122 lines
3.8 KiB
Python
122 lines
3.8 KiB
Python
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import numpy as np
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from scipy.linalg import bandwidth, issymmetric, ishermitian
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import pytest
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from pytest import raises
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def test_bandwidth_dtypes():
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n = 5
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for t in np.typecodes['All']:
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A = np.zeros([n, n], dtype=t)
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if t in 'eUVOMm':
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raises(TypeError, bandwidth, A)
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elif t == 'G': # No-op test. On win these pass on others fail.
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pass
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else:
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_ = bandwidth(A)
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def test_bandwidth_non2d_input():
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A = np.array([1, 2, 3])
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raises(ValueError, bandwidth, A)
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A = np.array([[[1, 2, 3], [4, 5, 6]]])
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raises(ValueError, bandwidth, A)
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@pytest.mark.parametrize('T', [x for x in np.typecodes['All']
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if x not in 'eGUVOMm'])
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def test_bandwidth_square_inputs(T):
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n = 20
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k = 4
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R = np.zeros([n, n], dtype=T, order='F')
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# form a banded matrix inplace
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R[[x for x in range(n)], [x for x in range(n)]] = 1
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R[[x for x in range(n-k)], [x for x in range(k, n)]] = 1
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R[[x for x in range(1, n)], [x for x in range(n-1)]] = 1
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R[[x for x in range(k, n)], [x for x in range(n-k)]] = 1
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assert bandwidth(R) == (k, k)
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@pytest.mark.parametrize('T', [x for x in np.typecodes['All']
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if x not in 'eGUVOMm'])
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def test_bandwidth_rect_inputs(T):
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n, m = 10, 20
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k = 5
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R = np.zeros([n, m], dtype=T, order='F')
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# form a banded matrix inplace
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R[[x for x in range(n)], [x for x in range(n)]] = 1
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R[[x for x in range(n-k)], [x for x in range(k, n)]] = 1
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R[[x for x in range(1, n)], [x for x in range(n-1)]] = 1
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R[[x for x in range(k, n)], [x for x in range(n-k)]] = 1
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assert bandwidth(R) == (k, k)
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def test_issymetric_ishermitian_dtypes():
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n = 5
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for t in np.typecodes['All']:
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A = np.zeros([n, n], dtype=t)
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if t in 'eUVOMm':
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raises(TypeError, issymmetric, A)
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raises(TypeError, ishermitian, A)
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elif t == 'G': # No-op test. On win these pass on others fail.
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pass
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else:
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assert issymmetric(A)
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assert ishermitian(A)
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def test_issymmetric_ishermitian_invalid_input():
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A = np.array([1, 2, 3])
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raises(ValueError, issymmetric, A)
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raises(ValueError, ishermitian, A)
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A = np.array([[[1, 2, 3], [4, 5, 6]]])
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raises(ValueError, issymmetric, A)
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raises(ValueError, ishermitian, A)
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A = np.array([[1, 2, 3], [4, 5, 6]])
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raises(ValueError, issymmetric, A)
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raises(ValueError, ishermitian, A)
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def test_issymetric_complex_decimals():
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A = np.arange(1, 10).astype(complex).reshape(3, 3)
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A += np.arange(-4, 5).astype(complex).reshape(3, 3)*1j
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# make entries decimal
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A /= np.pi
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A = A + A.T
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assert issymmetric(A)
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def test_ishermitian_complex_decimals():
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A = np.arange(1, 10).astype(complex).reshape(3, 3)
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A += np.arange(-4, 5).astype(complex).reshape(3, 3)*1j
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# make entries decimal
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A /= np.pi
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A = A + A.T.conj()
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assert ishermitian(A)
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def test_issymmetric_approximate_results():
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n = 20
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rng = np.random.RandomState(123456789)
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x = rng.uniform(high=5., size=[n, n])
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y = x @ x.T # symmetric
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p = rng.standard_normal([n, n])
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z = p @ y @ p.T
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assert issymmetric(z, atol=1e-10)
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assert issymmetric(z, atol=1e-10, rtol=0.)
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assert issymmetric(z, atol=0., rtol=1e-12)
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assert issymmetric(z, atol=1e-13, rtol=1e-12)
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def test_ishermitian_approximate_results():
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n = 20
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rng = np.random.RandomState(987654321)
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x = rng.uniform(high=5., size=[n, n])
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y = x @ x.T # symmetric
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p = rng.standard_normal([n, n]) + rng.standard_normal([n, n])*1j
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z = p @ y @ p.conj().T
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assert ishermitian(z, atol=1e-10)
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assert ishermitian(z, atol=1e-10, rtol=0.)
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assert ishermitian(z, atol=0., rtol=1e-12)
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assert ishermitian(z, atol=1e-13, rtol=1e-12)
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