test.py

import pypocketfft
import pyfftw
import numpy as np
import pytest
from numpy.testing import assert_

pmp = pytest.mark.parametrize

shapes1D = ((10,), (127,))
shapes2D = ((128, 128), (128, 129), (1, 129), (129,1))
shapes3D = ((32,17,39),)
shapes = shapes1D+shapes2D+shapes3D
len1D=range(1,2048)

def _l2error(a,b):
    return np.sqrt(np.sum(np.abs(a-b)**2)/np.sum(np.abs(a)**2))

def fftn(a, axes=None, inorm=0, inplace=False, nthreads=1):
    return pypocketfft.c2c(a, axes=axes, forward=True, inorm=inorm,
                           inplace=inplace, nthreads=nthreads)

def ifftn(a, axes=None, inorm=0, inplace=False, nthreads=1):
    return pypocketfft.c2c(a, axes=axes, forward=False, inorm=inorm,
                           inplace=inplace, nthreads=nthreads)

def rfftn(a, axes=None, inorm=0, nthreads=1):
    return pypocketfft.r2c(a, axes=axes, forward=True, inorm=inorm,
                           nthreads=nthreads)

def irfftn(a, axes=None, lastsize=0, inorm=0, nthreads=1):
    return pypocketfft.c2r(a, axes=axes, lastsize=lastsize,forward=False,
                           inorm=inorm, nthreads=nthreads)

def rfft_scipy(a, axis, inorm=0, inplace=False, nthreads=1):
    return pypocketfft.r2r_fftpack(a, axes=(axis,), input_halfcomplex=False,
                                   forward=True, inorm=inorm, inplace=inplace,
                                   nthreads=nthreads)
def irfft_scipy(a, axis, inorm=0, inplace=False, nthreads=1):
    return pypocketfft.r2r_fftpack(a, axes=(axis,), input_halfcomplex=True,
                                   forward=False, inorm=inorm, inplace=inplace,
                                   nthreads=nthreads)
@pmp("len", len1D)
@pmp("inorm", [0,1,2])
def test1D(len, inorm):
    a=np.random.rand(len)-0.5 + 1j*np.random.rand(len)-0.5j
    b=a.astype(np.complex64)
    c=a.astype(np.complex256)
    assert_(_l2error(a, ifftn(fftn(c,inorm=inorm), inorm=2-inorm))<1e-18)
    assert_(_l2error(a, ifftn(fftn(a,inorm=inorm), inorm=2-inorm))<1.5e-15)
    assert_(_l2error(a.real, ifftn(fftn(a.real,inorm=inorm), inorm=2-inorm))<1.5e-15)
    assert_(_l2error(a.real, fftn(ifftn(a.real,inorm=inorm), inorm=2-inorm))<1.5e-15)
    assert_(_l2error(a.real, irfftn(rfftn(a.real,inorm=inorm), inorm=2-inorm,lastsize=len))<1.5e-15)
    tmp=a.copy()
    assert_ (ifftn(fftn(tmp, inplace=True, inorm=inorm), inplace=True, inorm=2-inorm) is tmp)
    assert_(_l2error(tmp, a)<1.5e-15)
    assert_(_l2error(b, ifftn(fftn(b, inorm=inorm), inorm=2-inorm))<6e-7)
    assert_(_l2error(b.real, ifftn(fftn(b.real,inorm=inorm), inorm=2-inorm))<6e-7)
    assert_(_l2error(b.real, fftn(ifftn(b.real,inorm=inorm), inorm=2-inorm))<6e-7)
    assert_(_l2error(b.real, irfftn(rfftn(b.real, inorm=inorm), lastsize=len, inorm=2-inorm))<6e-7)
    tmp=b.copy()
    assert_ (ifftn(fftn(tmp, inplace=True, inorm=inorm), inplace=True, inorm=2-inorm) is tmp)
    assert_(_l2error(tmp, b)<6e-7)

@pmp("shp", shapes)
@pmp("nthreads", (0,1,2))
def test_fftn(shp, nthreads):
    a=np.random.rand(*shp)-0.5 + 1j*np.random.rand(*shp)-0.5j
    assert_(_l2error(pyfftw.interfaces.numpy_fft.fftn(a), fftn(a, nthreads=nthreads))<1e-15)
    a=a.astype(np.complex64)
    assert_(_l2error(pyfftw.interfaces.numpy_fft.fftn(a), fftn(a, nthreads=nthreads))<5e-7)

@pmp("shp", shapes2D)
@pmp("axes", ((0,),(1,),(0,1),(1,0)))
def test_fftn2D(shp, axes):
    a=np.random.rand(*shp)-0.5 + 1j*np.random.rand(*shp)-0.5j
    assert_(_l2error(pyfftw.interfaces.numpy_fft.fftn(a, axes=axes), fftn(a, axes=axes))<1e-15)
    a=a.astype(np.complex64)
    assert_(_l2error(pyfftw.interfaces.numpy_fft.fftn(a, axes=axes), fftn(a, axes=axes))<5e-7)

@pmp("shp", shapes)
def test_rfftn(shp):
    a=np.random.rand(*shp)-0.5
    assert_(_l2error(pyfftw.interfaces.numpy_fft.rfftn(a), rfftn(a))<1e-15)
    a=a.astype(np.float32)
    assert_(_l2error(pyfftw.interfaces.numpy_fft.rfftn(a), rfftn(a))<5e-7)

@pmp("shp", shapes)
def test_rfft_scipy(shp):
    for i in range(len(shp)):
        a=np.random.rand(*shp)-0.5
        assert_(_l2error(pyfftw.interfaces.scipy_fftpack.rfft(a,axis=i), rfft_scipy(a,axis=i))<1e-15)
        assert_(_l2error(pyfftw.interfaces.scipy_fftpack.irfft(a,axis=i), irfft_scipy(a,axis=i,inorm=2))<1e-15)

@pmp("shp", shapes2D)
@pmp("axes", ((0,),(1,),(0,1),(1,0)))
def test_rfftn2D(shp, axes):
    a=np.random.rand(*shp)-0.5
    assert_(_l2error(pyfftw.interfaces.numpy_fft.rfftn(a, axes=axes), rfftn(a, axes=axes))<1e-15)
    a=a.astype(np.float32)
    assert_(_l2error(pyfftw.interfaces.numpy_fft.rfftn(a, axes=axes), rfftn(a, axes=axes))<5e-7)

@pmp("shp", shapes)
def test_identity(shp):
    a=np.random.rand(*shp)-0.5 + 1j*np.random.rand(*shp)-0.5j
    assert_(_l2error(ifftn(fftn(a),inorm=2), a)<1.5e-15)
    assert_(_l2error(ifftn(fftn(a.real),inorm=2), a.real)<1.5e-15)
    assert_(_l2error(fftn(ifftn(a.real),inorm=2), a.real)<1.5e-15)
    tmp=a.copy()
    assert_ (ifftn(fftn(tmp, inplace=True), inorm=2, inplace=True) is tmp)
    assert_(_l2error(tmp, a)<1.5e-15)
    a=a.astype(np.complex64)
    assert_(_l2error(ifftn(fftn(a),inorm=2), a)<6e-7)

@pmp("shp", shapes)
def test_identity_r(shp):
    a=np.random.rand(*shp)-0.5
    b=a.astype(np.float32)
    for ax in range(a.ndim):
        n = a.shape[ax]
        assert_(_l2error(irfftn(rfftn(a,(ax,)),(ax,),lastsize=n,inorm=2), a)<1e-15)
        assert_(_l2error(irfftn(rfftn(b,(ax,)),(ax,),lastsize=n,inorm=2), b)<5e-7)

@pmp("shp", shapes)
def test_identity_r2(shp):
    a=np.random.rand(*shp)-0.5 + 1j*np.random.rand(*shp)-0.5j
    a=rfftn(irfftn(a))
    assert_(_l2error(rfftn(irfftn(a),inorm=2), a)<1e-15)

@pmp("shp", shapes2D+shapes3D)
def test_hartley2(shp):
    a=np.random.rand(*shp)-0.5
    v1 = pypocketfft.hartley2(a)
    v2 = fftn(a.astype(np.complex128))
    v2 = v2.real+v2.imag
    assert_(_l2error(v1, v2)<1e-15)

@pmp("shp", shapes)
def test_hartley_identity(shp):
    a=np.random.rand(*shp)-0.5
    v1 = pypocketfft.hartley(pypocketfft.hartley(a))/a.size
    assert_(_l2error(a, v1)<1e-15)

@pmp("shp", shapes)
def test_hartley2_identity(shp):
    a=np.random.rand(*shp)-0.5
    v1 = pypocketfft.hartley2(pypocketfft.hartley2(a))/a.size
    assert_(_l2error(a, v1)<1e-15)
    v1 = a.copy()
    assert_ (pypocketfft.hartley2(pypocketfft.hartley2(v1, inplace=True), inorm=2, inplace=True) is v1)
    assert_(_l2error(a, v1)<1e-15)

@pmp("shp", shapes2D)
@pmp("axes", ((0,),(1,),(0,1),(1,0)))
def test_hartley2_2D(shp, axes):
    a=np.random.rand(*shp)-0.5
    assert_(_l2error(pypocketfft.hartley2(pypocketfft.hartley2(a, axes=axes), axes=axes, inorm=2),a)<1e-15)