def _test_gen_schur(dtype):
rand = _Random()
a = rand.randmat(5, 5, dtype)
b = rand.randmat(5, 5, dtype)
s, t, q, z = gen_schur(a, b)[:4]
assert_array_almost_equal(dtype, np.dot(np.dot(q, s), z.T.conj()), a)
assert_array_almost_equal(dtype, np.dot(np.dot(q, t), z.T.conj()), b)
def _test_gen_schur(dtype):
rand = _Random()
a = rand.randmat(5, 5, dtype)
b = rand.randmat(5, 5, dtype)
s, t, q, z = gen_schur(a, b)[:4]
assert_array_almost_equal(dtype, np.dot(np.dot(q, s), z.T.conj()), a)
assert_array_almost_equal(dtype, np.dot(np.dot(q, t), z.T.conj()), b)
def _test_evecs_from_gen_schur(dtype):
rand = _Random()
a = rand.randmat(5, 5, dtype)
b = rand.randmat(5, 5, dtype)
s, t, q, z, alpha, beta = gen_schur(a, b)
vl, vr = evecs_from_gen_schur(s,
t,
q,
z,
select=None,
left=True,
right=True)
assert_array_almost_equal(dtype, np.dot(a, np.dot(vr, np.diag(beta))),
np.dot(b, np.dot(vr, np.diag(alpha))))
assert_array_almost_equal(
dtype, np.dot(np.dot(np.diag(beta), vl.T.conj()), a),
np.dot(np.dot(np.diag(alpha), vl.T.conj()), b))
select = np.array([True, True, False, False, False], dtype=bool)
vl, vr = evecs_from_gen_schur(s,
t,
q,
z,
select,
left=True,
right=True)
assert vr.shape[1] == 2
assert vl.shape[1] == 2
assert_array_almost_equal(
dtype, np.dot(a, np.dot(vr, np.diag(beta[select]))),
np.dot(b, np.dot(vr, np.diag(alpha[select]))))
assert_array_almost_equal(
dtype, np.dot(np.dot(np.diag(beta[select]), vl.T.conj()), a),
np.dot(np.dot(np.diag(alpha[select]), vl.T.conj()), b))
vl, vr = evecs_from_gen_schur(s,
t,
q,
z,
lambda i: i < 2,
left=True,
right=True)
assert vr.shape[1] == 2
assert vl.shape[1] == 2
assert_array_almost_equal(
dtype, np.dot(a, np.dot(vr, np.diag(beta[select]))),
np.dot(b, np.dot(vr, np.diag(alpha[select]))))
assert_array_almost_equal(
dtype, np.dot(np.dot(np.diag(beta[select]), vl.T.conj()), a),
np.dot(np.dot(np.diag(alpha[select]), vl.T.conj()), b))
def _test_evecs_from_gen_schur(dtype):
rand = _Random()
a = rand.randmat(5, 5, dtype)
b = rand.randmat(5, 5, dtype)
s, t, q, z, alpha, beta = gen_schur(a, b)
vl, vr = evecs_from_gen_schur(s, t, q, z , select=None,
left=True, right=True)
assert_array_almost_equal(dtype, np.dot(a, np.dot(vr, np.diag(beta))),
np.dot(b, np.dot(vr, np.diag(alpha))))
assert_array_almost_equal(dtype,
np.dot(np.dot(np.diag(beta), vl.T.conj()),
a),
np.dot(np.dot(np.diag(alpha), vl.T.conj()),
b))
select = np.array([True, True, False, False, False], dtype=bool)
vl, vr = evecs_from_gen_schur(s, t, q, z, select,
left=True, right=True)
assert_equal(vr.shape[1], 2)
assert_equal(vl.shape[1], 2)
assert_array_almost_equal(dtype,
np.dot(a, np.dot(vr,
np.diag(beta[select]))),
np.dot(b, np.dot(vr,
np.diag(alpha[select]))))
assert_array_almost_equal(dtype,
np.dot(np.dot(np.diag(beta[select]),
vl.T.conj()),
a),
np.dot(np.dot(np.diag(alpha[select]),
vl.T.conj()),
b))
vl, vr = evecs_from_gen_schur(s, t, q, z, lambda i: i<2, left=True,
right=True)
assert_equal(vr.shape[1], 2)
assert_equal(vl.shape[1], 2)
assert_array_almost_equal(dtype,
np.dot(a, np.dot(vr,
np.diag(beta[select]))),
np.dot(b, np.dot(vr,
np.diag(alpha[select]))))
assert_array_almost_equal(dtype,
np.dot(np.dot(np.diag(beta[select]),
vl.T.conj()),
a),
np.dot(np.dot(np.diag(alpha[select]),
vl.T.conj()),
b))
def _test_convert_r2c_gen_schur(dtype):
rand = _Random()
a = rand.randmat(10, 10, dtype)
b = rand.randmat(10, 10, dtype)
s, t, q, z = gen_schur(a, b)[:4]
s2, t2, q2, z2 = convert_r2c_gen_schur(s, t, q, z)
assert_array_almost_equal(dtype, np.dot(np.dot(q, s), z.T.conj()), a)
assert_array_almost_equal(dtype, np.dot(np.dot(q, t), z.T.conj()), b)
assert_array_almost_equal(dtype, np.dot(np.dot(q2, s2), z2.T.conj()),
a)
assert_array_almost_equal(dtype, np.dot(np.dot(q2, t2), z2.T.conj()),
b)
def _test_convert_r2c_gen_schur(dtype):
rand = _Random()
a = rand.randmat(10, 10, dtype)
b = rand.randmat(10, 10, dtype)
s, t, q, z = gen_schur(a, b)[:4]
s2, t2, q2, z2 = convert_r2c_gen_schur(s, t, q, z)
assert_array_almost_equal(dtype, np.dot(np.dot(q, s), z.T.conj()), a)
assert_array_almost_equal(dtype, np.dot(np.dot(q, t), z.T.conj()), b)
assert_array_almost_equal(dtype, np.dot(np.dot(q2, s2), z2.T.conj()),
a)
assert_array_almost_equal(dtype, np.dot(np.dot(q2, t2), z2.T.conj()),
b)
def _test_order_gen_schur(dtype):
rand = _Random()
a = rand.randmat(10, 10, dtype)
b = rand.randmat(10, 10, dtype)
s, t, q, z, alpha, beta = gen_schur(a, b)
s2, t2, q2, z2, alpha2, beta2 = order_gen_schur(
lambda i: i > 2 and i < 7, s, t, q, z)
assert_array_almost_equal(dtype, np.dot(np.dot(q, s), z.T.conj()), a)
assert_array_almost_equal(dtype, np.dot(np.dot(q, t), z.T.conj()), b)
assert_array_almost_equal(dtype, np.dot(np.dot(q2, s2), z2.T.conj()),
a)
assert_array_almost_equal(dtype, np.dot(np.dot(q2, t2), z2.T.conj()),
b)
#Sorting here is a bit tricky: For real matrices we expect
#for complex conjugated pairs identical real parts - however
#that seems messed up (only an error on the order of machine precision)
#in the division. The solution here is to sort and compare the real
#and imaginary parts separately. The only error that would not be
#catched in this comparison is if the real and imaginary parts would
#be assembled differently in the two arrays - an error that is highly
#unlikely.
assert_array_almost_equal(dtype, np.sort((alpha / beta).real),
np.sort((alpha2 / beta2).real))
assert_array_almost_equal(dtype, np.sort((alpha / beta).imag),
np.sort((alpha2 / beta2).imag))
assert_array_almost_equal(dtype, np.sort(
(alpha[3:7] / beta[3:7]).real),
np.sort((alpha2[:4] / beta2[:4]).real))
assert_array_almost_equal(dtype, np.sort(
(alpha[3:7] / beta[3:7]).imag),
np.sort((alpha2[:4] / beta2[:4]).imag))
sel = [False, False, 0, True, True, True, 1, False, False, False]
s3, t3, q3, z3 = order_gen_schur(sel, s, t, q, z)[:4]
assert_array_almost_equal(dtype, np.dot(np.dot(q3, s3), z3.T.conj()),
a)
assert_array_almost_equal(dtype, np.dot(np.dot(q3, t3), z3.T.conj()),
b)
assert_array_almost_equal(dtype, s2, s3)
assert_array_almost_equal(dtype, t2, t3)
assert_array_almost_equal(dtype, q2, q3)
assert_array_almost_equal(dtype, z2, z3)
def _test_order_gen_schur(dtype):
rand = _Random()
a = rand.randmat(10, 10, dtype)
b = rand.randmat(10, 10, dtype)
s, t, q, z, alpha, beta = gen_schur(a, b)
s2, t2, q2, z2, alpha2, beta2 = order_gen_schur(lambda i: i>2 and i<7,
s, t, q, z)
assert_array_almost_equal(dtype, np.dot(np.dot(q, s), z.T.conj()), a)
assert_array_almost_equal(dtype, np.dot(np.dot(q, t), z.T.conj()), b)
assert_array_almost_equal(dtype, np.dot(np.dot(q2, s2), z2.T.conj()),
a)
assert_array_almost_equal(dtype, np.dot(np.dot(q2, t2), z2.T.conj()),
b)
#Sorting here is a bit tricky: For real matrices we expect
#for complex conjugated pairs identical real parts - however
#that seems messed up (only an error on the order of machine precision)
#in the division. The solution here is to sort and compare the real
#and imaginary parts separately. The only error that would not be
#catched in this comparison is if the real and imaginary parts would
#be assembled differently in the two arrays - an error that is highly
#unlikely.
assert_array_almost_equal(dtype, np.sort((alpha/beta).real),
np.sort((alpha2/beta2).real))
assert_array_almost_equal(dtype, np.sort((alpha/beta).imag),
np.sort((alpha2/beta2).imag))
assert_array_almost_equal(dtype, np.sort((alpha[3:7]/beta[3:7]).real),
np.sort((alpha2[:4]/beta2[:4]).real))
assert_array_almost_equal(dtype, np.sort((alpha[3:7]/beta[3:7]).imag),
np.sort((alpha2[:4]/beta2[:4]).imag))
sel = [False, False, 0, True, True, True, 1, False, False, False]
s3, t3, q3, z3 = order_gen_schur(sel, s, t, q, z)[:4]
assert_array_almost_equal(dtype, np.dot(np.dot(q3, s3), z3.T.conj()),
a)
assert_array_almost_equal(dtype, np.dot(np.dot(q3, t3), z3.T.conj()),
b)
assert_array_almost_equal(dtype, s2, s3)
assert_array_almost_equal(dtype, t2, t3)
assert_array_almost_equal(dtype, q2, q3)
assert_array_almost_equal(dtype, z2, z3)