - '0';
+        }
+    }
+    *ts = t;
+    return count;
+}
+static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
+    int number = __Pyx_BufFmt_ParseNumber(ts);
+    if (number == -1)
+        PyErr_Format(PyExc_ValueError,\
+                     "Does not understand character buffer dtype format string ('%c')", **ts);
+    return number;
+}
+static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
+  PyErr_Format(PyExc_ValueError,
+               "Unexpected format string character: '%c'", ch);
+}
+static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
+  switch (ch) {
+    case '?': return "'bool'";
+    case 'c': return "'char'";
+    case 'b': return "'signed char'";
+    case 'B': return "'unsigned char'";
+    case 'h': return "'short'";
+    case 'H': return "'unsigned short'";
+    case 'i': return "'int'";
+    case 'I': return "'unsigned int'";
+    case 'l': return "'long'";
+    case 'L': return "'unsigned long'";
+    case 'q': return "'long long'";
+    case 'Q': return "'unsigned long long'";
+    case 'f': return (is_complex ? "'complex float'" : "'float'");
+    case 'd': return (is_complex ? "'complex double'" : "'double'");
+    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
+    case 'T': return "a struct";
+    case 'O': return "Python object";
+    case 'P': return "a pointer";
+    case 's': case 'p': return "a string";
+    case 0: return "end";
+    default: return "unparseable format string";
+  }
+}
+static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return 2;
+    case 'i': case 'I': case 'l': case 'L': return 4;
+    case 'q': case 'Q': return 8;
+    case 'f': return (is_complex ? 8 : 4);
+    case 'd': return (is_complex ? 16 : 8);
+    case 'g': {
+      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
+      return 0;
+    }
+    case 'O': case 'P': return sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(short);
+    case 'i': case 'I': return sizeof(int);
+    case 'l': case 'L': return sizeof(long);
+    #ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
+    #endif
+    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
+    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
+    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
+    case 'O': case 'P': return sizeof(void*);
+    default: {
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+  }
+}
+typedef struct { char c; short x; } __Pyx_st_short;
+typedef struct { char c; int x; } __Pyx_st_int;
+typedef struct { char c; long x; } __Pyx_st_long;
+typedef struct { char c; float x; } __Pyx_st_float;
+typedef struct { char c; double x; } __Pyx_st_double;
+typedef struct { char c; long double x; } __Pyx_st_longdouble;
+typedef struct { char c; void *x; } __Pyx_st_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
+#endif
+static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
+    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
+    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
+#endif
+    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
+    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
+    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
+    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+/* These are for computing the padding at the end of the struct to align
+   on the first member of the struct. This will probably the same as above,
+   but we don't have any guarantees.
+ */
+typedef struct { short x; char c; } __Pyx_pad_short;
+typedef struct { int x; char c; } __Pyx_pad_int;
+typedef struct { long x; char c; } __Pyx_pad_long;
+typedef struct { float x; char c; } __Pyx_pad_float;
+typedef struct { double x; char c; } __Pyx_pad_double;
+typedef struct { long double x; char c; } __Pyx_pad_longdouble;
+typedef struct { void *x; char c; } __Pyx_pad_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
+#endif
+static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
+    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
+    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
+#endif
+    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
+    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
+    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
+    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
+  switch (ch) {
+    case 'c':
+        return 'H';
+    case 'b': case 'h': case 'i':
+    case 'l': case 'q': case 's': case 'p':
+        return 'I';
+    case '?': case 'B': case 'H': case 'I': case 'L': case 'Q':
+        return 'U';
+    case 'f': case 'd': case 'g':
+        return (is_complex ? 'C' : 'R');
+    case 'O':
+        return 'O';
+    case 'P':
+        return 'P';
+    default: {
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+  }
+}
+static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
+  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
+    const char* expected;
+    const char* quote;
+    if (ctx->head == NULL) {
+      expected = "end";
+      quote = "";
+    } else {
+      expected = ctx->head->field->type->name;
+      quote = "'";
+    }
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer dtype mismatch, expected %s%s%s but got %s",
+                 quote, expected, quote,
+                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
+  } else {
+    __Pyx_StructField* field = ctx->head->field;
+    __Pyx_StructField* parent = (ctx->head - 1)->field;
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
+                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
+                 parent->type->name, field->name);
+  }
+}
+static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
+  char group;
+  size_t size, offset, arraysize = 1;
+  if (ctx->enc_type == 0) return 0;
+  if (ctx->head->field->type->arraysize[0]) {
+    int i, ndim = 0;
+    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
+        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
+        ndim = 1;
+        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
+            PyErr_Format(PyExc_ValueError,
+                         "Expected a dimension of size %zu, got %zu",
+                         ctx->head->field->type->arraysize[0], ctx->enc_count);
+            return -1;
+        }
+    }
+    if (!ctx->is_valid_array) {
+      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
+                   ctx->head->field->type->ndim, ndim);
+      return -1;
+    }
+    for (i = 0; i < ctx->head->field->type->ndim; i++) {
+      arraysize *= ctx->head->field->type->arraysize[i];
+    }
+    ctx->is_valid_array = 0;
+    ctx->enc_count = 1;
+  }
+  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
+  do {
+    __Pyx_StructField* field = ctx->head->field;
+    __Pyx_TypeInfo* type = field->type;
+    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
+      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
+    } else {
+      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
+    }
+    if (ctx->enc_packmode == '@') {
+      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
+      size_t align_mod_offset;
+      if (align_at == 0) return -1;
+      align_mod_offset = ctx->fmt_offset % align_at;
+      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
+      if (ctx->struct_alignment == 0)
+          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
+                                                                 ctx->is_complex);
+    }
+    if (type->size != size || type->typegroup != group) {
+      if (type->typegroup == 'C' && type->fields != NULL) {
+        size_t parent_offset = ctx->head->parent_offset + field->offset;
+        ++ctx->head;
+        ctx->head->field = type->fields;
+        ctx->head->parent_offset = parent_offset;
+        continue;
+      }
+      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
+      } else {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return -1;
+      }
+    }
+    offset = ctx->head->parent_offset + field->offset;
+    if (ctx->fmt_offset != offset) {
+      PyErr_Format(PyExc_ValueError,
+                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
+                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
+      return -1;
+    }
+    ctx->fmt_offset += size;
+    if (arraysize)
+      ctx->fmt_offset += (arraysize - 1) * size;
+    --ctx->enc_count;
+    while (1) {
+      if (field == &ctx->root) {
+        ctx->head = NULL;
+        if (ctx->enc_count != 0) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return -1;
+        }
+        break;
+      }
+      ctx->head->field = ++field;
+      if (field->type == NULL) {
+        --ctx->head;
+        field = ctx->head->field;
+        continue;
+      } else if (field->type->typegroup == 'S') {
+        size_t parent_offset = ctx->head->parent_offset + field->offset;
+        if (field->type->fields->type == NULL) continue;
+        field = field->type->fields;
+        ++ctx->head;
+        ctx->head->field = field;
+        ctx->head->parent_offset = parent_offset;
+        break;
+      } else {
+        break;
+      }
+    }
+  } while (ctx->enc_count);
+  ctx->enc_type = 0;
+  ctx->is_complex = 0;
+  return 0;
+}
+static PyObject *
+__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
+{
+    const char *ts = *tsp;
+    int i = 0, number, ndim;
+    ++ts;
+    if (ctx->new_count != 1) {
+        PyErr_SetString(PyExc_ValueError,
+                        "Cannot handle repeated arrays in format string");
+        return NULL;
+    }
+    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+    ndim = ctx->head->field->type->ndim;
+    while (*ts && *ts != ')') {
+        switch (*ts) {
+            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
+            default:  break;
+        }
+        number = __Pyx_BufFmt_ExpectNumber(&ts);
+        if (number == -1) return NULL;
+        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
+            return PyErr_Format(PyExc_ValueError,
+                        "Expected a dimension of size %zu, got %d",
+                        ctx->head->field->type->arraysize[i], number);
+        if (*ts != ',' && *ts != ')')
+            return PyErr_Format(PyExc_ValueError,
+                                "Expected a comma in format string, got '%c'", *ts);
+        if (*ts == ',') ts++;
+        i++;
+    }
+    if (i != ndim)
+        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
+                            ctx->head->field->type->ndim, i);
+    if (!*ts) {
+        PyErr_SetString(PyExc_ValueError,
+                        "Unexpected end of format string, expected ')'");
+        return NULL;
+    }
+    ctx->is_valid_array = 1;
+    ctx->new_count = 1;
+    *tsp = ++ts;
+    return Py_None;
+}
+static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
+  int got_Z = 0;
+  while (1) {
+    switch(*ts) {
+      case 0:
+        if (ctx->enc_type != 0 && ctx->head == NULL) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return NULL;
+        }
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        if (ctx->head != NULL) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return NULL;
+        }
+        return ts;
+      case ' ':
+      case '\r':
+      case '\n':
+        ++ts;
+        break;
+      case '<':
+        if (!__Pyx_Is_Little_Endian()) {
+          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
+          return NULL;
+        }
+        ctx->new_packmode = '=';
+        ++ts;
+        break;
+      case '>':
+      case '!':
+        if (__Pyx_Is_Little_Endian()) {
+          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
+          return NULL;
+        }
+        ctx->new_packmode = '=';
+        ++ts;
+        break;
+      case '=':
+      case '@':
+      case '^':
+        ctx->new_packmode = *ts++;
+        break;
+      case 'T':
+        {
+          const char* ts_after_sub;
+          size_t i, struct_count = ctx->new_count;
+          size_t struct_alignment = ctx->struct_alignment;
+          ctx->new_count = 1;
+          ++ts;
+          if (*ts != '{') {
+            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
+            return NULL;
+          }
+          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+          ctx->enc_type = 0;
+          ctx->enc_count = 0;
+          ctx->struct_alignment = 0;
+          ++ts;
+          ts_after_sub = ts;
+          for (i = 0; i != struct_count; ++i) {
+            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
+            if (!ts_after_sub) return NULL;
+          }
+          ts = ts_after_sub;
+          if (struct_alignment) ctx->struct_alignment = struct_alignment;
+        }
+        break;
+      case '}':
+        {
+          size_t alignment = ctx->struct_alignment;
+          ++ts;
+          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+          ctx->enc_type = 0;
+          if (alignment && ctx->fmt_offset % alignment) {
+            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
+          }
+        }
+        return ts;
+      case 'x':
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        ctx->fmt_offset += ctx->new_count;
+        ctx->new_count = 1;
+        ctx->enc_count = 0;
+        ctx->enc_type = 0;
+        ctx->enc_packmode = ctx->new_packmode;
+        ++ts;
+        break;
+      case 'Z':
+        got_Z = 1;
+        ++ts;
+        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
+          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
+          return NULL;
+        }
+        CYTHON_FALLTHROUGH;
+      case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
+      case 'l': case 'L': case 'q': case 'Q':
+      case 'f': case 'd': case 'g':
+      case 'O': case 'p':
+        if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) &&
+            (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) {
+          ctx->enc_count += ctx->new_count;
+          ctx->new_count = 1;
+          got_Z = 0;
+          ++ts;
+          break;
+        }
+        CYTHON_FALLTHROUGH;
+      case 's':
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        ctx->enc_count = ctx->new_count;
+        ctx->enc_packmode = ctx->new_packmode;
+        ctx->enc_type = *ts;
+        ctx->is_complex = got_Z;
+        ++ts;
+        ctx->new_count = 1;
+        got_Z = 0;
+        break;
+      case ':':
+        ++ts;
+        while(*ts != ':') ++ts;
+        ++ts;
+        break;
+      case '(':
+        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
+        break;
+      default:
+        {
+          int number = __Pyx_BufFmt_ExpectNumber(&ts);
+          if (number == -1) return NULL;
+          ctx->new_count = (size_t)number;
+        }
+    }
+  }
+}
+
+/* BufferGetAndValidate */
+  static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
+  if (unlikely(info->buf == NULL)) return;
+  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
+  __Pyx_ReleaseBuffer(info);
+}
+static void __Pyx_ZeroBuffer(Py_buffer* buf) {
+  buf->buf = NULL;
+  buf->obj = NULL;
+  buf->strides = __Pyx_zeros;
+  buf->shape = __Pyx_zeros;
+  buf->suboffsets = __Pyx_minusones;
+}
+static int __Pyx__GetBufferAndValidate(
+        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
+        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
+{
+  buf->buf = NULL;
+  if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) {
+    __Pyx_ZeroBuffer(buf);
+    return -1;
+  }
+  if (unlikely(buf->ndim != nd)) {
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer has wrong number of dimensions (expected %d, got %d)",
+                 nd, buf->ndim);
+    goto fail;
+  }
+  if (!cast) {
+    __Pyx_BufFmt_Context ctx;
+    __Pyx_BufFmt_Init(&ctx, stack, dtype);
+    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
+  }
+  if (unlikely((size_t)buf->itemsize != dtype->size)) {
+    PyErr_Format(PyExc_ValueError,
+      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
+      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
+      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
+    goto fail;
+  }
+  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
+  return 0;
+fail:;
+  __Pyx_SafeReleaseBuffer(buf);
+  return -1;
+}
+
+/* BufferIndexError */
+  static void __Pyx_RaiseBufferIndexError(int axis) {
+  PyErr_Format(PyExc_IndexError,
+     "Out of bounds on buffer access (axis %d)", axis);
+}
+
+/* PyErrFetchRestore */
+  #if CYTHON_FAST_THREAD_STATE
+static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    tmp_type = tstate->curexc_type;
+    tmp_value = tstate->curexc_value;
+    tmp_tb = tstate->curexc_traceback;
+    tstate->curexc_type = type;
+    tstate->curexc_value = value;
+    tstate->curexc_traceback = tb;
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+}
+static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
+    *type = tstate->curexc_type;
+    *value = tstate->curexc_value;
+    *tb = tstate->curexc_traceback;
+    tstate->curexc_type = 0;
+    tstate->curexc_value = 0;
+    tstate->curexc_traceback = 0;
+}
+#endif
+
+/* WriteUnraisableException */
+  static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
+                                  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
+                                  int full_traceback, CYTHON_UNUSED int nogil) {
+    PyObject *old_exc, *old_val, *old_tb;
+    PyObject *ctx;
+    __Pyx_PyThreadState_declare
+#ifdef WITH_THREAD
+    PyGILState_STATE state;
+    if (nogil)
+        state = PyGILState_Ensure();
+#ifdef _MSC_VER
+    else state = (PyGILState_STATE)-1;
+#endif
+#endif
+    __Pyx_PyThreadState_assign
+    __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
+    if (full_traceback) {
+        Py_XINCREF(old_exc);
+        Py_XINCREF(old_val);
+        Py_XINCREF(old_tb);
+        __Pyx_ErrRestore(old_exc, old_val, old_tb);
+        PyErr_PrintEx(1);
+    }
+    #if PY_MAJOR_VERSION < 3
+    ctx = PyString_FromString(name);
+    #else
+    ctx = PyUnicode_FromString(name);
+    #endif
+    __Pyx_ErrRestore(old_exc, old_val, old_tb);
+    if (!ctx) {
+        PyErr_WriteUnraisable(Py_None);
+    } else {
+        PyErr_WriteUnraisable(ctx);
+        Py_DECREF(ctx);
+    }
+#ifdef WITH_THREAD
+    if (nogil)
+        PyGILState_Release(state);
+#endif
+}
+
+/* RaiseArgTupleInvalid */
+  static void __Pyx_RaiseArgtupleInvalid(
+    const char* func_name,
+    int exact,
+    Py_ssize_t num_min,
+    Py_ssize_t num_max,
+    Py_ssize_t num_found)
+{
+    Py_ssize_t num_expected;
+    const char *more_or_less;
+    if (num_found < num_min) {
+        num_expected = num_min;
+        more_or_less = "at least";
+    } else {
+        num_expected = num_max;
+        more_or_less = "at most";
+    }
+    if (exact) {
+        more_or_less = "exactly";
+    }
+    PyErr_Format(PyExc_TypeError,
+                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                 func_name, more_or_less, num_expected,
+                 (num_expected == 1) ? "" : "s", num_found);
+}
+
+/* RaiseDoubleKeywords */
+  static void __Pyx_RaiseDoubleKeywordsError(
+    const char* func_name,
+    PyObject* kw_name)
+{
+    PyErr_Format(PyExc_TypeError,
+        #if PY_MAJOR_VERSION >= 3
+        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
+        #else
+        "%s() got multiple values for keyword argument '%s'", func_name,
+        PyString_AsString(kw_name));
+        #endif
+}
+
+/* ParseKeywords */
+  static int __Pyx_ParseOptionalKeywords(
+    PyObject *kwds,
+    PyObject **argnames[],
+    PyObject *kwds2,
+    PyObject *values[],
+    Py_ssize_t num_pos_args,
+    const char* function_name)
+{
+    PyObject *key = 0, *value = 0;
+    Py_ssize_t pos = 0;
+    PyObject*** name;
+    PyObject*** first_kw_arg = argnames + num_pos_args;
+    while (PyDict_Next(kwds, &pos, &key, &value)) {
+        name = first_kw_arg;
+        while (*name && (**name != key)) name++;
+        if (*name) {
+            values[name-argnames] = value;
+            continue;
+        }
+        name = first_kw_arg;
+        #if PY_MAJOR_VERSION < 3
+        if (likely(PyString_Check(key))) {
+            while (*name) {
+                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
+                        && _PyString_Eq(**name, key)) {
+                    values[name-argnames] = value;
+                    break;
+                }
+                name++;
+            }
+            if (*name) continue;
+            else {
+                PyObject*** argname = argnames;
+                while (argname != first_kw_arg) {
+                    if ((**argname == key) || (
+                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
+                             && _PyString_Eq(**argname, key))) {
+                        goto arg_passed_twice;
+                    }
+                    argname++;
+                }
+            }
+        } else
+        #endif
+        if (likely(PyUnicode_Check(key))) {
+            while (*name) {
+                int cmp = (**name == key) ? 0 :
+                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
+                    (__Pyx_PyUnicode_GET_LENGTH(**name) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
+                #endif
+                    PyUnicode_Compare(**name, key);
+                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
+                if (cmp == 0) {
+                    values[name-argnames] = value;
+                    break;
+                }
+                name++;
+            }
+            if (*name) continue;
+            else {
+                PyObject*** argname = argnames;
+                while (argname != first_kw_arg) {
+                    int cmp = (**argname == key) ? 0 :
+                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
+                        (__Pyx_PyUnicode_GET_LENGTH(**argname) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
+                    #endif
+                        PyUnicode_Compare(**argname, key);
+                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
+                    if (cmp == 0) goto arg_passed_twice;
+                    argname++;
+                }
+            }
+        } else
+            goto invalid_keyword_type;
+        if (kwds2) {
+            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
+        } else {
+            goto invalid_keyword;
+        }
+    }
+    return 0;
+arg_passed_twice:
+    __Pyx_RaiseDoubleKeywordsError(function_name, key);
+    goto bad;
+invalid_keyword_type:
+    PyErr_Format(PyExc_TypeError,
+        "%.200s() keywords must be strings", function_name);
+    goto bad;
+invalid_keyword:
+    PyErr_Format(PyExc_TypeError,
+    #if PY_MAJOR_VERSION < 3
+        "%.200s() got an unexpected keyword argument '%.200s'",
+        function_name, PyString_AsString(key));
+    #else
+        "%s() got an unexpected keyword argument '%U'",
+        function_name, key);
+    #endif
+bad:
+    return -1;
+}
+
+/* ArgTypeTest */
+  static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
+{
+    if (unlikely(!type)) {
+        PyErr_SetString(PyExc_SystemError, "Missing type object");
+        return 0;
+    }
+    else if (exact) {
+        #if PY_MAJOR_VERSION == 2
+        if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
+        #endif
+    }
+    else {
+        if (likely(__Pyx_TypeCheck(obj, type))) return 1;
+    }
+    PyErr_Format(PyExc_TypeError,
+        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
+        name, type->tp_name, Py_TYPE(obj)->tp_name);
+    return 0;
+}
+
+/* PyObjectGetAttrStr */
+  #if CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
+    PyTypeObject* tp = Py_TYPE(obj);
+    if (likely(tp->tp_getattro))
+        return tp->tp_getattro(obj, attr_name);
+#if PY_MAJOR_VERSION < 3
+    if (likely(tp->tp_getattr))
+        return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
+#endif
+    return PyObject_GetAttr(obj, attr_name);
+}
+#endif
+
+/* GetBuiltinName */
+  static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
+    PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
+    if (unlikely(!result)) {
+        PyErr_Format(PyExc_NameError,
+#if PY_MAJOR_VERSION >= 3
+            "name '%U' is not defined", name);
+#else
+            "name '%.200s' is not defined", PyString_AS_STRING(name));
+#endif
+    }
+    return result;
+}
+
+/* PyDictVersioning */
+  #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
+    PyObject *dict = Py_TYPE(obj)->tp_dict;
+    return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
+}
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
+    PyObject **dictptr = NULL;
+    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
+    if (offset) {
+#if CYTHON_COMPILING_IN_CPYTHON
+        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
+#else
+        dictptr = _PyObject_GetDictPtr(obj);
+#endif
+    }
+    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
+}
+static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
+    PyObject *dict = Py_TYPE(obj)->tp_dict;
+    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
+        return 0;
+    return obj_dict_version == __Pyx_get_object_dict_version(obj);
+}
+#endif
+
+/* GetModuleGlobalName */
+  #if CYTHON_USE_DICT_VERSIONS
+static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)
+#else
+static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)
+#endif
+{
+    PyObject *result;
+#if !CYTHON_AVOID_BORROWED_REFS
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
+    result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
+    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
+    if (likely(result)) {
+        return __Pyx_NewRef(result);
+    } else if (unlikely(PyErr_Occurred())) {
+        return NULL;
+    }
+#else
+    result = PyDict_GetItem(__pyx_d, name);
+    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
+    if (likely(result)) {
+        return __Pyx_NewRef(result);
+    }
+#endif
+#else
+    result = PyObject_GetItem(__pyx_d, name);
+    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
+    if (likely(result)) {
+        return __Pyx_NewRef(result);
+    }
+    PyErr_Clear();
+#endif
+    return __Pyx_GetBuiltinName(name);
+}
+
+/* PyObjectCall */
+  #if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
+    PyObject *result;
+    ternaryfunc call = Py_TYPE(func)->tp_call;
+    if (unlikely(!call))
+        return PyObject_Call(func, arg, kw);
+    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
+        return NULL;
+    result = (*call)(func, arg, kw);
+    Py_LeaveRecursiveCall();
+    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
+        PyErr_SetString(
+            PyExc_SystemError,
+            "NULL result without error in PyObject_Call");
+    }
+    return result;
+}
+#endif
+
+/* ExtTypeTest */
+  static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
+    if (unlikely(!type)) {
+        PyErr_SetString(PyExc_SystemError, "Missing type object");
+        return 0;
+    }
+    if (likely(__Pyx_TypeCheck(obj, type)))
+        return 1;
+    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
+                 Py_TYPE(obj)->tp_name, type->tp_name);
+    return 0;
+}
+
+/* PyCFunctionFastCall */
+  #if CYTHON_FAST_PYCCALL
+static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
+    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
+    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
+    PyObject *self = PyCFunction_GET_SELF(func);
+    int flags = PyCFunction_GET_FLAGS(func);
+    assert(PyCFunction_Check(func));
+    assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)));
+    assert(nargs >= 0);
+    assert(nargs == 0 || args != NULL);
+    /* _PyCFunction_FastCallDict() must not be called with an exception set,
+       because it may clear it (directly or indirectly) and so the
+       caller loses its exception */
+    assert(!PyErr_Occurred());
+    if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
+        return (*((__Pyx_PyCFunctionFastWithKeywords)(void*)meth)) (self, args, nargs, NULL);
+    } else {
+        return (*((__Pyx_PyCFunctionFast)(void*)meth)) (self, args, nargs);
+    }
+}
+#endif
+
+/* PyFunctionFastCall */
+  #if CYTHON_FAST_PYCALL
+static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
+                                               PyObject *globals) {
+    PyFrameObject *f;
+    PyThreadState *tstate = __Pyx_PyThreadState_Current;
+    PyObject **fastlocals;
+    Py_ssize_t i;
+    PyObject *result;
+    assert(globals != NULL);
+    /* XXX Perhaps we should create a specialized
+       PyFrame_New() that doesn't take locals, but does
+       take builtins without sanity checking them.
+       */
+    assert(tstate != NULL);
+    f = PyFrame_New(tstate, co, globals, NULL);
+    if (f == NULL) {
+        return NULL;
+    }
+    fastlocals = __Pyx_PyFrame_GetLocalsplus(f);
+    for (i = 0; i < na; i++) {
+        Py_INCREF(*args);
+        fastlocals[i] = *args++;
+    }
+    result = PyEval_EvalFrameEx(f,0);
+    ++tstate->recursion_depth;
+    Py_DECREF(f);
+    --tstate->recursion_depth;
+    return result;
+}
+#if 1 || PY_VERSION_HEX < 0x030600B1
+static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs) {
+    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
+    PyObject *globals = PyFunction_GET_GLOBALS(func);
+    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
+    PyObject *closure;
+#if PY_MAJOR_VERSION >= 3
+    PyObject *kwdefs;
+#endif
+    PyObject *kwtuple, **k;
+    PyObject **d;
+    Py_ssize_t nd;
+    Py_ssize_t nk;
+    PyObject *result;
+    assert(kwargs == NULL || PyDict_Check(kwargs));
+    nk = kwargs ? PyDict_Size(kwargs) : 0;
+    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
+        return NULL;
+    }
+    if (
+#if PY_MAJOR_VERSION >= 3
+            co->co_kwonlyargcount == 0 &&
+#endif
+            likely(kwargs == NULL || nk == 0) &&
+            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
+        if (argdefs == NULL && co->co_argcount == nargs) {
+            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
+            goto done;
+        }
+        else if (nargs == 0 && argdefs != NULL
+                 && co->co_argcount == Py_SIZE(argdefs)) {
+            /* function called with no arguments, but all parameters have
+               a default value: use default values as arguments .*/
+            args = &PyTuple_GET_ITEM(argdefs, 0);
+            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
+            goto done;
+        }
+    }
+    if (kwargs != NULL) {
+        Py_ssize_t pos, i;
+        kwtuple = PyTuple_New(2 * nk);
+        if (kwtuple == NULL) {
+            result = NULL;
+            goto done;
+        }
+        k = &PyTuple_GET_ITEM(kwtuple, 0);
+        pos = i = 0;
+        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
+            Py_INCREF(k[i]);
+            Py_INCREF(k[i+1]);
+            i += 2;
+        }
+        nk = i / 2;
+    }
+    else {
+        kwtuple = NULL;
+        k = NULL;
+    }
+    closure = PyFunction_GET_CLOSURE(func);
+#if PY_MAJOR_VERSION >= 3
+    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
+#endif
+    if (argdefs != NULL) {
+        d = &PyTuple_GET_ITEM(argdefs, 0);
+        nd = Py_SIZE(argdefs);
+    }
+    else {
+        d = NULL;
+        nd = 0;
+    }
+#if PY_MAJOR_VERSION >= 3
+    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
+                               args, (int)nargs,
+                               k, (int)nk,
+                               d, (int)nd, kwdefs, closure);
+#else
+    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
+                               args, (int)nargs,
+                               k, (int)nk,
+                               d, (int)nd, closure);
+#endif
+    Py_XDECREF(kwtuple);
+done:
+    Py_LeaveRecursiveCall();
+    return result;
+}
+#endif
+#endif
+
+/* PyObjectCall2Args */
+  static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) {
+    PyObject *args, *result = NULL;
+    #if CYTHON_FAST_PYCALL
+    if (PyFunction_Check(function)) {
+        PyObject *args[2] = {arg1, arg2};
+        return __Pyx_PyFunction_FastCall(function, args, 2);
+    }
+    #endif
+    #if CYTHON_FAST_PYCCALL
+    if (__Pyx_PyFastCFunction_Check(function)) {
+        PyObject *args[2] = {arg1, arg2};
+        return __Pyx_PyCFunction_FastCall(function, args, 2);
+    }
+    #endif
+    args = PyTuple_New(2);
+    if (unlikely(!args)) goto done;
+    Py_INCREF(arg1);
+    PyTuple_SET_ITEM(args, 0, arg1);
+    Py_INCREF(arg2);
+    PyTuple_SET_ITEM(args, 1, arg2);
+    Py_INCREF(function);
+    result = __Pyx_PyObject_Call(function, args, NULL);
+    Py_DECREF(args);
+    Py_DECREF(function);
+done:
+    return result;
+}
+
+/* PyObjectCallMethO */
+  #if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
+    PyObject *self, *result;
+    PyCFunction cfunc;
+    cfunc = PyCFunction_GET_FUNCTION(func);
+    self = PyCFunction_GET_SELF(func);
+    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
+        return NULL;
+    result = cfunc(self, arg);
+    Py_LeaveRecursiveCall();
+    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
+        PyErr_SetString(
+            PyExc_SystemError,
+            "NULL result without error in PyObject_Call");
+    }
+    return result;
+}
+#endif
+
+/* PyObjectCallOneArg */
+  #if CYTHON_COMPILING_IN_CPYTHON
+static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+    PyObject *result;
+    PyObject *args = PyTuple_New(1);
+    if (unlikely(!args)) return NULL;
+    Py_INCREF(arg);
+    PyTuple_SET_ITEM(args, 0, arg);
+    result = __Pyx_PyObject_Call(func, args, NULL);
+    Py_DECREF(args);
+    return result;
+}
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+#if CYTHON_FAST_PYCALL
+    if (PyFunction_Check(func)) {
+        return __Pyx_PyFunction_FastCall(func, &arg, 1);
+    }
+#endif
+    if (likely(PyCFunction_Check(func))) {
+        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
+            return __Pyx_PyObject_CallMethO(func, arg);
+#if CYTHON_FAST_PYCCALL
+        } else if (__Pyx_PyFastCFunction_Check(func)) {
+            return __Pyx_PyCFunction_FastCall(func, &arg, 1);
+#endif
+        }
+    }
+    return __Pyx__PyObject_CallOneArg(func, arg);
+}
+#else
+static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
+    PyObject *result;
+    PyObject *args = PyTuple_Pack(1, arg);
+    if (unlikely(!args)) return NULL;
+    result = __Pyx_PyObject_Call(func, args, NULL);
+    Py_DECREF(args);
+    return result;
+}
+#endif
+
+/* GetItemInt */
+  static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
+    PyObject *r;
+    if (!j) return NULL;
+    r = PyObject_GetItem(o, j);
+    Py_DECREF(j);
+    return r;
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
+                                                              CYTHON_NCP_UNUSED int wraparound,
+                                                              CYTHON_NCP_UNUSED int boundscheck) {
+#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+    Py_ssize_t wrapped_i = i;
+    if (wraparound & unlikely(i < 0)) {
+        wrapped_i += PyList_GET_SIZE(o);
+    }
+    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyList_GET_SIZE(o)))) {
+        PyObject *r = PyList_GET_ITEM(o, wrapped_i);
+        Py_INCREF(r);
+        return r;
+    }
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+#else
+    return PySequence_GetItem(o, i);
+#endif
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
+                                                              CYTHON_NCP_UNUSED int wraparound,
+                                                              CYTHON_NCP_UNUSED int boundscheck) {
+#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+    Py_ssize_t wrapped_i = i;
+    if (wraparound & unlikely(i < 0)) {
+        wrapped_i += PyTuple_GET_SIZE(o);
+    }
+    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyTuple_GET_SIZE(o)))) {
+        PyObject *r = PyTuple_GET_ITEM(o, wrapped_i);
+        Py_INCREF(r);
+        return r;
+    }
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+#else
+    return PySequence_GetItem(o, i);
+#endif
+}
+static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
+                                                     CYTHON_NCP_UNUSED int wraparound,
+                                                     CYTHON_NCP_UNUSED int boundscheck) {
+#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
+    if (is_list || PyList_CheckExact(o)) {
+        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
+        if ((!boundscheck) || (likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o))))) {
+            PyObject *r = PyList_GET_ITEM(o, n);
+            Py_INCREF(r);
+            return r;
+        }
+    }
+    else if (PyTuple_CheckExact(o)) {
+        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
+        if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyTuple_GET_SIZE(o)))) {
+            PyObject *r = PyTuple_GET_ITEM(o, n);
+            Py_INCREF(r);
+            return r;
+        }
+    } else {
+        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
+        if (likely(m && m->sq_item)) {
+            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
+                Py_ssize_t l = m->sq_length(o);
+                if (likely(l >= 0)) {
+                    i += l;
+                } else {
+                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
+                        return NULL;
+                    PyErr_Clear();
+                }
+            }
+            return m->sq_item(o, i);
+        }
+    }
+#else
+    if (is_list || PySequence_Check(o)) {
+        return PySequence_GetItem(o, i);
+    }
+#endif
+    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
+}
+
+/* ObjectGetItem */
+  #if CYTHON_USE_TYPE_SLOTS
+static PyObject *__Pyx_PyObject_GetIndex(PyObject *obj, PyObject* index) {
+    PyObject *runerr;
+    Py_ssize_t key_value;
+    PySequenceMethods *m = Py_TYPE(obj)->tp_as_sequence;
+    if (unlikely(!(m && m->sq_item))) {
+        PyErr_Format(PyExc_TypeError, "'%.200s' object is not subscriptable", Py_TYPE(obj)->tp_name);
+        return NULL;
+    }
+    key_value = __Pyx_PyIndex_AsSsize_t(index);
+    if (likely(key_value != -1 || !(runerr = PyErr_Occurred()))) {
+        return __Pyx_GetItemInt_Fast(obj, key_value, 0, 1, 1);
+    }
+    if (PyErr_GivenExceptionMatches(runerr, PyExc_OverflowError)) {
+        PyErr_Clear();
+        PyErr_Format(PyExc_IndexError, "cannot fit '%.200s' into an index-sized integer", Py_TYPE(index)->tp_name);
+    }
+    return NULL;
+}
+static PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key) {
+    PyMappingMethods *m = Py_TYPE(obj)->tp_as_mapping;
+    if (likely(m && m->mp_subscript)) {
+        return m->mp_subscript(obj, key);
+    }
+    return __Pyx_PyObject_GetIndex(obj, key);
+}
+#endif
+
+/* GetTopmostException */
+  #if CYTHON_USE_EXC_INFO_STACK
+static _PyErr_StackItem *
+__Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
+{
+    _PyErr_StackItem *exc_info = tstate->exc_info;
+    while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) &&
+           exc_info->previous_item != NULL)
+    {
+        exc_info = exc_info->previous_item;
+    }
+    return exc_info;
+}
+#endif
+
+/* SaveResetException */
+  #if CYTHON_FAST_THREAD_STATE
+static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
+    #if CYTHON_USE_EXC_INFO_STACK
+    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
+    *type = exc_info->exc_type;
+    *value = exc_info->exc_value;
+    *tb = exc_info->exc_traceback;
+    #else
+    *type = tstate->exc_type;
+    *value = tstate->exc_value;
+    *tb = tstate->exc_traceback;
+    #endif
+    Py_XINCREF(*type);
+    Py_XINCREF(*value);
+    Py_XINCREF(*tb);
+}
+static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    #if CYTHON_USE_EXC_INFO_STACK
+    _PyErr_StackItem *exc_info = tstate->exc_info;
+    tmp_type = exc_info->exc_type;
+    tmp_value = exc_info->exc_value;
+    tmp_tb = exc_info->exc_traceback;
+    exc_info->exc_type = type;
+    exc_info->exc_value = value;
+    exc_info->exc_traceback = tb;
+    #else
+    tmp_type = tstate->exc_type;
+    tmp_value = tstate->exc_value;
+    tmp_tb = tstate->exc_traceback;
+    tstate->exc_type = type;
+    tstate->exc_value = value;
+    tstate->exc_traceback = tb;
+    #endif
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+}
+#endif
+
+/* PyErrExceptionMatches */
+  #if CYTHON_FAST_THREAD_STATE
+static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
+    Py_ssize_t i, n;
+    n = PyTuple_GET_SIZE(tuple);
+#if PY_MAJOR_VERSION >= 3
+    for (i=0; i<n; i++) {
+        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
+    }
+#endif
+    for (i=0; i<n; i++) {
+        if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
+    }
+    return 0;
+}
+static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
+    PyObject *exc_type = tstate->curexc_type;
+    if (exc_type == err) return 1;
+    if (unlikely(!exc_type)) return 0;
+    if (unlikely(PyTuple_Check(err)))
+        return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
+    return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
+}
+#endif
+
+/* GetException */
+  #if CYTHON_FAST_THREAD_STATE
+static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)
+#else
+static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)
+#endif
+{
+    PyObject *local_type, *local_value, *local_tb;
+#if CYTHON_FAST_THREAD_STATE
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    local_type = tstate->curexc_type;
+    local_value = tstate->curexc_value;
+    local_tb = tstate->curexc_traceback;
+    tstate->curexc_type = 0;
+    tstate->curexc_value = 0;
+    tstate->curexc_traceback = 0;
+#else
+    PyErr_Fetch(&local_type, &local_value, &local_tb);
+#endif
+    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
+#if CYTHON_FAST_THREAD_STATE
+    if (unlikely(tstate->curexc_type))
+#else
+    if (unlikely(PyErr_Occurred()))
+#endif
+        goto bad;
+    #if PY_MAJOR_VERSION >= 3
+    if (local_tb) {
+        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
+            goto bad;
+    }
+    #endif
+    Py_XINCREF(local_tb);
+    Py_XINCREF(local_type);
+    Py_XINCREF(local_value);
+    *type = local_type;
+    *value = local_value;
+    *tb = local_tb;
+#if CYTHON_FAST_THREAD_STATE
+    #if CYTHON_USE_EXC_INFO_STACK
+    {
+        _PyErr_StackItem *exc_info = tstate->exc_info;
+        tmp_type = exc_info->exc_type;
+        tmp_value = exc_info->exc_value;
+        tmp_tb = exc_info->exc_traceback;
+        exc_info->exc_type = local_type;
+        exc_info->exc_value = local_value;
+        exc_info->exc_traceback = local_tb;
+    }
+    #else
+    tmp_type = tstate->exc_type;
+    tmp_value = tstate->exc_value;
+    tmp_tb = tstate->exc_traceback;
+    tstate->exc_type = local_type;
+    tstate->exc_value = local_value;
+    tstate->exc_traceback = local_tb;
+    #endif
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+#else
+    PyErr_SetExcInfo(local_type, local_value, local_tb);
+#endif
+    return 0;
+bad:
+    *type = 0;
+    *value = 0;
+    *tb = 0;
+    Py_XDECREF(local_type);
+    Py_XDECREF(local_value);
+    Py_XDECREF(local_tb);
+    return -1;
+}
+
+/* RaiseException */
+  #if PY_MAJOR_VERSION < 3
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
+                        CYTHON_UNUSED PyObject *cause) {
+    __Pyx_PyThreadState_declare
+    Py_XINCREF(type);
+    if (!value || value == Py_None)
+        value = NULL;
+    else
+        Py_INCREF(value);
+    if (!tb || tb == Py_None)
+        tb = NULL;
+    else {
+        Py_INCREF(tb);
+        if (!PyTraceBack_Check(tb)) {
+            PyErr_SetString(PyExc_TypeError,
+                "raise: arg 3 must be a traceback or None");
+            goto raise_error;
+        }
+    }
+    if (PyType_Check(type)) {
+#if CYTHON_COMPILING_IN_PYPY
+        if (!value) {
+            Py_INCREF(Py_None);
+            value = Py_None;
+        }
+#endif
+        PyErr_NormalizeException(&type, &value, &tb);
+    } else {
+        if (value) {
+            PyErr_SetString(PyExc_TypeError,
+                "instance exception may not have a separate value");
+            goto raise_error;
+        }
+        value = type;
+        type = (PyObject*) Py_TYPE(type);
+        Py_INCREF(type);
+        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
+            PyErr_SetString(PyExc_TypeError,
+                "raise: exception class must be a subclass of BaseException");
+            goto raise_error;
+        }
+    }
+    __Pyx_PyThreadState_assign
+    __Pyx_ErrRestore(type, value, tb);
+    return;
+raise_error:
+    Py_XDECREF(value);
+    Py_XDECREF(type);
+    Py_XDECREF(tb);
+    return;
+}
+#else
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
+    PyObject* owned_instance = NULL;
+    if (tb == Py_None) {
+        tb = 0;
+    } else if (tb && !PyTraceBack_Check(tb)) {
+        PyErr_SetString(PyExc_TypeError,
+            "raise: arg 3 must be a traceback or None");
+        goto bad;
+    }
+    if (value == Py_None)
+        value = 0;
+    if (PyExceptionInstance_Check(type)) {
+        if (value) {
+            PyErr_SetString(PyExc_TypeError,
+                "instance exception may not have a separate value");
+            goto bad;
+        }
+        value = type;
+        type = (PyObject*) Py_TYPE(value);
+    } else if (PyExceptionClass_Check(type)) {
+        PyObject *instance_class = NULL;
+        if (value && PyExceptionInstance_Check(value)) {
+            instance_class = (PyObject*) Py_TYPE(value);
+            if (instance_class != type) {
+                int is_subclass = PyObject_IsSubclass(instance_class, type);
+                if (!is_subclass) {
+                    instance_class = NULL;
+                } else if (unlikely(is_subclass == -1)) {
+                    goto bad;
+                } else {
+                    type = instance_class;
+                }
+            }
+        }
+        if (!instance_class) {
+            PyObject *args;
+            if (!value)
+                args = PyTuple_New(0);
+            else if (PyTuple_Check(value)) {
+                Py_INCREF(value);
+                args = value;
+            } else
+                args = PyTuple_Pack(1, value);
+            if (!args)
+                goto bad;
+            owned_instance = PyObject_Call(type, args, NULL);
+            Py_DECREF(args);
+            if (!owned_instance)
+                goto bad;
+            value = owned_instance;
+            if (!PyExceptionInstance_Check(value)) {
+                PyErr_Format(PyExc_TypeError,
+                             "calling %R should have returned an instance of "
+                             "BaseException, not %R",
+                             type, Py_TYPE(value));
+                goto bad;
+            }
+        }
+    } else {
+        PyErr_SetString(PyExc_TypeError,
+            "raise: exception class must be a subclass of BaseException");
+        goto bad;
+    }
+    if (cause) {
+        PyObject *fixed_cause;
+        if (cause == Py_None) {
+            fixed_cause = NULL;
+        } else if (PyExceptionClass_Check(cause)) {
+            fixed_cause = PyObject_CallObject(cause, NULL);
+            if (fixed_cause == NULL)
+                goto bad;
+        } else if (PyExceptionInstance_Check(cause)) {
+            fixed_cause = cause;
+            Py_INCREF(fixed_cause);
+        } else {
+            PyErr_SetString(PyExc_TypeError,
+                            "exception causes must derive from "
+                            "BaseException");
+            goto bad;
+        }
+        PyException_SetCause(value, fixed_cause);
+    }
+    PyErr_SetObject(type, value);
+    if (tb) {
+#if CYTHON_COMPILING_IN_PYPY
+        PyObject *tmp_type, *tmp_value, *tmp_tb;
+        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
+        Py_INCREF(tb);
+        PyErr_Restore(tmp_type, tmp_value, tb);
+        Py_XDECREF(tmp_tb);
+#else
+        PyThreadState *tstate = __Pyx_PyThreadState_Current;
+        PyObject* tmp_tb = tstate->curexc_traceback;
+        if (tb != tmp_tb) {
+            Py_INCREF(tb);
+            tstate->curexc_traceback = tb;
+            Py_XDECREF(tmp_tb);
+        }
+#endif
+    }
+bad:
+    Py_XDECREF(owned_instance);
+    return;
+}
+#endif
+
+/* TypeImport */
+  #ifndef __PYX_HAVE_RT_ImportType
+#define __PYX_HAVE_RT_ImportType
+static PyTypeObject *__Pyx_ImportType(PyObject *module, const char *module_name, const char *class_name,
+    size_t size, enum __Pyx_ImportType_CheckSize check_size)
+{
+    PyObject *result = 0;
+    char warning[200];
+    Py_ssize_t basicsize;
+#ifdef Py_LIMITED_API
+    PyObject *py_basicsize;
+#endif
+    result = PyObject_GetAttrString(module, class_name);
+    if (!result)
+        goto bad;
+    if (!PyType_Check(result)) {
+        PyErr_Format(PyExc_TypeError,
+            "%.200s.%.200s is not a type object",
+            module_name, class_name);
+        goto bad;
+    }
+#ifndef Py_LIMITED_API
+    basicsize = ((PyTypeObject *)result)->tp_basicsize;
+#else
+    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
+    if (!py_basicsize)
+        goto bad;
+    basicsize = PyLong_AsSsize_t(py_basicsize);
+    Py_DECREF(py_basicsize);
+    py_basicsize = 0;
+    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
+        goto bad;
+#endif
+    if ((size_t)basicsize < size) {
+        PyErr_Format(PyExc_ValueError,
+            "%.200s.%.200s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd from PyObject",
+            module_name, class_name, size, basicsize);
+        goto bad;
+    }
+    if (check_size == __Pyx_ImportType_CheckSize_Error && (size_t)basicsize != size) {
+        PyErr_Format(PyExc_ValueError,
+            "%.200s.%.200s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd from PyObject",
+            module_name, class_name, size, basicsize);
+        goto bad;
+    }
+    else if (check_size == __Pyx_ImportType_CheckSize_Warn && (size_t)basicsize > size) {
+        PyOS_snprintf(warning, sizeof(warning),
+            "%s.%s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd from PyObject",
+            module_name, class_name, size, basicsize);
+        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
+    }
+    return (PyTypeObject *)result;
+bad:
+    Py_XDECREF(result);
+    return NULL;
+}
+#endif
+
+/* Import */
+  static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
+    PyObject *empty_list = 0;
+    PyObject *module = 0;
+    PyObject *global_dict = 0;
+    PyObject *empty_dict = 0;
+    PyObject *list;
+    #if PY_MAJOR_VERSION < 3
+    PyObject *py_import;
+    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
+    if (!py_import)
+        goto bad;
+    #endif
+    if (from_list)
+        list = from_list;
+    else {
+        empty_list = PyList_New(0);
+        if (!empty_list)
+            goto bad;
+        list = empty_list;
+    }
+    global_dict = PyModule_GetDict(__pyx_m);
+    if (!global_dict)
+        goto bad;
+    empty_dict = PyDict_New();
+    if (!empty_dict)
+        goto bad;
+    {
+        #if PY_MAJOR_VERSION >= 3
+        if (level == -1) {
+            if ((1) && (strchr(__Pyx_MODULE_NAME, '.'))) {
+                module = PyImport_ImportModuleLevelObject(
+                    name, global_dict, empty_dict, list, 1);
+                if (!module) {
+                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
+                        goto bad;
+                    PyErr_Clear();
+                }
+            }
+            level = 0;
+        }
+        #endif
+        if (!module) {
+            #if PY_MAJOR_VERSION < 3
+            PyObject *py_level = PyInt_FromLong(level);
+            if (!py_level)
+                goto bad;
+            module = PyObject_CallFunctionObjArgs(py_import,
+                name, global_dict, empty_dict, list, py_level, (PyObject *)NULL);
+            Py_DECREF(py_level);
+            #else
+            module = PyImport_ImportModuleLevelObject(
+                name, global_dict, empty_dict, list, level);
+            #endif
+        }
+    }
+bad:
+    #if PY_MAJOR_VERSION < 3
+    Py_XDECREF(py_import);
+    #endif
+    Py_XDECREF(empty_list);
+    Py_XDECREF(empty_dict);
+    return module;
+}
+
+/* ImportFrom */
+  static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
+    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
+    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
+        PyErr_Format(PyExc_ImportError,
+        #if PY_MAJOR_VERSION < 3
+            "cannot import name %.230s", PyString_AS_STRING(name));
+        #else
+            "cannot import name %S", name);
+        #endif
+    }
+    return value;
+}
+
+/* CLineInTraceback */
+  #ifndef CYTHON_CLINE_IN_TRACEBACK
+static int __Pyx_CLineForTraceback(CYTHON_NCP_UNUSED PyThreadState *tstate, int c_line) {
+    PyObject *use_cline;
+    PyObject *ptype, *pvalue, *ptraceback;
+#if CYTHON_COMPILING_IN_CPYTHON
+    PyObject **cython_runtime_dict;
+#endif
+    if (unlikely(!__pyx_cython_runtime)) {
+        return c_line;
+    }
+    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
+#if CYTHON_COMPILING_IN_CPYTHON
+    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
+    if (likely(cython_runtime_dict)) {
+        __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
+            use_cline, *cython_runtime_dict,
+            __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback))
+    } else
+#endif
+    {
+      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
+      if (use_cline_obj) {
+        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
+        Py_DECREF(use_cline_obj);
+      } else {
+        PyErr_Clear();
+        use_cline = NULL;
+      }
+    }
+    if (!use_cline) {
+        c_line = 0;
+        PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
+    }
+    else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
+        c_line = 0;
+    }
+    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
+    return c_line;
+}
+#endif
+
+/* CodeObjectCache */
+  static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
+    int start = 0, mid = 0, end = count - 1;
+    if (end >= 0 && code_line > entries[end].code_line) {
+        return count;
+    }
+    while (start < end) {
+        mid = start + (end - start) / 2;
+        if (code_line < entries[mid].code_line) {
+            end = mid;
+        } else if (code_line > entries[mid].code_line) {
+             start = mid + 1;
+        } else {
+            return mid;
+        }
+    }
+    if (code_line <= entries[mid].code_line) {
+        return mid;
+    } else {
+        return mid + 1;
+    }
+}
+static PyCodeObject *__pyx_find_code_object(int code_line) {
+    PyCodeObject* code_object;
+    int pos;
+    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
+        return NULL;
+    }
+    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
+    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
+        return NULL;
+    }
+    code_object = __pyx_code_cache.entries[pos].code_object;
+    Py_INCREF(code_object);
+    return code_object;
+}
+static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
+    int pos, i;
+    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
+    if (unlikely(!code_line)) {
+        return;
+    }
+    if (unlikely(!entries)) {
+        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
+        if (likely(entries)) {
+            __pyx_code_cache.entries = entries;
+            __pyx_code_cache.max_count = 64;
+            __pyx_code_cache.count = 1;
+            entries[0].code_line = code_line;
+            entries[0].code_object = code_object;
+            Py_INCREF(code_object);
+        }
+        return;
+    }
+    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
+    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
+        PyCodeObject* tmp = entries[pos].code_object;
+        entries[pos].code_object = code_object;
+        Py_DECREF(tmp);
+        return;
+    }
+    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
+        int new_max = __pyx_code_cache.max_count + 64;
+        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
+            __pyx_code_cache.entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry));
+        if (unlikely(!entries)) {
+            return;
+        }
+        __pyx_code_cache.entries = entries;
+        __pyx_code_cache.max_count = new_max;
+    }
+    for (i=__pyx_code_cache.count; i>pos; i--) {
+        entries[i] = entries[i-1];
+    }
+    entries[pos].code_line = code_line;
+    entries[pos].code_object = code_object;
+    __pyx_code_cache.count++;
+    Py_INCREF(code_object);
+}
+
+/* AddTraceback */
+  #include "compile.h"
+#include "frameobject.h"
+#include "traceback.h"
+static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
+            const char *funcname, int c_line,
+            int py_line, const char *filename) {
+    PyCodeObject *py_code = 0;
+    PyObject *py_srcfile = 0;
+    PyObject *py_funcname = 0;
+    #if PY_MAJOR_VERSION < 3
+    py_srcfile = PyString_FromString(filename);
+    #else
+    py_srcfile = PyUnicode_FromString(filename);
+    #endif
+    if (!py_srcfile) goto bad;
+    if (c_line) {
+        #if PY_MAJOR_VERSION < 3
+        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
+        #else
+        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
+        #endif
+    }
+    else {
+        #if PY_MAJOR_VERSION < 3
+        py_funcname = PyString_FromString(funcname);
+        #else
+        py_funcname = PyUnicode_FromString(funcname);
+        #endif
+    }
+    if (!py_funcname) goto bad;
+    py_code = __Pyx_PyCode_New(
+        0,
+        0,
+        0,
+        0,
+        0,
+        __pyx_empty_bytes, /*PyObject *code,*/
+        __pyx_empty_tuple, /*PyObject *consts,*/
+        __pyx_empty_tuple, /*PyObject *names,*/
+        __pyx_empty_tuple, /*PyObject *varnames,*/
+        __pyx_empty_tuple, /*PyObject *freevars,*/
+        __pyx_empty_tuple, /*PyObject *cellvars,*/
+        py_srcfile,   /*PyObject *filename,*/
+        py_funcname,  /*PyObject *name,*/
+        py_line,
+        __pyx_empty_bytes  /*PyObject *lnotab*/
+    );
+    Py_DECREF(py_srcfile);
+    Py_DECREF(py_funcname);
+    return py_code;
+bad:
+    Py_XDECREF(py_srcfile);
+    Py_XDECREF(py_funcname);
+    return NULL;
+}
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename) {
+    PyCodeObject *py_code = 0;
+    PyFrameObject *py_frame = 0;
+    PyThreadState *tstate = __Pyx_PyThreadState_Current;
+    if (c_line) {
+        c_line = __Pyx_CLineForTraceback(tstate, c_line);
+    }
+    py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
+    if (!py_code) {
+        py_code = __Pyx_CreateCodeObjectForTraceback(
+            funcname, c_line, py_line, filename);
+        if (!py_code) goto bad;
+        __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
+    }
+    py_frame = PyFrame_New(
+        tstate,            /*PyThreadState *tstate,*/
+        py_code,           /*PyCodeObject *code,*/
+        __pyx_d,    /*PyObject *globals,*/
+        0                  /*PyObject *locals*/
+    );
+    if (!py_frame) goto bad;
+    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
+    PyTraceBack_Here(py_frame);
+bad:
+    Py_XDECREF(py_code);
+    Py_XDECREF(py_frame);
+}
+
+#if PY_MAJOR_VERSION < 3
+static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
+    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
+    PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
+    return -1;
+}
+static void __Pyx_ReleaseBuffer(Py_buffer *view) {
+    PyObject *obj = view->obj;
+    if (!obj) return;
+    if (PyObject_CheckBuffer(obj)) {
+        PyBuffer_Release(view);
+        return;
+    }
+    if ((0)) {}
+    view->obj = NULL;
+    Py_DECREF(obj);
+}
+#endif
+
+
+  /* CIntFromPyVerify */
+  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
+    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
+#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
+    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
+#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
+    {\
+        func_type value = func_value;\
+        if (sizeof(target_type) < sizeof(func_type)) {\
+            if (unlikely(value != (func_type) (target_type) value)) {\
+                func_type zero = 0;\
+                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
+                    return (target_type) -1;\
+                if (is_unsigned && unlikely(value < zero))\
+                    goto raise_neg_overflow;\
+                else\
+                    goto raise_overflow;\
+            }\
+        }\
+        return (target_type) value;\
+    }
+
+/* Print */
+  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION < 3
+static PyObject *__Pyx_GetStdout(void) {
+    PyObject *f = PySys_GetObject((char *)"stdout");
+    if (!f) {
+        PyErr_SetString(PyExc_RuntimeError, "lost sys.stdout");
+    }
+    return f;
+}
+static int __Pyx_Print(PyObject* f, PyObject *arg_tuple, int newline) {
+    int i;
+    if (!f) {
+        if (!(f = __Pyx_GetStdout()))
+            return -1;
+    }
+    Py_INCREF(f);
+    for (i=0; i < PyTuple_GET_SIZE(arg_tuple); i++) {
+        PyObject* v;
+        if (PyFile_SoftSpace(f, 1)) {
+            if (PyFile_WriteString(" ", f) < 0)
+                goto error;
+        }
+        v = PyTuple_GET_ITEM(arg_tuple, i);
+        if (PyFile_WriteObject(v, f, Py_PRINT_RAW) < 0)
+            goto error;
+        if (PyString_Check(v)) {
+            char *s = PyString_AsString(v);
+            Py_ssize_t len = PyString_Size(v);
+            if (len > 0) {
+                switch (s[len-1]) {
+                    case ' ': break;
+                    case '\f': case '\r': case '\n': case '\t': case '\v':
+                        PyFile_SoftSpace(f, 0);
+                        break;
+                    default:  break;
+                }
+            }
+        }
+    }
+    if (newline) {
+        if (PyFile_WriteString("\n", f) < 0)
+            goto error;
+        PyFile_SoftSpace(f, 0);
+    }
+    Py_DECREF(f);
+    return 0;
+error:
+    Py_DECREF(f);
+    return -1;
+}
+#else
+static int __Pyx_Print(PyObject* stream, PyObject *arg_tuple, int newline) {
+    PyObject* kwargs = 0;
+    PyObject* result = 0;
+    PyObject* end_string;
+    if (unlikely(!__pyx_print)) {
+        __pyx_print = PyObject_GetAttr(__pyx_b, __pyx_n_s_print);
+        if (!__pyx_print)
+            return -1;
+    }
+    if (stream) {
+        kwargs = PyDict_New();
+        if (unlikely(!kwargs))
+            return -1;
+        if (unlikely(PyDict_SetItem(kwargs, __pyx_n_s_file, stream) < 0))
+            goto bad;
+        if (!newline) {
+            end_string = PyUnicode_FromStringAndSize(" ", 1);
+            if (unlikely(!end_string))
+                goto bad;
+            if (PyDict_SetItem(kwargs, __pyx_n_s_end, end_string) < 0) {
+                Py_DECREF(end_string);
+                goto bad;
+            }
+            Py_DECREF(end_string);
+        }
+    } else if (!newline) {
+        if (unlikely(!__pyx_print_kwargs)) {
+            __pyx_print_kwargs = PyDict_New();
+            if (unlikely(!__pyx_print_kwargs))
+                return -1;
+            end_string = PyUnicode_FromStringAndSize(" ", 1);
+            if (unlikely(!end_string))
+                return -1;
+            if (PyDict_SetItem(__pyx_print_kwargs, __pyx_n_s_end, end_string) < 0) {
+                Py_DECREF(end_string);
+                return -1;
+            }
+            Py_DECREF(end_string);
+        }
+        kwargs = __pyx_print_kwargs;
+    }
+    result = PyObject_Call(__pyx_print, arg_tuple, kwargs);
+    if (unlikely(kwargs) && (kwargs != __pyx_print_kwargs))
+        Py_DECREF(kwargs);
+    if (!result)
+        return -1;
+    Py_DECREF(result);
+    return 0;
+bad:
+    if (kwargs != __pyx_print_kwargs)
+        Py_XDECREF(kwargs);
+    return -1;
+}
+#endif
+
+/* Declarations */
+  #if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      return ::std::complex< float >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      return x + y*(__pyx_t_float_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      __pyx_t_float_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+/* Arithmetic */
+  #if CYTHON_CCOMPLEX
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    #if 1
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else if (fabsf(b.real) >= fabsf(b.imag)) {
+            if (b.real == 0 && b.imag == 0) {
+                return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);
+            } else {
+                float r = b.imag / b.real;
+                float s = (float)(1.0) / (b.real + b.imag * r);
+                return __pyx_t_float_complex_from_parts(
+                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
+            }
+        } else {
+            float r = b.real / b.imag;
+            float s = (float)(1.0) / (b.imag + b.real * r);
+            return __pyx_t_float_complex_from_parts(
+                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
+        }
+    }
+    #else
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else {
+            float denom = b.real * b.real + b.imag * b.imag;
+            return __pyx_t_float_complex_from_parts(
+                (a.real * b.real + a.imag * b.imag) / denom,
+                (a.imag * b.real - a.real * b.imag) / denom);
+        }
+    }
+    #endif
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) {
+        __pyx_t_float_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) {
+        __pyx_t_float_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrtf(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypotf(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+            __pyx_t_float_complex z;
+            float r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    float denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        return __Pyx_c_prod_float(a, a);
+                    case 3:
+                        z = __Pyx_c_prod_float(a, a);
+                        return __Pyx_c_prod_float(z, a);
+                    case 4:
+                        z = __Pyx_c_prod_float(a, a);
+                        return __Pyx_c_prod_float(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                } else if (b.imag == 0) {
+                    z.real = powf(a.real, b.real);
+                    z.imag = 0;
+                    return z;
+                } else if (a.real > 0) {
+                    r = a.real;
+                    theta = 0;
+                } else {
+                    r = -a.real;
+                    theta = atan2f(0.0, -1.0);
+                }
+            } else {
+                r = __Pyx_c_abs_float(a);
+                theta = atan2f(a.imag, a.real);
+            }
+            lnr = logf(r);
+            z_r = expf(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cosf(z_theta);
+            z.imag = z_r * sinf(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+/* Declarations */
+  #if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      return ::std::complex< double >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      return x + y*(__pyx_t_double_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      __pyx_t_double_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+/* Arithmetic */
+  #if CYTHON_CCOMPLEX
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    #if 1
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else if (fabs(b.real) >= fabs(b.imag)) {
+            if (b.real == 0 && b.imag == 0) {
+                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
+            } else {
+                double r = b.imag / b.real;
+                double s = (double)(1.0) / (b.real + b.imag * r);
+                return __pyx_t_double_complex_from_parts(
+                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
+            }
+        } else {
+            double r = b.real / b.imag;
+            double s = (double)(1.0) / (b.imag + b.real * r);
+            return __pyx_t_double_complex_from_parts(
+                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
+        }
+    }
+    #else
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else {
+            double denom = b.real * b.real + b.imag * b.imag;
+            return __pyx_t_double_complex_from_parts(
+                (a.real * b.real + a.imag * b.imag) / denom,
+                (a.imag * b.real - a.real * b.imag) / denom);
+        }
+    }
+    #endif
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) {
+        __pyx_t_double_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) {
+        __pyx_t_double_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrt(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypot(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+            __pyx_t_double_complex z;
+            double r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    double denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        return __Pyx_c_prod_double(a, a);
+                    case 3:
+                        z = __Pyx_c_prod_double(a, a);
+                        return __Pyx_c_prod_double(z, a);
+                    case 4:
+                        z = __Pyx_c_prod_double(a, a);
+                        return __Pyx_c_prod_double(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                } else if (b.imag == 0) {
+                    z.real = pow(a.real, b.real);
+                    z.imag = 0;
+                    return z;
+                } else if (a.real > 0) {
+                    r = a.real;
+                    theta = 0;
+                } else {
+                    r = -a.real;
+                    theta = atan2(0.0, -1.0);
+                }
+            } else {
+                r = __Pyx_c_abs_double(a);
+                theta = atan2(a.imag, a.real);
+            }
+            lnr = log(r);
+            z_r = exp(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cos(z_theta);
+            z.imag = z_r * sin(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+/* CIntToPy */
+  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const int neg_one = (int) -1, const_zero = (int) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+    if (is_unsigned) {
+        if (sizeof(int) < sizeof(long)) {
+            return PyInt_FromLong((long) value);
+        } else if (sizeof(int) <= sizeof(unsigned long)) {
+            return PyLong_FromUnsignedLong((unsigned long) value);
+#ifdef HAVE_LONG_LONG
+        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
+            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
+#endif
+        }
+    } else {
+        if (sizeof(int) <= sizeof(long)) {
+            return PyInt_FromLong((long) value);
+#ifdef HAVE_LONG_LONG
+        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
+            return PyLong_FromLongLong((PY_LONG_LONG) value);
+#endif
+        }
+    }
+    {
+        int one = 1; int little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&value;
+        return _PyLong_FromByteArray(bytes, sizeof(int),
+                                     little, !is_unsigned);
+    }
+}
+
+/* CIntFromPy */
+  static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const int neg_one = (int) -1, const_zero = (int) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if (sizeof(int) < sizeof(long)) {
+            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (int) val;
+        }
+    } else
+#endif
+    if (likely(PyLong_Check(x))) {
+        if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (int) 0;
+                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
+                case 2:
+                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
+                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
+                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
+                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+            }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON
+            if (unlikely(Py_SIZE(x) < 0)) {
+                goto raise_neg_overflow;
+            }
+#else
+            {
+                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+                if (unlikely(result < 0))
+                    return (int) -1;
+                if (unlikely(result == 1))
+                    goto raise_neg_overflow;
+            }
+#endif
+            if (sizeof(int) <= sizeof(unsigned long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+            }
+        } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (int) 0;
+                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
+                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
+                case -2:
+                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
+                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
+                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
+                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
+                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
+                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
+                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+            }
+#endif
+            if (sizeof(int) <= sizeof(long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+            }
+        }
+        {
+#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
+            PyErr_SetString(PyExc_RuntimeError,
+                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
+#else
+            int val;
+            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
+ #if PY_MAJOR_VERSION < 3
+            if (likely(v) && !PyLong_Check(v)) {
+                PyObject *tmp = v;
+                v = PyNumber_Long(tmp);
+                Py_DECREF(tmp);
+            }
+ #endif
+            if (likely(v)) {
+                int one = 1; int is_little = (int)*(unsigned char *)&one;
+                unsigned char *bytes = (unsigned char *)&val;
+                int ret = _PyLong_AsByteArray((PyLongObject *)v,
+                                              bytes, sizeof(val),
+                                              is_little, !is_unsigned);
+                Py_DECREF(v);
+                if (likely(!ret))
+                    return val;
+            }
+#endif
+            return (int) -1;
+        }
+    } else {
+        int val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (int) -1;
+        val = __Pyx_PyInt_As_int(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to int");
+    return (int) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to int");
+    return (int) -1;
+}
+
+/* PrintOne */
+  #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION < 3
+static int __Pyx_PrintOne(PyObject* f, PyObject *o) {
+    if (!f) {
+        if (!(f = __Pyx_GetStdout()))
+            return -1;
+    }
+    Py_INCREF(f);
+    if (PyFile_SoftSpace(f, 0)) {
+        if (PyFile_WriteString(" ", f) < 0)
+            goto error;
+    }
+    if (PyFile_WriteObject(o, f, Py_PRINT_RAW) < 0)
+        goto error;
+    if (PyFile_WriteString("\n", f) < 0)
+        goto error;
+    Py_DECREF(f);
+    return 0;
+error:
+    Py_DECREF(f);
+    return -1;
+    /* the line below is just to avoid C compiler
+     * warnings about unused functions */
+    return __Pyx_Print(f, NULL, 0);
+}
+#else
+static int __Pyx_PrintOne(PyObject* stream, PyObject *o) {
+    int res;
+    PyObject* arg_tuple = PyTuple_Pack(1, o);
+    if (unlikely(!arg_tuple))
+        return -1;
+    res = __Pyx_Print(stream, arg_tuple, 1);
+    Py_DECREF(arg_tuple);
+    return res;
+}
+#endif
+
+/* CIntToPy */
+  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const long neg_one = (long) -1, const_zero = (long) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+    if (is_unsigned) {
+        if (sizeof(long) < sizeof(long)) {
+            return PyInt_FromLong((long) value);
+        } else if (sizeof(long) <= sizeof(unsigned long)) {
+            return PyLong_FromUnsignedLong((unsigned long) value);
+#ifdef HAVE_LONG_LONG
+        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
+            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
+#endif
+        }
+    } else {
+        if (sizeof(long) <= sizeof(long)) {
+            return PyInt_FromLong((long) value);
+#ifdef HAVE_LONG_LONG
+        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
+            return PyLong_FromLongLong((PY_LONG_LONG) value);
+#endif
+        }
+    }
+    {
+        int one = 1; int little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&value;
+        return _PyLong_FromByteArray(bytes, sizeof(long),
+                                     little, !is_unsigned);
+    }
+}
+
+/* CIntFromPy */
+  static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const long neg_one = (long) -1, const_zero = (long) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if (sizeof(long) < sizeof(long)) {
+            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (long) val;
+        }
+    } else
+#endif
+    if (likely(PyLong_Check(x))) {
+        if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (long) 0;
+                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
+                case 2:
+                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
+                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
+                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
+                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+            }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON
+            if (unlikely(Py_SIZE(x) < 0)) {
+                goto raise_neg_overflow;
+            }
+#else
+            {
+                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+                if (unlikely(result < 0))
+                    return (long) -1;
+                if (unlikely(result == 1))
+                    goto raise_neg_overflow;
+            }
+#endif
+            if (sizeof(long) <= sizeof(unsigned long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+            }
+        } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+            const digit* digits = ((PyLongObject*)x)->ob_digit;
+            switch (Py_SIZE(x)) {
+                case  0: return (long) 0;
+                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
+                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
+                case -2:
+                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
+                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
+                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
+                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+            }
+#endif
+            if (sizeof(long) <= sizeof(long)) {
+                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
+                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+            }
+        }
+        {
+#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
+            PyErr_SetString(PyExc_RuntimeError,
+                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
+#else
+            long val;
+            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
+ #if PY_MAJOR_VERSION < 3
+            if (likely(v) && !PyLong_Check(v)) {
+                PyObject *tmp = v;
+                v = PyNumber_Long(tmp);
+                Py_DECREF(tmp);
+            }
+ #endif
+            if (likely(v)) {
+                int one = 1; int is_little = (int)*(unsigned char *)&one;
+                unsigned char *bytes = (unsigned char *)&val;
+                int ret = _PyLong_AsByteArray((PyLongObject *)v,
+                                              bytes, sizeof(val),
+                                              is_little, !is_unsigned);
+                Py_DECREF(v);
+                if (likely(!ret))
+                    return val;
+            }
+#endif
+            return (long) -1;
+        }
+    } else {
+        long val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (long) -1;
+        val = __Pyx_PyInt_As_long(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to long");
+    return (long) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to long");
+    return (long) -1;
+}
+
+/* FastTypeChecks */
+  #if CYTHON_COMPILING_IN_CPYTHON
+static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
+    while (a) {
+        a = a->tp_base;
+        if (a == b)
+            return 1;
+    }
+    return b == &PyBaseObject_Type;
+}
+static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
+    PyObject *mro;
+    if (a == b) return 1;
+    mro = a->tp_mro;
+    if (likely(mro)) {
+        Py_ssize_t i, n;
+        n = PyTuple_GET_SIZE(mro);
+        for (i = 0; i < n; i++) {
+            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
+                return 1;
+        }
+        return 0;
+    }
+    return __Pyx_InBases(a, b);
+}
+#if PY_MAJOR_VERSION == 2
+static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
+    PyObject *exception, *value, *tb;
+    int res;
+    __Pyx_PyThreadState_declare
+    __Pyx_PyThreadState_assign
+    __Pyx_ErrFetch(&exception, &value, &tb);
+    res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
+    if (unlikely(res == -1)) {
+        PyErr_WriteUnraisable(err);
+        res = 0;
+    }
+    if (!res) {
+        res = PyObject_IsSubclass(err, exc_type2);
+        if (unlikely(res == -1)) {
+            PyErr_WriteUnraisable(err);
+            res = 0;
+        }
+    }
+    __Pyx_ErrRestore(exception, value, tb);
+    return res;
+}
+#else
+static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
+    int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
+    if (!res) {
+        res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
+    }
+    return res;
+}
+#endif
+static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
+    Py_ssize_t i, n;
+    assert(PyExceptionClass_Check(exc_type));
+    n = PyTuple_GET_SIZE(tuple);
+#if PY_MAJOR_VERSION >= 3
+    for (i=0; i<n; i++) {
+        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
+    }
+#endif
+    for (i=0; i<n; i++) {
+        PyObject *t = PyTuple_GET_ITEM(tuple, i);
+        #if PY_MAJOR_VERSION < 3
+        if (likely(exc_type == t)) return 1;
+        #endif
+        if (likely(PyExceptionClass_Check(t))) {
+            if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
+        } else {
+        }
+    }
+    return 0;
+}
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
+    if (likely(err == exc_type)) return 1;
+    if (likely(PyExceptionClass_Check(err))) {
+        if (likely(PyExceptionClass_Check(exc_type))) {
+            return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
+        } else if (likely(PyTuple_Check(exc_type))) {
+            return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
+        } else {
+        }
+    }
+    return PyErr_GivenExceptionMatches(err, exc_type);
+}
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
+    assert(PyExceptionClass_Check(exc_type1));
+    assert(PyExceptionClass_Check(exc_type2));
+    if (likely(err == exc_type1 || err == exc_type2)) return 1;
+    if (likely(PyExceptionClass_Check(err))) {
+        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
+    }
+    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
+}
+#endif
+
+/* CheckBinaryVersion */
+  static int __Pyx_check_binary_version(void) {
+    char ctversion[4], rtversion[4];
+    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
+    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
+    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
+        char message[200];
+        PyOS_snprintf(message, sizeof(message),
+                      "compiletime version %s of module '%.100s' "
+                      "does not match runtime version %s",
+                      ctversion, __Pyx_MODULE_NAME, rtversion);
+        return PyErr_WarnEx(NULL, message, 1);
+    }
+    return 0;
+}
+
+/* InitStrings */
+  static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
+    while (t->p) {
+        #if PY_MAJOR_VERSION < 3
+        if (t->is_unicode) {
+            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
+        } else if (t->intern) {
+            *t->p = PyString_InternFromString(t->s);
+        } else {
+            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
+        }
+        #else
+        if (t->is_unicode | t->is_str) {
+            if (t->intern) {
+                *t->p = PyUnicode_InternFromString(t->s);
+            } else if (t->encoding) {
+                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
+            } else {
+                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
+            }
+        } else {
+            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
+        }
+        #endif
+        if (!*t->p)
+            return -1;
+        if (PyObject_Hash(*t->p) == -1)
+            return -1;
+        ++t;
+    }
+    return 0;
+}
+
+static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
+    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
+}
+static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
+    Py_ssize_t ignore;
+    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
+}
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+#if !CYTHON_PEP393_ENABLED
+static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+    char* defenc_c;
+    PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
+    if (!defenc) return NULL;
+    defenc_c = PyBytes_AS_STRING(defenc);
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+    {
+        char* end = defenc_c + PyBytes_GET_SIZE(defenc);
+        char* c;
+        for (c = defenc_c; c < end; c++) {
+            if ((unsigned char) (*c) >= 128) {
+                PyUnicode_AsASCIIString(o);
+                return NULL;
+            }
+        }
+    }
+#endif
+    *length = PyBytes_GET_SIZE(defenc);
+    return defenc_c;
+}
+#else
+static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+    if (likely(PyUnicode_IS_ASCII(o))) {
+        *length = PyUnicode_GET_LENGTH(o);
+        return PyUnicode_AsUTF8(o);
+    } else {
+        PyUnicode_AsASCIIString(o);
+        return NULL;
+    }
+#else
+    return PyUnicode_AsUTF8AndSize(o, length);
+#endif
+}
+#endif
+#endif
+static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+    if (
+#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+            __Pyx_sys_getdefaultencoding_not_ascii &&
+#endif
+            PyUnicode_Check(o)) {
+        return __Pyx_PyUnicode_AsStringAndSize(o, length);
+    } else
+#endif
+#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
+    if (PyByteArray_Check(o)) {
+        *length = PyByteArray_GET_SIZE(o);
+        return PyByteArray_AS_STRING(o);
+    } else
+#endif
+    {
+        char* result;
+        int r = PyBytes_AsStringAndSize(o, &result, length);
+        if (unlikely(r < 0)) {
+            return NULL;
+        } else {
+            return result;
+        }
+    }
+}
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
+   int is_true = x == Py_True;
+   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
+   else return PyObject_IsTrue(x);
+}
+static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
+    int retval;
+    if (unlikely(!x)) return -1;
+    retval = __Pyx_PyObject_IsTrue(x);
+    Py_DECREF(x);
+    return retval;
+}
+static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
+#if PY_MAJOR_VERSION >= 3
+    if (PyLong_Check(result)) {
+        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
+                "__int__ returned non-int (type %.200s).  "
+                "The ability to return an instance of a strict subclass of int "
+                "is deprecated, and may be removed in a future version of Python.",
+                Py_TYPE(result)->tp_name)) {
+            Py_DECREF(result);
+            return NULL;
+        }
+        return result;
+    }
+#endif
+    PyErr_Format(PyExc_TypeError,
+                 "__%.4s__ returned non-%.4s (type %.200s)",
+                 type_name, type_name, Py_TYPE(result)->tp_name);
+    Py_DECREF(result);
+    return NULL;
+}
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
+#if CYTHON_USE_TYPE_SLOTS
+  PyNumberMethods *m;
+#endif
+  const char *name = NULL;
+  PyObject *res = NULL;
+#if PY_MAJOR_VERSION < 3
+  if (likely(PyInt_Check(x) || PyLong_Check(x)))
+#else
+  if (likely(PyLong_Check(x)))
+#endif
+    return __Pyx_NewRef(x);
+#if CYTHON_USE_TYPE_SLOTS
+  m = Py_TYPE(x)->tp_as_number;
+  #if PY_MAJOR_VERSION < 3
+  if (m && m->nb_int) {
+    name = "int";
+    res = m->nb_int(x);
+  }
+  else if (m && m->nb_long) {
+    name = "long";
+    res = m->nb_long(x);
+  }
+  #else
+  if (likely(m && m->nb_int)) {
+    name = "int";
+    res = m->nb_int(x);
+  }
+  #endif
+#else
+  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
+    res = PyNumber_Int(x);
+  }
+#endif
+  if (likely(res)) {
+#if PY_MAJOR_VERSION < 3
+    if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
+#else
+    if (unlikely(!PyLong_CheckExact(res))) {
+#endif
+        return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
+    }
+  }
+  else if (!PyErr_Occurred()) {
+    PyErr_SetString(PyExc_TypeError,
+                    "an integer is required");
+  }
+  return res;
+}
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
+  Py_ssize_t ival;
+  PyObject *x;
+#if PY_MAJOR_VERSION < 3
+  if (likely(PyInt_CheckExact(b))) {
+    if (sizeof(Py_ssize_t) >= sizeof(long))
+        return PyInt_AS_LONG(b);
+    else
+        return PyInt_AsSsize_t(b);
+  }
+#endif
+  if (likely(PyLong_CheckExact(b))) {
+    #if CYTHON_USE_PYLONG_INTERNALS
+    const digit* digits = ((PyLongObject*)b)->ob_digit;
+    const Py_ssize_t size = Py_SIZE(b);
+    if (likely(__Pyx_sst_abs(size) <= 1)) {
+        ival = likely(size) ? digits[0] : 0;
+        if (size == -1) ival = -ival;
+        return ival;
+    } else {
+      switch (size) {
+         case 2:
+           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -2:
+           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case 3:
+           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -3:
+           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case 4:
+           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -4:
+           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+      }
+    }
+    #endif
+    return PyLong_AsSsize_t(b);
+  }
+  x = PyNumber_Index(b);
+  if (!x) return -1;
+  ival = PyInt_AsSsize_t(x);
+  Py_DECREF(x);
+  return ival;
+}
+static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
+  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
+}
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
+    return PyInt_FromSize_t(ival);
+}
+
+
+#endif /* Py_PYTHON_H */
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new file mode 100644
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diff --git a/tool/algorithm/xml/AnalysisXml.py b/tool/algorithm/xml/AnalysisXml.py
new file mode 100644
index 00000000..8bbc228a
--- /dev/null
+++ b/tool/algorithm/xml/AnalysisXml.py
@@ -0,0 +1,135 @@
+from xml.etree.ElementTree import ElementTree
+import os
+
+
+class DictXml:
+    def __init__(self, xml_path):
+        self.xml_path = xml_path
+        self.__tree = ElementTree()
+        self.__root = None
+        self.init_xml()
+
+    def init_xml(self):
+        self.__root = self.__tree.parse(self.xml_path)
+        if self.__root is None:
+            raise Exception("get root failed")
+
+    def get_extend(self):
+        productInfo = self.__root.find("imageinfo")
+        if productInfo is None:
+            raise Exception("get imageInfo failed")
+
+        corner = productInfo.find("corner")
+        if corner is None:
+            raise Exception("get corner failed")
+
+        topLeft = corner.find("topLeft")
+        if topLeft is None:
+            raise Exception("get topLeft failed")
+
+        topRight = corner.find("topRight")
+        if topRight is None:
+            raise Exception("get topRight failed")
+
+        bottomLeft = corner.find("bottomLeft")
+        if bottomLeft is None:
+            raise Exception("get bottomLeft failed")
+
+        bottomRight = corner.find("bottomRight")
+        if bottomRight is None:
+            raise Exception("get bottomRight failed")
+
+        point_upleft = [float(topLeft.find("longitude").text), float(topLeft.find("latitude").text)]
+        point_upright = [float(topRight.find("longitude").text), float(topRight.find("latitude").text)]
+        point_downleft = [float(bottomLeft.find("longitude").text), float(bottomLeft.find("latitude").text)]
+        point_downright = [float(bottomRight.find("longitude").text), float(bottomRight.find("latitude").text)]
+        scopes = [point_upleft, point_upright, point_downleft, point_downright]
+
+        point_upleft_buf = [float(topLeft.find("longitude").text) - 0.5, float(topLeft.find("latitude").text) + 0.5]
+        point_upright_buf = [float(topRight.find("longitude").text) + 0.5, float(topRight.find("latitude").text) + 0.5]
+        point_downleft_buf = [float(bottomLeft.find("longitude").text) - 0.5,
+                              float(bottomLeft.find("latitude").text) - 0.5]
+        point_downright_buf = [float(bottomRight.find("longitude").text) + 0.5,
+                               float(bottomRight.find("latitude").text) - 0.5]
+        scopes_buf = [point_upleft_buf, point_upright_buf, point_downleft_buf, point_downright_buf]
+        return scopes
+
+
+class xml_extend:
+    def __init__(self, xml_path):
+        self.xml_path = xml_path
+        self.__tree = ElementTree()
+        self.__root = None
+        self.init_xml()
+
+    def init_xml(self):
+        self.__root = self.__tree.parse(self.xml_path)
+        if self.__root is None:
+            raise Exception("get root failed")
+
+    def get_extend(self):
+        ProductBasicInfo = self.__root.find("ProductBasicInfo")
+        if ProductBasicInfo is None:
+            raise Exception("get ProductBasicInfo failed")
+
+        SpatialCoverageInformation = ProductBasicInfo.find("SpatialCoverageInformation")
+        if SpatialCoverageInformation is None:
+            raise Exception("get SpatialCoverageInformation failed")
+
+        TopLeftLongitude = SpatialCoverageInformation.find("TopLeftLongitude")
+        if TopLeftLongitude is None:
+            raise Exception("get TopLeftLongitude failed")
+
+        TopLeftLatitude = SpatialCoverageInformation.find("TopLeftLatitude")
+        if TopLeftLatitude is None:
+            raise Exception("get TopLeftLatitude failed")
+
+        TopRightLongitude = SpatialCoverageInformation.find("TopRightLongitude")
+        if TopRightLongitude is None:
+            raise Exception("get TopRightLongitude failed")
+
+        TopRightLatitude = SpatialCoverageInformation.find("TopRightLatitude")
+        if TopRightLatitude is None:
+            raise Exception("get TopRightLatitude failed")
+
+        BottomRightLongitude = SpatialCoverageInformation.find("BottomRightLongitude")
+        if BottomRightLongitude is None:
+            raise Exception("get BottomRightLongitude failed")
+
+        BottomRightLatitude = SpatialCoverageInformation.find("BottomRightLatitude")
+        if BottomRightLatitude is None:
+            raise Exception("get BottomRightLatitude failed")
+
+        BottomLeftLongitude = SpatialCoverageInformation.find("BottomLeftLongitude")
+        if BottomLeftLongitude is None:
+            raise Exception("get BottomLeftLongitude failed")
+
+        BottomLeftLatitude = SpatialCoverageInformation.find("BottomLeftLatitude")
+        if BottomLeftLatitude is None:
+            raise Exception("get BottomLeftLatitude failed")
+
+        point_upleft = [float(TopLeftLongitude.text), float(TopLeftLatitude.text)]
+        point_upright = [float(TopRightLongitude.text), float(TopRightLatitude.text)]
+        point_downleft = [float(BottomLeftLongitude.text), float(BottomLeftLatitude.text)]
+        point_downright = [float(BottomRightLongitude.text), float(BottomRightLatitude.text)]
+        scopes = [point_upleft, point_upright, point_downleft, point_downright]
+
+        point_upleft_buf = [float(TopLeftLongitude.text) - 0.5, float(TopLeftLatitude.text) + 0.5]
+        point_upright_buf = [float(TopRightLongitude.text) + 0.5, float(TopRightLatitude.text) + 0.5]
+        point_downleft_buf = [float(BottomLeftLongitude.text) - 0.5, float(BottomLeftLatitude.text) - 0.5]
+        point_downright_buf = [float(BottomRightLongitude.text) + 0.5, float(BottomRightLatitude.text) - 0.5]
+        scopes_buf = [point_upleft_buf, point_upright_buf, point_downleft_buf, point_downright_buf]
+        return scopes
+
+
+if __name__ == '__main__':
+    xml_path = r'E:\MicroWorkspace\GF3A_nanjing\GF3_SAY_QPSI_011444_E118.9_N31.4_20181012_L1A_AHV_L10003515422\GF3_SAY_QPSI_011444_E118.9_N31.4_20181012_L1A_AHV_L10003515422.meta.xml'
+    scopes, scopes_buf = DictXml(xml_path).get_extend()
+    print(scopes)
+    print(scopes_buf)
+#     path = r'D:\BaiduNetdiskDownload\GZ\lon.rdr'
+#     path2 = r'D:\BaiduNetdiskDownload\GZ\lat.rdr'
+#     path3 = r'D:\BaiduNetdiskDownload\GZ\lon_lat.tif'
+#     s = ImageHandler().band_merge(path, path2, path3)
+#     print(s)
+#     pass