217 lines
7.4 KiB
Python
217 lines
7.4 KiB
Python
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import numpy as np
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from numpy.testing import assert_allclose, assert_array_equal
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import pytest
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from scipy.fft import dct, idct, dctn, idctn, dst, idst, dstn, idstn
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import scipy.fft as fft
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from scipy import fftpack
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import math
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SQRT_2 = math.sqrt(2)
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# scipy.fft wraps the fftpack versions but with normalized inverse transforms.
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# So, the forward transforms and definitions are already thoroughly tested in
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# fftpack/test_real_transforms.py
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@pytest.mark.parametrize("forward, backward", [(dct, idct), (dst, idst)])
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@pytest.mark.parametrize("type", [1, 2, 3, 4])
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@pytest.mark.parametrize("n", [2, 3, 4, 5, 10, 16])
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@pytest.mark.parametrize("axis", [0, 1])
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@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
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@pytest.mark.parametrize("orthogonalize", [False, True])
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def test_identity_1d(forward, backward, type, n, axis, norm, orthogonalize):
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# Test the identity f^-1(f(x)) == x
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x = np.random.rand(n, n)
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y = forward(x, type, axis=axis, norm=norm, orthogonalize=orthogonalize)
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z = backward(y, type, axis=axis, norm=norm, orthogonalize=orthogonalize)
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assert_allclose(z, x)
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pad = [(0, 0)] * 2
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pad[axis] = (0, 4)
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y2 = np.pad(y, pad, mode='edge')
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z2 = backward(y2, type, n, axis, norm, orthogonalize=orthogonalize)
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assert_allclose(z2, x)
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@pytest.mark.parametrize("forward, backward", [(dct, idct), (dst, idst)])
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@pytest.mark.parametrize("type", [1, 2, 3, 4])
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@pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64,
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np.complex64, np.complex128])
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@pytest.mark.parametrize("axis", [0, 1])
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@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
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@pytest.mark.parametrize("overwrite_x", [True, False])
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def test_identity_1d_overwrite(forward, backward, type, dtype, axis, norm,
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overwrite_x):
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# Test the identity f^-1(f(x)) == x
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x = np.random.rand(7, 8).astype(dtype)
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x_orig = x.copy()
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y = forward(x, type, axis=axis, norm=norm, overwrite_x=overwrite_x)
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y_orig = y.copy()
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z = backward(y, type, axis=axis, norm=norm, overwrite_x=overwrite_x)
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if not overwrite_x:
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assert_allclose(z, x, rtol=1e-6, atol=1e-6)
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assert_array_equal(x, x_orig)
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assert_array_equal(y, y_orig)
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else:
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assert_allclose(z, x_orig, rtol=1e-6, atol=1e-6)
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@pytest.mark.parametrize("forward, backward", [(dctn, idctn), (dstn, idstn)])
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@pytest.mark.parametrize("type", [1, 2, 3, 4])
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@pytest.mark.parametrize("shape, axes",
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[
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((4, 4), 0),
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((4, 4), 1),
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((4, 4), None),
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((4, 4), (0, 1)),
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((10, 12), None),
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((10, 12), (0, 1)),
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((4, 5, 6), None),
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((4, 5, 6), 1),
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((4, 5, 6), (0, 2)),
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])
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@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
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@pytest.mark.parametrize("orthogonalize", [False, True])
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def test_identity_nd(forward, backward, type, shape, axes, norm,
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orthogonalize):
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# Test the identity f^-1(f(x)) == x
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x = np.random.random(shape)
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if axes is not None:
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shape = np.take(shape, axes)
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y = forward(x, type, axes=axes, norm=norm, orthogonalize=orthogonalize)
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z = backward(y, type, axes=axes, norm=norm, orthogonalize=orthogonalize)
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assert_allclose(z, x)
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if axes is None:
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pad = [(0, 4)] * x.ndim
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elif isinstance(axes, int):
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pad = [(0, 0)] * x.ndim
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pad[axes] = (0, 4)
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else:
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pad = [(0, 0)] * x.ndim
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for a in axes:
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pad[a] = (0, 4)
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y2 = np.pad(y, pad, mode='edge')
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z2 = backward(y2, type, shape, axes, norm, orthogonalize=orthogonalize)
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assert_allclose(z2, x)
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@pytest.mark.parametrize("forward, backward", [(dctn, idctn), (dstn, idstn)])
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@pytest.mark.parametrize("type", [1, 2, 3, 4])
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@pytest.mark.parametrize("shape, axes",
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[
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((4, 5), 0),
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((4, 5), 1),
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((4, 5), None),
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])
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@pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64,
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np.complex64, np.complex128])
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@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
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@pytest.mark.parametrize("overwrite_x", [False, True])
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def test_identity_nd_overwrite(forward, backward, type, shape, axes, dtype,
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norm, overwrite_x):
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# Test the identity f^-1(f(x)) == x
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x = np.random.random(shape).astype(dtype)
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x_orig = x.copy()
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if axes is not None:
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shape = np.take(shape, axes)
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y = forward(x, type, axes=axes, norm=norm)
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y_orig = y.copy()
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z = backward(y, type, axes=axes, norm=norm)
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if overwrite_x:
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assert_allclose(z, x_orig, rtol=1e-6, atol=1e-6)
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else:
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assert_allclose(z, x, rtol=1e-6, atol=1e-6)
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assert_array_equal(x, x_orig)
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assert_array_equal(y, y_orig)
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@pytest.mark.parametrize("func", ['dct', 'dst', 'dctn', 'dstn'])
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@pytest.mark.parametrize("type", [1, 2, 3, 4])
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@pytest.mark.parametrize("norm", [None, 'backward', 'ortho', 'forward'])
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def test_fftpack_equivalience(func, type, norm):
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x = np.random.rand(8, 16)
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fft_res = getattr(fft, func)(x, type, norm=norm)
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fftpack_res = getattr(fftpack, func)(x, type, norm=norm)
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assert_allclose(fft_res, fftpack_res)
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@pytest.mark.parametrize("func", [dct, dst, dctn, dstn])
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@pytest.mark.parametrize("type", [1, 2, 3, 4])
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def test_orthogonalize_default(func, type):
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# Test orthogonalize is the default when norm="ortho", but not otherwise
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x = np.random.rand(100)
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for norm, ortho in [
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("forward", False),
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("backward", False),
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("ortho", True),
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]:
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a = func(x, type=type, norm=norm, orthogonalize=ortho)
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b = func(x, type=type, norm=norm)
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assert_allclose(a, b)
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@pytest.mark.parametrize("norm", ["backward", "ortho", "forward"])
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@pytest.mark.parametrize("func, type", [
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(dct, 4), (dst, 1), (dst, 4)])
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def test_orthogonalize_noop(func, type, norm):
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# Transforms where orthogonalize is a no-op
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x = np.random.rand(100)
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y1 = func(x, type=type, norm=norm, orthogonalize=True)
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y2 = func(x, type=type, norm=norm, orthogonalize=False)
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assert_allclose(y1, y2)
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@pytest.mark.parametrize("norm", ["backward", "ortho", "forward"])
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def test_orthogonalize_dct1(norm):
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x = np.random.rand(100)
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x2 = x.copy()
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x2[0] *= SQRT_2
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x2[-1] *= SQRT_2
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y1 = dct(x, type=1, norm=norm, orthogonalize=True)
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y2 = dct(x2, type=1, norm=norm, orthogonalize=False)
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y2[0] /= SQRT_2
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y2[-1] /= SQRT_2
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assert_allclose(y1, y2)
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@pytest.mark.parametrize("norm", ["backward", "ortho", "forward"])
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@pytest.mark.parametrize("func", [dct, dst])
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def test_orthogonalize_dcst2(func, norm):
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x = np.random.rand(100)
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y1 = func(x, type=2, norm=norm, orthogonalize=True)
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y2 = func(x, type=2, norm=norm, orthogonalize=False)
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y2[0] /= SQRT_2
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assert_allclose(y1, y2)
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@pytest.mark.parametrize("norm", ["backward", "ortho", "forward"])
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@pytest.mark.parametrize("func", [dct, dst])
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def test_orthogonalize_dcst3(func, norm):
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x = np.random.rand(100)
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x2 = x.copy()
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x2[0] *= SQRT_2
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y1 = func(x, type=3, norm=norm, orthogonalize=True)
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y2 = func(x2, type=3, norm=norm, orthogonalize=False)
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assert_allclose(y1, y2)
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