def test_shift():
A, b = get_sample_problem()
shift = 0.5
shifted_A = A - shift * np.eye(10)
x1, info1 = minres(A, b, shift=shift)
x2, info2 = minres(shifted_A, b)
assert_equal(info1, 0)
assert_allclose(x1, x2, rtol=1e-5)
def test_shift():
A, b = get_sample_problem()
shift = 0.5
shifted_A = A - shift * np.eye(10)
x1, info1 = minres(A, b, shift=shift)
x2, info2 = minres(shifted_A, b)
assert_equal(info1, 0)
assert_allclose(x1, x2, rtol=1e-5)
def test_asymmetric_fail():
"""Asymmetric matrix should raise `ValueError` when check=True"""
A, b = get_sample_problem()
A[1, 2] = 1
A[2, 1] = 2
with assert_raises(ValueError):
xp, info = minres(A, b, check=True)
def test_gh_6843():
"""check if x0 is being used by tracing iterates"""
A, b = get_sample_problem()
# Random x0 to feed minres
np.random.seed(12345)
x0 = np.random.rand(10)
trace = []
def trace_iterates(xk):
trace.append(xk)
minres(A, b, x0=x0, callback=trace_iterates)
trace_with_x0 = trace
trace = []
minres(A, b, callback=trace_iterates)
assert_(not np.array_equal(trace_with_x0[0], trace[0]))
def test_singular():
A, b = get_sample_problem()
A[0, ] = 0
b[0] = 0
xp, info = minres(A, b)
assert_equal(info, 0)
assert_normclose(A.dot(xp), b, tol=1e-5)
def test_asymmetric_fail():
"""Asymmetric matrix should raise `ValueError` when check=True"""
A, b = get_sample_problem()
A[1, 2] = 1
A[2, 1] = 2
with assert_raises(ValueError):
xp, info = minres(A, b, check=True)
def test_gh_6843():
"""check if x0 is being used by tracing iterates"""
A, b = get_sample_problem()
# Random x0 to feed minres
np.random.seed(12345)
x0 = np.random.rand(10)
trace = []
def trace_iterates(xk):
trace.append(xk)
minres(A, b, x0=x0, callback=trace_iterates)
trace_with_x0 = trace
trace = []
minres(A, b, callback=trace_iterates)
assert_(not np.array_equal(trace_with_x0[0], trace[0]))
def test_singular():
A, b = get_sample_problem()
A[0, ] = 0
b[0] = 0
xp, info = minres(A, b)
assert_equal(info, 0)
assert_normclose(A.dot(xp), b, tol=1e-5)
def test_x0_is_used_by():
A, b = get_sample_problem()
# Random x0 to feed minres
np.random.seed(12345)
x0 = np.random.rand(10)
trace = []
def trace_iterates(xk):
trace.append(xk)
minres(A, b, x0=x0, callback=trace_iterates)
trace_with_x0 = trace
trace = []
minres(A, b, callback=trace_iterates)
assert_(not np.array_equal(trace_with_x0[0], trace[0]))
def test_minres_non_default_x0():
np.random.seed(1234)
tol = 10**(-6)
a = np.random.randn(5, 5)
a = np.dot(a, a.T)
b = np.random.randn(5)
c = np.random.randn(5)
x = minres(a, b, x0=c, tol=tol)[0]
assert norm(a.dot(x) - b) < tol
def test_minres_precond_exact_x0():
np.random.seed(1234)
tol = 10**(-6)
a = np.eye(10)
b = np.ones(10)
c = np.ones(10)
m = np.random.randn(10, 10)
m = np.dot(m, m.T)
x = minres(a, b, M=m, x0=c, tol=tol)[0]
assert norm(a.dot(x) - b) < tol
def test_minres_precond_non_default_x0():
np.random.seed(12345)
tol = 10**(-6)
a = np.random.randn(5, 5)
a = np.dot(a, a.T)
b = np.random.randn(5)
c = np.random.randn(5)
m = np.random.randn(5, 5)
m = np.dot(m, m.T)
x = minres(a, b, M=m, x0=c, tol=tol)[0]
assert_normclose(a.dot(x), b, tol=tol)
