manyi/venv/Lib/site-packages/scipy/fftpack/tests/test_basic.py

# 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()'
Run tests if fftpack is not installed:
  python tests/test_basic.py
"""

from numpy.testing import (assert_, assert_equal, assert_array_almost_equal,
                           assert_array_almost_equal_nulp, assert_array_less)
import pytest
from pytest import raises as assert_raises
from scipy.fftpack import ifft, fft, fftn, ifftn, rfft, irfft, fft2
from scipy.fftpack import _fftpack as fftpack
from scipy.fftpack.basic import _is_safe_size

from numpy import (arange, add, array, asarray, zeros, dot, exp, pi,
                   swapaxes, double, cdouble)
import numpy as np
import numpy.fft
from numpy.random import rand

# "large" composite numbers supported by FFTPACK
LARGE_COMPOSITE_SIZES = [
    2**13,
    2**5 * 3**5,
    2**3 * 3**3 * 5**2,
]
SMALL_COMPOSITE_SIZES = [
    2,
    2*3*5,
    2*2*3*3,
]
# prime
LARGE_PRIME_SIZES = [
    2011
]
SMALL_PRIME_SIZES = [
    29
]


def _assert_close_in_norm(x, y, rtol, size, rdt):
    # helper function for testing
    err_msg = "size: %s  rdt: %s" % (size, rdt)
    assert_array_less(np.linalg.norm(x - y), rtol*np.linalg.norm(x), err_msg)


def random(size):
    return rand(*size)


def get_mat(n):
    data = arange(n)
    data = add.outer(data, data)
    return data


def direct_dft(x):
    x = asarray(x)
    n = len(x)
    y = zeros(n, dtype=cdouble)
    w = -arange(n)*(2j*pi/n)
    for i in range(n):
        y[i] = dot(exp(i*w), x)
    return y


def direct_idft(x):
    x = asarray(x)
    n = len(x)
    y = zeros(n, dtype=cdouble)
    w = arange(n)*(2j*pi/n)
    for i in range(n):
        y[i] = dot(exp(i*w), x)/n
    return y


def direct_dftn(x):
    x = asarray(x)
    for axis in range(len(x.shape)):
        x = fft(x, axis=axis)
    return x


def direct_idftn(x):
    x = asarray(x)
    for axis in range(len(x.shape)):
        x = ifft(x, axis=axis)
    return x


def direct_rdft(x):
    x = asarray(x)
    n = len(x)
    w = -arange(n)*(2j*pi/n)
    r = zeros(n, dtype=double)
    for i in range(n//2+1):
        y = dot(exp(i*w), x)
        if i:
            r[2*i-1] = y.real
            if 2*i < n:
                r[2*i] = y.imag
        else:
            r[0] = y.real
    return r


def direct_irdft(x):
    x = asarray(x)
    n = len(x)
    x1 = zeros(n, dtype=cdouble)
    for i in range(n//2+1):
        if i:
            if 2*i < n:
                x1[i] = x[2*i-1] + 1j*x[2*i]
                x1[n-i] = x[2*i-1] - 1j*x[2*i]
            else:
                x1[i] = x[2*i-1]
        else:
            x1[0] = x[0]
    return direct_idft(x1).real


class _TestFFTBase(object):
    def setup_method(self):
        self.cdt = None
        self.rdt = None
        np.random.seed(1234)

    def test_definition(self):
        x = np.array([1,2,3,4+1j,1,2,3,4+2j], dtype=self.cdt)
        y = fft(x)
        assert_equal(y.dtype, self.cdt)
        y1 = direct_dft(x)
        assert_array_almost_equal(y,y1)
        x = np.array([1,2,3,4+0j,5], dtype=self.cdt)
        assert_array_almost_equal(fft(x),direct_dft(x))

    def test_n_argument_real(self):
        x1 = np.array([1,2,3,4], dtype=self.rdt)
        x2 = np.array([1,2,3,4], dtype=self.rdt)
        y = fft([x1,x2],n=4)
        assert_equal(y.dtype, self.cdt)
        assert_equal(y.shape,(2,4))
        assert_array_almost_equal(y[0],direct_dft(x1))
        assert_array_almost_equal(y[1],direct_dft(x2))

    def _test_n_argument_complex(self):
        x1 = np.array([1,2,3,4+1j], dtype=self.cdt)
        x2 = np.array([1,2,3,4+1j], dtype=self.cdt)
        y = fft([x1,x2],n=4)
        assert_equal(y.dtype, self.cdt)
        assert_equal(y.shape,(2,4))
        assert_array_almost_equal(y[0],direct_dft(x1))
        assert_array_almost_equal(y[1],direct_dft(x2))

    def test_djbfft(self):
        for i in range(2,14):
            n = 2**i
            x = list(range(n))
            y = fftpack.zfft(x)
            y2 = numpy.fft.fft(x)
            assert_array_almost_equal(y,y2)
            y = fftpack.zrfft(x)
            assert_array_almost_equal(y,y2)

    def test_invalid_sizes(self):
        assert_raises(ValueError, fft, [])
        assert_raises(ValueError, fft, [[1,1],[2,2]], -5)

    def test__is_safe_size(self):
        vals = [(0, True), (1, True), (2, True), (3, True), (4, True), (5, True), (6, True), (7, False),
                (15, True), (16, True), (17, False), (18, True), (21, False), (25, True), (50, True),
                (120, True), (210, False)]
        for n, is_safe in vals:
            assert_equal(_is_safe_size(n), is_safe)


class TestDoubleFFT(_TestFFTBase):
    def setup_method(self):
        self.cdt = np.cdouble
        self.rdt = np.double


class TestSingleFFT(_TestFFTBase):
    def setup_method(self):
        self.cdt = np.complex64
        self.rdt = np.float32

    @pytest.mark.xfail(run=False, reason="single-precision FFT implementation is partially disabled, until accuracy issues with large prime powers are resolved")
    def test_notice(self):
        pass


class TestFloat16FFT(object):

    def test_1_argument_real(self):
        x1 = np.array([1, 2, 3, 4], dtype=np.float16)
        y = fft(x1, n=4)
        assert_equal(y.dtype, np.complex64)
        assert_equal(y.shape, (4, ))
        assert_array_almost_equal(y, direct_dft(x1.astype(np.float32)))

    def test_n_argument_real(self):
        x1 = np.array([1, 2, 3, 4], dtype=np.float16)
        x2 = np.array([1, 2, 3, 4], dtype=np.float16)
        y = fft([x1, x2], n=4)
        assert_equal(y.dtype, np.complex64)
        assert_equal(y.shape, (2, 4))
        assert_array_almost_equal(y[0], direct_dft(x1.astype(np.float32)))
        assert_array_almost_equal(y[1], direct_dft(x2.astype(np.float32)))


class _TestIFFTBase(object):
    def setup_method(self):
        np.random.seed(1234)

    def test_definition(self):
        x = np.array([1,2,3,4+1j,1,2,3,4+2j], self.cdt)
        y = ifft(x)
        y1 = direct_idft(x)
        assert_equal(y.dtype, self.cdt)
        assert_array_almost_equal(y,y1)

        x = np.array([1,2,3,4+0j,5], self.cdt)
        assert_array_almost_equal(ifft(x),direct_idft(x))

    def test_definition_real(self):
        x = np.array([1,2,3,4,1,2,3,4], self.rdt)
        y = ifft(x)
        assert_equal(y.dtype, self.cdt)
        y1 = direct_idft(x)
        assert_array_almost_equal(y,y1)

        x = np.array([1,2,3,4,5], dtype=self.rdt)
        assert_equal(y.dtype, self.cdt)
        assert_array_almost_equal(ifft(x),direct_idft(x))

    def test_djbfft(self):
        for i in range(2,14):
            n = 2**i
            x = list(range(n))
            y = fftpack.zfft(x,direction=-1)
            y2 = numpy.fft.ifft(x)
            assert_array_almost_equal(y,y2)
            y = fftpack.zrfft(x,direction=-1)
            assert_array_almost_equal(y,y2)

    def test_random_complex(self):
        for size in [1,51,111,100,200,64,128,256,1024]:
            x = random([size]).astype(self.cdt)
            x = random([size]).astype(self.cdt) + 1j*x
            y1 = ifft(fft(x))
            y2 = fft(ifft(x))
            assert_equal(y1.dtype, self.cdt)
            assert_equal(y2.dtype, self.cdt)
            assert_array_almost_equal(y1, x)
            assert_array_almost_equal(y2, x)

    def test_random_real(self):
        for size in [1,51,111,100,200,64,128,256,1024]:
            x = random([size]).astype(self.rdt)
            y1 = ifft(fft(x))
            y2 = fft(ifft(x))
            assert_equal(y1.dtype, self.cdt)
            assert_equal(y2.dtype, self.cdt)
            assert_array_almost_equal(y1, x)
            assert_array_almost_equal(y2, x)

    def test_size_accuracy(self):
        # Sanity check for the accuracy for prime and non-prime sized inputs
        if self.rdt == np.float32:
            rtol = 1e-5
        elif self.rdt == np.float64:
            rtol = 1e-10

        for size in LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES:
            np.random.seed(1234)
            x = np.random.rand(size).astype(self.rdt)
            y = ifft(fft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)
            y = fft(ifft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)

            x = (x + 1j*np.random.rand(size)).astype(self.cdt)
            y = ifft(fft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)
            y = fft(ifft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)

    def test_invalid_sizes(self):
        assert_raises(ValueError, ifft, [])
        assert_raises(ValueError, ifft, [[1,1],[2,2]], -5)


class TestDoubleIFFT(_TestIFFTBase):
    def setup_method(self):
        self.cdt = np.cdouble
        self.rdt = np.double


class TestSingleIFFT(_TestIFFTBase):
    def setup_method(self):
        self.cdt = np.complex64
        self.rdt = np.float32


class _TestRFFTBase(object):
    def setup_method(self):
        np.random.seed(1234)

    def test_definition(self):
        for t in [[1, 2, 3, 4, 1, 2, 3, 4], [1, 2, 3, 4, 1, 2, 3, 4, 5]]:
            x = np.array(t, dtype=self.rdt)
            y = rfft(x)
            y1 = direct_rdft(x)
            assert_array_almost_equal(y,y1)
            assert_equal(y.dtype, self.rdt)

    def test_djbfft(self):
        from numpy.fft import fft as numpy_fft
        for i in range(2,14):
            n = 2**i
            x = list(range(n))
            y2 = numpy_fft(x)
            y1 = zeros((n,),dtype=double)
            y1[0] = y2[0].real
            y1[-1] = y2[n//2].real
            for k in range(1, n//2):
                y1[2*k-1] = y2[k].real
                y1[2*k] = y2[k].imag
            y = fftpack.drfft(x)
            assert_array_almost_equal(y,y1)

    def test_invalid_sizes(self):
        assert_raises(ValueError, rfft, [])
        assert_raises(ValueError, rfft, [[1,1],[2,2]], -5)

    # See gh-5790
    class MockSeries(object):
        def __init__(self, data):
            self.data = np.asarray(data)

        def __getattr__(self, item):
            try:
                return getattr(self.data, item)
            except AttributeError:
                raise AttributeError(("'MockSeries' object "
                                      "has no attribute '{attr}'".
                                      format(attr=item)))

    def test_non_ndarray_with_dtype(self):
        x = np.array([1., 2., 3., 4., 5.])
        xs = _TestRFFTBase.MockSeries(x)

        expected = [1, 2, 3, 4, 5]
        out = rfft(xs)

        # Data should not have been overwritten
        assert_equal(x, expected)
        assert_equal(xs.data, expected)

class TestRFFTDouble(_TestRFFTBase):
    def setup_method(self):
        self.cdt = np.cdouble
        self.rdt = np.double


class TestRFFTSingle(_TestRFFTBase):
    def setup_method(self):
        self.cdt = np.complex64
        self.rdt = np.float32


class _TestIRFFTBase(object):
    def setup_method(self):
        np.random.seed(1234)

    def test_definition(self):
        x1 = [1,2,3,4,1,2,3,4]
        x1_1 = [1,2+3j,4+1j,2+3j,4,2-3j,4-1j,2-3j]
        x2 = [1,2,3,4,1,2,3,4,5]
        x2_1 = [1,2+3j,4+1j,2+3j,4+5j,4-5j,2-3j,4-1j,2-3j]

        def _test(x, xr):
            y = irfft(np.array(x, dtype=self.rdt))
            y1 = direct_irdft(x)
            assert_equal(y.dtype, self.rdt)
            assert_array_almost_equal(y,y1, decimal=self.ndec)
            assert_array_almost_equal(y,ifft(xr), decimal=self.ndec)

        _test(x1, x1_1)
        _test(x2, x2_1)

    def test_djbfft(self):
        from numpy.fft import ifft as numpy_ifft
        for i in range(2,14):
            n = 2**i
            x = list(range(n))
            x1 = zeros((n,),dtype=cdouble)
            x1[0] = x[0]
            for k in range(1, n//2):
                x1[k] = x[2*k-1]+1j*x[2*k]
                x1[n-k] = x[2*k-1]-1j*x[2*k]
            x1[n//2] = x[-1]
            y1 = numpy_ifft(x1)
            y = fftpack.drfft(x,direction=-1)
            assert_array_almost_equal(y,y1)

    def test_random_real(self):
        for size in [1,51,111,100,200,64,128,256,1024]:
            x = random([size]).astype(self.rdt)
            y1 = irfft(rfft(x))
            y2 = rfft(irfft(x))
            assert_equal(y1.dtype, self.rdt)
            assert_equal(y2.dtype, self.rdt)
            assert_array_almost_equal(y1, x, decimal=self.ndec,
                                       err_msg="size=%d" % size)
            assert_array_almost_equal(y2, x, decimal=self.ndec,
                                       err_msg="size=%d" % size)

    def test_size_accuracy(self):
        # Sanity check for the accuracy for prime and non-prime sized inputs
        if self.rdt == np.float32:
            rtol = 1e-5
        elif self.rdt == np.float64:
            rtol = 1e-10

        for size in LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES:
            np.random.seed(1234)
            x = np.random.rand(size).astype(self.rdt)
            y = irfft(rfft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)
            y = rfft(irfft(x))
            _assert_close_in_norm(x, y, rtol, size, self.rdt)

    def test_invalid_sizes(self):
        assert_raises(ValueError, irfft, [])
        assert_raises(ValueError, irfft, [[1,1],[2,2]], -5)


# self.ndec is bogus; we should have a assert_array_approx_equal for number of
# significant digits

class TestIRFFTDouble(_TestIRFFTBase):
    def setup_method(self):
        self.cdt = np.cdouble
        self.rdt = np.double
        self.ndec = 14


class TestIRFFTSingle(_TestIRFFTBase):
    def setup_method(self):
        self.cdt = np.complex64
        self.rdt = np.float32
        self.ndec = 5


class Testfft2(object):
    def setup_method(self):
        np.random.seed(1234)

    def test_regression_244(self):
        """FFT returns wrong result with axes parameter."""
        # fftn (and hence fft2) used to break when both axes and shape were
        # used
        x = numpy.ones((4, 4, 2))
        y = fft2(x, shape=(8, 8), axes=(-3, -2))
        y_r = numpy.fft.fftn(x, s=(8, 8), axes=(-3, -2))
        assert_array_almost_equal(y, y_r)

    def test_invalid_sizes(self):
        assert_raises(ValueError, fft2, [[]])
        assert_raises(ValueError, fft2, [[1, 1], [2, 2]], (4, -3))


class TestFftnSingle(object):
    def setup_method(self):
        np.random.seed(1234)

    def test_definition(self):
        x = [[1, 2, 3],
             [4, 5, 6],
             [7, 8, 9]]
        y = fftn(np.array(x, np.float32))
        assert_(y.dtype == np.complex64,
                msg="double precision output with single precision")

        y_r = np.array(fftn(x), np.complex64)
        assert_array_almost_equal_nulp(y, y_r)

    @pytest.mark.parametrize('size', SMALL_COMPOSITE_SIZES + SMALL_PRIME_SIZES)
    def test_size_accuracy_small(self, size):
        x = np.random.rand(size, size) + 1j*np.random.rand(size, size)
        y1 = fftn(x.real.astype(np.float32))
        y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)

        assert_equal(y1.dtype, np.complex64)
        assert_array_almost_equal_nulp(y1, y2, 2000)

    @pytest.mark.parametrize('size', LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES)
    def test_size_accuracy_large(self, size):
        x = np.random.rand(size, 3) + 1j*np.random.rand(size, 3)
        y1 = fftn(x.real.astype(np.float32))
        y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)

        assert_equal(y1.dtype, np.complex64)
        assert_array_almost_equal_nulp(y1, y2, 2000)

    def test_definition_float16(self):
        x = [[1, 2, 3],
             [4, 5, 6],
             [7, 8, 9]]
        y = fftn(np.array(x, np.float16))
        assert_equal(y.dtype, np.complex64)
        y_r = np.array(fftn(x), np.complex64)
        assert_array_almost_equal_nulp(y, y_r)

    @pytest.mark.parametrize('size', SMALL_COMPOSITE_SIZES + SMALL_PRIME_SIZES)
    def test_float16_input_small(self, size):
        x = np.random.rand(size, size) + 1j*np.random.rand(size, size)
        y1 = fftn(x.real.astype(np.float16))
        y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)

        assert_equal(y1.dtype, np.complex64)
        assert_array_almost_equal_nulp(y1, y2, 5e5)

    @pytest.mark.parametrize('size', LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES)
    def test_float16_input_large(self, size):
        x = np.random.rand(size, 3) + 1j*np.random.rand(size, 3)
        y1 = fftn(x.real.astype(np.float16))
        y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)

        assert_equal(y1.dtype, np.complex64)
        assert_array_almost_equal_nulp(y1, y2, 2e6)


class TestFftn(object):
    def setup_method(self):
        np.random.seed(1234)

    def test_definition(self):
        x = [[1, 2, 3],
             [4, 5, 6],
             [7, 8, 9]]
        y = fftn(x)
        assert_array_almost_equal(y, direct_dftn(x))

        x = random((20, 26))
        assert_array_almost_equal(fftn(x), direct_dftn(x))

        x = random((5, 4, 3, 20))
        assert_array_almost_equal(fftn(x), direct_dftn(x))

    def test_axes_argument(self):
        # plane == ji_plane, x== kji_space
        plane1 = [[1, 2, 3],
                  [4, 5, 6],
                  [7, 8, 9]]
        plane2 = [[10, 11, 12],
                  [13, 14, 15],
                  [16, 17, 18]]
        plane3 = [[19, 20, 21],
                  [22, 23, 24],
                  [25, 26, 27]]
        ki_plane1 = [[1, 2, 3],
                     [10, 11, 12],
                     [19, 20, 21]]
        ki_plane2 = [[4, 5, 6],
                     [13, 14, 15],
                     [22, 23, 24]]
        ki_plane3 = [[7, 8, 9],
                     [16, 17, 18],
                     [25, 26, 27]]
        jk_plane1 = [[1, 10, 19],
                     [4, 13, 22],
                     [7, 16, 25]]
        jk_plane2 = [[2, 11, 20],
                     [5, 14, 23],
                     [8, 17, 26]]
        jk_plane3 = [[3, 12, 21],
                     [6, 15, 24],
                     [9, 18, 27]]
        kj_plane1 = [[1, 4, 7],
                     [10, 13, 16], [19, 22, 25]]
        kj_plane2 = [[2, 5, 8],
                     [11, 14, 17], [20, 23, 26]]
        kj_plane3 = [[3, 6, 9],
                     [12, 15, 18], [21, 24, 27]]
        ij_plane1 = [[1, 4, 7],
                     [2, 5, 8],
                     [3, 6, 9]]
        ij_plane2 = [[10, 13, 16],
                     [11, 14, 17],
                     [12, 15, 18]]
        ij_plane3 = [[19, 22, 25],
                     [20, 23, 26],
                     [21, 24, 27]]
        ik_plane1 = [[1, 10, 19],
                     [2, 11, 20],
                     [3, 12, 21]]
        ik_plane2 = [[4, 13, 22],
                     [5, 14, 23],
                     [6, 15, 24]]
        ik_plane3 = [[7, 16, 25],
                     [8, 17, 26],
                     [9, 18, 27]]
        ijk_space = [jk_plane1, jk_plane2, jk_plane3]
        ikj_space = [kj_plane1, kj_plane2, kj_plane3]
        jik_space = [ik_plane1, ik_plane2, ik_plane3]
        jki_space = [ki_plane1, ki_plane2, ki_plane3]
        kij_space = [ij_plane1, ij_plane2, ij_plane3]
        x = array([plane1, plane2, plane3])

        assert_array_almost_equal(fftn(x),
                                  fftn(x, axes=(-3, -2, -1)))  # kji_space
        assert_array_almost_equal(fftn(x), fftn(x, axes=(0, 1, 2)))
        assert_array_almost_equal(fftn(x, axes=(0, 2)), fftn(x, axes=(0, -1)))
        y = fftn(x, axes=(2, 1, 0))  # ijk_space
        assert_array_almost_equal(swapaxes(y, -1, -3), fftn(ijk_space))
        y = fftn(x, axes=(2, 0, 1))  # ikj_space
        assert_array_almost_equal(swapaxes(swapaxes(y, -1, -3), -1, -2),
                                  fftn(ikj_space))
        y = fftn(x, axes=(1, 2, 0))  # jik_space
        assert_array_almost_equal(swapaxes(swapaxes(y, -1, -3), -3, -2),
                                  fftn(jik_space))
        y = fftn(x, axes=(1, 0, 2))  # jki_space
        assert_array_almost_equal(swapaxes(y, -2, -3), fftn(jki_space))
        y = fftn(x, axes=(0, 2, 1))  # kij_space
        assert_array_almost_equal(swapaxes(y, -2, -1), fftn(kij_space))

        y = fftn(x, axes=(-2, -1))  # ji_plane
        assert_array_almost_equal(fftn(plane1), y[0])
        assert_array_almost_equal(fftn(plane2), y[1])
        assert_array_almost_equal(fftn(plane3), y[2])

        y = fftn(x, axes=(1, 2))  # ji_plane
        assert_array_almost_equal(fftn(plane1), y[0])
        assert_array_almost_equal(fftn(plane2), y[1])
        assert_array_almost_equal(fftn(plane3), y[2])

        y = fftn(x, axes=(-3, -2))  # kj_plane
        assert_array_almost_equal(fftn(x[:, :, 0]), y[:, :, 0])
        assert_array_almost_equal(fftn(x[:, :, 1]), y[:, :, 1])
        assert_array_almost_equal(fftn(x[:, :, 2]), y[:, :, 2])

        y = fftn(x, axes=(-3, -1))  # ki_plane
        assert_array_almost_equal(fftn(x[:, 0, :]), y[:, 0, :])
        assert_array_almost_equal(fftn(x[:, 1, :]), y[:, 1, :])
        assert_array_almost_equal(fftn(x[:, 2, :]), y[:, 2, :])

        y = fftn(x, axes=(-1, -2))  # ij_plane
        assert_array_almost_equal(fftn(ij_plane1), swapaxes(y[0], -2, -1))
        assert_array_almost_equal(fftn(ij_plane2), swapaxes(y[1], -2, -1))
        assert_array_almost_equal(fftn(ij_plane3), swapaxes(y[2], -2, -1))

        y = fftn(x, axes=(-1, -3))  # ik_plane
        assert_array_almost_equal(fftn(ik_plane1),
                                  swapaxes(y[:, 0, :], -1, -2))
        assert_array_almost_equal(fftn(ik_plane2),
                                  swapaxes(y[:, 1, :], -1, -2))
        assert_array_almost_equal(fftn(ik_plane3),
                                  swapaxes(y[:, 2, :], -1, -2))

        y = fftn(x, axes=(-2, -3))  # jk_plane
        assert_array_almost_equal(fftn(jk_plane1),
                                  swapaxes(y[:, :, 0], -1, -2))
        assert_array_almost_equal(fftn(jk_plane2),
                                  swapaxes(y[:, :, 1], -1, -2))
        assert_array_almost_equal(fftn(jk_plane3),
                                  swapaxes(y[:, :, 2], -1, -2))

        y = fftn(x, axes=(-1,))  # i_line
        for i in range(3):
            for j in range(3):
                assert_array_almost_equal(fft(x[i, j, :]), y[i, j, :])
        y = fftn(x, axes=(-2,))  # j_line
        for i in range(3):
            for j in range(3):
                assert_array_almost_equal(fft(x[i, :, j]), y[i, :, j])
        y = fftn(x, axes=(0,))  # k_line
        for i in range(3):
            for j in range(3):
                assert_array_almost_equal(fft(x[:, i, j]), y[:, i, j])

        y = fftn(x, axes=())  # point
        assert_array_almost_equal(y, x)

    def test_shape_argument(self):
        small_x = [[1, 2, 3],
                   [4, 5, 6]]
        large_x1 = [[1, 2, 3, 0],
                    [4, 5, 6, 0],
                    [0, 0, 0, 0],
                    [0, 0, 0, 0]]

        y = fftn(small_x, shape=(4, 4))
        assert_array_almost_equal(y, fftn(large_x1))

        y = fftn(small_x, shape=(3, 4))
        assert_array_almost_equal(y, fftn(large_x1[:-1]))

    def test_shape_axes_argument(self):
        small_x = [[1, 2, 3],
                   [4, 5, 6],
                   [7, 8, 9]]
        large_x1 = array([[1, 2, 3, 0],
                          [4, 5, 6, 0],
                          [7, 8, 9, 0],
                          [0, 0, 0, 0]])
        y = fftn(small_x, shape=(4, 4), axes=(-2, -1))
        assert_array_almost_equal(y, fftn(large_x1))
        y = fftn(small_x, shape=(4, 4), axes=(-1, -2))

        assert_array_almost_equal(y, swapaxes(
            fftn(swapaxes(large_x1, -1, -2)), -1, -2))

    def test_shape_axes_argument2(self):
        # Change shape of the last axis
        x = numpy.random.random((10, 5, 3, 7))
        y = fftn(x, axes=(-1,), shape=(8,))
        assert_array_almost_equal(y, fft(x, axis=-1, n=8))

        # Change shape of an arbitrary axis which is not the last one
        x = numpy.random.random((10, 5, 3, 7))
        y = fftn(x, axes=(-2,), shape=(8,))
        assert_array_almost_equal(y, fft(x, axis=-2, n=8))

        # Change shape of axes: cf #244, where shape and axes were mixed up
        x = numpy.random.random((4, 4, 2))
        y = fftn(x, axes=(-3, -2), shape=(8, 8))
        assert_array_almost_equal(y,
                                  numpy.fft.fftn(x, axes=(-3, -2), s=(8, 8)))

    def test_shape_argument_more(self):
        x = zeros((4, 4, 2))
        with assert_raises(ValueError,
                           match="when given, axes and shape arguments"
                           " have to be of the same length"):
            fftn(x, shape=(8, 8, 2, 1))

    def test_invalid_sizes(self):
        with assert_raises(ValueError,
                           match="invalid number of data points"
                           r" \(\[1 0\]\) specified"):
            fftn([[]])

        with assert_raises(ValueError,
                           match="invalid number of data points"
                           r" \(\[ 4 -3\]\) specified"):
            fftn([[1, 1], [2, 2]], (4, -3))


class TestIfftn(object):
    dtype = None
    cdtype = None

    def setup_method(self):
        np.random.seed(1234)

    @pytest.mark.parametrize('dtype,cdtype,maxnlp',
                             [(np.float64, np.complex128, 2000),
                              (np.float32, np.complex64, 3500)])
    def test_definition(self, dtype, cdtype, maxnlp):
        x = np.array([[1, 2, 3],
                      [4, 5, 6],
                      [7, 8, 9]], dtype=dtype)
        y = ifftn(x)
        assert_equal(y.dtype, cdtype)
        assert_array_almost_equal_nulp(y, direct_idftn(x), maxnlp)

        x = random((20, 26))
        assert_array_almost_equal_nulp(ifftn(x), direct_idftn(x), maxnlp)

        x = random((5, 4, 3, 20))
        assert_array_almost_equal_nulp(ifftn(x), direct_idftn(x), maxnlp)

    @pytest.mark.parametrize('maxnlp', [2000, 3500])
    @pytest.mark.parametrize('size', [1, 2, 51, 32, 64, 92])
    def test_random_complex(self, maxnlp, size):
        x = random([size, size]) + 1j*random([size, size])
        assert_array_almost_equal_nulp(ifftn(fftn(x)), x, maxnlp)
        assert_array_almost_equal_nulp(fftn(ifftn(x)), x, maxnlp)

    def test_invalid_sizes(self):
        with assert_raises(ValueError,
                           match="invalid number of data points"
                           r" \(\[1 0\]\) specified"):
            ifftn([[]])

        with assert_raises(ValueError,
                           match="invalid number of data points"
                           r" \(\[ 4 -3\]\) specified"):
            ifftn([[1, 1], [2, 2]], (4, -3))


class TestLongDoubleFailure(object):
    def setup_method(self):
        np.random.seed(1234)

    def test_complex(self):
        if np.dtype(np.longcomplex).itemsize == np.dtype(complex).itemsize:
            # longdouble == double; so fft is supported
            return

        x = np.random.randn(10).astype(np.longdouble) + \
                1j * np.random.randn(10).astype(np.longdouble)

        for f in [fft, ifft]:
            try:
                f(x)
                raise AssertionError("Type {0} not supported but does not fail" %
                                     np.longcomplex)
            except ValueError:
                pass

    def test_real(self):
        if np.dtype(np.longdouble).itemsize == np.dtype(np.double).itemsize:
            # longdouble == double; so fft is supported
            return

        x = np.random.randn(10).astype(np.longcomplex)

        for f in [fft, ifft]:
            try:
                f(x)
                raise AssertionError("Type %r not supported but does not fail" %
                                     np.longcomplex)
            except ValueError:
                pass


class FakeArray(object):
    def __init__(self, data):
        self._data = data
        self.__array_interface__ = data.__array_interface__


class FakeArray2(object):
    def __init__(self, data):
        self._data = data

    def __array__(self):
        return self._data


class TestOverwrite(object):
    """Check input overwrite behavior of the FFT functions."""

    real_dtypes = [np.float32, np.float64]
    dtypes = real_dtypes + [np.complex64, np.complex128]
    fftsizes = [8, 16, 32]

    def _check(self, x, routine, fftsize, axis, overwrite_x, should_overwrite):
        x2 = x.copy()
        for fake in [lambda x: x, FakeArray, FakeArray2]:
            routine(fake(x2), fftsize, axis, overwrite_x=overwrite_x)

            sig = "%s(%s%r, %r, axis=%r, overwrite_x=%r)" % (
                routine.__name__, x.dtype, x.shape, fftsize, axis, overwrite_x)
            if not should_overwrite:
                assert_equal(x2, x, err_msg="spurious overwrite in %s" % sig)

    def _check_1d(self, routine, dtype, shape, axis, overwritable_dtypes,
                  fftsize, overwrite_x):
        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)

        should_overwrite = (overwrite_x
                            and dtype in overwritable_dtypes
                            and fftsize <= shape[axis]
                            and (len(shape) == 1 or
                                 (axis % len(shape) == len(shape)-1
                                  and fftsize == shape[axis])))
        self._check(data, routine, fftsize, axis,
                    overwrite_x=overwrite_x,
                    should_overwrite=should_overwrite)

    @pytest.mark.parametrize('dtype', dtypes)
    @pytest.mark.parametrize('fftsize', fftsizes)
    @pytest.mark.parametrize('overwrite_x', [True, False])
    @pytest.mark.parametrize('shape,axes', [((16,), -1),
                                            ((16, 2), 0),
                                            ((2, 16), 1)])
    def test_fft_ifft(self, dtype, fftsize, overwrite_x, shape, axes):
        overwritable = (np.complex128, np.complex64)
        self._check_1d(fft, dtype, shape, axes, overwritable,
                       fftsize, overwrite_x)
        self._check_1d(ifft, dtype, shape, axes, overwritable,
                       fftsize, overwrite_x)

    @pytest.mark.parametrize('dtype', real_dtypes)
    @pytest.mark.parametrize('fftsize', fftsizes)
    @pytest.mark.parametrize('overwrite_x', [True, False])
    @pytest.mark.parametrize('shape,axes', [((16,), -1),
                                            ((16, 2), 0),
                                            ((2, 16), 1)])
    def test_rfft_irfft(self, dtype, fftsize, overwrite_x, shape, axes):
        overwritable = self.real_dtypes
        self._check_1d(irfft, dtype, shape, axes, overwritable,
                       fftsize, overwrite_x)
        self._check_1d(rfft, dtype, shape, axes, overwritable,
                       fftsize, overwrite_x)

    def _check_nd_one(self, routine, dtype, shape, axes, overwritable_dtypes,
                      overwrite_x):
        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)

        def fftshape_iter(shp):
            if len(shp) <= 0:
                yield ()
            else:
                for j in (shp[0]//2, shp[0], shp[0]*2):
                    for rest in fftshape_iter(shp[1:]):
                        yield (j,) + rest

        if axes is None:
            part_shape = shape
        else:
            part_shape = tuple(np.take(shape, axes))

        for fftshape in fftshape_iter(part_shape):
            should_overwrite = (overwrite_x
                                and data.ndim == 1
                                and np.all([x < y for x, y in zip(fftshape,
                                                                  part_shape)])
                                and dtype in overwritable_dtypes)
            self._check(data, routine, fftshape, axes,
                        overwrite_x=overwrite_x,
                        should_overwrite=should_overwrite)
            if data.ndim > 1:
                # check fortran order: it never overwrites
                self._check(data.T, routine, fftshape, axes,
                            overwrite_x=overwrite_x,
                            should_overwrite=False)

    @pytest.mark.parametrize('dtype', dtypes)
    @pytest.mark.parametrize('overwrite_x', [True, False])
    @pytest.mark.parametrize('shape,axes', [((16,), None),
                                            ((16,), (0,)),
                                            ((16, 2), (0,)),
                                            ((2, 16), (1,)),
                                            ((8, 16), None),
                                            ((8, 16), (0, 1)),
                                            ((8, 16, 2), (0, 1)),
                                            ((8, 16, 2), (1, 2)),
                                            ((8, 16, 2), (0,)),
                                            ((8, 16, 2), (1,)),
                                            ((8, 16, 2), (2,)),
                                            ((8, 16, 2), None),
                                            ((8, 16, 2), (0, 1, 2))])
    def test_fftn_ifftn(self, dtype, overwrite_x, shape, axes):
        overwritable = (np.complex128, np.complex64)
        self._check_nd_one(fftn, dtype, shape, axes, overwritable,
                           overwrite_x)
        self._check_nd_one(ifftn, dtype, shape, axes, overwritable,
                           overwrite_x)