def tsqr_hr(a):
"""Algorithm 6 from http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-175.pdf"""
q, r_temp = tsqr(a)
y, u, s = single.modified_lu(assemble(q))
s_full = np.diag(s)
b = q.shape[1]
y_top = y[:b, :b]
t = -1 * np.dot(u, np.dot(s_full, np.linalg.inv(y_top).T))
r = np.dot(s_full, r_temp)
return y, t, y_top, r
def test_modified_lu(d1, d2):
print "testing modified_lu with d1 = " + str(d1) + ", d2 = " + str(d2)
assert d1 >= d2
k = min(d1, d2)
m = np.random.normal(size=(d1, d2))
q, r = np.linalg.qr(m)
l, u, s = single.modified_lu(q)
s_mat = np.zeros((d1, d2))
for i in range(len(s)):
s_mat[i, i] = s[i]
np.testing.assert_allclose(q - s_mat, np.dot(l, u)) # check that q - s = l * u
np.testing.assert_allclose(np.triu(u), u) # check that u is upper triangular
np.testing.assert_allclose(np.tril(l), l) # check that u is lower triangular
def test_modified_lu(d1, d2):
print "testing modified_lu with d1 = " + str(d1) + ", d2 = " + str(d2)
assert d1 >= d2
k = min(d1, d2)
m = np.random.normal(size=(d1, d2))
q, r = np.linalg.qr(m)
l, u, s = single.modified_lu(q)
s_mat = np.zeros((d1, d2))
for i in range(len(s)):
s_mat[i, i] = s[i]
np.testing.assert_allclose(q - s_mat,
np.dot(l, u)) # check that q - s = l * u
np.testing.assert_allclose(np.triu(u),
u) # check that u is upper triangular
np.testing.assert_allclose(np.tril(l),
l) # check that u is lower triangular
