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#!/usr/bin/env python
# Created by Pearu Peterson, September 2002
from __future__ import division, print_function, absolute_import
__usage__ = """
Build fftpack:
python setup_fftpack.py build
Run tests if scipy is installed:
python -c 'import scipy;scipy.fftpack.test(<level>)'
Run tests if fftpack is not installed:
python tests/test_pseudo_diffs.py [<level>]
"""
from numpy.testing import (TestCase, assert_equal, assert_almost_equal,
assert_array_almost_equal, run_module_suite)
from scipy.fftpack import (diff, fft, ifft, tilbert, itilbert, hilbert,
ihilbert, shift, fftfreq, cs_diff, sc_diff,
ss_diff, cc_diff)
import numpy as np
from numpy import arange, sin, cos, pi, exp, tanh, sum, sign
from numpy.random import random
def direct_diff(x,k=1,period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2*pi
w = fftfreq(n)*2j*pi/period*n
if k < 0:
w = 1 / w**k
w[0] = 0.0
else:
w = w**k
if n > 2000:
w[250:n-250] = 0.0
return ifft(w*fx).real
def direct_tilbert(x,h=1,period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2*pi
w = fftfreq(n)*h*2*pi/period*n
w[0] = 1
w = 1j/tanh(w)
w[0] = 0j
return ifft(w*fx)
def direct_itilbert(x,h=1,period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2*pi
w = fftfreq(n)*h*2*pi/period*n
w = -1j*tanh(w)
return ifft(w*fx)
def direct_hilbert(x):
fx = fft(x)
n = len(fx)
w = fftfreq(n)*n
w = 1j*sign(w)
return ifft(w*fx)
def direct_ihilbert(x):
return -direct_hilbert(x)
def direct_shift(x,a,period=None):
n = len(x)
if period is None:
k = fftfreq(n)*1j*n
else:
k = fftfreq(n)*2j*pi/period*n
return ifft(fft(x)*exp(k*a)).real
class TestDiff(TestCase):
def test_definition(self):
for n in [16,17,64,127,32]:
x = arange(n)*2*pi/n
assert_array_almost_equal(diff(sin(x)),direct_diff(sin(x)))
assert_array_almost_equal(diff(sin(x),2),direct_diff(sin(x),2))
assert_array_almost_equal(diff(sin(x),3),direct_diff(sin(x),3))
assert_array_almost_equal(diff(sin(x),4),direct_diff(sin(x),4))
assert_array_almost_equal(diff(sin(x),5),direct_diff(sin(x),5))
assert_array_almost_equal(diff(sin(2*x),3),direct_diff(sin(2*x),3))
assert_array_almost_equal(diff(sin(2*x),4),direct_diff(sin(2*x),4))
assert_array_almost_equal(diff(cos(x)),direct_diff(cos(x)))
assert_array_almost_equal(diff(cos(x),2),direct_diff(cos(x),2))
assert_array_almost_equal(diff(cos(x),3),direct_diff(cos(x),3))
assert_array_almost_equal(diff(cos(x),4),direct_diff(cos(x),4))
assert_array_almost_equal(diff(cos(2*x)),direct_diff(cos(2*x)))
assert_array_almost_equal(diff(sin(x*n/8)),direct_diff(sin(x*n/8)))
assert_array_almost_equal(diff(cos(x*n/8)),direct_diff(cos(x*n/8)))
for k in range(5):
assert_array_almost_equal(diff(sin(4*x),k),direct_diff(sin(4*x),k))
assert_array_almost_equal(diff(cos(4*x),k),direct_diff(cos(4*x),k))
def test_period(self):
for n in [17,64]:
x = arange(n)/float(n)
assert_array_almost_equal(diff(sin(2*pi*x),period=1),
2*pi*cos(2*pi*x))
assert_array_almost_equal(diff(sin(2*pi*x),3,period=1),
-(2*pi)**3*cos(2*pi*x))
def test_sin(self):
for n in [32,64,77]:
x = arange(n)*2*pi/n
assert_array_almost_equal(diff(sin(x)),cos(x))
assert_array_almost_equal(diff(cos(x)),-sin(x))
assert_array_almost_equal(diff(sin(x),2),-sin(x))
assert_array_almost_equal(diff(sin(x),4),sin(x))
assert_array_almost_equal(diff(sin(4*x)),4*cos(4*x))
assert_array_almost_equal(diff(sin(sin(x))),cos(x)*cos(sin(x)))
def test_expr(self):
for n in [64,77,100,128,256,512,1024,2048,4096,8192][:5]:
x = arange(n)*2*pi/n
f = sin(x)*cos(4*x)+exp(sin(3*x))
df = cos(x)*cos(4*x)-4*sin(x)*sin(4*x)+3*cos(3*x)*exp(sin(3*x))
ddf = -17*sin(x)*cos(4*x)-8*cos(x)*sin(4*x)\
- 9*sin(3*x)*exp(sin(3*x))+9*cos(3*x)**2*exp(sin(3*x))
d1 = diff(f)
assert_array_almost_equal(d1,df)
assert_array_almost_equal(diff(df),ddf)
assert_array_almost_equal(diff(f,2),ddf)
assert_array_almost_equal(diff(ddf,-1),df)
def test_expr_large(self):
for n in [2048,4096]:
x = arange(n)*2*pi/n
f = sin(x)*cos(4*x)+exp(sin(3*x))
df = cos(x)*cos(4*x)-4*sin(x)*sin(4*x)+3*cos(3*x)*exp(sin(3*x))
ddf = -17*sin(x)*cos(4*x)-8*cos(x)*sin(4*x)\
- 9*sin(3*x)*exp(sin(3*x))+9*cos(3*x)**2*exp(sin(3*x))
assert_array_almost_equal(diff(f),df)
assert_array_almost_equal(diff(df),ddf)
assert_array_almost_equal(diff(ddf,-1),df)
assert_array_almost_equal(diff(f,2),ddf)
def test_int(self):
n = 64
x = arange(n)*2*pi/n
assert_array_almost_equal(diff(sin(x),-1),-cos(x))
assert_array_almost_equal(diff(sin(x),-2),-sin(x))
assert_array_almost_equal(diff(sin(x),-4),sin(x))
assert_array_almost_equal(diff(2*cos(2*x),-1),sin(2*x))
def test_random_even(self):
for k in [0,2,4,6]:
for n in [60,32,64,56,55]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
# zeroing Nyquist mode:
f = diff(diff(f,1),-1)
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(diff(diff(f,k),-k),f)
assert_array_almost_equal(diff(diff(f,-k),k),f)
def test_random_odd(self):
for k in [0,1,2,3,4,5,6]:
for n in [33,65,55]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(diff(diff(f,k),-k),f)
assert_array_almost_equal(diff(diff(f,-k),k),f)
def test_zero_nyquist(self):
for k in [0,1,2,3,4,5,6]:
for n in [32,33,64,56,55]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
# zeroing Nyquist mode:
f = diff(diff(f,1),-1)
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(diff(diff(f,k),-k),f)
assert_array_almost_equal(diff(diff(f,-k),k),f)
class TestTilbert(TestCase):
def test_definition(self):
for h in [0.1,0.5,1,5.5,10]:
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
y = tilbert(sin(x),h)
y1 = direct_tilbert(sin(x),h)
assert_array_almost_equal(y,y1)
assert_array_almost_equal(tilbert(sin(x),h),
direct_tilbert(sin(x),h))
assert_array_almost_equal(tilbert(sin(2*x),h),
direct_tilbert(sin(2*x),h))
def test_random_even(self):
for h in [0.1,0.5,1,5.5,10]:
for n in [32,64,56]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(direct_tilbert(direct_itilbert(f,h),h),f)
def test_random_odd(self):
for h in [0.1,0.5,1,5.5,10]:
for n in [33,65,55]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(itilbert(tilbert(f,h),h),f)
assert_array_almost_equal(tilbert(itilbert(f,h),h),f)
class TestITilbert(TestCase):
def test_definition(self):
for h in [0.1,0.5,1,5.5,10]:
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
y = itilbert(sin(x),h)
y1 = direct_itilbert(sin(x),h)
assert_array_almost_equal(y,y1)
assert_array_almost_equal(itilbert(sin(x),h),
direct_itilbert(sin(x),h))
assert_array_almost_equal(itilbert(sin(2*x),h),
direct_itilbert(sin(2*x),h))
class TestHilbert(TestCase):
def test_definition(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
y = hilbert(sin(x))
y1 = direct_hilbert(sin(x))
assert_array_almost_equal(y,y1)
assert_array_almost_equal(hilbert(sin(2*x)),
direct_hilbert(sin(2*x)))
def test_tilbert_relation(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
f = sin(x)+cos(2*x)*sin(x)
y = hilbert(f)
y1 = direct_hilbert(f)
assert_array_almost_equal(y,y1)
y2 = tilbert(f,h=10)
assert_array_almost_equal(y,y2)
def test_random_odd(self):
for n in [33,65,55]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(ihilbert(hilbert(f)),f)
assert_array_almost_equal(hilbert(ihilbert(f)),f)
def test_random_even(self):
for n in [32,64,56]:
f = random((n,))
af = sum(f,axis=0)/n
f = f-af
# zeroing Nyquist mode:
f = diff(diff(f,1),-1)
assert_almost_equal(sum(f,axis=0),0.0)
assert_array_almost_equal(direct_hilbert(direct_ihilbert(f)),f)
assert_array_almost_equal(hilbert(ihilbert(f)),f)
class TestIHilbert(TestCase):
def test_definition(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
y = ihilbert(sin(x))
y1 = direct_ihilbert(sin(x))
assert_array_almost_equal(y,y1)
assert_array_almost_equal(ihilbert(sin(2*x)),
direct_ihilbert(sin(2*x)))
def test_itilbert_relation(self):
for n in [16,17,64,127]:
x = arange(n)*2*pi/n
f = sin(x)+cos(2*x)*sin(x)
y = ihilbert(f)
y1 = direct_ihilbert(f)
assert_array_almost_equal(y,y1)
y2 = itilbert(f,h=10)
assert_array_almost_equal(y,y2)
class TestShift(TestCase):
def test_definition(self):
for n in [18,17,64,127,32,2048,256]:
x = arange(n)*2*pi/n
for a in [0.1,3]:
assert_array_almost_equal(shift(sin(x),a),direct_shift(sin(x),a))
assert_array_almost_equal(shift(sin(x),a),sin(x+a))
assert_array_almost_equal(shift(cos(x),a),cos(x+a))
assert_array_almost_equal(shift(cos(2*x)+sin(x),a),
cos(2*(x+a))+sin(x+a))
assert_array_almost_equal(shift(exp(sin(x)),a),exp(sin(x+a)))
assert_array_almost_equal(shift(sin(x),2*pi),sin(x))
assert_array_almost_equal(shift(sin(x),pi),-sin(x))
assert_array_almost_equal(shift(sin(x),pi/2),cos(x))
class TestOverwrite(object):
"""Check input overwrite behavior """
real_dtypes = [np.float32, np.float64]
dtypes = real_dtypes + [np.complex64, np.complex128]
def _check(self, x, routine, *args, **kwargs):
x2 = x.copy()
routine(x2, *args, **kwargs)
sig = routine.__name__
if args:
sig += repr(args)
if kwargs:
sig += repr(kwargs)
assert_equal(x2, x, err_msg="spurious overwrite in %s" % sig)
def _check_1d(self, routine, dtype, shape, *args, **kwargs):
np.random.seed(1234)
if np.issubdtype(dtype, np.complexfloating):
data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
else:
data = np.random.randn(*shape)
data = data.astype(dtype)
self._check(data, routine, *args, **kwargs)
def test_diff(self):
for dtype in self.dtypes:
self._check_1d(diff, dtype, (16,))
def test_tilbert(self):
for dtype in self.dtypes:
self._check_1d(tilbert, dtype, (16,), 1.6)
def test_itilbert(self):
for dtype in self.dtypes:
self._check_1d(itilbert, dtype, (16,), 1.6)
def test_hilbert(self):
for dtype in self.dtypes:
self._check_1d(hilbert, dtype, (16,))
def test_cs_diff(self):
for dtype in self.dtypes:
self._check_1d(cs_diff, dtype, (16,), 1.0, 4.0)
def test_sc_diff(self):
for dtype in self.dtypes:
self._check_1d(sc_diff, dtype, (16,), 1.0, 4.0)
def test_ss_diff(self):
for dtype in self.dtypes:
self._check_1d(ss_diff, dtype, (16,), 1.0, 4.0)
def test_cc_diff(self):
for dtype in self.dtypes:
self._check_1d(cc_diff, dtype, (16,), 1.0, 4.0)
def test_shift(self):
for dtype in self.dtypes:
self._check_1d(shift, dtype, (16,), 1.0)
if __name__ == "__main__":
run_module_suite()
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