127 lines
4.3 KiB
Python
Executable File
127 lines
4.3 KiB
Python
Executable File
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# Copyright 2012 California Institute of Technology. ALL RIGHTS RESERVED.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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#
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# United States Government Sponsorship acknowledged. This software is subject to
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# U.S. export control laws and regulations and has been classified as 'EAR99 NLR'
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# (No [Export] License Required except when exporting to an embargoed country,
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# end user, or in support of a prohibited end use). By downloading this software,
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# the user agrees to comply with all applicable U.S. export laws and regulations.
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# The user has the responsibility to obtain export licenses, or other export
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# authority as may be required before exporting this software to any 'EAR99'
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# embargoed foreign country or citizen of those countries.
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#
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# Author: Eric Belz
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#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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"""A very simple 1st order differentiator"""
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## \namespace ::geo::dxdt A simple differentiator
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## numerical derivative algorithm \n
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## see http://docs.scipy.org/doc/scipy/reference/misc.html for other
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## functions (maybe better).
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def deriv(x,y=None):
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"""(dy/dx) = deriv(x [,y=None])"""
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import numpy
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if y is None: return deriv(numpy.arange(len(x), dtype=float), x)
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n = len(x)
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if n < 3:
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print('Parameters must have at least 3 points')
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raise ValueError
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if n != len(y):
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print('x and y must have same length')
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raise ValueError
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Sleft = Shifter(1)
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Sright = ~Sleft
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x12 = x - Sleft(x) #x1 - x2
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x01 = Sright(x) - x #x0 - x1
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x02 = Sright(x) - Sleft(x) #x0 - x2
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d = (Sright(y) * (x12 / (x01*x02)) + y * (1./x12 - 1./x01) - Sleft(y) * (x01 / (x02 * x12)))
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d[0] = y[0] * (x01[1]+x02[1])/(x01[1]*x02[1]) - y[1] * x02[1]/(x01[1]*x12[1]) + y[2] * x01[1]/(x02[1]*x12[1])
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n2 = n-2
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d[n-1] = -y[n-3] * x12[n2]/(x01[n2]*x02[n2]) + y[n-2] * x02[n2]/(x01[n2]*x12[n2]) -y[n-1] * (x02[n2]+x12[n2]) / (x02[n2]*x12[n2])
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return d
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## integer index shift of an array \f$ x'_i = x_{(i+n)\, \bmod\, {\rm len}\, x} \f$, with wrapping
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def ishift(x, m=0):
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"""shift index, e.g.:
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In [4]: dsp.ishift([0,1,2,3,4,5], 2)
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Out[4]: [2, 3, 4, 5, 0, 1] """
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import numpy
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L = len(x)
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y = numpy.zeros_like(x)
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n = m%L
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y[:L-n] = x[n:]
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y[L-n:] = x[:n]
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return y
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## \f$ [S_n(x)]_i \rightarrow x_{i+n} \f$ \n Shifter wraps ishift() ir fshift() with fixed n as a circular buffer (http://en.wikipedia.org/wiki/Circular_buffer ) \n For fixed length, the frequency domain phase ramp is precomputed, so it will be faster for repeated use.
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class Shifter(object):
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## number of indices to shift:
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def __init__(self, n, length = None):
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## \f$n\f$ is the number of indices to shift
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self.n = n
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self.length = length
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if isinstance(n, (int, long)):
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F = lambda x: ishift(x, self.n)
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else:
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if length is None:
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F = lambda x: fshift(x, self.n)
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else:
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f_shifter = fshifter(self.length, self.n)
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F = lambda x: fftpack.ifft(fftpack.fft(x)*f_shifter)
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pass
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self.F = F
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return None
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## int(self) = self.n
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def __int__(self):
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return self.n
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## float(self) = self.n
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def __float__(self):
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return self.n
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## len(self) = self.length, which is optional\n If self.length is not None, then the shifter is created at __init__(), not __call__().
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def __len__(self):
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return self.length if self.length else 0
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## inverse shift
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def __invert__(self):
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return self.__class__(-self.n)
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## self(n)(x) = ::ishift(x, self.n)
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def __call__(self, x):
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return self.F(x)
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pass
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