def _test_lu(dtype):
rand = _Random()
a = rand.randmat(4, 4, dtype)
bmat = rand.randmat(4, 4, dtype)
bvec = rand.randvec(4, dtype)
lu = lu_factor(a)
xmat = lu_solve(lu, bmat)
xvec = lu_solve(lu, bvec)
assert_array_almost_equal(dtype, np.dot(a, xmat), bmat)
assert_array_almost_equal(dtype, np.dot(a, xvec), bvec)
def _test_lu(dtype):
rand = _Random()
a = rand.randmat(4, 4, dtype)
bmat = rand.randmat(4, 4, dtype)
bvec = rand.randvec(4, dtype)
lu = lu_factor(a)
xmat = lu_solve(lu, bmat)
xvec = lu_solve(lu, bvec)
assert_array_almost_equal(dtype, np.dot(a, xmat), bmat)
assert_array_almost_equal(dtype, np.dot(a, xvec), bvec)
def _test_rcond_from_lu(dtype):
rand = _Random()
a = rand.randmat(10, 10, dtype)
norm1_a = np.linalg.norm(a, 1)
normI_a = np.linalg.norm(a, np.inf)
lu = lu_factor(a)
rcond1 = rcond_from_lu(lu, norm1_a, '1')
rcondI = rcond_from_lu(lu, normI_a, 'I')
err1 = abs(rcond1 -
1/(norm1_a * np.linalg.norm(np.linalg.inv(a), 1)))
errI = abs(rcondI -
1/(normI_a * np.linalg.norm(np.linalg.inv(a), np.inf)))
#rcond_from_lu returns an estimate for the reciprocal
#condition number only; hence we shouldn't be too strict about
#the assertions here
#Note: in my experience the estimate is excellent for somewhat
#larger matrices
assert_true(err1/rcond1 < 0.1)
assert_true(errI/rcondI < 0.1)
def _test_rcond_from_lu(dtype):
rand = _Random()
a = rand.randmat(10, 10, dtype)
norm1_a = np.linalg.norm(a, 1)
normI_a = np.linalg.norm(a, np.inf)
lu = lu_factor(a)
rcond1 = rcond_from_lu(lu, norm1_a, '1')
rcondI = rcond_from_lu(lu, normI_a, 'I')
err1 = abs(rcond1 - 1 /
(norm1_a * np.linalg.norm(np.linalg.inv(a), 1)))
errI = abs(rcondI - 1 /
(normI_a * np.linalg.norm(np.linalg.inv(a), np.inf)))
#rcond_from_lu returns an estimate for the reciprocal
#condition number only; hence we shouldn't be too strict about
#the assertions here
#Note: in my experience the estimate is excellent for somewhat
#larger matrices
assert err1 / rcond1 < 0.1
assert errI / rcondI < 0.1
