def test_householder_tfm(self):
a = [[1.0, 2.0, 3.0], [2.0, 0.0, -1.0]]
svd._householder_tfm_rows_tail_inplace(a, [1.0, 0.0, 0.0])
self.assertTrue(mat_eq(a, [[-1.0, 2.0, 3.0], [-2.0, 0.0, -1.0]]))
svd._householder_tfm_rows_tail_inplace(a, [1.0, 0.0, 0.0])
self.assertTrue(mat_eq(a, [[1.0, 2.0, 3.0], [2.0, 0.0, -1.0]]))
def test_householder_bring2(self):
v = [1.0, 2.0, 3.0]
b = svd._householder_bring_vector(v, -1)
m = copy_mat( [v] )
svd._householder_tfm_rows_tail_inplace( m, b )
self.assertTrue( abs(m[0][0]) < 1e-5 )
self.assertTrue( abs(m[0][1]) < 1e-5 )
self.assertTrue( abs(m[0][2]) > 0 )
self.assertTrue( abs(abs(m[0][2]) - vec_norm2(v)) < 1e-5 )
def test_householder_bring2(self):
v = [1.0, 2.0, 3.0]
b = svd._householder_bring_vector(v, -1)
m = copy_mat([v])
svd._householder_tfm_rows_tail_inplace(m, b)
self.assertTrue(abs(m[0][0]) < 1e-5)
self.assertTrue(abs(m[0][1]) < 1e-5)
self.assertTrue(abs(m[0][2]) > 0)
self.assertTrue(abs(abs(m[0][2]) - vec_norm2(v)) < 1e-5)
def test_householder_tfm(self):
a = [[1.0, 2.0, 3.0],
[2.0, 0.0, -1.0]]
svd._householder_tfm_rows_tail_inplace( a, [1.0, 0.0, 0.0] )
self.assertTrue( mat_eq( a,
[[-1.0, 2.0, 3.0],
[-2.0, 0.0, -1.0]] ) )
svd._householder_tfm_rows_tail_inplace( a, [1.0, 0.0, 0.0] )
self.assertTrue( mat_eq( a,
[[1.0, 2.0, 3.0],
[2.0, 0.0, -1.0]] ) )
def test_householder_tfm_tail_numpy(self):
"""Big test on arbitrary householder transformations"""
import numpy
N, M = 2,3
for i in xrange(100):
a = numpy.random.rand( N,M) - 0.5
v = numpy.random.rand( M ) - 0.5
vn = numpy.array(normalized_vec( v ))
H = numpy.eye(M) - 2*numpy.dot( vn.reshape((M,1)), vn.reshape((1,M)) ) # H = E - 2*vv'
a1 = numpy.dot(a, H)
svd._householder_tfm_rows_tail_inplace( a, vn )
self.assertTrue( mat_eq( a1, a, tol=1e-5 ) )
def test_householder_tfm_tail_numpy(self):
"""Big test on arbitrary householder transformations"""
import numpy
N, M = 2, 3
for i in xrange(100):
a = numpy.random.rand(N, M) - 0.5
v = numpy.random.rand(M) - 0.5
vn = numpy.array(normalized_vec(v))
H = numpy.eye(M) - 2 * numpy.dot(vn.reshape(
(M, 1)), vn.reshape((1, M))) # H = E - 2*vv'
a1 = numpy.dot(a, H)
svd._householder_tfm_rows_tail_inplace(a, vn)
self.assertTrue(mat_eq(a1, a, tol=1e-5))
