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# Test interfaces to fortran blas.
#
# The tests are more of interface than they are of the underlying blas.
# Only very small matrices checked -- N=3 or so.
#
# !! Complex calculations really aren't checked that carefully.
# !! Only real valued complex numbers are used in tests.
from numpy import float32, float64, complex64, complex128, arange, array, \
zeros, shape, transpose, newaxis, common_type, conjugate
from scipy.linalg import _fblas as fblas
from numpy.testing import assert_array_equal, \
assert_allclose, assert_array_almost_equal, assert_
import pytest
# decimal accuracy to require between Python and LAPACK/BLAS calculations
accuracy = 5
# Since numpy.dot likely uses the same blas, use this routine
# to check.
def matrixmultiply(a, b):
if len(b.shape) == 1:
b_is_vector = True
b = b[:, newaxis]
else:
b_is_vector = False
assert_(a.shape[1] == b.shape[0])
c = zeros((a.shape[0], b.shape[1]), common_type(a, b))
for i in range(a.shape[0]):
for j in range(b.shape[1]):
s = 0
for k in range(a.shape[1]):
s += a[i, k] * b[k, j]
c[i, j] = s
if b_is_vector:
c = c.reshape((a.shape[0],))
return c
##################################################
# Test blas ?axpy
class BaseAxpy:
''' Mixin class for axpy tests '''
def test_default_a(self):
x = arange(3., dtype=self.dtype)
y = arange(3., dtype=x.dtype)
real_y = x*1.+y
y = self.blas_func(x, y)
assert_array_equal(real_y, y)
def test_simple(self):
x = arange(3., dtype=self.dtype)
y = arange(3., dtype=x.dtype)
real_y = x*3.+y
y = self.blas_func(x, y, a=3.)
assert_array_equal(real_y, y)
def test_x_stride(self):
x = arange(6., dtype=self.dtype)
y = zeros(3, x.dtype)
y = arange(3., dtype=x.dtype)
real_y = x[::2]*3.+y
y = self.blas_func(x, y, a=3., n=3, incx=2)
assert_array_equal(real_y, y)
def test_y_stride(self):
x = arange(3., dtype=self.dtype)
y = zeros(6, x.dtype)
real_y = x*3.+y[::2]
y = self.blas_func(x, y, a=3., n=3, incy=2)
assert_array_equal(real_y, y[::2])
def test_x_and_y_stride(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
real_y = x[::4]*3.+y[::2]
y = self.blas_func(x, y, a=3., n=3, incx=4, incy=2)
assert_array_equal(real_y, y[::2])
def test_x_bad_size(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
with pytest.raises(Exception, match='failed for 1st keyword'):
self.blas_func(x, y, n=4, incx=5)
def test_y_bad_size(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
with pytest.raises(Exception, match='failed for 1st keyword'):
self.blas_func(x, y, n=3, incy=5)
try:
class TestSaxpy(BaseAxpy):
blas_func = fblas.saxpy
dtype = float32
except AttributeError:
class TestSaxpy:
pass
class TestDaxpy(BaseAxpy):
blas_func = fblas.daxpy
dtype = float64
try:
class TestCaxpy(BaseAxpy):
blas_func = fblas.caxpy
dtype = complex64
except AttributeError:
class TestCaxpy:
pass
class TestZaxpy(BaseAxpy):
blas_func = fblas.zaxpy
dtype = complex128
##################################################
# Test blas ?scal
class BaseScal:
''' Mixin class for scal testing '''
def test_simple(self):
x = arange(3., dtype=self.dtype)
real_x = x*3.
x = self.blas_func(3., x)
assert_array_equal(real_x, x)
def test_x_stride(self):
x = arange(6., dtype=self.dtype)
real_x = x.copy()
real_x[::2] = x[::2]*array(3., self.dtype)
x = self.blas_func(3., x, n=3, incx=2)
assert_array_equal(real_x, x)
def test_x_bad_size(self):
x = arange(12., dtype=self.dtype)
with pytest.raises(Exception, match='failed for 1st keyword'):
self.blas_func(2., x, n=4, incx=5)
try:
class TestSscal(BaseScal):
blas_func = fblas.sscal
dtype = float32
except AttributeError:
class TestSscal:
pass
class TestDscal(BaseScal):
blas_func = fblas.dscal
dtype = float64
try:
class TestCscal(BaseScal):
blas_func = fblas.cscal
dtype = complex64
except AttributeError:
class TestCscal:
pass
class TestZscal(BaseScal):
blas_func = fblas.zscal
dtype = complex128
##################################################
# Test blas ?copy
class BaseCopy:
''' Mixin class for copy testing '''
def test_simple(self):
x = arange(3., dtype=self.dtype)
y = zeros(shape(x), x.dtype)
y = self.blas_func(x, y)
assert_array_equal(x, y)
def test_x_stride(self):
x = arange(6., dtype=self.dtype)
y = zeros(3, x.dtype)
y = self.blas_func(x, y, n=3, incx=2)
assert_array_equal(x[::2], y)
def test_y_stride(self):
x = arange(3., dtype=self.dtype)
y = zeros(6, x.dtype)
y = self.blas_func(x, y, n=3, incy=2)
assert_array_equal(x, y[::2])
def test_x_and_y_stride(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
y = self.blas_func(x, y, n=3, incx=4, incy=2)
assert_array_equal(x[::4], y[::2])
def test_x_bad_size(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
with pytest.raises(Exception, match='failed for 1st keyword'):
self.blas_func(x, y, n=4, incx=5)
def test_y_bad_size(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
with pytest.raises(Exception, match='failed for 1st keyword'):
self.blas_func(x, y, n=3, incy=5)
# def test_y_bad_type(self):
## Hmmm. Should this work? What should be the output.
# x = arange(3.,dtype=self.dtype)
# y = zeros(shape(x))
# self.blas_func(x,y)
# assert_array_equal(x,y)
try:
class TestScopy(BaseCopy):
blas_func = fblas.scopy
dtype = float32
except AttributeError:
class TestScopy:
pass
class TestDcopy(BaseCopy):
blas_func = fblas.dcopy
dtype = float64
try:
class TestCcopy(BaseCopy):
blas_func = fblas.ccopy
dtype = complex64
except AttributeError:
class TestCcopy:
pass
class TestZcopy(BaseCopy):
blas_func = fblas.zcopy
dtype = complex128
##################################################
# Test blas ?swap
class BaseSwap:
''' Mixin class for swap tests '''
def test_simple(self):
x = arange(3., dtype=self.dtype)
y = zeros(shape(x), x.dtype)
desired_x = y.copy()
desired_y = x.copy()
x, y = self.blas_func(x, y)
assert_array_equal(desired_x, x)
assert_array_equal(desired_y, y)
def test_x_stride(self):
x = arange(6., dtype=self.dtype)
y = zeros(3, x.dtype)
desired_x = y.copy()
desired_y = x.copy()[::2]
x, y = self.blas_func(x, y, n=3, incx=2)
assert_array_equal(desired_x, x[::2])
assert_array_equal(desired_y, y)
def test_y_stride(self):
x = arange(3., dtype=self.dtype)
y = zeros(6, x.dtype)
desired_x = y.copy()[::2]
desired_y = x.copy()
x, y = self.blas_func(x, y, n=3, incy=2)
assert_array_equal(desired_x, x)
assert_array_equal(desired_y, y[::2])
def test_x_and_y_stride(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
desired_x = y.copy()[::2]
desired_y = x.copy()[::4]
x, y = self.blas_func(x, y, n=3, incx=4, incy=2)
assert_array_equal(desired_x, x[::4])
assert_array_equal(desired_y, y[::2])
def test_x_bad_size(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
with pytest.raises(Exception, match='failed for 1st keyword'):
self.blas_func(x, y, n=4, incx=5)
def test_y_bad_size(self):
x = arange(12., dtype=self.dtype)
y = zeros(6, x.dtype)
with pytest.raises(Exception, match='failed for 1st keyword'):
self.blas_func(x, y, n=3, incy=5)
try:
class TestSswap(BaseSwap):
blas_func = fblas.sswap
dtype = float32
except AttributeError:
class TestSswap:
pass
class TestDswap(BaseSwap):
blas_func = fblas.dswap
dtype = float64
try:
class TestCswap(BaseSwap):
blas_func = fblas.cswap
dtype = complex64
except AttributeError:
class TestCswap:
pass
class TestZswap(BaseSwap):
blas_func = fblas.zswap
dtype = complex128
##################################################
# Test blas ?gemv
# This will be a mess to test all cases.
class BaseGemv:
''' Mixin class for gemv tests '''
def get_data(self, x_stride=1, y_stride=1):
mult = array(1, dtype=self.dtype)
if self.dtype in [complex64, complex128]:
mult = array(1+1j, dtype=self.dtype)
from numpy.random import normal, seed
seed(1234)
alpha = array(1., dtype=self.dtype) * mult
beta = array(1., dtype=self.dtype) * mult
a = normal(0., 1., (3, 3)).astype(self.dtype) * mult
x = arange(shape(a)[0]*x_stride, dtype=self.dtype) * mult
y = arange(shape(a)[1]*y_stride, dtype=self.dtype) * mult
return alpha, beta, a, x, y
def test_simple(self):
alpha, beta, a, x, y = self.get_data()
desired_y = alpha*matrixmultiply(a, x)+beta*y
y = self.blas_func(alpha, a, x, beta, y)
assert_array_almost_equal(desired_y, y)
def test_default_beta_y(self):
alpha, beta, a, x, y = self.get_data()
desired_y = matrixmultiply(a, x)
y = self.blas_func(1, a, x)
assert_array_almost_equal(desired_y, y)
def test_simple_transpose(self):
alpha, beta, a, x, y = self.get_data()
desired_y = alpha*matrixmultiply(transpose(a), x)+beta*y
y = self.blas_func(alpha, a, x, beta, y, trans=1)
assert_array_almost_equal(desired_y, y)
def test_simple_transpose_conj(self):
alpha, beta, a, x, y = self.get_data()
desired_y = alpha*matrixmultiply(transpose(conjugate(a)), x)+beta*y
y = self.blas_func(alpha, a, x, beta, y, trans=2)
assert_array_almost_equal(desired_y, y)
def test_x_stride(self):
alpha, beta, a, x, y = self.get_data(x_stride=2)
desired_y = alpha*matrixmultiply(a, x[::2])+beta*y
y = self.blas_func(alpha, a, x, beta, y, incx=2)
assert_array_almost_equal(desired_y, y)
def test_x_stride_transpose(self):
alpha, beta, a, x, y = self.get_data(x_stride=2)
desired_y = alpha*matrixmultiply(transpose(a), x[::2])+beta*y
y = self.blas_func(alpha, a, x, beta, y, trans=1, incx=2)
assert_array_almost_equal(desired_y, y)
def test_x_stride_assert(self):
# What is the use of this test?
alpha, beta, a, x, y = self.get_data(x_stride=2)
with pytest.raises(Exception, match='failed for 3rd argument'):
y = self.blas_func(1, a, x, 1, y, trans=0, incx=3)
with pytest.raises(Exception, match='failed for 3rd argument'):
y = self.blas_func(1, a, x, 1, y, trans=1, incx=3)
def test_y_stride(self):
alpha, beta, a, x, y = self.get_data(y_stride=2)
desired_y = y.copy()
desired_y[::2] = alpha*matrixmultiply(a, x)+beta*y[::2]
y = self.blas_func(alpha, a, x, beta, y, incy=2)
assert_array_almost_equal(desired_y, y)
def test_y_stride_transpose(self):
alpha, beta, a, x, y = self.get_data(y_stride=2)
desired_y = y.copy()
desired_y[::2] = alpha*matrixmultiply(transpose(a), x)+beta*y[::2]
y = self.blas_func(alpha, a, x, beta, y, trans=1, incy=2)
assert_array_almost_equal(desired_y, y)
def test_y_stride_assert(self):
# What is the use of this test?
alpha, beta, a, x, y = self.get_data(y_stride=2)
with pytest.raises(Exception, match='failed for 2nd keyword'):
y = self.blas_func(1, a, x, 1, y, trans=0, incy=3)
with pytest.raises(Exception, match='failed for 2nd keyword'):
y = self.blas_func(1, a, x, 1, y, trans=1, incy=3)
try:
class TestSgemv(BaseGemv):
blas_func = fblas.sgemv
dtype = float32
def test_sgemv_on_osx(self):
from itertools import product
import sys
import numpy as np
if sys.platform != 'darwin':
return
def aligned_array(shape, align, dtype, order='C'):
# Make array shape `shape` with aligned at `align` bytes
d = dtype()
# Make array of correct size with `align` extra bytes
N = np.prod(shape)
tmp = np.zeros(N * d.nbytes + align, dtype=np.uint8)
address = tmp.__array_interface__["data"][0]
# Find offset into array giving desired alignment
for offset in range(align):
if (address + offset) % align == 0:
break
tmp = tmp[offset:offset+N*d.nbytes].view(dtype=dtype)
return tmp.reshape(shape, order=order)
def as_aligned(arr, align, dtype, order='C'):
# Copy `arr` into an aligned array with same shape
aligned = aligned_array(arr.shape, align, dtype, order)
aligned[:] = arr[:]
return aligned
def assert_dot_close(A, X, desired):
assert_allclose(self.blas_func(1.0, A, X), desired,
rtol=1e-5, atol=1e-7)
testdata = product((15, 32), (10000,), (200, 89), ('C', 'F'))
for align, m, n, a_order in testdata:
A_d = np.random.rand(m, n)
X_d = np.random.rand(n)
desired = np.dot(A_d, X_d)
# Calculation with aligned single precision
A_f = as_aligned(A_d, align, np.float32, order=a_order)
X_f = as_aligned(X_d, align, np.float32, order=a_order)
assert_dot_close(A_f, X_f, desired)
except AttributeError:
class TestSgemv:
pass
class TestDgemv(BaseGemv):
blas_func = fblas.dgemv
dtype = float64
try:
class TestCgemv(BaseGemv):
blas_func = fblas.cgemv
dtype = complex64
except AttributeError:
class TestCgemv:
pass
class TestZgemv(BaseGemv):
blas_func = fblas.zgemv
dtype = complex128
"""
##################################################
### Test blas ?ger
### This will be a mess to test all cases.
class BaseGer:
def get_data(self,x_stride=1,y_stride=1):
from numpy.random import normal, seed
seed(1234)
alpha = array(1., dtype = self.dtype)
a = normal(0.,1.,(3,3)).astype(self.dtype)
x = arange(shape(a)[0]*x_stride,dtype=self.dtype)
y = arange(shape(a)[1]*y_stride,dtype=self.dtype)
return alpha,a,x,y
def test_simple(self):
alpha,a,x,y = self.get_data()
# transpose takes care of Fortran vs. C(and Python) memory layout
desired_a = alpha*transpose(x[:,newaxis]*y) + a
self.blas_func(x,y,a)
assert_array_almost_equal(desired_a,a)
def test_x_stride(self):
alpha,a,x,y = self.get_data(x_stride=2)
desired_a = alpha*transpose(x[::2,newaxis]*y) + a
self.blas_func(x,y,a,incx=2)
assert_array_almost_equal(desired_a,a)
def test_x_stride_assert(self):
alpha,a,x,y = self.get_data(x_stride=2)
with pytest.raises(ValueError, match='foo'):
self.blas_func(x,y,a,incx=3)
def test_y_stride(self):
alpha,a,x,y = self.get_data(y_stride=2)
desired_a = alpha*transpose(x[:,newaxis]*y[::2]) + a
self.blas_func(x,y,a,incy=2)
assert_array_almost_equal(desired_a,a)
def test_y_stride_assert(self):
alpha,a,x,y = self.get_data(y_stride=2)
with pytest.raises(ValueError, match='foo'):
self.blas_func(a,x,y,incy=3)
class TestSger(BaseGer):
blas_func = fblas.sger
dtype = float32
class TestDger(BaseGer):
blas_func = fblas.dger
dtype = float64
"""
##################################################
# Test blas ?gerc
# This will be a mess to test all cases.
"""
class BaseGerComplex(BaseGer):
def get_data(self,x_stride=1,y_stride=1):
from numpy.random import normal, seed
seed(1234)
alpha = array(1+1j, dtype = self.dtype)
a = normal(0.,1.,(3,3)).astype(self.dtype)
a = a + normal(0.,1.,(3,3)) * array(1j, dtype = self.dtype)
x = normal(0.,1.,shape(a)[0]*x_stride).astype(self.dtype)
x = x + x * array(1j, dtype = self.dtype)
y = normal(0.,1.,shape(a)[1]*y_stride).astype(self.dtype)
y = y + y * array(1j, dtype = self.dtype)
return alpha,a,x,y
def test_simple(self):
alpha,a,x,y = self.get_data()
# transpose takes care of Fortran vs. C(and Python) memory layout
a = a * array(0.,dtype = self.dtype)
#desired_a = alpha*transpose(x[:,newaxis]*self.transform(y)) + a
desired_a = alpha*transpose(x[:,newaxis]*y) + a
#self.blas_func(x,y,a,alpha = alpha)
fblas.cgeru(x,y,a,alpha = alpha)
assert_array_almost_equal(desired_a,a)
#def test_x_stride(self):
# alpha,a,x,y = self.get_data(x_stride=2)
# desired_a = alpha*transpose(x[::2,newaxis]*self.transform(y)) + a
# self.blas_func(x,y,a,incx=2)
# assert_array_almost_equal(desired_a,a)
#def test_y_stride(self):
# alpha,a,x,y = self.get_data(y_stride=2)
# desired_a = alpha*transpose(x[:,newaxis]*self.transform(y[::2])) + a
# self.blas_func(x,y,a,incy=2)
# assert_array_almost_equal(desired_a,a)
class TestCgeru(BaseGerComplex):
blas_func = fblas.cgeru
dtype = complex64
def transform(self,x):
return x
class TestZgeru(BaseGerComplex):
blas_func = fblas.zgeru
dtype = complex128
def transform(self,x):
return x
class TestCgerc(BaseGerComplex):
blas_func = fblas.cgerc
dtype = complex64
def transform(self,x):
return conjugate(x)
class TestZgerc(BaseGerComplex):
blas_func = fblas.zgerc
dtype = complex128
def transform(self,x):
return conjugate(x)
"""
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