1097 lines
39 KiB
Python
1097 lines
39 KiB
Python
#
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# Created by: Pearu Peterson, April 2002
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#
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__usage__ = """
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Build linalg:
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python setup.py build
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Run tests if scipy is installed:
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python -c 'import scipy;scipy.linalg.test()'
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"""
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import math
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import pytest
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import numpy as np
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from numpy.testing import (assert_equal, assert_almost_equal, assert_,
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assert_array_almost_equal, assert_allclose)
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from pytest import raises as assert_raises
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from numpy import float32, float64, complex64, complex128, arange, triu, \
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tril, zeros, tril_indices, ones, mod, diag, append, eye, \
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nonzero
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from numpy.random import rand, seed
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from scipy.linalg import _fblas as fblas, get_blas_funcs, toeplitz, solve
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try:
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from scipy.linalg import _cblas as cblas
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except ImportError:
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cblas = None
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REAL_DTYPES = [float32, float64]
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COMPLEX_DTYPES = [complex64, complex128]
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DTYPES = REAL_DTYPES + COMPLEX_DTYPES
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def test_get_blas_funcs():
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# check that it returns Fortran code for arrays that are
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# fortran-ordered
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f1, f2, f3 = get_blas_funcs(
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('axpy', 'axpy', 'axpy'),
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(np.empty((2, 2), dtype=np.complex64, order='F'),
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np.empty((2, 2), dtype=np.complex128, order='C'))
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)
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# get_blas_funcs will choose libraries depending on most generic
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# array
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assert_equal(f1.typecode, 'z')
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assert_equal(f2.typecode, 'z')
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if cblas is not None:
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assert_equal(f1.module_name, 'cblas')
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assert_equal(f2.module_name, 'cblas')
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# check defaults.
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f1 = get_blas_funcs('rotg')
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assert_equal(f1.typecode, 'd')
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# check also dtype interface
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f1 = get_blas_funcs('gemm', dtype=np.complex64)
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assert_equal(f1.typecode, 'c')
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f1 = get_blas_funcs('gemm', dtype='F')
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assert_equal(f1.typecode, 'c')
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# extended precision complex
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f1 = get_blas_funcs('gemm', dtype=np.longcomplex)
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assert_equal(f1.typecode, 'z')
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# check safe complex upcasting
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f1 = get_blas_funcs('axpy',
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(np.empty((2, 2), dtype=np.float64),
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np.empty((2, 2), dtype=np.complex64))
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)
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assert_equal(f1.typecode, 'z')
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def test_get_blas_funcs_alias():
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# check alias for get_blas_funcs
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f, g = get_blas_funcs(('nrm2', 'dot'), dtype=np.complex64)
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assert f.typecode == 'c'
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assert g.typecode == 'c'
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f, g, h = get_blas_funcs(('dot', 'dotc', 'dotu'), dtype=np.float64)
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assert f is g
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assert f is h
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class TestCBLAS1Simple:
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def test_axpy(self):
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for p in 'sd':
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f = getattr(cblas, p+'axpy', None)
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if f is None:
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continue
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assert_array_almost_equal(f([1, 2, 3], [2, -1, 3], a=5),
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[7, 9, 18])
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for p in 'cz':
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f = getattr(cblas, p+'axpy', None)
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if f is None:
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continue
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assert_array_almost_equal(f([1, 2j, 3], [2, -1, 3], a=5),
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[7, 10j-1, 18])
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class TestFBLAS1Simple:
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def test_axpy(self):
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for p in 'sd':
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f = getattr(fblas, p+'axpy', None)
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if f is None:
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continue
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assert_array_almost_equal(f([1, 2, 3], [2, -1, 3], a=5),
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[7, 9, 18])
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for p in 'cz':
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f = getattr(fblas, p+'axpy', None)
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if f is None:
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continue
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assert_array_almost_equal(f([1, 2j, 3], [2, -1, 3], a=5),
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[7, 10j-1, 18])
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def test_copy(self):
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for p in 'sd':
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f = getattr(fblas, p+'copy', None)
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if f is None:
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continue
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assert_array_almost_equal(f([3, 4, 5], [8]*3), [3, 4, 5])
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for p in 'cz':
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f = getattr(fblas, p+'copy', None)
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if f is None:
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continue
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assert_array_almost_equal(f([3, 4j, 5+3j], [8]*3), [3, 4j, 5+3j])
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def test_asum(self):
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for p in 'sd':
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f = getattr(fblas, p+'asum', None)
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if f is None:
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continue
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assert_almost_equal(f([3, -4, 5]), 12)
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for p in ['sc', 'dz']:
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f = getattr(fblas, p+'asum', None)
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if f is None:
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continue
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assert_almost_equal(f([3j, -4, 3-4j]), 14)
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def test_dot(self):
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for p in 'sd':
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f = getattr(fblas, p+'dot', None)
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if f is None:
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continue
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assert_almost_equal(f([3, -4, 5], [2, 5, 1]), -9)
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def test_complex_dotu(self):
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for p in 'cz':
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f = getattr(fblas, p+'dotu', None)
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if f is None:
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continue
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assert_almost_equal(f([3j, -4, 3-4j], [2, 3, 1]), -9+2j)
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def test_complex_dotc(self):
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for p in 'cz':
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f = getattr(fblas, p+'dotc', None)
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if f is None:
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continue
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assert_almost_equal(f([3j, -4, 3-4j], [2, 3j, 1]), 3-14j)
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def test_nrm2(self):
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for p in 'sd':
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f = getattr(fblas, p+'nrm2', None)
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if f is None:
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continue
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assert_almost_equal(f([3, -4, 5]), math.sqrt(50))
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for p in ['c', 'z', 'sc', 'dz']:
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f = getattr(fblas, p+'nrm2', None)
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if f is None:
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continue
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assert_almost_equal(f([3j, -4, 3-4j]), math.sqrt(50))
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def test_scal(self):
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for p in 'sd':
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f = getattr(fblas, p+'scal', None)
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if f is None:
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continue
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assert_array_almost_equal(f(2, [3, -4, 5]), [6, -8, 10])
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for p in 'cz':
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f = getattr(fblas, p+'scal', None)
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if f is None:
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continue
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assert_array_almost_equal(f(3j, [3j, -4, 3-4j]), [-9, -12j, 12+9j])
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for p in ['cs', 'zd']:
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f = getattr(fblas, p+'scal', None)
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if f is None:
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continue
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assert_array_almost_equal(f(3, [3j, -4, 3-4j]), [9j, -12, 9-12j])
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def test_swap(self):
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for p in 'sd':
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f = getattr(fblas, p+'swap', None)
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if f is None:
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continue
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x, y = [2, 3, 1], [-2, 3, 7]
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x1, y1 = f(x, y)
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assert_array_almost_equal(x1, y)
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assert_array_almost_equal(y1, x)
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for p in 'cz':
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f = getattr(fblas, p+'swap', None)
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if f is None:
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continue
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x, y = [2, 3j, 1], [-2, 3, 7-3j]
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x1, y1 = f(x, y)
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assert_array_almost_equal(x1, y)
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assert_array_almost_equal(y1, x)
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def test_amax(self):
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for p in 'sd':
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f = getattr(fblas, 'i'+p+'amax')
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assert_equal(f([-2, 4, 3]), 1)
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for p in 'cz':
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f = getattr(fblas, 'i'+p+'amax')
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assert_equal(f([-5, 4+3j, 6]), 1)
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# XXX: need tests for rot,rotm,rotg,rotmg
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class TestFBLAS2Simple:
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def test_gemv(self):
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for p in 'sd':
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f = getattr(fblas, p+'gemv', None)
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if f is None:
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continue
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assert_array_almost_equal(f(3, [[3]], [-4]), [-36])
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assert_array_almost_equal(f(3, [[3]], [-4], 3, [5]), [-21])
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for p in 'cz':
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f = getattr(fblas, p+'gemv', None)
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if f is None:
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continue
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assert_array_almost_equal(f(3j, [[3-4j]], [-4]), [-48-36j])
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assert_array_almost_equal(f(3j, [[3-4j]], [-4], 3, [5j]),
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[-48-21j])
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def test_ger(self):
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for p in 'sd':
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f = getattr(fblas, p+'ger', None)
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if f is None:
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continue
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assert_array_almost_equal(f(1, [1, 2], [3, 4]), [[3, 4], [6, 8]])
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assert_array_almost_equal(f(2, [1, 2, 3], [3, 4]),
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[[6, 8], [12, 16], [18, 24]])
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assert_array_almost_equal(f(1, [1, 2], [3, 4],
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a=[[1, 2], [3, 4]]), [[4, 6], [9, 12]])
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for p in 'cz':
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f = getattr(fblas, p+'geru', None)
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if f is None:
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continue
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assert_array_almost_equal(f(1, [1j, 2], [3, 4]),
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[[3j, 4j], [6, 8]])
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assert_array_almost_equal(f(-2, [1j, 2j, 3j], [3j, 4j]),
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[[6, 8], [12, 16], [18, 24]])
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for p in 'cz':
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for name in ('ger', 'gerc'):
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f = getattr(fblas, p+name, None)
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if f is None:
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continue
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assert_array_almost_equal(f(1, [1j, 2], [3, 4]),
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[[3j, 4j], [6, 8]])
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assert_array_almost_equal(f(2, [1j, 2j, 3j], [3j, 4j]),
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[[6, 8], [12, 16], [18, 24]])
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def test_syr_her(self):
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x = np.arange(1, 5, dtype='d')
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resx = np.triu(x[:, np.newaxis] * x)
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resx_reverse = np.triu(x[::-1, np.newaxis] * x[::-1])
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y = np.linspace(0, 8.5, 17, endpoint=False)
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z = np.arange(1, 9, dtype='d').view('D')
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resz = np.triu(z[:, np.newaxis] * z)
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resz_reverse = np.triu(z[::-1, np.newaxis] * z[::-1])
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rehz = np.triu(z[:, np.newaxis] * z.conj())
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rehz_reverse = np.triu(z[::-1, np.newaxis] * z[::-1].conj())
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w = np.c_[np.zeros(4), z, np.zeros(4)].ravel()
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for p, rtol in zip('sd', [1e-7, 1e-14]):
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f = getattr(fblas, p+'syr', None)
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if f is None:
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continue
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assert_allclose(f(1.0, x), resx, rtol=rtol)
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assert_allclose(f(1.0, x, lower=True), resx.T, rtol=rtol)
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assert_allclose(f(1.0, y, incx=2, offx=2, n=4), resx, rtol=rtol)
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# negative increments imply reversed vectors in blas
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assert_allclose(f(1.0, y, incx=-2, offx=2, n=4),
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resx_reverse, rtol=rtol)
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a = np.zeros((4, 4), 'f' if p == 's' else 'd', 'F')
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b = f(1.0, x, a=a, overwrite_a=True)
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assert_allclose(a, resx, rtol=rtol)
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b = f(2.0, x, a=a)
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assert_(a is not b)
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assert_allclose(b, 3*resx, rtol=rtol)
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assert_raises(Exception, f, 1.0, x, incx=0)
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assert_raises(Exception, f, 1.0, x, offx=5)
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assert_raises(Exception, f, 1.0, x, offx=-2)
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assert_raises(Exception, f, 1.0, x, n=-2)
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assert_raises(Exception, f, 1.0, x, n=5)
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assert_raises(Exception, f, 1.0, x, lower=2)
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assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
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for p, rtol in zip('cz', [1e-7, 1e-14]):
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f = getattr(fblas, p+'syr', None)
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if f is None:
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continue
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assert_allclose(f(1.0, z), resz, rtol=rtol)
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assert_allclose(f(1.0, z, lower=True), resz.T, rtol=rtol)
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assert_allclose(f(1.0, w, incx=3, offx=1, n=4), resz, rtol=rtol)
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# negative increments imply reversed vectors in blas
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assert_allclose(f(1.0, w, incx=-3, offx=1, n=4),
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resz_reverse, rtol=rtol)
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a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
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b = f(1.0, z, a=a, overwrite_a=True)
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assert_allclose(a, resz, rtol=rtol)
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b = f(2.0, z, a=a)
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assert_(a is not b)
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assert_allclose(b, 3*resz, rtol=rtol)
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assert_raises(Exception, f, 1.0, x, incx=0)
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assert_raises(Exception, f, 1.0, x, offx=5)
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assert_raises(Exception, f, 1.0, x, offx=-2)
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assert_raises(Exception, f, 1.0, x, n=-2)
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assert_raises(Exception, f, 1.0, x, n=5)
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assert_raises(Exception, f, 1.0, x, lower=2)
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assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
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for p, rtol in zip('cz', [1e-7, 1e-14]):
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f = getattr(fblas, p+'her', None)
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if f is None:
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continue
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assert_allclose(f(1.0, z), rehz, rtol=rtol)
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assert_allclose(f(1.0, z, lower=True), rehz.T.conj(), rtol=rtol)
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assert_allclose(f(1.0, w, incx=3, offx=1, n=4), rehz, rtol=rtol)
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# negative increments imply reversed vectors in blas
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assert_allclose(f(1.0, w, incx=-3, offx=1, n=4),
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rehz_reverse, rtol=rtol)
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a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
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b = f(1.0, z, a=a, overwrite_a=True)
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assert_allclose(a, rehz, rtol=rtol)
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b = f(2.0, z, a=a)
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assert_(a is not b)
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assert_allclose(b, 3*rehz, rtol=rtol)
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assert_raises(Exception, f, 1.0, x, incx=0)
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assert_raises(Exception, f, 1.0, x, offx=5)
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assert_raises(Exception, f, 1.0, x, offx=-2)
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assert_raises(Exception, f, 1.0, x, n=-2)
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assert_raises(Exception, f, 1.0, x, n=5)
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assert_raises(Exception, f, 1.0, x, lower=2)
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assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
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def test_syr2(self):
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x = np.arange(1, 5, dtype='d')
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y = np.arange(5, 9, dtype='d')
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resxy = np.triu(x[:, np.newaxis] * y + y[:, np.newaxis] * x)
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resxy_reverse = np.triu(x[::-1, np.newaxis] * y[::-1]
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+ y[::-1, np.newaxis] * x[::-1])
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q = np.linspace(0, 8.5, 17, endpoint=False)
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for p, rtol in zip('sd', [1e-7, 1e-14]):
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f = getattr(fblas, p+'syr2', None)
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if f is None:
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continue
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assert_allclose(f(1.0, x, y), resxy, rtol=rtol)
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assert_allclose(f(1.0, x, y, n=3), resxy[:3, :3], rtol=rtol)
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assert_allclose(f(1.0, x, y, lower=True), resxy.T, rtol=rtol)
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assert_allclose(f(1.0, q, q, incx=2, offx=2, incy=2, offy=10),
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resxy, rtol=rtol)
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assert_allclose(f(1.0, q, q, incx=2, offx=2, incy=2, offy=10, n=3),
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resxy[:3, :3], rtol=rtol)
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# negative increments imply reversed vectors in blas
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assert_allclose(f(1.0, q, q, incx=-2, offx=2, incy=-2, offy=10),
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resxy_reverse, rtol=rtol)
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a = np.zeros((4, 4), 'f' if p == 's' else 'd', 'F')
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b = f(1.0, x, y, a=a, overwrite_a=True)
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assert_allclose(a, resxy, rtol=rtol)
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b = f(2.0, x, y, a=a)
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assert_(a is not b)
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assert_allclose(b, 3*resxy, rtol=rtol)
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assert_raises(Exception, f, 1.0, x, y, incx=0)
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assert_raises(Exception, f, 1.0, x, y, offx=5)
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assert_raises(Exception, f, 1.0, x, y, offx=-2)
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assert_raises(Exception, f, 1.0, x, y, incy=0)
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assert_raises(Exception, f, 1.0, x, y, offy=5)
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assert_raises(Exception, f, 1.0, x, y, offy=-2)
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assert_raises(Exception, f, 1.0, x, y, n=-2)
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assert_raises(Exception, f, 1.0, x, y, n=5)
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assert_raises(Exception, f, 1.0, x, y, lower=2)
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assert_raises(Exception, f, 1.0, x, y,
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a=np.zeros((2, 2), 'd', 'F'))
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def test_her2(self):
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x = np.arange(1, 9, dtype='d').view('D')
|
|
y = np.arange(9, 17, dtype='d').view('D')
|
|
resxy = x[:, np.newaxis] * y.conj() + y[:, np.newaxis] * x.conj()
|
|
resxy = np.triu(resxy)
|
|
|
|
resxy_reverse = x[::-1, np.newaxis] * y[::-1].conj()
|
|
resxy_reverse += y[::-1, np.newaxis] * x[::-1].conj()
|
|
resxy_reverse = np.triu(resxy_reverse)
|
|
|
|
u = np.c_[np.zeros(4), x, np.zeros(4)].ravel()
|
|
v = np.c_[np.zeros(4), y, np.zeros(4)].ravel()
|
|
|
|
for p, rtol in zip('cz', [1e-7, 1e-14]):
|
|
f = getattr(fblas, p+'her2', None)
|
|
if f is None:
|
|
continue
|
|
assert_allclose(f(1.0, x, y), resxy, rtol=rtol)
|
|
assert_allclose(f(1.0, x, y, n=3), resxy[:3, :3], rtol=rtol)
|
|
assert_allclose(f(1.0, x, y, lower=True), resxy.T.conj(),
|
|
rtol=rtol)
|
|
|
|
assert_allclose(f(1.0, u, v, incx=3, offx=1, incy=3, offy=1),
|
|
resxy, rtol=rtol)
|
|
assert_allclose(f(1.0, u, v, incx=3, offx=1, incy=3, offy=1, n=3),
|
|
resxy[:3, :3], rtol=rtol)
|
|
# negative increments imply reversed vectors in blas
|
|
assert_allclose(f(1.0, u, v, incx=-3, offx=1, incy=-3, offy=1),
|
|
resxy_reverse, rtol=rtol)
|
|
|
|
a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
|
|
b = f(1.0, x, y, a=a, overwrite_a=True)
|
|
assert_allclose(a, resxy, rtol=rtol)
|
|
|
|
b = f(2.0, x, y, a=a)
|
|
assert_(a is not b)
|
|
assert_allclose(b, 3*resxy, rtol=rtol)
|
|
|
|
assert_raises(Exception, f, 1.0, x, y, incx=0)
|
|
assert_raises(Exception, f, 1.0, x, y, offx=5)
|
|
assert_raises(Exception, f, 1.0, x, y, offx=-2)
|
|
assert_raises(Exception, f, 1.0, x, y, incy=0)
|
|
assert_raises(Exception, f, 1.0, x, y, offy=5)
|
|
assert_raises(Exception, f, 1.0, x, y, offy=-2)
|
|
assert_raises(Exception, f, 1.0, x, y, n=-2)
|
|
assert_raises(Exception, f, 1.0, x, y, n=5)
|
|
assert_raises(Exception, f, 1.0, x, y, lower=2)
|
|
assert_raises(Exception, f, 1.0, x, y,
|
|
a=np.zeros((2, 2), 'd', 'F'))
|
|
|
|
def test_gbmv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 7
|
|
m = 5
|
|
kl = 1
|
|
ku = 2
|
|
# fake a banded matrix via toeplitz
|
|
A = toeplitz(append(rand(kl+1), zeros(m-kl-1)),
|
|
append(rand(ku+1), zeros(n-ku-1)))
|
|
A = A.astype(dtype)
|
|
Ab = zeros((kl+ku+1, n), dtype=dtype)
|
|
|
|
# Form the banded storage
|
|
Ab[2, :5] = A[0, 0] # diag
|
|
Ab[1, 1:6] = A[0, 1] # sup1
|
|
Ab[0, 2:7] = A[0, 2] # sup2
|
|
Ab[3, :4] = A[1, 0] # sub1
|
|
|
|
x = rand(n).astype(dtype)
|
|
y = rand(m).astype(dtype)
|
|
alpha, beta = dtype(3), dtype(-5)
|
|
|
|
func, = get_blas_funcs(('gbmv',), dtype=dtype)
|
|
y1 = func(m=m, n=n, ku=ku, kl=kl, alpha=alpha, a=Ab,
|
|
x=x, y=y, beta=beta)
|
|
y2 = alpha * A.dot(x) + beta * y
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
def test_sbmv_hbmv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 6
|
|
k = 2
|
|
A = zeros((n, n), dtype=dtype)
|
|
Ab = zeros((k+1, n), dtype=dtype)
|
|
|
|
# Form the array and its packed banded storage
|
|
A[arange(n), arange(n)] = rand(n)
|
|
for ind2 in range(1, k+1):
|
|
temp = rand(n-ind2)
|
|
A[arange(n-ind2), arange(ind2, n)] = temp
|
|
Ab[-1-ind2, ind2:] = temp
|
|
A = A.astype(dtype)
|
|
A = A + A.T if ind < 2 else A + A.conj().T
|
|
Ab[-1, :] = diag(A)
|
|
x = rand(n).astype(dtype)
|
|
y = rand(n).astype(dtype)
|
|
alpha, beta = dtype(1.25), dtype(3)
|
|
|
|
if ind > 1:
|
|
func, = get_blas_funcs(('hbmv',), dtype=dtype)
|
|
else:
|
|
func, = get_blas_funcs(('sbmv',), dtype=dtype)
|
|
y1 = func(k=k, alpha=alpha, a=Ab, x=x, y=y, beta=beta)
|
|
y2 = alpha * A.dot(x) + beta * y
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
def test_spmv_hpmv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES+COMPLEX_DTYPES):
|
|
n = 3
|
|
A = rand(n, n).astype(dtype)
|
|
if ind > 1:
|
|
A += rand(n, n)*1j
|
|
A = A.astype(dtype)
|
|
A = A + A.T if ind < 4 else A + A.conj().T
|
|
c, r = tril_indices(n)
|
|
Ap = A[r, c]
|
|
x = rand(n).astype(dtype)
|
|
y = rand(n).astype(dtype)
|
|
xlong = arange(2*n).astype(dtype)
|
|
ylong = ones(2*n).astype(dtype)
|
|
alpha, beta = dtype(1.25), dtype(2)
|
|
|
|
if ind > 3:
|
|
func, = get_blas_funcs(('hpmv',), dtype=dtype)
|
|
else:
|
|
func, = get_blas_funcs(('spmv',), dtype=dtype)
|
|
y1 = func(n=n, alpha=alpha, ap=Ap, x=x, y=y, beta=beta)
|
|
y2 = alpha * A.dot(x) + beta * y
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
# Test inc and offsets
|
|
y1 = func(n=n-1, alpha=alpha, beta=beta, x=xlong, y=ylong, ap=Ap,
|
|
incx=2, incy=2, offx=n, offy=n)
|
|
y2 = (alpha * A[:-1, :-1]).dot(xlong[3::2]) + beta * ylong[3::2]
|
|
assert_array_almost_equal(y1[3::2], y2)
|
|
assert_almost_equal(y1[4], ylong[4])
|
|
|
|
def test_spr_hpr(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES+COMPLEX_DTYPES):
|
|
n = 3
|
|
A = rand(n, n).astype(dtype)
|
|
if ind > 1:
|
|
A += rand(n, n)*1j
|
|
A = A.astype(dtype)
|
|
A = A + A.T if ind < 4 else A + A.conj().T
|
|
c, r = tril_indices(n)
|
|
Ap = A[r, c]
|
|
x = rand(n).astype(dtype)
|
|
alpha = (DTYPES+COMPLEX_DTYPES)[mod(ind, 4)](2.5)
|
|
|
|
if ind > 3:
|
|
func, = get_blas_funcs(('hpr',), dtype=dtype)
|
|
y2 = alpha * x[:, None].dot(x[None, :].conj()) + A
|
|
else:
|
|
func, = get_blas_funcs(('spr',), dtype=dtype)
|
|
y2 = alpha * x[:, None].dot(x[None, :]) + A
|
|
|
|
y1 = func(n=n, alpha=alpha, ap=Ap, x=x)
|
|
y1f = zeros((3, 3), dtype=dtype)
|
|
y1f[r, c] = y1
|
|
y1f[c, r] = y1.conj() if ind > 3 else y1
|
|
assert_array_almost_equal(y1f, y2)
|
|
|
|
def test_spr2_hpr2(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 3
|
|
A = rand(n, n).astype(dtype)
|
|
if ind > 1:
|
|
A += rand(n, n)*1j
|
|
A = A.astype(dtype)
|
|
A = A + A.T if ind < 2 else A + A.conj().T
|
|
c, r = tril_indices(n)
|
|
Ap = A[r, c]
|
|
x = rand(n).astype(dtype)
|
|
y = rand(n).astype(dtype)
|
|
alpha = dtype(2)
|
|
|
|
if ind > 1:
|
|
func, = get_blas_funcs(('hpr2',), dtype=dtype)
|
|
else:
|
|
func, = get_blas_funcs(('spr2',), dtype=dtype)
|
|
|
|
u = alpha.conj() * x[:, None].dot(y[None, :].conj())
|
|
y2 = A + u + u.conj().T
|
|
y1 = func(n=n, alpha=alpha, x=x, y=y, ap=Ap)
|
|
y1f = zeros((3, 3), dtype=dtype)
|
|
y1f[r, c] = y1
|
|
y1f[[1, 2, 2], [0, 0, 1]] = y1[[1, 3, 4]].conj()
|
|
assert_array_almost_equal(y1f, y2)
|
|
|
|
def test_tbmv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 10
|
|
k = 3
|
|
x = rand(n).astype(dtype)
|
|
A = zeros((n, n), dtype=dtype)
|
|
# Banded upper triangular array
|
|
for sup in range(k+1):
|
|
A[arange(n-sup), arange(sup, n)] = rand(n-sup)
|
|
|
|
# Add complex parts for c,z
|
|
if ind > 1:
|
|
A[nonzero(A)] += 1j * rand((k+1)*n-(k*(k+1)//2)).astype(dtype)
|
|
|
|
# Form the banded storage
|
|
Ab = zeros((k+1, n), dtype=dtype)
|
|
for row in range(k+1):
|
|
Ab[-row-1, row:] = diag(A, k=row)
|
|
func, = get_blas_funcs(('tbmv',), dtype=dtype)
|
|
|
|
y1 = func(k=k, a=Ab, x=x)
|
|
y2 = A.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(k=k, a=Ab, x=x, diag=1)
|
|
A[arange(n), arange(n)] = dtype(1)
|
|
y2 = A.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(k=k, a=Ab, x=x, diag=1, trans=1)
|
|
y2 = A.T.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(k=k, a=Ab, x=x, diag=1, trans=2)
|
|
y2 = A.conj().T.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
def test_tbsv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 6
|
|
k = 3
|
|
x = rand(n).astype(dtype)
|
|
A = zeros((n, n), dtype=dtype)
|
|
# Banded upper triangular array
|
|
for sup in range(k+1):
|
|
A[arange(n-sup), arange(sup, n)] = rand(n-sup)
|
|
|
|
# Add complex parts for c,z
|
|
if ind > 1:
|
|
A[nonzero(A)] += 1j * rand((k+1)*n-(k*(k+1)//2)).astype(dtype)
|
|
|
|
# Form the banded storage
|
|
Ab = zeros((k+1, n), dtype=dtype)
|
|
for row in range(k+1):
|
|
Ab[-row-1, row:] = diag(A, k=row)
|
|
func, = get_blas_funcs(('tbsv',), dtype=dtype)
|
|
|
|
y1 = func(k=k, a=Ab, x=x)
|
|
y2 = solve(A, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(k=k, a=Ab, x=x, diag=1)
|
|
A[arange(n), arange(n)] = dtype(1)
|
|
y2 = solve(A, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(k=k, a=Ab, x=x, diag=1, trans=1)
|
|
y2 = solve(A.T, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(k=k, a=Ab, x=x, diag=1, trans=2)
|
|
y2 = solve(A.conj().T, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
def test_tpmv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 10
|
|
x = rand(n).astype(dtype)
|
|
# Upper triangular array
|
|
A = triu(rand(n, n)) if ind < 2 else triu(rand(n, n)+rand(n, n)*1j)
|
|
# Form the packed storage
|
|
c, r = tril_indices(n)
|
|
Ap = A[r, c]
|
|
func, = get_blas_funcs(('tpmv',), dtype=dtype)
|
|
|
|
y1 = func(n=n, ap=Ap, x=x)
|
|
y2 = A.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(n=n, ap=Ap, x=x, diag=1)
|
|
A[arange(n), arange(n)] = dtype(1)
|
|
y2 = A.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(n=n, ap=Ap, x=x, diag=1, trans=1)
|
|
y2 = A.T.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(n=n, ap=Ap, x=x, diag=1, trans=2)
|
|
y2 = A.conj().T.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
def test_tpsv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 10
|
|
x = rand(n).astype(dtype)
|
|
# Upper triangular array
|
|
A = triu(rand(n, n)) if ind < 2 else triu(rand(n, n)+rand(n, n)*1j)
|
|
A += eye(n)
|
|
# Form the packed storage
|
|
c, r = tril_indices(n)
|
|
Ap = A[r, c]
|
|
func, = get_blas_funcs(('tpsv',), dtype=dtype)
|
|
|
|
y1 = func(n=n, ap=Ap, x=x)
|
|
y2 = solve(A, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(n=n, ap=Ap, x=x, diag=1)
|
|
A[arange(n), arange(n)] = dtype(1)
|
|
y2 = solve(A, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(n=n, ap=Ap, x=x, diag=1, trans=1)
|
|
y2 = solve(A.T, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(n=n, ap=Ap, x=x, diag=1, trans=2)
|
|
y2 = solve(A.conj().T, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
def test_trmv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 3
|
|
A = (rand(n, n)+eye(n)).astype(dtype)
|
|
x = rand(3).astype(dtype)
|
|
func, = get_blas_funcs(('trmv',), dtype=dtype)
|
|
|
|
y1 = func(a=A, x=x)
|
|
y2 = triu(A).dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(a=A, x=x, diag=1)
|
|
A[arange(n), arange(n)] = dtype(1)
|
|
y2 = triu(A).dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(a=A, x=x, diag=1, trans=1)
|
|
y2 = triu(A).T.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(a=A, x=x, diag=1, trans=2)
|
|
y2 = triu(A).conj().T.dot(x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
def test_trsv(self):
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
n = 15
|
|
A = (rand(n, n)+eye(n)).astype(dtype)
|
|
x = rand(n).astype(dtype)
|
|
func, = get_blas_funcs(('trsv',), dtype=dtype)
|
|
|
|
y1 = func(a=A, x=x)
|
|
y2 = solve(triu(A), x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(a=A, x=x, lower=1)
|
|
y2 = solve(tril(A), x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(a=A, x=x, diag=1)
|
|
A[arange(n), arange(n)] = dtype(1)
|
|
y2 = solve(triu(A), x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(a=A, x=x, diag=1, trans=1)
|
|
y2 = solve(triu(A).T, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
y1 = func(a=A, x=x, diag=1, trans=2)
|
|
y2 = solve(triu(A).conj().T, x)
|
|
assert_array_almost_equal(y1, y2)
|
|
|
|
|
|
class TestFBLAS3Simple:
|
|
|
|
def test_gemm(self):
|
|
for p in 'sd':
|
|
f = getattr(fblas, p+'gemm', None)
|
|
if f is None:
|
|
continue
|
|
assert_array_almost_equal(f(3, [3], [-4]), [[-36]])
|
|
assert_array_almost_equal(f(3, [3], [-4], 3, [5]), [-21])
|
|
for p in 'cz':
|
|
f = getattr(fblas, p+'gemm', None)
|
|
if f is None:
|
|
continue
|
|
assert_array_almost_equal(f(3j, [3-4j], [-4]), [[-48-36j]])
|
|
assert_array_almost_equal(f(3j, [3-4j], [-4], 3, [5j]), [-48-21j])
|
|
|
|
|
|
def _get_func(func, ps='sdzc'):
|
|
"""Just a helper: return a specified BLAS function w/typecode."""
|
|
for p in ps:
|
|
f = getattr(fblas, p+func, None)
|
|
if f is None:
|
|
continue
|
|
yield f
|
|
|
|
|
|
class TestBLAS3Symm:
|
|
|
|
def setup_method(self):
|
|
self.a = np.array([[1., 2.],
|
|
[0., 1.]])
|
|
self.b = np.array([[1., 0., 3.],
|
|
[0., -1., 2.]])
|
|
self.c = np.ones((2, 3))
|
|
self.t = np.array([[2., -1., 8.],
|
|
[3., 0., 9.]])
|
|
|
|
def test_symm(self):
|
|
for f in _get_func('symm'):
|
|
res = f(a=self.a, b=self.b, c=self.c, alpha=1., beta=1.)
|
|
assert_array_almost_equal(res, self.t)
|
|
|
|
res = f(a=self.a.T, b=self.b, lower=1, c=self.c, alpha=1., beta=1.)
|
|
assert_array_almost_equal(res, self.t)
|
|
|
|
res = f(a=self.a, b=self.b.T, side=1, c=self.c.T,
|
|
alpha=1., beta=1.)
|
|
assert_array_almost_equal(res, self.t.T)
|
|
|
|
def test_summ_wrong_side(self):
|
|
f = getattr(fblas, 'dsymm', None)
|
|
if f is not None:
|
|
assert_raises(Exception, f, **{'a': self.a, 'b': self.b,
|
|
'alpha': 1, 'side': 1})
|
|
# `side=1` means C <- B*A, hence shapes of A and B are to be
|
|
# compatible. Otherwise, f2py exception is raised
|
|
|
|
def test_symm_wrong_uplo(self):
|
|
"""SYMM only considers the upper/lower part of A. Hence setting
|
|
wrong value for `lower` (default is lower=0, meaning upper triangle)
|
|
gives a wrong result.
|
|
"""
|
|
f = getattr(fblas, 'dsymm', None)
|
|
if f is not None:
|
|
res = f(a=self.a, b=self.b, c=self.c, alpha=1., beta=1.)
|
|
assert np.allclose(res, self.t)
|
|
|
|
res = f(a=self.a, b=self.b, lower=1, c=self.c, alpha=1., beta=1.)
|
|
assert not np.allclose(res, self.t)
|
|
|
|
|
|
class TestBLAS3Syrk:
|
|
def setup_method(self):
|
|
self.a = np.array([[1., 0.],
|
|
[0., -2.],
|
|
[2., 3.]])
|
|
self.t = np.array([[1., 0., 2.],
|
|
[0., 4., -6.],
|
|
[2., -6., 13.]])
|
|
self.tt = np.array([[5., 6.],
|
|
[6., 13.]])
|
|
|
|
def test_syrk(self):
|
|
for f in _get_func('syrk'):
|
|
c = f(a=self.a, alpha=1.)
|
|
assert_array_almost_equal(np.triu(c), np.triu(self.t))
|
|
|
|
c = f(a=self.a, alpha=1., lower=1)
|
|
assert_array_almost_equal(np.tril(c), np.tril(self.t))
|
|
|
|
c0 = np.ones(self.t.shape)
|
|
c = f(a=self.a, alpha=1., beta=1., c=c0)
|
|
assert_array_almost_equal(np.triu(c), np.triu(self.t+c0))
|
|
|
|
c = f(a=self.a, alpha=1., trans=1)
|
|
assert_array_almost_equal(np.triu(c), np.triu(self.tt))
|
|
|
|
# prints '0-th dimension must be fixed to 3 but got 5',
|
|
# FIXME: suppress?
|
|
# FIXME: how to catch the _fblas.error?
|
|
def test_syrk_wrong_c(self):
|
|
f = getattr(fblas, 'dsyrk', None)
|
|
if f is not None:
|
|
assert_raises(Exception, f, **{'a': self.a, 'alpha': 1.,
|
|
'c': np.ones((5, 8))})
|
|
# if C is supplied, it must have compatible dimensions
|
|
|
|
|
|
class TestBLAS3Syr2k:
|
|
def setup_method(self):
|
|
self.a = np.array([[1., 0.],
|
|
[0., -2.],
|
|
[2., 3.]])
|
|
self.b = np.array([[0., 1.],
|
|
[1., 0.],
|
|
[0, 1.]])
|
|
self.t = np.array([[0., -1., 3.],
|
|
[-1., 0., 0.],
|
|
[3., 0., 6.]])
|
|
self.tt = np.array([[0., 1.],
|
|
[1., 6]])
|
|
|
|
def test_syr2k(self):
|
|
for f in _get_func('syr2k'):
|
|
c = f(a=self.a, b=self.b, alpha=1.)
|
|
assert_array_almost_equal(np.triu(c), np.triu(self.t))
|
|
|
|
c = f(a=self.a, b=self.b, alpha=1., lower=1)
|
|
assert_array_almost_equal(np.tril(c), np.tril(self.t))
|
|
|
|
c0 = np.ones(self.t.shape)
|
|
c = f(a=self.a, b=self.b, alpha=1., beta=1., c=c0)
|
|
assert_array_almost_equal(np.triu(c), np.triu(self.t+c0))
|
|
|
|
c = f(a=self.a, b=self.b, alpha=1., trans=1)
|
|
assert_array_almost_equal(np.triu(c), np.triu(self.tt))
|
|
|
|
# prints '0-th dimension must be fixed to 3 but got 5', FIXME: suppress?
|
|
def test_syr2k_wrong_c(self):
|
|
f = getattr(fblas, 'dsyr2k', None)
|
|
if f is not None:
|
|
assert_raises(Exception, f, **{'a': self.a,
|
|
'b': self.b,
|
|
'alpha': 1.,
|
|
'c': np.zeros((15, 8))})
|
|
# if C is supplied, it must have compatible dimensions
|
|
|
|
|
|
class TestSyHe:
|
|
"""Quick and simple tests for (zc)-symm, syrk, syr2k."""
|
|
|
|
def setup_method(self):
|
|
self.sigma_y = np.array([[0., -1.j],
|
|
[1.j, 0.]])
|
|
|
|
def test_symm_zc(self):
|
|
for f in _get_func('symm', 'zc'):
|
|
# NB: a is symmetric w/upper diag of ONLY
|
|
res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
|
|
assert_array_almost_equal(np.triu(res), np.diag([1, -1]))
|
|
|
|
def test_hemm_zc(self):
|
|
for f in _get_func('hemm', 'zc'):
|
|
# NB: a is hermitian w/upper diag of ONLY
|
|
res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
|
|
assert_array_almost_equal(np.triu(res), np.diag([1, 1]))
|
|
|
|
def test_syrk_zr(self):
|
|
for f in _get_func('syrk', 'zc'):
|
|
res = f(a=self.sigma_y, alpha=1.)
|
|
assert_array_almost_equal(np.triu(res), np.diag([-1, -1]))
|
|
|
|
def test_herk_zr(self):
|
|
for f in _get_func('herk', 'zc'):
|
|
res = f(a=self.sigma_y, alpha=1.)
|
|
assert_array_almost_equal(np.triu(res), np.diag([1, 1]))
|
|
|
|
def test_syr2k_zr(self):
|
|
for f in _get_func('syr2k', 'zc'):
|
|
res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
|
|
assert_array_almost_equal(np.triu(res), 2.*np.diag([-1, -1]))
|
|
|
|
def test_her2k_zr(self):
|
|
for f in _get_func('her2k', 'zc'):
|
|
res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
|
|
assert_array_almost_equal(np.triu(res), 2.*np.diag([1, 1]))
|
|
|
|
|
|
class TestTRMM:
|
|
"""Quick and simple tests for dtrmm."""
|
|
|
|
def setup_method(self):
|
|
self.a = np.array([[1., 2., ],
|
|
[-2., 1.]])
|
|
self.b = np.array([[3., 4., -1.],
|
|
[5., 6., -2.]])
|
|
|
|
self.a2 = np.array([[1, 1, 2, 3],
|
|
[0, 1, 4, 5],
|
|
[0, 0, 1, 6],
|
|
[0, 0, 0, 1]], order="f")
|
|
self.b2 = np.array([[1, 4], [2, 5], [3, 6], [7, 8], [9, 10]],
|
|
order="f")
|
|
|
|
@pytest.mark.parametrize("dtype_", DTYPES)
|
|
def test_side(self, dtype_):
|
|
trmm = get_blas_funcs("trmm", dtype=dtype_)
|
|
# Provide large A array that works for side=1 but not 0 (see gh-10841)
|
|
assert_raises(Exception, trmm, 1.0, self.a2, self.b2)
|
|
res = trmm(1.0, self.a2.astype(dtype_), self.b2.astype(dtype_),
|
|
side=1)
|
|
k = self.b2.shape[1]
|
|
assert_allclose(res, self.b2 @ self.a2[:k, :k], rtol=0.,
|
|
atol=100*np.finfo(dtype_).eps)
|
|
|
|
def test_ab(self):
|
|
f = getattr(fblas, 'dtrmm', None)
|
|
if f is not None:
|
|
result = f(1., self.a, self.b)
|
|
# default a is upper triangular
|
|
expected = np.array([[13., 16., -5.],
|
|
[5., 6., -2.]])
|
|
assert_array_almost_equal(result, expected)
|
|
|
|
def test_ab_lower(self):
|
|
f = getattr(fblas, 'dtrmm', None)
|
|
if f is not None:
|
|
result = f(1., self.a, self.b, lower=True)
|
|
expected = np.array([[3., 4., -1.],
|
|
[-1., -2., 0.]]) # now a is lower triangular
|
|
assert_array_almost_equal(result, expected)
|
|
|
|
def test_b_overwrites(self):
|
|
# BLAS dtrmm modifies B argument in-place.
|
|
# Here the default is to copy, but this can be overridden
|
|
f = getattr(fblas, 'dtrmm', None)
|
|
if f is not None:
|
|
for overwr in [True, False]:
|
|
bcopy = self.b.copy()
|
|
result = f(1., self.a, bcopy, overwrite_b=overwr)
|
|
# C-contiguous arrays are copied
|
|
assert_(bcopy.flags.f_contiguous is False and
|
|
np.may_share_memory(bcopy, result) is False)
|
|
assert_equal(bcopy, self.b)
|
|
|
|
bcopy = np.asfortranarray(self.b.copy()) # or just transpose it
|
|
result = f(1., self.a, bcopy, overwrite_b=True)
|
|
assert_(bcopy.flags.f_contiguous is True and
|
|
np.may_share_memory(bcopy, result) is True)
|
|
assert_array_almost_equal(bcopy, result)
|
|
|
|
|
|
def test_trsm():
|
|
seed(1234)
|
|
for ind, dtype in enumerate(DTYPES):
|
|
tol = np.finfo(dtype).eps*1000
|
|
func, = get_blas_funcs(('trsm',), dtype=dtype)
|
|
|
|
# Test protection against size mismatches
|
|
A = rand(4, 5).astype(dtype)
|
|
B = rand(4, 4).astype(dtype)
|
|
alpha = dtype(1)
|
|
assert_raises(Exception, func, alpha, A, B)
|
|
assert_raises(Exception, func, alpha, A.T, B)
|
|
|
|
n = 8
|
|
m = 7
|
|
alpha = dtype(-2.5)
|
|
A = (rand(m, m) if ind < 2 else rand(m, m) + rand(m, m)*1j) + eye(m)
|
|
A = A.astype(dtype)
|
|
Au = triu(A)
|
|
Al = tril(A)
|
|
B1 = rand(m, n).astype(dtype)
|
|
B2 = rand(n, m).astype(dtype)
|
|
|
|
x1 = func(alpha=alpha, a=A, b=B1)
|
|
assert_equal(B1.shape, x1.shape)
|
|
x2 = solve(Au, alpha*B1)
|
|
assert_allclose(x1, x2, atol=tol)
|
|
|
|
x1 = func(alpha=alpha, a=A, b=B1, trans_a=1)
|
|
x2 = solve(Au.T, alpha*B1)
|
|
assert_allclose(x1, x2, atol=tol)
|
|
|
|
x1 = func(alpha=alpha, a=A, b=B1, trans_a=2)
|
|
x2 = solve(Au.conj().T, alpha*B1)
|
|
assert_allclose(x1, x2, atol=tol)
|
|
|
|
x1 = func(alpha=alpha, a=A, b=B1, diag=1)
|
|
Au[arange(m), arange(m)] = dtype(1)
|
|
x2 = solve(Au, alpha*B1)
|
|
assert_allclose(x1, x2, atol=tol)
|
|
|
|
x1 = func(alpha=alpha, a=A, b=B2, diag=1, side=1)
|
|
x2 = solve(Au.conj().T, alpha*B2.conj().T)
|
|
assert_allclose(x1, x2.conj().T, atol=tol)
|
|
|
|
x1 = func(alpha=alpha, a=A, b=B2, diag=1, side=1, lower=1)
|
|
Al[arange(m), arange(m)] = dtype(1)
|
|
x2 = solve(Al.conj().T, alpha*B2.conj().T)
|
|
assert_allclose(x1, x2.conj().T, atol=tol)
|