1698 lines
67 KiB
Python
1698 lines
67 KiB
Python
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import itertools
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import numpy as np
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from numpy.testing import assert_, assert_allclose, assert_equal
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from pytest import raises as assert_raises
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from scipy import linalg
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import scipy.linalg._decomp_update as _decomp_update
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from scipy.linalg._decomp_update import qr_delete, qr_update, qr_insert
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def assert_unitary(a, rtol=None, atol=None, assert_sqr=True):
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if rtol is None:
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rtol = 10.0 ** -(np.finfo(a.dtype).precision-2)
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if atol is None:
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atol = 10*np.finfo(a.dtype).eps
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if assert_sqr:
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assert_(a.shape[0] == a.shape[1], 'unitary matrices must be square')
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aTa = np.dot(a.T.conj(), a)
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assert_allclose(aTa, np.eye(a.shape[1]), rtol=rtol, atol=atol)
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def assert_upper_tri(a, rtol=None, atol=None):
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if rtol is None:
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rtol = 10.0 ** -(np.finfo(a.dtype).precision-2)
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if atol is None:
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atol = 2*np.finfo(a.dtype).eps
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mask = np.tri(a.shape[0], a.shape[1], -1, np.bool_)
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assert_allclose(a[mask], 0.0, rtol=rtol, atol=atol)
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def check_qr(q, r, a, rtol, atol, assert_sqr=True):
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assert_unitary(q, rtol, atol, assert_sqr)
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assert_upper_tri(r, rtol, atol)
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assert_allclose(q.dot(r), a, rtol=rtol, atol=atol)
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def make_strided(arrs):
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strides = [(3, 7), (2, 2), (3, 4), (4, 2), (5, 4), (2, 3), (2, 1), (4, 5)]
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kmax = len(strides)
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k = 0
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ret = []
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for a in arrs:
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if a.ndim == 1:
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s = strides[k % kmax]
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k += 1
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base = np.zeros(s[0]*a.shape[0]+s[1], a.dtype)
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view = base[s[1]::s[0]]
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view[...] = a
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elif a.ndim == 2:
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s = strides[k % kmax]
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t = strides[(k+1) % kmax]
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k += 2
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base = np.zeros((s[0]*a.shape[0]+s[1], t[0]*a.shape[1]+t[1]),
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a.dtype)
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view = base[s[1]::s[0], t[1]::t[0]]
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view[...] = a
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else:
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raise ValueError('make_strided only works for ndim = 1 or'
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' 2 arrays')
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ret.append(view)
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return ret
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def negate_strides(arrs):
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ret = []
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for a in arrs:
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b = np.zeros_like(a)
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if b.ndim == 2:
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b = b[::-1, ::-1]
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elif b.ndim == 1:
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b = b[::-1]
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else:
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raise ValueError('negate_strides only works for ndim = 1 or'
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' 2 arrays')
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b[...] = a
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ret.append(b)
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return ret
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def nonitemsize_strides(arrs):
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out = []
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for a in arrs:
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a_dtype = a.dtype
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b = np.zeros(a.shape, [('a', a_dtype), ('junk', 'S1')])
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c = b.getfield(a_dtype)
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c[...] = a
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out.append(c)
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return out
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def make_nonnative(arrs):
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return [a.astype(a.dtype.newbyteorder()) for a in arrs]
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class BaseQRdeltas(object):
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def setup_method(self):
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self.rtol = 10.0 ** -(np.finfo(self.dtype).precision-2)
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self.atol = 10 * np.finfo(self.dtype).eps
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def generate(self, type, mode='full'):
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np.random.seed(29382)
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shape = {'sqr': (8, 8), 'tall': (12, 7), 'fat': (7, 12),
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'Mx1': (8, 1), '1xN': (1, 8), '1x1': (1, 1)}[type]
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a = np.random.random(shape)
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if np.iscomplexobj(self.dtype.type(1)):
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b = np.random.random(shape)
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a = a + 1j * b
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a = a.astype(self.dtype)
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q, r = linalg.qr(a, mode=mode)
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return a, q, r
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class BaseQRdelete(BaseQRdeltas):
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def test_sqr_1_row(self):
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a, q, r = self.generate('sqr')
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for row in range(r.shape[0]):
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q1, r1 = qr_delete(q, r, row, overwrite_qr=False)
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a1 = np.delete(a, row, 0)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_sqr_p_row(self):
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a, q, r = self.generate('sqr')
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for ndel in range(2, 6):
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for row in range(a.shape[0]-ndel):
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q1, r1 = qr_delete(q, r, row, ndel, overwrite_qr=False)
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a1 = np.delete(a, slice(row, row+ndel), 0)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_sqr_1_col(self):
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a, q, r = self.generate('sqr')
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for col in range(r.shape[1]):
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q1, r1 = qr_delete(q, r, col, which='col', overwrite_qr=False)
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a1 = np.delete(a, col, 1)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_sqr_p_col(self):
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a, q, r = self.generate('sqr')
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for ndel in range(2, 6):
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for col in range(r.shape[1]-ndel):
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q1, r1 = qr_delete(q, r, col, ndel, which='col',
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overwrite_qr=False)
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a1 = np.delete(a, slice(col, col+ndel), 1)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_tall_1_row(self):
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a, q, r = self.generate('tall')
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for row in range(r.shape[0]):
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q1, r1 = qr_delete(q, r, row, overwrite_qr=False)
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a1 = np.delete(a, row, 0)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_tall_p_row(self):
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a, q, r = self.generate('tall')
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for ndel in range(2, 6):
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for row in range(a.shape[0]-ndel):
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q1, r1 = qr_delete(q, r, row, ndel, overwrite_qr=False)
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a1 = np.delete(a, slice(row, row+ndel), 0)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_tall_1_col(self):
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a, q, r = self.generate('tall')
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for col in range(r.shape[1]):
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q1, r1 = qr_delete(q, r, col, which='col', overwrite_qr=False)
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a1 = np.delete(a, col, 1)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_tall_p_col(self):
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a, q, r = self.generate('tall')
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for ndel in range(2, 6):
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for col in range(r.shape[1]-ndel):
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q1, r1 = qr_delete(q, r, col, ndel, which='col',
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overwrite_qr=False)
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a1 = np.delete(a, slice(col, col+ndel), 1)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_fat_1_row(self):
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a, q, r = self.generate('fat')
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for row in range(r.shape[0]):
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q1, r1 = qr_delete(q, r, row, overwrite_qr=False)
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a1 = np.delete(a, row, 0)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_fat_p_row(self):
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a, q, r = self.generate('fat')
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for ndel in range(2, 6):
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for row in range(a.shape[0]-ndel):
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q1, r1 = qr_delete(q, r, row, ndel, overwrite_qr=False)
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a1 = np.delete(a, slice(row, row+ndel), 0)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_fat_1_col(self):
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a, q, r = self.generate('fat')
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for col in range(r.shape[1]):
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q1, r1 = qr_delete(q, r, col, which='col', overwrite_qr=False)
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a1 = np.delete(a, col, 1)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_fat_p_col(self):
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a, q, r = self.generate('fat')
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for ndel in range(2, 6):
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for col in range(r.shape[1]-ndel):
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q1, r1 = qr_delete(q, r, col, ndel, which='col',
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overwrite_qr=False)
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a1 = np.delete(a, slice(col, col+ndel), 1)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_economic_1_row(self):
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# this test always starts and ends with an economic decomp.
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a, q, r = self.generate('tall', 'economic')
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for row in range(r.shape[0]):
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q1, r1 = qr_delete(q, r, row, overwrite_qr=False)
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a1 = np.delete(a, row, 0)
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check_qr(q1, r1, a1, self.rtol, self.atol, False)
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# for economic row deletes
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# eco - prow = eco
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# eco - prow = sqr
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# eco - prow = fat
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def base_economic_p_row_xxx(self, ndel):
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a, q, r = self.generate('tall', 'economic')
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for row in range(a.shape[0]-ndel):
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q1, r1 = qr_delete(q, r, row, ndel, overwrite_qr=False)
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a1 = np.delete(a, slice(row, row+ndel), 0)
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check_qr(q1, r1, a1, self.rtol, self.atol, False)
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def test_economic_p_row_economic(self):
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# (12, 7) - (3, 7) = (9,7) --> stays economic
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self.base_economic_p_row_xxx(3)
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def test_economic_p_row_sqr(self):
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# (12, 7) - (5, 7) = (7, 7) --> becomes square
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self.base_economic_p_row_xxx(5)
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def test_economic_p_row_fat(self):
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# (12, 7) - (7,7) = (5, 7) --> becomes fat
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self.base_economic_p_row_xxx(7)
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def test_economic_1_col(self):
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a, q, r = self.generate('tall', 'economic')
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for col in range(r.shape[1]):
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q1, r1 = qr_delete(q, r, col, which='col', overwrite_qr=False)
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a1 = np.delete(a, col, 1)
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check_qr(q1, r1, a1, self.rtol, self.atol, False)
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def test_economic_p_col(self):
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a, q, r = self.generate('tall', 'economic')
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for ndel in range(2, 6):
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for col in range(r.shape[1]-ndel):
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q1, r1 = qr_delete(q, r, col, ndel, which='col',
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overwrite_qr=False)
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a1 = np.delete(a, slice(col, col+ndel), 1)
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check_qr(q1, r1, a1, self.rtol, self.atol, False)
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def test_Mx1_1_row(self):
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a, q, r = self.generate('Mx1')
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for row in range(r.shape[0]):
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q1, r1 = qr_delete(q, r, row, overwrite_qr=False)
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a1 = np.delete(a, row, 0)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_Mx1_p_row(self):
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a, q, r = self.generate('Mx1')
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for ndel in range(2, 6):
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for row in range(a.shape[0]-ndel):
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q1, r1 = qr_delete(q, r, row, ndel, overwrite_qr=False)
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a1 = np.delete(a, slice(row, row+ndel), 0)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_1xN_1_col(self):
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a, q, r = self.generate('1xN')
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for col in range(r.shape[1]):
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q1, r1 = qr_delete(q, r, col, which='col', overwrite_qr=False)
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a1 = np.delete(a, col, 1)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_1xN_p_col(self):
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a, q, r = self.generate('1xN')
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for ndel in range(2, 6):
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for col in range(r.shape[1]-ndel):
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q1, r1 = qr_delete(q, r, col, ndel, which='col',
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overwrite_qr=False)
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a1 = np.delete(a, slice(col, col+ndel), 1)
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check_qr(q1, r1, a1, self.rtol, self.atol)
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def test_Mx1_economic_1_row(self):
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a, q, r = self.generate('Mx1', 'economic')
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for row in range(r.shape[0]):
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q1, r1 = qr_delete(q, r, row, overwrite_qr=False)
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a1 = np.delete(a, row, 0)
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check_qr(q1, r1, a1, self.rtol, self.atol, False)
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def test_Mx1_economic_p_row(self):
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a, q, r = self.generate('Mx1', 'economic')
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for ndel in range(2, 6):
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for row in range(a.shape[0]-ndel):
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q1, r1 = qr_delete(q, r, row, ndel, overwrite_qr=False)
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a1 = np.delete(a, slice(row, row+ndel), 0)
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check_qr(q1, r1, a1, self.rtol, self.atol, False)
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def test_delete_last_1_row(self):
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# full and eco are the same for 1xN
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a, q, r = self.generate('1xN')
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q1, r1 = qr_delete(q, r, 0, 1, 'row')
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assert_equal(q1, np.ndarray(shape=(0, 0), dtype=q.dtype))
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assert_equal(r1, np.ndarray(shape=(0, r.shape[1]), dtype=r.dtype))
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def test_delete_last_p_row(self):
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a, q, r = self.generate('tall', 'full')
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q1, r1 = qr_delete(q, r, 0, a.shape[0], 'row')
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assert_equal(q1, np.ndarray(shape=(0, 0), dtype=q.dtype))
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assert_equal(r1, np.ndarray(shape=(0, r.shape[1]), dtype=r.dtype))
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||
|
|
|
||
|
|
a, q, r = self.generate('tall', 'economic')
|
||
|
|
q1, r1 = qr_delete(q, r, 0, a.shape[0], 'row')
|
||
|
|
assert_equal(q1, np.ndarray(shape=(0, 0), dtype=q.dtype))
|
||
|
|
assert_equal(r1, np.ndarray(shape=(0, r.shape[1]), dtype=r.dtype))
|
||
|
|
|
||
|
|
def test_delete_last_1_col(self):
|
||
|
|
a, q, r = self.generate('Mx1', 'economic')
|
||
|
|
q1, r1 = qr_delete(q, r, 0, 1, 'col')
|
||
|
|
assert_equal(q1, np.ndarray(shape=(q.shape[0], 0), dtype=q.dtype))
|
||
|
|
assert_equal(r1, np.ndarray(shape=(0, 0), dtype=r.dtype))
|
||
|
|
|
||
|
|
a, q, r = self.generate('Mx1', 'full')
|
||
|
|
q1, r1 = qr_delete(q, r, 0, 1, 'col')
|
||
|
|
assert_unitary(q1)
|
||
|
|
assert_(q1.dtype == q.dtype)
|
||
|
|
assert_(q1.shape == q.shape)
|
||
|
|
assert_equal(r1, np.ndarray(shape=(r.shape[0], 0), dtype=r.dtype))
|
||
|
|
|
||
|
|
def test_delete_last_p_col(self):
|
||
|
|
a, q, r = self.generate('tall', 'full')
|
||
|
|
q1, r1 = qr_delete(q, r, 0, a.shape[1], 'col')
|
||
|
|
assert_unitary(q1)
|
||
|
|
assert_(q1.dtype == q.dtype)
|
||
|
|
assert_(q1.shape == q.shape)
|
||
|
|
assert_equal(r1, np.ndarray(shape=(r.shape[0], 0), dtype=r.dtype))
|
||
|
|
|
||
|
|
a, q, r = self.generate('tall', 'economic')
|
||
|
|
q1, r1 = qr_delete(q, r, 0, a.shape[1], 'col')
|
||
|
|
assert_equal(q1, np.ndarray(shape=(q.shape[0], 0), dtype=q.dtype))
|
||
|
|
assert_equal(r1, np.ndarray(shape=(0, 0), dtype=r.dtype))
|
||
|
|
|
||
|
|
def test_delete_1x1_row_col(self):
|
||
|
|
a, q, r = self.generate('1x1')
|
||
|
|
q1, r1 = qr_delete(q, r, 0, 1, 'row')
|
||
|
|
assert_equal(q1, np.ndarray(shape=(0, 0), dtype=q.dtype))
|
||
|
|
assert_equal(r1, np.ndarray(shape=(0, r.shape[1]), dtype=r.dtype))
|
||
|
|
|
||
|
|
a, q, r = self.generate('1x1')
|
||
|
|
q1, r1 = qr_delete(q, r, 0, 1, 'col')
|
||
|
|
assert_unitary(q1)
|
||
|
|
assert_(q1.dtype == q.dtype)
|
||
|
|
assert_(q1.shape == q.shape)
|
||
|
|
assert_equal(r1, np.ndarray(shape=(r.shape[0], 0), dtype=r.dtype))
|
||
|
|
|
||
|
|
# all full qr, row deletes and single column deletes should be able to
|
||
|
|
# handle any non negative strides. (only row and column vector
|
||
|
|
# operations are used.) p column delete require fortran ordered
|
||
|
|
# Q and R and will make a copy as necessary. Economic qr row deletes
|
||
|
|
# requre a contigous q.
|
||
|
|
|
||
|
|
def base_non_simple_strides(self, adjust_strides, ks, p, which,
|
||
|
|
overwriteable):
|
||
|
|
if which == 'row':
|
||
|
|
qind = (slice(p,None), slice(p,None))
|
||
|
|
rind = (slice(p,None), slice(None))
|
||
|
|
else:
|
||
|
|
qind = (slice(None), slice(None))
|
||
|
|
rind = (slice(None), slice(None,-p))
|
||
|
|
|
||
|
|
for type, k in itertools.product(['sqr', 'tall', 'fat'], ks):
|
||
|
|
a, q0, r0, = self.generate(type)
|
||
|
|
qs, rs = adjust_strides((q0, r0))
|
||
|
|
if p == 1:
|
||
|
|
a1 = np.delete(a, k, 0 if which == 'row' else 1)
|
||
|
|
else:
|
||
|
|
s = slice(k,k+p)
|
||
|
|
if k < 0:
|
||
|
|
s = slice(k, k + p +
|
||
|
|
(a.shape[0] if which == 'row' else a.shape[1]))
|
||
|
|
a1 = np.delete(a, s, 0 if which == 'row' else 1)
|
||
|
|
|
||
|
|
# for each variable, q, r we try with it strided and
|
||
|
|
# overwrite=False. Then we try with overwrite=True, and make
|
||
|
|
# sure that q and r are still overwritten.
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
q1, r1 = qr_delete(qs, r, k, p, which, False)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
q1o, r1o = qr_delete(qs, r, k, p, which, True)
|
||
|
|
check_qr(q1o, r1o, a1, self.rtol, self.atol)
|
||
|
|
if overwriteable:
|
||
|
|
assert_allclose(q1o, qs[qind], rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r1o, r[rind], rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
q2, r2 = qr_delete(q, rs, k, p, which, False)
|
||
|
|
check_qr(q2, r2, a1, self.rtol, self.atol)
|
||
|
|
q2o, r2o = qr_delete(q, rs, k, p, which, True)
|
||
|
|
check_qr(q2o, r2o, a1, self.rtol, self.atol)
|
||
|
|
if overwriteable:
|
||
|
|
assert_allclose(q2o, q[qind], rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r2o, rs[rind], rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
# since some of these were consumed above
|
||
|
|
qs, rs = adjust_strides((q, r))
|
||
|
|
q3, r3 = qr_delete(qs, rs, k, p, which, False)
|
||
|
|
check_qr(q3, r3, a1, self.rtol, self.atol)
|
||
|
|
q3o, r3o = qr_delete(qs, rs, k, p, which, True)
|
||
|
|
check_qr(q3o, r3o, a1, self.rtol, self.atol)
|
||
|
|
if overwriteable:
|
||
|
|
assert_allclose(q2o, qs[qind], rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r3o, rs[rind], rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
def test_non_unit_strides_1_row(self):
|
||
|
|
self.base_non_simple_strides(make_strided, [0], 1, 'row', True)
|
||
|
|
|
||
|
|
def test_non_unit_strides_p_row(self):
|
||
|
|
self.base_non_simple_strides(make_strided, [0], 3, 'row', True)
|
||
|
|
|
||
|
|
def test_non_unit_strides_1_col(self):
|
||
|
|
self.base_non_simple_strides(make_strided, [0], 1, 'col', True)
|
||
|
|
|
||
|
|
def test_non_unit_strides_p_col(self):
|
||
|
|
self.base_non_simple_strides(make_strided, [0], 3, 'col', False)
|
||
|
|
|
||
|
|
def test_neg_strides_1_row(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, [0], 1, 'row', False)
|
||
|
|
|
||
|
|
def test_neg_strides_p_row(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, [0], 3, 'row', False)
|
||
|
|
|
||
|
|
def test_neg_strides_1_col(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, [0], 1, 'col', False)
|
||
|
|
|
||
|
|
def test_neg_strides_p_col(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, [0], 3, 'col', False)
|
||
|
|
|
||
|
|
def test_non_itemize_strides_1_row(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, [0], 1, 'row', False)
|
||
|
|
|
||
|
|
def test_non_itemize_strides_p_row(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, [0], 3, 'row', False)
|
||
|
|
|
||
|
|
def test_non_itemize_strides_1_col(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, [0], 1, 'col', False)
|
||
|
|
|
||
|
|
def test_non_itemize_strides_p_col(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, [0], 3, 'col', False)
|
||
|
|
|
||
|
|
def test_non_native_byte_order_1_row(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, [0], 1, 'row', False)
|
||
|
|
|
||
|
|
def test_non_native_byte_order_p_row(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, [0], 3, 'row', False)
|
||
|
|
|
||
|
|
def test_non_native_byte_order_1_col(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, [0], 1, 'col', False)
|
||
|
|
|
||
|
|
def test_non_native_byte_order_p_col(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, [0], 3, 'col', False)
|
||
|
|
|
||
|
|
def test_neg_k(self):
|
||
|
|
a, q, r = self.generate('sqr')
|
||
|
|
for k, p, w in itertools.product([-3, -7], [1, 3], ['row', 'col']):
|
||
|
|
q1, r1 = qr_delete(q, r, k, p, w, overwrite_qr=False)
|
||
|
|
if w == 'row':
|
||
|
|
a1 = np.delete(a, slice(k+a.shape[0], k+p+a.shape[0]), 0)
|
||
|
|
else:
|
||
|
|
a1 = np.delete(a, slice(k+a.shape[0], k+p+a.shape[1]), 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def base_overwrite_qr(self, which, p, test_C, test_F, mode='full'):
|
||
|
|
assert_sqr = True if mode == 'full' else False
|
||
|
|
if which == 'row':
|
||
|
|
qind = (slice(p,None), slice(p,None))
|
||
|
|
rind = (slice(p,None), slice(None))
|
||
|
|
else:
|
||
|
|
qind = (slice(None), slice(None))
|
||
|
|
rind = (slice(None), slice(None,-p))
|
||
|
|
a, q0, r0 = self.generate('sqr', mode)
|
||
|
|
if p == 1:
|
||
|
|
a1 = np.delete(a, 3, 0 if which == 'row' else 1)
|
||
|
|
else:
|
||
|
|
a1 = np.delete(a, slice(3, 3+p), 0 if which == 'row' else 1)
|
||
|
|
|
||
|
|
# don't overwrite
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
q1, r1 = qr_delete(q, r, 3, p, which, False)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, assert_sqr)
|
||
|
|
check_qr(q, r, a, self.rtol, self.atol, assert_sqr)
|
||
|
|
|
||
|
|
if test_F:
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
q2, r2 = qr_delete(q, r, 3, p, which, True)
|
||
|
|
check_qr(q2, r2, a1, self.rtol, self.atol, assert_sqr)
|
||
|
|
# verify the overwriting
|
||
|
|
assert_allclose(q2, q[qind], rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r2, r[rind], rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
if test_C:
|
||
|
|
q = q0.copy('C')
|
||
|
|
r = r0.copy('C')
|
||
|
|
q3, r3 = qr_delete(q, r, 3, p, which, True)
|
||
|
|
check_qr(q3, r3, a1, self.rtol, self.atol, assert_sqr)
|
||
|
|
assert_allclose(q3, q[qind], rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r3, r[rind], rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
def test_overwrite_qr_1_row(self):
|
||
|
|
# any positively strided q and r.
|
||
|
|
self.base_overwrite_qr('row', 1, True, True)
|
||
|
|
|
||
|
|
def test_overwrite_economic_qr_1_row(self):
|
||
|
|
# Any contiguous q and positively strided r.
|
||
|
|
self.base_overwrite_qr('row', 1, True, True, 'economic')
|
||
|
|
|
||
|
|
def test_overwrite_qr_1_col(self):
|
||
|
|
# any positively strided q and r.
|
||
|
|
# full and eco share code paths
|
||
|
|
self.base_overwrite_qr('col', 1, True, True)
|
||
|
|
|
||
|
|
def test_overwrite_qr_p_row(self):
|
||
|
|
# any positively strided q and r.
|
||
|
|
self.base_overwrite_qr('row', 3, True, True)
|
||
|
|
|
||
|
|
def test_overwrite_economic_qr_p_row(self):
|
||
|
|
# any contiguous q and positively strided r
|
||
|
|
self.base_overwrite_qr('row', 3, True, True, 'economic')
|
||
|
|
|
||
|
|
def test_overwrite_qr_p_col(self):
|
||
|
|
# only F orderd q and r can be overwritten for cols
|
||
|
|
# full and eco share code paths
|
||
|
|
self.base_overwrite_qr('col', 3, False, True)
|
||
|
|
|
||
|
|
def test_bad_which(self):
|
||
|
|
a, q, r = self.generate('sqr')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, 0, which='foo')
|
||
|
|
|
||
|
|
def test_bad_k(self):
|
||
|
|
a, q, r = self.generate('tall')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, q.shape[0], 1)
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, -q.shape[0]-1, 1)
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, r.shape[0], 1, 'col')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, -r.shape[0]-1, 1, 'col')
|
||
|
|
|
||
|
|
def test_bad_p(self):
|
||
|
|
a, q, r = self.generate('tall')
|
||
|
|
# p must be positive
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, 0, -1)
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, 0, -1, 'col')
|
||
|
|
|
||
|
|
# and nonzero
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, 0, 0)
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, 0, 0, 'col')
|
||
|
|
|
||
|
|
# must have at least k+p rows or cols, depending.
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, 3, q.shape[0]-2)
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, 3, r.shape[1]-2, 'col')
|
||
|
|
|
||
|
|
def test_empty_q(self):
|
||
|
|
a, q, r = self.generate('tall')
|
||
|
|
# same code path for 'row' and 'col'
|
||
|
|
assert_raises(ValueError, qr_delete, np.array([]), r, 0, 1)
|
||
|
|
|
||
|
|
def test_empty_r(self):
|
||
|
|
a, q, r = self.generate('tall')
|
||
|
|
# same code path for 'row' and 'col'
|
||
|
|
assert_raises(ValueError, qr_delete, q, np.array([]), 0, 1)
|
||
|
|
|
||
|
|
def test_mismatched_q_and_r(self):
|
||
|
|
a, q, r = self.generate('tall')
|
||
|
|
r = r[1:]
|
||
|
|
assert_raises(ValueError, qr_delete, q, r, 0, 1)
|
||
|
|
|
||
|
|
def test_unsupported_dtypes(self):
|
||
|
|
dts = ['int8', 'int16', 'int32', 'int64',
|
||
|
|
'uint8', 'uint16', 'uint32', 'uint64',
|
||
|
|
'float16', 'longdouble', 'longcomplex',
|
||
|
|
'bool']
|
||
|
|
a, q0, r0 = self.generate('tall')
|
||
|
|
for dtype in dts:
|
||
|
|
q = q0.real.astype(dtype)
|
||
|
|
r = r0.real.astype(dtype)
|
||
|
|
assert_raises(ValueError, qr_delete, q, r0, 0, 1, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r0, 0, 2, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r0, 0, 1, 'col')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r0, 0, 2, 'col')
|
||
|
|
|
||
|
|
assert_raises(ValueError, qr_delete, q0, r, 0, 1, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q0, r, 0, 2, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q0, r, 0, 1, 'col')
|
||
|
|
assert_raises(ValueError, qr_delete, q0, r, 0, 2, 'col')
|
||
|
|
|
||
|
|
def test_check_finite(self):
|
||
|
|
a0, q0, r0 = self.generate('tall')
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
q[1,1] = np.nan
|
||
|
|
assert_raises(ValueError, qr_delete, q, r0, 0, 1, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r0, 0, 3, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r0, 0, 1, 'col')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r0, 0, 3, 'col')
|
||
|
|
|
||
|
|
r = r0.copy('F')
|
||
|
|
r[1,1] = np.nan
|
||
|
|
assert_raises(ValueError, qr_delete, q0, r, 0, 1, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q0, r, 0, 3, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q0, r, 0, 1, 'col')
|
||
|
|
assert_raises(ValueError, qr_delete, q0, r, 0, 3, 'col')
|
||
|
|
|
||
|
|
def test_qr_scalar(self):
|
||
|
|
a, q, r = self.generate('1x1')
|
||
|
|
assert_raises(ValueError, qr_delete, q[0, 0], r, 0, 1, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r[0, 0], 0, 1, 'row')
|
||
|
|
assert_raises(ValueError, qr_delete, q[0, 0], r, 0, 1, 'col')
|
||
|
|
assert_raises(ValueError, qr_delete, q, r[0, 0], 0, 1, 'col')
|
||
|
|
|
||
|
|
class TestQRdelete_f(BaseQRdelete):
|
||
|
|
dtype = np.dtype('f')
|
||
|
|
|
||
|
|
class TestQRdelete_F(BaseQRdelete):
|
||
|
|
dtype = np.dtype('F')
|
||
|
|
|
||
|
|
class TestQRdelete_d(BaseQRdelete):
|
||
|
|
dtype = np.dtype('d')
|
||
|
|
|
||
|
|
class TestQRdelete_D(BaseQRdelete):
|
||
|
|
dtype = np.dtype('D')
|
||
|
|
|
||
|
|
class BaseQRinsert(BaseQRdeltas):
|
||
|
|
def generate(self, type, mode='full', which='row', p=1):
|
||
|
|
a, q, r = super(BaseQRinsert, self).generate(type, mode)
|
||
|
|
|
||
|
|
assert_(p > 0)
|
||
|
|
|
||
|
|
# super call set the seed...
|
||
|
|
if which == 'row':
|
||
|
|
if p == 1:
|
||
|
|
u = np.random.random(a.shape[1])
|
||
|
|
else:
|
||
|
|
u = np.random.random((p, a.shape[1]))
|
||
|
|
elif which == 'col':
|
||
|
|
if p == 1:
|
||
|
|
u = np.random.random(a.shape[0])
|
||
|
|
else:
|
||
|
|
u = np.random.random((a.shape[0], p))
|
||
|
|
else:
|
||
|
|
ValueError('which should be either "row" or "col"')
|
||
|
|
|
||
|
|
if np.iscomplexobj(self.dtype.type(1)):
|
||
|
|
b = np.random.random(u.shape)
|
||
|
|
u = u + 1j * b
|
||
|
|
|
||
|
|
u = u.astype(self.dtype)
|
||
|
|
return a, q, r, u
|
||
|
|
|
||
|
|
def test_sqr_1_row(self):
|
||
|
|
a, q, r, u = self.generate('sqr', which='row')
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, row, u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_sqr_p_row(self):
|
||
|
|
# sqr + rows --> fat always
|
||
|
|
a, q, r, u = self.generate('sqr', which='row', p=3)
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, np.full(3, row, np.intp), u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_sqr_1_col(self):
|
||
|
|
a, q, r, u = self.generate('sqr', which='col')
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, col, u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_sqr_p_col(self):
|
||
|
|
# sqr + cols --> fat always
|
||
|
|
a, q, r, u = self.generate('sqr', which='col', p=3)
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(3, col, np.intp), u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_tall_1_row(self):
|
||
|
|
a, q, r, u = self.generate('tall', which='row')
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, row, u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_tall_p_row(self):
|
||
|
|
# tall + rows --> tall always
|
||
|
|
a, q, r, u = self.generate('tall', which='row', p=3)
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, np.full(3, row, np.intp), u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_tall_1_col(self):
|
||
|
|
a, q, r, u = self.generate('tall', which='col')
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, col, u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
# for column adds to tall matrices there are three cases to test
|
||
|
|
# tall + pcol --> tall
|
||
|
|
# tall + pcol --> sqr
|
||
|
|
# tall + pcol --> fat
|
||
|
|
def base_tall_p_col_xxx(self, p):
|
||
|
|
a, q, r, u = self.generate('tall', which='col', p=p)
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(p, col, np.intp), u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_tall_p_col_tall(self):
|
||
|
|
# 12x7 + 12x3 = 12x10 --> stays tall
|
||
|
|
self.base_tall_p_col_xxx(3)
|
||
|
|
|
||
|
|
def test_tall_p_col_sqr(self):
|
||
|
|
# 12x7 + 12x5 = 12x12 --> becomes sqr
|
||
|
|
self.base_tall_p_col_xxx(5)
|
||
|
|
|
||
|
|
def test_tall_p_col_fat(self):
|
||
|
|
# 12x7 + 12x7 = 12x14 --> becomes fat
|
||
|
|
self.base_tall_p_col_xxx(7)
|
||
|
|
|
||
|
|
def test_fat_1_row(self):
|
||
|
|
a, q, r, u = self.generate('fat', which='row')
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, row, u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
# for row adds to fat matrices there are three cases to test
|
||
|
|
# fat + prow --> fat
|
||
|
|
# fat + prow --> sqr
|
||
|
|
# fat + prow --> tall
|
||
|
|
def base_fat_p_row_xxx(self, p):
|
||
|
|
a, q, r, u = self.generate('fat', which='row', p=p)
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, np.full(p, row, np.intp), u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_fat_p_row_fat(self):
|
||
|
|
# 7x12 + 3x12 = 10x12 --> stays fat
|
||
|
|
self.base_fat_p_row_xxx(3)
|
||
|
|
|
||
|
|
def test_fat_p_row_sqr(self):
|
||
|
|
# 7x12 + 5x12 = 12x12 --> becomes sqr
|
||
|
|
self.base_fat_p_row_xxx(5)
|
||
|
|
|
||
|
|
def test_fat_p_row_tall(self):
|
||
|
|
# 7x12 + 7x12 = 14x12 --> becomes tall
|
||
|
|
self.base_fat_p_row_xxx(7)
|
||
|
|
|
||
|
|
def test_fat_1_col(self):
|
||
|
|
a, q, r, u = self.generate('fat', which='col')
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, col, u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_fat_p_col(self):
|
||
|
|
# fat + cols --> fat always
|
||
|
|
a, q, r, u = self.generate('fat', which='col', p=3)
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(3, col, np.intp), u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_economic_1_row(self):
|
||
|
|
a, q, r, u = self.generate('tall', 'economic', 'row')
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row, overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, row, u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_economic_p_row(self):
|
||
|
|
# tall + rows --> tall always
|
||
|
|
a, q, r, u = self.generate('tall', 'economic', 'row', 3)
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row, overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(3, row, np.intp), u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_economic_1_col(self):
|
||
|
|
a, q, r, u = self.generate('tall', 'economic', which='col')
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u.copy(), col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, col, u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_economic_1_col_bad_update(self):
|
||
|
|
# When the column to be added lies in the span of Q, the update is
|
||
|
|
# not meaningful. This is detected, and a LinAlgError is issued.
|
||
|
|
q = np.eye(5, 3, dtype=self.dtype)
|
||
|
|
r = np.eye(3, dtype=self.dtype)
|
||
|
|
u = np.array([1, 0, 0, 0, 0], self.dtype)
|
||
|
|
assert_raises(linalg.LinAlgError, qr_insert, q, r, u, 0, 'col')
|
||
|
|
|
||
|
|
# for column adds to economic matrices there are three cases to test
|
||
|
|
# eco + pcol --> eco
|
||
|
|
# eco + pcol --> sqr
|
||
|
|
# eco + pcol --> fat
|
||
|
|
def base_economic_p_col_xxx(self, p):
|
||
|
|
a, q, r, u = self.generate('tall', 'economic', which='col', p=p)
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(p, col, np.intp), u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_economic_p_col_eco(self):
|
||
|
|
# 12x7 + 12x3 = 12x10 --> stays eco
|
||
|
|
self.base_economic_p_col_xxx(3)
|
||
|
|
|
||
|
|
def test_economic_p_col_sqr(self):
|
||
|
|
# 12x7 + 12x5 = 12x12 --> becomes sqr
|
||
|
|
self.base_economic_p_col_xxx(5)
|
||
|
|
|
||
|
|
def test_economic_p_col_fat(self):
|
||
|
|
# 12x7 + 12x7 = 12x14 --> becomes fat
|
||
|
|
self.base_economic_p_col_xxx(7)
|
||
|
|
|
||
|
|
def test_Mx1_1_row(self):
|
||
|
|
a, q, r, u = self.generate('Mx1', which='row')
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, row, u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_Mx1_p_row(self):
|
||
|
|
a, q, r, u = self.generate('Mx1', which='row', p=3)
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, np.full(3, row, np.intp), u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_Mx1_1_col(self):
|
||
|
|
a, q, r, u = self.generate('Mx1', which='col')
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, col, u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_Mx1_p_col(self):
|
||
|
|
a, q, r, u = self.generate('Mx1', which='col', p=3)
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(3, col, np.intp), u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_Mx1_economic_1_row(self):
|
||
|
|
a, q, r, u = self.generate('Mx1', 'economic', 'row')
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, row, u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_Mx1_economic_p_row(self):
|
||
|
|
a, q, r, u = self.generate('Mx1', 'economic', 'row', 3)
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, np.full(3, row, np.intp), u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_Mx1_economic_1_col(self):
|
||
|
|
a, q, r, u = self.generate('Mx1', 'economic', 'col')
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, col, u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_Mx1_economic_p_col(self):
|
||
|
|
a, q, r, u = self.generate('Mx1', 'economic', 'col', 3)
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(3, col, np.intp), u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_1xN_1_row(self):
|
||
|
|
a, q, r, u = self.generate('1xN', which='row')
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, row, u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1xN_p_row(self):
|
||
|
|
a, q, r, u = self.generate('1xN', which='row', p=3)
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, np.full(3, row, np.intp), u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1xN_1_col(self):
|
||
|
|
a, q, r, u = self.generate('1xN', which='col')
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, col, u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1xN_p_col(self):
|
||
|
|
a, q, r, u = self.generate('1xN', which='col', p=3)
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(3, col, np.intp), u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1x1_1_row(self):
|
||
|
|
a, q, r, u = self.generate('1x1', which='row')
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, row, u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1x1_p_row(self):
|
||
|
|
a, q, r, u = self.generate('1x1', which='row', p=3)
|
||
|
|
for row in range(r.shape[0] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, row)
|
||
|
|
a1 = np.insert(a, np.full(3, row, np.intp), u, 0)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1x1_1_col(self):
|
||
|
|
a, q, r, u = self.generate('1x1', which='col')
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, col, u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1x1_p_col(self):
|
||
|
|
a, q, r, u = self.generate('1x1', which='col', p=3)
|
||
|
|
for col in range(r.shape[1] + 1):
|
||
|
|
q1, r1 = qr_insert(q, r, u, col, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, np.full(3, col, np.intp), u, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1x1_1_scalar(self):
|
||
|
|
a, q, r, u = self.generate('1x1', which='row')
|
||
|
|
assert_raises(ValueError, qr_insert, q[0, 0], r, u, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r[0, 0], u, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r, u[0], 0, 'row')
|
||
|
|
|
||
|
|
assert_raises(ValueError, qr_insert, q[0, 0], r, u, 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r[0, 0], u, 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r, u[0], 0, 'col')
|
||
|
|
|
||
|
|
def base_non_simple_strides(self, adjust_strides, k, p, which):
|
||
|
|
for type in ['sqr', 'tall', 'fat']:
|
||
|
|
a, q0, r0, u0 = self.generate(type, which=which, p=p)
|
||
|
|
qs, rs, us = adjust_strides((q0, r0, u0))
|
||
|
|
if p == 1:
|
||
|
|
ai = np.insert(a, k, u0, 0 if which == 'row' else 1)
|
||
|
|
else:
|
||
|
|
ai = np.insert(a, np.full(p, k, np.intp),
|
||
|
|
u0 if which == 'row' else u0,
|
||
|
|
0 if which == 'row' else 1)
|
||
|
|
|
||
|
|
# for each variable, q, r, u we try with it strided and
|
||
|
|
# overwrite=False. Then we try with overwrite=True. Nothing
|
||
|
|
# is checked to see if it can be overwritten, since only
|
||
|
|
# F ordered Q can be overwritten when adding columns.
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
q1, r1 = qr_insert(qs, r, u, k, which, overwrite_qru=False)
|
||
|
|
check_qr(q1, r1, ai, self.rtol, self.atol)
|
||
|
|
q1o, r1o = qr_insert(qs, r, u, k, which, overwrite_qru=True)
|
||
|
|
check_qr(q1o, r1o, ai, self.rtol, self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
q2, r2 = qr_insert(q, rs, u, k, which, overwrite_qru=False)
|
||
|
|
check_qr(q2, r2, ai, self.rtol, self.atol)
|
||
|
|
q2o, r2o = qr_insert(q, rs, u, k, which, overwrite_qru=True)
|
||
|
|
check_qr(q2o, r2o, ai, self.rtol, self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
q3, r3 = qr_insert(q, r, us, k, which, overwrite_qru=False)
|
||
|
|
check_qr(q3, r3, ai, self.rtol, self.atol)
|
||
|
|
q3o, r3o = qr_insert(q, r, us, k, which, overwrite_qru=True)
|
||
|
|
check_qr(q3o, r3o, ai, self.rtol, self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
# since some of these were consumed above
|
||
|
|
qs, rs, us = adjust_strides((q, r, u))
|
||
|
|
q5, r5 = qr_insert(qs, rs, us, k, which, overwrite_qru=False)
|
||
|
|
check_qr(q5, r5, ai, self.rtol, self.atol)
|
||
|
|
q5o, r5o = qr_insert(qs, rs, us, k, which, overwrite_qru=True)
|
||
|
|
check_qr(q5o, r5o, ai, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_non_unit_strides_1_row(self):
|
||
|
|
self.base_non_simple_strides(make_strided, 0, 1, 'row')
|
||
|
|
|
||
|
|
def test_non_unit_strides_p_row(self):
|
||
|
|
self.base_non_simple_strides(make_strided, 0, 3, 'row')
|
||
|
|
|
||
|
|
def test_non_unit_strides_1_col(self):
|
||
|
|
self.base_non_simple_strides(make_strided, 0, 1, 'col')
|
||
|
|
|
||
|
|
def test_non_unit_strides_p_col(self):
|
||
|
|
self.base_non_simple_strides(make_strided, 0, 3, 'col')
|
||
|
|
|
||
|
|
def test_neg_strides_1_row(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, 0, 1, 'row')
|
||
|
|
|
||
|
|
def test_neg_strides_p_row(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, 0, 3, 'row')
|
||
|
|
|
||
|
|
def test_neg_strides_1_col(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, 0, 1, 'col')
|
||
|
|
|
||
|
|
def test_neg_strides_p_col(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, 0, 3, 'col')
|
||
|
|
|
||
|
|
def test_non_itemsize_strides_1_row(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, 0, 1, 'row')
|
||
|
|
|
||
|
|
def test_non_itemsize_strides_p_row(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, 0, 3, 'row')
|
||
|
|
|
||
|
|
def test_non_itemsize_strides_1_col(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, 0, 1, 'col')
|
||
|
|
|
||
|
|
def test_non_itemsize_strides_p_col(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, 0, 3, 'col')
|
||
|
|
|
||
|
|
def test_non_native_byte_order_1_row(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, 0, 1, 'row')
|
||
|
|
|
||
|
|
def test_non_native_byte_order_p_row(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, 0, 3, 'row')
|
||
|
|
|
||
|
|
def test_non_native_byte_order_1_col(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, 0, 1, 'col')
|
||
|
|
|
||
|
|
def test_non_native_byte_order_p_col(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, 0, 3, 'col')
|
||
|
|
|
||
|
|
def test_overwrite_qu_rank_1(self):
|
||
|
|
# when inserting rows, the size of both Q and R change, so only
|
||
|
|
# column inserts can overwrite q. Only complex column inserts
|
||
|
|
# with C ordered Q overwrite u. Any contiguous Q is overwritten
|
||
|
|
# when inserting 1 column
|
||
|
|
a, q0, r, u, = self.generate('sqr', which='col', p=1)
|
||
|
|
q = q0.copy('C')
|
||
|
|
u0 = u.copy()
|
||
|
|
# don't overwrite
|
||
|
|
q1, r1 = qr_insert(q, r, u, 0, 'col', overwrite_qru=False)
|
||
|
|
a1 = np.insert(a, 0, u0, 1)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
check_qr(q, r, a, self.rtol, self.atol)
|
||
|
|
|
||
|
|
# try overwriting
|
||
|
|
q2, r2 = qr_insert(q, r, u, 0, 'col', overwrite_qru=True)
|
||
|
|
check_qr(q2, r2, a1, self.rtol, self.atol)
|
||
|
|
# verify the overwriting
|
||
|
|
assert_allclose(q2, q, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(u, u0.conj(), self.rtol, self.atol)
|
||
|
|
|
||
|
|
# now try with a fortran ordered Q
|
||
|
|
qF = q0.copy('F')
|
||
|
|
u1 = u0.copy()
|
||
|
|
q3, r3 = qr_insert(qF, r, u1, 0, 'col', overwrite_qru=False)
|
||
|
|
check_qr(q3, r3, a1, self.rtol, self.atol)
|
||
|
|
check_qr(qF, r, a, self.rtol, self.atol)
|
||
|
|
|
||
|
|
# try overwriting
|
||
|
|
q4, r4 = qr_insert(qF, r, u1, 0, 'col', overwrite_qru=True)
|
||
|
|
check_qr(q4, r4, a1, self.rtol, self.atol)
|
||
|
|
assert_allclose(q4, qF, rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
def test_overwrite_qu_rank_p(self):
|
||
|
|
# when inserting rows, the size of both Q and R change, so only
|
||
|
|
# column inserts can potentially overwrite Q. In practice, only
|
||
|
|
# F ordered Q are overwritten with a rank p update.
|
||
|
|
a, q0, r, u, = self.generate('sqr', which='col', p=3)
|
||
|
|
q = q0.copy('F')
|
||
|
|
a1 = np.insert(a, np.zeros(3, np.intp), u, 1)
|
||
|
|
|
||
|
|
# don't overwrite
|
||
|
|
q1, r1 = qr_insert(q, r, u, 0, 'col', overwrite_qru=False)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
check_qr(q, r, a, self.rtol, self.atol)
|
||
|
|
|
||
|
|
# try overwriting
|
||
|
|
q2, r2 = qr_insert(q, r, u, 0, 'col', overwrite_qru=True)
|
||
|
|
check_qr(q2, r2, a1, self.rtol, self.atol)
|
||
|
|
assert_allclose(q2, q, rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
def test_empty_inputs(self):
|
||
|
|
a, q, r, u = self.generate('sqr', which='row')
|
||
|
|
assert_raises(ValueError, qr_insert, np.array([]), r, u, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, np.array([]), u, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r, np.array([]), 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, np.array([]), r, u, 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q, np.array([]), u, 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r, np.array([]), 0, 'col')
|
||
|
|
|
||
|
|
def test_mismatched_shapes(self):
|
||
|
|
a, q, r, u = self.generate('tall', which='row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r[1:], u, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q[:-2], r, u, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r, u[1:], 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r[1:], u, 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q[:-2], r, u, 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r, u[1:], 0, 'col')
|
||
|
|
|
||
|
|
def test_unsupported_dtypes(self):
|
||
|
|
dts = ['int8', 'int16', 'int32', 'int64',
|
||
|
|
'uint8', 'uint16', 'uint32', 'uint64',
|
||
|
|
'float16', 'longdouble', 'longcomplex',
|
||
|
|
'bool']
|
||
|
|
a, q0, r0, u0 = self.generate('sqr', which='row')
|
||
|
|
for dtype in dts:
|
||
|
|
q = q0.real.astype(dtype)
|
||
|
|
r = r0.real.astype(dtype)
|
||
|
|
u = u0.real.astype(dtype)
|
||
|
|
assert_raises(ValueError, qr_insert, q, r0, u0, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r0, u0, 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r, u0, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r, u0, 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r0, u, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r0, u, 0, 'col')
|
||
|
|
|
||
|
|
def test_check_finite(self):
|
||
|
|
a0, q0, r0, u0 = self.generate('sqr', which='row', p=3)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
q[1,1] = np.nan
|
||
|
|
assert_raises(ValueError, qr_insert, q, r0, u0[:,0], 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r0, u0, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r0, u0[:,0], 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q, r0, u0, 0, 'col')
|
||
|
|
|
||
|
|
r = r0.copy('F')
|
||
|
|
r[1,1] = np.nan
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r, u0[:,0], 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r, u0, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r, u0[:,0], 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r, u0, 0, 'col')
|
||
|
|
|
||
|
|
u = u0.copy('F')
|
||
|
|
u[0,0] = np.nan
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r0, u[:,0], 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r0, u, 0, 'row')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r0, u[:,0], 0, 'col')
|
||
|
|
assert_raises(ValueError, qr_insert, q0, r0, u, 0, 'col')
|
||
|
|
|
||
|
|
class TestQRinsert_f(BaseQRinsert):
|
||
|
|
dtype = np.dtype('f')
|
||
|
|
|
||
|
|
class TestQRinsert_F(BaseQRinsert):
|
||
|
|
dtype = np.dtype('F')
|
||
|
|
|
||
|
|
class TestQRinsert_d(BaseQRinsert):
|
||
|
|
dtype = np.dtype('d')
|
||
|
|
|
||
|
|
class TestQRinsert_D(BaseQRinsert):
|
||
|
|
dtype = np.dtype('D')
|
||
|
|
|
||
|
|
class BaseQRupdate(BaseQRdeltas):
|
||
|
|
def generate(self, type, mode='full', p=1):
|
||
|
|
a, q, r = super(BaseQRupdate, self).generate(type, mode)
|
||
|
|
|
||
|
|
# super call set the seed...
|
||
|
|
if p == 1:
|
||
|
|
u = np.random.random(q.shape[0])
|
||
|
|
v = np.random.random(r.shape[1])
|
||
|
|
else:
|
||
|
|
u = np.random.random((q.shape[0], p))
|
||
|
|
v = np.random.random((r.shape[1], p))
|
||
|
|
|
||
|
|
if np.iscomplexobj(self.dtype.type(1)):
|
||
|
|
b = np.random.random(u.shape)
|
||
|
|
u = u + 1j * b
|
||
|
|
|
||
|
|
c = np.random.random(v.shape)
|
||
|
|
v = v + 1j * c
|
||
|
|
|
||
|
|
u = u.astype(self.dtype)
|
||
|
|
v = v.astype(self.dtype)
|
||
|
|
return a, q, r, u, v
|
||
|
|
|
||
|
|
def test_sqr_rank_1(self):
|
||
|
|
a, q, r, u, v = self.generate('sqr')
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_sqr_rank_p(self):
|
||
|
|
# test ndim = 2, rank 1 updates here too
|
||
|
|
for p in [1, 2, 3, 5]:
|
||
|
|
a, q, r, u, v = self.generate('sqr', p=p)
|
||
|
|
if p == 1:
|
||
|
|
u = u.reshape(u.size, 1)
|
||
|
|
v = v.reshape(v.size, 1)
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.dot(u, v.T.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_tall_rank_1(self):
|
||
|
|
a, q, r, u, v = self.generate('tall')
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_tall_rank_p(self):
|
||
|
|
for p in [1, 2, 3, 5]:
|
||
|
|
a, q, r, u, v = self.generate('tall', p=p)
|
||
|
|
if p == 1:
|
||
|
|
u = u.reshape(u.size, 1)
|
||
|
|
v = v.reshape(v.size, 1)
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.dot(u, v.T.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_fat_rank_1(self):
|
||
|
|
a, q, r, u, v = self.generate('fat')
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_fat_rank_p(self):
|
||
|
|
for p in [1, 2, 3, 5]:
|
||
|
|
a, q, r, u, v = self.generate('fat', p=p)
|
||
|
|
if p == 1:
|
||
|
|
u = u.reshape(u.size, 1)
|
||
|
|
v = v.reshape(v.size, 1)
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.dot(u, v.T.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_economic_rank_1(self):
|
||
|
|
a, q, r, u, v = self.generate('tall', 'economic')
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_economic_rank_p(self):
|
||
|
|
for p in [1, 2, 3, 5]:
|
||
|
|
a, q, r, u, v = self.generate('tall', 'economic', p)
|
||
|
|
if p == 1:
|
||
|
|
u = u.reshape(u.size, 1)
|
||
|
|
v = v.reshape(v.size, 1)
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.dot(u, v.T.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_Mx1_rank_1(self):
|
||
|
|
a, q, r, u, v = self.generate('Mx1')
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_Mx1_rank_p(self):
|
||
|
|
# when M or N == 1, only a rank 1 update is allowed. This isn't
|
||
|
|
# fundamental limitation, but the code does not support it.
|
||
|
|
a, q, r, u, v = self.generate('Mx1', p=1)
|
||
|
|
u = u.reshape(u.size, 1)
|
||
|
|
v = v.reshape(v.size, 1)
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.dot(u, v.T.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_Mx1_economic_rank_1(self):
|
||
|
|
a, q, r, u, v = self.generate('Mx1', 'economic')
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_Mx1_economic_rank_p(self):
|
||
|
|
# when M or N == 1, only a rank 1 update is allowed. This isn't
|
||
|
|
# fundamental limitation, but the code does not support it.
|
||
|
|
a, q, r, u, v = self.generate('Mx1', 'economic', p=1)
|
||
|
|
u = u.reshape(u.size, 1)
|
||
|
|
v = v.reshape(v.size, 1)
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.dot(u, v.T.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
def test_1xN_rank_1(self):
|
||
|
|
a, q, r, u, v = self.generate('1xN')
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1xN_rank_p(self):
|
||
|
|
# when M or N == 1, only a rank 1 update is allowed. This isn't
|
||
|
|
# fundamental limitation, but the code does not support it.
|
||
|
|
a, q, r, u, v = self.generate('1xN', p=1)
|
||
|
|
u = u.reshape(u.size, 1)
|
||
|
|
v = v.reshape(v.size, 1)
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.dot(u, v.T.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1x1_rank_1(self):
|
||
|
|
a, q, r, u, v = self.generate('1x1')
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1x1_rank_p(self):
|
||
|
|
# when M or N == 1, only a rank 1 update is allowed. This isn't
|
||
|
|
# fundamental limitation, but the code does not support it.
|
||
|
|
a, q, r, u, v = self.generate('1x1', p=1)
|
||
|
|
u = u.reshape(u.size, 1)
|
||
|
|
v = v.reshape(v.size, 1)
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
a1 = a + np.dot(u, v.T.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
|
||
|
|
def test_1x1_rank_1_scalar(self):
|
||
|
|
a, q, r, u, v = self.generate('1x1')
|
||
|
|
assert_raises(ValueError, qr_update, q[0, 0], r, u, v)
|
||
|
|
assert_raises(ValueError, qr_update, q, r[0, 0], u, v)
|
||
|
|
assert_raises(ValueError, qr_update, q, r, u[0], v)
|
||
|
|
assert_raises(ValueError, qr_update, q, r, u, v[0])
|
||
|
|
|
||
|
|
def base_non_simple_strides(self, adjust_strides, mode, p, overwriteable):
|
||
|
|
assert_sqr = False if mode == 'economic' else True
|
||
|
|
for type in ['sqr', 'tall', 'fat']:
|
||
|
|
a, q0, r0, u0, v0 = self.generate(type, mode, p)
|
||
|
|
qs, rs, us, vs = adjust_strides((q0, r0, u0, v0))
|
||
|
|
if p == 1:
|
||
|
|
aup = a + np.outer(u0, v0.conj())
|
||
|
|
else:
|
||
|
|
aup = a + np.dot(u0, v0.T.conj())
|
||
|
|
|
||
|
|
# for each variable, q, r, u, v we try with it strided and
|
||
|
|
# overwrite=False. Then we try with overwrite=True, and make
|
||
|
|
# sure that if p == 1, r and v are still overwritten.
|
||
|
|
# a strided q and u must always be copied.
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
v = v0.copy('C')
|
||
|
|
q1, r1 = qr_update(qs, r, u, v, False)
|
||
|
|
check_qr(q1, r1, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
q1o, r1o = qr_update(qs, r, u, v, True)
|
||
|
|
check_qr(q1o, r1o, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
if overwriteable:
|
||
|
|
assert_allclose(r1o, r, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(v, v0.conj(), rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
v = v0.copy('C')
|
||
|
|
q2, r2 = qr_update(q, rs, u, v, False)
|
||
|
|
check_qr(q2, r2, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
q2o, r2o = qr_update(q, rs, u, v, True)
|
||
|
|
check_qr(q2o, r2o, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
if overwriteable:
|
||
|
|
assert_allclose(r2o, rs, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(v, v0.conj(), rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
v = v0.copy('C')
|
||
|
|
q3, r3 = qr_update(q, r, us, v, False)
|
||
|
|
check_qr(q3, r3, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
q3o, r3o = qr_update(q, r, us, v, True)
|
||
|
|
check_qr(q3o, r3o, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
if overwriteable:
|
||
|
|
assert_allclose(r3o, r, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(v, v0.conj(), rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
v = v0.copy('C')
|
||
|
|
q4, r4 = qr_update(q, r, u, vs, False)
|
||
|
|
check_qr(q4, r4, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
q4o, r4o = qr_update(q, r, u, vs, True)
|
||
|
|
check_qr(q4o, r4o, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
if overwriteable:
|
||
|
|
assert_allclose(r4o, r, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(vs, v0.conj(), rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
v = v0.copy('C')
|
||
|
|
# since some of these were consumed above
|
||
|
|
qs, rs, us, vs = adjust_strides((q, r, u, v))
|
||
|
|
q5, r5 = qr_update(qs, rs, us, vs, False)
|
||
|
|
check_qr(q5, r5, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
q5o, r5o = qr_update(qs, rs, us, vs, True)
|
||
|
|
check_qr(q5o, r5o, aup, self.rtol, self.atol, assert_sqr)
|
||
|
|
if overwriteable:
|
||
|
|
assert_allclose(r5o, rs, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(vs, v0.conj(), rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
def test_non_unit_strides_rank_1(self):
|
||
|
|
self.base_non_simple_strides(make_strided, 'full', 1, True)
|
||
|
|
|
||
|
|
def test_non_unit_strides_economic_rank_1(self):
|
||
|
|
self.base_non_simple_strides(make_strided, 'economic', 1, True)
|
||
|
|
|
||
|
|
def test_non_unit_strides_rank_p(self):
|
||
|
|
self.base_non_simple_strides(make_strided, 'full', 3, False)
|
||
|
|
|
||
|
|
def test_non_unit_strides_economic_rank_p(self):
|
||
|
|
self.base_non_simple_strides(make_strided, 'economic', 3, False)
|
||
|
|
|
||
|
|
def test_neg_strides_rank_1(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, 'full', 1, False)
|
||
|
|
|
||
|
|
def test_neg_strides_economic_rank_1(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, 'economic', 1, False)
|
||
|
|
|
||
|
|
def test_neg_strides_rank_p(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, 'full', 3, False)
|
||
|
|
|
||
|
|
def test_neg_strides_economic_rank_p(self):
|
||
|
|
self.base_non_simple_strides(negate_strides, 'economic', 3, False)
|
||
|
|
|
||
|
|
def test_non_itemsize_strides_rank_1(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, 'full', 1, False)
|
||
|
|
|
||
|
|
def test_non_itemsize_strides_economic_rank_1(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, 'economic', 1, False)
|
||
|
|
|
||
|
|
def test_non_itemsize_strides_rank_p(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, 'full', 3, False)
|
||
|
|
|
||
|
|
def test_non_itemsize_strides_economic_rank_p(self):
|
||
|
|
self.base_non_simple_strides(nonitemsize_strides, 'economic', 3, False)
|
||
|
|
|
||
|
|
def test_non_native_byte_order_rank_1(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, 'full', 1, False)
|
||
|
|
|
||
|
|
def test_non_native_byte_order_economic_rank_1(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, 'economic', 1, False)
|
||
|
|
|
||
|
|
def test_non_native_byte_order_rank_p(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, 'full', 3, False)
|
||
|
|
|
||
|
|
def test_non_native_byte_order_economic_rank_p(self):
|
||
|
|
self.base_non_simple_strides(make_nonnative, 'economic', 3, False)
|
||
|
|
|
||
|
|
def test_overwrite_qruv_rank_1(self):
|
||
|
|
# Any positive strided q, r, u, and v can be overwritten for a rank 1
|
||
|
|
# update, only checking C and F contiguous.
|
||
|
|
a, q0, r0, u0, v0 = self.generate('sqr')
|
||
|
|
a1 = a + np.outer(u0, v0.conj())
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
v = v0.copy('F')
|
||
|
|
|
||
|
|
# don't overwrite
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
check_qr(q, r, a, self.rtol, self.atol)
|
||
|
|
|
||
|
|
q2, r2 = qr_update(q, r, u, v, True)
|
||
|
|
check_qr(q2, r2, a1, self.rtol, self.atol)
|
||
|
|
# verify the overwriting, no good way to check u and v.
|
||
|
|
assert_allclose(q2, q, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r2, r, rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('C')
|
||
|
|
r = r0.copy('C')
|
||
|
|
u = u0.copy('C')
|
||
|
|
v = v0.copy('C')
|
||
|
|
q3, r3 = qr_update(q, r, u, v, True)
|
||
|
|
check_qr(q3, r3, a1, self.rtol, self.atol)
|
||
|
|
assert_allclose(q3, q, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r3, r, rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
def test_overwrite_qruv_rank_1_economic(self):
|
||
|
|
# updating economic decompositions can overwrite any contigous r,
|
||
|
|
# and positively strided r and u. V is only ever read.
|
||
|
|
# only checking C and F contiguous.
|
||
|
|
a, q0, r0, u0, v0 = self.generate('tall', 'economic')
|
||
|
|
a1 = a + np.outer(u0, v0.conj())
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
v = v0.copy('F')
|
||
|
|
|
||
|
|
# don't overwrite
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
check_qr(q, r, a, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
q2, r2 = qr_update(q, r, u, v, True)
|
||
|
|
check_qr(q2, r2, a1, self.rtol, self.atol, False)
|
||
|
|
# verify the overwriting, no good way to check u and v.
|
||
|
|
assert_allclose(q2, q, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r2, r, rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
q = q0.copy('C')
|
||
|
|
r = r0.copy('C')
|
||
|
|
u = u0.copy('C')
|
||
|
|
v = v0.copy('C')
|
||
|
|
q3, r3 = qr_update(q, r, u, v, True)
|
||
|
|
check_qr(q3, r3, a1, self.rtol, self.atol, False)
|
||
|
|
assert_allclose(q3, q, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r3, r, rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
def test_overwrite_qruv_rank_p(self):
|
||
|
|
# for rank p updates, q r must be F contiguous, v must be C (v.T --> F)
|
||
|
|
# and u can be C or F, but is only overwritten if Q is C and complex
|
||
|
|
a, q0, r0, u0, v0 = self.generate('sqr', p=3)
|
||
|
|
a1 = a + np.dot(u0, v0.T.conj())
|
||
|
|
q = q0.copy('F')
|
||
|
|
r = r0.copy('F')
|
||
|
|
u = u0.copy('F')
|
||
|
|
v = v0.copy('C')
|
||
|
|
|
||
|
|
# don't overwrite
|
||
|
|
q1, r1 = qr_update(q, r, u, v, False)
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol)
|
||
|
|
check_qr(q, r, a, self.rtol, self.atol)
|
||
|
|
|
||
|
|
q2, r2 = qr_update(q, r, u, v, True)
|
||
|
|
check_qr(q2, r2, a1, self.rtol, self.atol)
|
||
|
|
# verify the overwriting, no good way to check u and v.
|
||
|
|
assert_allclose(q2, q, rtol=self.rtol, atol=self.atol)
|
||
|
|
assert_allclose(r2, r, rtol=self.rtol, atol=self.atol)
|
||
|
|
|
||
|
|
def test_empty_inputs(self):
|
||
|
|
a, q, r, u, v = self.generate('tall')
|
||
|
|
assert_raises(ValueError, qr_update, np.array([]), r, u, v)
|
||
|
|
assert_raises(ValueError, qr_update, q, np.array([]), u, v)
|
||
|
|
assert_raises(ValueError, qr_update, q, r, np.array([]), v)
|
||
|
|
assert_raises(ValueError, qr_update, q, r, u, np.array([]))
|
||
|
|
|
||
|
|
def test_mismatched_shapes(self):
|
||
|
|
a, q, r, u, v = self.generate('tall')
|
||
|
|
assert_raises(ValueError, qr_update, q, r[1:], u, v)
|
||
|
|
assert_raises(ValueError, qr_update, q[:-2], r, u, v)
|
||
|
|
assert_raises(ValueError, qr_update, q, r, u[1:], v)
|
||
|
|
assert_raises(ValueError, qr_update, q, r, u, v[1:])
|
||
|
|
|
||
|
|
def test_unsupported_dtypes(self):
|
||
|
|
dts = ['int8', 'int16', 'int32', 'int64',
|
||
|
|
'uint8', 'uint16', 'uint32', 'uint64',
|
||
|
|
'float16', 'longdouble', 'longcomplex',
|
||
|
|
'bool']
|
||
|
|
a, q0, r0, u0, v0 = self.generate('tall')
|
||
|
|
for dtype in dts:
|
||
|
|
q = q0.real.astype(dtype)
|
||
|
|
r = r0.real.astype(dtype)
|
||
|
|
u = u0.real.astype(dtype)
|
||
|
|
v = v0.real.astype(dtype)
|
||
|
|
assert_raises(ValueError, qr_update, q, r0, u0, v0)
|
||
|
|
assert_raises(ValueError, qr_update, q0, r, u0, v0)
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u, v0)
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u0, v)
|
||
|
|
|
||
|
|
def test_integer_input(self):
|
||
|
|
q = np.arange(16).reshape(4, 4)
|
||
|
|
r = q.copy() # doesn't matter
|
||
|
|
u = q[:, 0].copy()
|
||
|
|
v = r[0, :].copy()
|
||
|
|
assert_raises(ValueError, qr_update, q, r, u, v)
|
||
|
|
|
||
|
|
def test_check_finite(self):
|
||
|
|
a0, q0, r0, u0, v0 = self.generate('tall', p=3)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
q[1,1] = np.nan
|
||
|
|
assert_raises(ValueError, qr_update, q, r0, u0[:,0], v0[:,0])
|
||
|
|
assert_raises(ValueError, qr_update, q, r0, u0, v0)
|
||
|
|
|
||
|
|
r = r0.copy('F')
|
||
|
|
r[1,1] = np.nan
|
||
|
|
assert_raises(ValueError, qr_update, q0, r, u0[:,0], v0[:,0])
|
||
|
|
assert_raises(ValueError, qr_update, q0, r, u0, v0)
|
||
|
|
|
||
|
|
u = u0.copy('F')
|
||
|
|
u[0,0] = np.nan
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u[:,0], v0[:,0])
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u, v0)
|
||
|
|
|
||
|
|
v = v0.copy('F')
|
||
|
|
v[0,0] = np.nan
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u[:,0], v[:,0])
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u, v)
|
||
|
|
|
||
|
|
def test_economic_check_finite(self):
|
||
|
|
a0, q0, r0, u0, v0 = self.generate('tall', mode='economic', p=3)
|
||
|
|
|
||
|
|
q = q0.copy('F')
|
||
|
|
q[1,1] = np.nan
|
||
|
|
assert_raises(ValueError, qr_update, q, r0, u0[:,0], v0[:,0])
|
||
|
|
assert_raises(ValueError, qr_update, q, r0, u0, v0)
|
||
|
|
|
||
|
|
r = r0.copy('F')
|
||
|
|
r[1,1] = np.nan
|
||
|
|
assert_raises(ValueError, qr_update, q0, r, u0[:,0], v0[:,0])
|
||
|
|
assert_raises(ValueError, qr_update, q0, r, u0, v0)
|
||
|
|
|
||
|
|
u = u0.copy('F')
|
||
|
|
u[0,0] = np.nan
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u[:,0], v0[:,0])
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u, v0)
|
||
|
|
|
||
|
|
v = v0.copy('F')
|
||
|
|
v[0,0] = np.nan
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u[:,0], v[:,0])
|
||
|
|
assert_raises(ValueError, qr_update, q0, r0, u, v)
|
||
|
|
|
||
|
|
def test_u_exactly_in_span_q(self):
|
||
|
|
q = np.array([[0, 0], [0, 0], [1, 0], [0, 1]], self.dtype)
|
||
|
|
r = np.array([[1, 0], [0, 1]], self.dtype)
|
||
|
|
u = np.array([0, 0, 0, -1], self.dtype)
|
||
|
|
v = np.array([1, 2], self.dtype)
|
||
|
|
q1, r1 = qr_update(q, r, u, v)
|
||
|
|
a1 = np.dot(q, r) + np.outer(u, v.conj())
|
||
|
|
check_qr(q1, r1, a1, self.rtol, self.atol, False)
|
||
|
|
|
||
|
|
class TestQRupdate_f(BaseQRupdate):
|
||
|
|
dtype = np.dtype('f')
|
||
|
|
|
||
|
|
class TestQRupdate_F(BaseQRupdate):
|
||
|
|
dtype = np.dtype('F')
|
||
|
|
|
||
|
|
class TestQRupdate_d(BaseQRupdate):
|
||
|
|
dtype = np.dtype('d')
|
||
|
|
|
||
|
|
class TestQRupdate_D(BaseQRupdate):
|
||
|
|
dtype = np.dtype('D')
|
||
|
|
|
||
|
|
def test_form_qTu():
|
||
|
|
# We want to ensure that all of the code paths through this function are
|
||
|
|
# tested. Most of them should be hit with the rest of test suite, but
|
||
|
|
# explicit tests make clear precisely what is being tested.
|
||
|
|
#
|
||
|
|
# This function expects that Q is either C or F contiguous and square.
|
||
|
|
# Economic mode decompositions (Q is (M, N), M != N) do not go through this
|
||
|
|
# function. U may have any positive strides.
|
||
|
|
#
|
||
|
|
# Some of these test are duplicates, since contiguous 1d arrays are both C
|
||
|
|
# and F.
|
||
|
|
|
||
|
|
q_order = ['F', 'C']
|
||
|
|
q_shape = [(8, 8), ]
|
||
|
|
u_order = ['F', 'C', 'A'] # here A means is not F not C
|
||
|
|
u_shape = [1, 3]
|
||
|
|
dtype = ['f', 'd', 'F', 'D']
|
||
|
|
|
||
|
|
for qo, qs, uo, us, d in \
|
||
|
|
itertools.product(q_order, q_shape, u_order, u_shape, dtype):
|
||
|
|
if us == 1:
|
||
|
|
check_form_qTu(qo, qs, uo, us, 1, d)
|
||
|
|
check_form_qTu(qo, qs, uo, us, 2, d)
|
||
|
|
else:
|
||
|
|
check_form_qTu(qo, qs, uo, us, 2, d)
|
||
|
|
|
||
|
|
def check_form_qTu(q_order, q_shape, u_order, u_shape, u_ndim, dtype):
|
||
|
|
np.random.seed(47)
|
||
|
|
if u_shape == 1 and u_ndim == 1:
|
||
|
|
u_shape = (q_shape[0],)
|
||
|
|
else:
|
||
|
|
u_shape = (q_shape[0], u_shape)
|
||
|
|
dtype = np.dtype(dtype)
|
||
|
|
|
||
|
|
if dtype.char in 'fd':
|
||
|
|
q = np.random.random(q_shape)
|
||
|
|
u = np.random.random(u_shape)
|
||
|
|
elif dtype.char in 'FD':
|
||
|
|
q = np.random.random(q_shape) + 1j*np.random.random(q_shape)
|
||
|
|
u = np.random.random(u_shape) + 1j*np.random.random(u_shape)
|
||
|
|
else:
|
||
|
|
ValueError("form_qTu doesn't support this dtype")
|
||
|
|
|
||
|
|
q = np.require(q, dtype, q_order)
|
||
|
|
if u_order != 'A':
|
||
|
|
u = np.require(u, dtype, u_order)
|
||
|
|
else:
|
||
|
|
u, = make_strided((u.astype(dtype),))
|
||
|
|
|
||
|
|
rtol = 10.0 ** -(np.finfo(dtype).precision-2)
|
||
|
|
atol = 2*np.finfo(dtype).eps
|
||
|
|
|
||
|
|
expected = np.dot(q.T.conj(), u)
|
||
|
|
res = _decomp_update._form_qTu(q, u)
|
||
|
|
assert_allclose(res, expected, rtol=rtol, atol=atol)
|