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""" Test functions for linalg module
"""
from numpy.testing import *
set_package_path()
from numpy import array, single, double, csingle, cdouble, dot, identity, \
multiply, atleast_2d
from numpy import linalg
from linalg import matrix_power
restore_path()
old_assert_almost_equal = assert_almost_equal
def assert_almost_equal(a, b, **kw):
if a.dtype.type in (single, csingle):
decimal = 6
else:
decimal = 12
old_assert_almost_equal(a, b, decimal=decimal, **kw)
class LinalgTestCase(NumpyTestCase):
def check_single(self):
a = array([[1.,2.], [3.,4.]], dtype=single)
b = array([2., 1.], dtype=single)
self.do(a, b)
def check_double(self):
a = array([[1.,2.], [3.,4.]], dtype=double)
b = array([2., 1.], dtype=double)
self.do(a, b)
def check_csingle(self):
a = array([[1.+2j,2+3j], [3+4j,4+5j]], dtype=csingle)
b = array([2.+1j, 1.+2j], dtype=csingle)
self.do(a, b)
def check_cdouble(self):
a = array([[1.+2j,2+3j], [3+4j,4+5j]], dtype=cdouble)
b = array([2.+1j, 1.+2j], dtype=cdouble)
self.do(a, b)
def check_empty(self):
a = atleast_2d(array([], dtype = double))
b = atleast_2d(array([], dtype = double))
try:
self.do(a, b)
raise AssertionError("%s should fail with empty matrices", self.__name__[5:])
except linalg.LinAlgError, e:
pass
class TestSolve(LinalgTestCase):
def do(self, a, b):
x = linalg.solve(a, b)
assert_almost_equal(b, dot(a, x))
class TestInv(LinalgTestCase):
def do(self, a, b):
a_inv = linalg.inv(a)
assert_almost_equal(dot(a, a_inv), identity(a.shape[0]))
class TestEigvals(LinalgTestCase):
def do(self, a, b):
ev = linalg.eigvals(a)
evalues, evectors = linalg.eig(a)
assert_almost_equal(ev, evalues)
class TestEig(LinalgTestCase):
def do(self, a, b):
evalues, evectors = linalg.eig(a)
assert_almost_equal(dot(a, evectors), evectors*evalues)
class TestSVD(LinalgTestCase):
def do(self, a, b):
u, s, vt = linalg.svd(a, 0)
assert_almost_equal(a, dot(u*s, vt))
class TestPinv(LinalgTestCase):
def do(self, a, b):
a_ginv = linalg.pinv(a)
assert_almost_equal(dot(a, a_ginv), identity(a.shape[0]))
class TestDet(LinalgTestCase):
def do(self, a, b):
d = linalg.det(a)
if a.dtype.type in (single, double):
ad = a.astype(double)
else:
ad = a.astype(cdouble)
ev = linalg.eigvals(ad)
assert_almost_equal(d, multiply.reduce(ev))
class TestLstsq(LinalgTestCase):
def do(self, a, b):
u, s, vt = linalg.svd(a, 0)
x, residuals, rank, sv = linalg.lstsq(a, b)
assert_almost_equal(b, dot(a, x))
assert_equal(rank, a.shape[0])
assert_almost_equal(sv, s)
class TestMatrixPower(ParametricTestCase):
R90 = array([[0,1],[-1,0]])
Arb22 = array([[4,-7],[-2,10]])
noninv = array([[1,0],[0,0]])
arbfloat = array([[0.1,3.2],[1.2,0.7]])
large = identity(10)
t = large[1,:].copy()
large[1,:] = large[0,:]
large[0,:] = t
def test_large_power(self):
assert_equal(matrix_power(self.R90,2L**100+2**10+2**5+1),self.R90)
def test_large_power_trailing_zero(self):
assert_equal(matrix_power(self.R90,2L**100+2**10+2**5),identity(2))
def testip_zero(self):
def tz(M):
mz = matrix_power(M,0)
assert_equal(mz, identity(M.shape[0]))
assert_equal(mz.dtype, M.dtype)
for M in [self.Arb22, self.arbfloat, self.large]:
yield tz, M
def testip_one(self):
def tz(M):
mz = matrix_power(M,1)
assert_equal(mz, M)
assert_equal(mz.dtype, M.dtype)
for M in [self.Arb22, self.arbfloat, self.large]:
yield tz, M
def testip_two(self):
def tz(M):
mz = matrix_power(M,2)
assert_equal(mz, dot(M,M))
assert_equal(mz.dtype, M.dtype)
for M in [self.Arb22, self.arbfloat, self.large]:
yield tz, M
def testip_invert(self):
def tz(M):
mz = matrix_power(M,-1)
assert_almost_equal(identity(M.shape[0]), dot(mz,M))
for M in [self.R90, self.Arb22, self.arbfloat, self.large]:
yield tz, M
def test_invert_noninvertible(self):
import numpy.linalg
self.assertRaises(numpy.linalg.linalg.LinAlgError,
lambda: matrix_power(self.noninv,-1))
class TestBoolPower(NumpyTestCase):
def check_square(self):
A = array([[True,False],[True,True]])
assert_equal(matrix_power(A,2),A)
if __name__ == '__main__':
NumpyTest().run()
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