def test_dot(d1, d2, d3):
print "testing dot with d1 = " + str(d1) + ", d2 = " + str(d2) + ", d3 = " + str(d3)
a = dist.random_normal([d1, d2])
b = dist.random_normal([d2, d3])
c = dist.dot(a, b)
a_val = a.assemble()
b_val = b.assemble()
c_val = c.assemble()
np.testing.assert_allclose(np.dot(a_val, b_val), c_val)
def test_dot(d1, d2, d3):
print "testing dot with d1 = " + str(d1) + ", d2 = " + str(
d2) + ", d3 = " + str(d3)
a = dist.random_normal([d1, d2])
b = dist.random_normal([d2, d3])
c = dist.dot(a, b)
a_val = a.assemble()
b_val = b.assemble()
c_val = c.assemble()
np.testing.assert_allclose(np.dot(a_val, b_val), c_val)
def test_tsqr(d1, d2):
print "testing tsqr with d1 = " + str(d1) + ", d2 = " + str(d2)
a = dist.random_normal([d1, d2])
q, r = dist.tsqr(a)
a_val = a.assemble()
q_val = q.assemble()
np.testing.assert_allclose(np.dot(q_val, r), a_val) # check that a = q * r
np.testing.assert_allclose(np.dot(q_val.T, q_val), np.eye(min(d1, d2)), atol=1e-6) # check that q.T * q = I
np.testing.assert_allclose(np.triu(r), r) # check that r is upper triangular
def test_tsqr_hr(d1, d2):
print "testing tsqr_hr with d1 = " + str(d1) + ", d2 = " + str(d2)
a = dist.random_normal([d1, d2])
a_val = a.assemble()
y, t, y_top, r = dist.tsqr_hr(a)
tall_eye = np.zeros((d1, min(d1, d2)))
np.fill_diagonal(tall_eye, 1)
q = tall_eye - np.dot(y, np.dot(t, y_top.T))
np.testing.assert_allclose(np.dot(q.T, q), np.eye(min(d1, d2)), atol=1e-6) # check that q.T * q = I
np.testing.assert_allclose(np.dot(q, r), a_val) # check that a = (I - y * t * y_top.T) * r
def test_tsqr_hr(d1, d2):
print "testing tsqr_hr with d1 = " + str(d1) + ", d2 = " + str(d2)
a = dist.random_normal([d1, d2])
a_val = a.assemble()
y, t, y_top, r = dist.tsqr_hr(a)
tall_eye = np.zeros((d1, min(d1, d2)))
np.fill_diagonal(tall_eye, 1)
q = tall_eye - np.dot(y, np.dot(t, y_top.T))
np.testing.assert_allclose(np.dot(q.T, q),
np.eye(min(d1, d2)),
atol=1e-6) # check that q.T * q = I
np.testing.assert_allclose(np.dot(
q, r), a_val) # check that a = (I - y * t * y_top.T) * r
def test_tsqr(d1, d2):
print "testing tsqr with d1 = " + str(d1) + ", d2 = " + str(d2)
a = dist.random_normal([d1, d2])
q, r = dist.tsqr(a)
a_val = a.assemble()
q_val = q.assemble()
np.testing.assert_allclose(np.dot(q_val, r),
a_val) # check that a = q * r
np.testing.assert_allclose(np.dot(q_val.T, q_val),
np.eye(min(d1, d2)),
atol=1e-6) # check that q.T * q = I
np.testing.assert_allclose(np.triu(r),
r) # check that r is upper triangular
def test_qr(d1, d2):
print "testing qr with d1 = " + str(d1) + ", d2 = " + str(d2)
a = dist.random_normal([d1, d2])
a_val = a.assemble()
Ts, y_res, r_res = dist.qr(a)
r_val = r_res.assemble()
y_val = y_res.assemble()
q = np.eye(d1)
for i in range(min(a.num_blocks[0], a.num_blocks[1])):
q = np.dot(q, np.eye(d1) - np.dot(y_val[:, (i * 10):((i + 1) * 10)], np.dot(Ts[i], y_val[:, (i * 10):((i + 1) * 10)].T)))
q = q[:, :min(d1, d2)]
np.testing.assert_allclose(np.triu(r_val), r_val) # check that r is upper triangular
np.testing.assert_allclose(np.dot(q.T, q), np.eye(min(d1, d2)), atol=1e-6) # check that q.T * q = I
np.testing.assert_allclose(np.dot(q, r_val), a_val) # check that a = q * r
def test_qr(d1, d2):
print "testing qr with d1 = " + str(d1) + ", d2 = " + str(d2)
a = dist.random_normal([d1, d2])
a_val = a.assemble()
Ts, y_res, r_res = dist.qr(a)
r_val = r_res.assemble()
y_val = y_res.assemble()
q = np.eye(d1)
for i in range(min(a.num_blocks[0], a.num_blocks[1])):
q = np.dot(
q,
np.eye(d1) -
np.dot(y_val[:, (i * 10):((i + 1) * 10)],
np.dot(Ts[i], y_val[:, (i * 10):((i + 1) * 10)].T)))
q = q[:, :min(d1, d2)]
np.testing.assert_allclose(np.triu(r_val),
r_val) # check that r is upper triangular
np.testing.assert_allclose(np.dot(q.T, q),
np.eye(min(d1, d2)),
atol=1e-6) # check that q.T * q = I
np.testing.assert_allclose(np.dot(q, r_val),
a_val) # check that a = q * r