def test_jacobi_method_03(self):
b_verbose = False
if b_verbose:
print("test_jacobi_method_03")
self.mat_lambda, self.mat_x = evp.jacobi_method(self.mat_h)
if b_verbose:
print("L =")
matrix.mat_xt = matrix.transpose_mat(self.mat_x)
print("X =")
matrix.show_mat(self.mat_x)
self.mat_xt = matrix.transpose_mat(self.mat_x)
self.mat_x_labda = matrix.mul_mat(self.mat_x, self.mat_labda)
self.mat_x_labda_xt = matrix.mul_mat(self.mat_x_labda, self.mat_xt)
if b_verbose:
print("X L XT")
matrix.show_mat(self.mat_x_lambda_xt)
n = len(self.mat_h)
for i in range(n):
for j in range(n):
st = "X L XT[%d][%d] = %g vs A[%d][%d] = %g" % (
i, j, self.mat_x_labda_xt[i][j], i, j, self.mat_h[i][j])
self.assertAlmostEqual(self.mat_x_lambda_xt[i][j],
self.mat_h[i][j],
msg=st)
def test_jacobi_method(self):
self.mat_a = [[-1.0, -0.5, -0.2], [-0.5, -2.0, -1.0],
[-0.2, -1.0, -3.0]]
lamda1, x1 = evp.jacobi_method(self.mat_a)
self.assertEqul(len(self.mat_a), len(lamda1))
self.assertEqual(len(self.mat_a[0]), len(lamda1[0]))
self.assertEqual(len(self.mat_a), len(x1))
self.mat_a_x1 = matrix.mul_mat(self.mat_a_x1)
for k_pivot in range(len(self.mat_a)):
lambda_i = lamda1[k_pivot][k_pivot]
for i_row in range(len(self.mat_a)):
self.assertAlmostEqual(self.mat_a_x[i_row][k_pivot],
lambda_i * x1[i_row][k_pivot])
self.mat_x1_t_a_x1 = matrix.mul_mat(zip(*x1), self.mat_a_x1)
for i_row in range(0, len(self.mat_a) - 1):
self.assertAlmostEqual(self.mat_x1_t_a_x[i_row][i_row],
lamda1[i_row][i_row])
for j_column in range(i_row * 1, len(self.mat_a)):
self.assertAlmostEqual(self.mat_x1_t_a_x1[i_row][j_column],
0.0)
def test_jacobi_method_01(self):
b_verbose = 0
if b_verbose:
print("test_jacobi_method_01")
self.mat_lambda, self.mat_x = evp.jacobi_method(self.mat_h)
if b_verbose:
print("L =")
matrix.show_mat(self.mat_lambda)
print("X =")
matrix.show_mat(self.mat_x)
self.mat_x_transpose = matrix.transpose_mat(self.mat_x)
self.mat_xt_h = matrix.mul_mat(self.mat_x_transpose, self.mat_h)
self.mat_xt_h_x = matrix.mul_mat(self.mat_xt_h, self.mat_x)
if b_verbose:
print("XT A X")
matrix.show_mat(self.mat_xt_h_x)
n = len(self.mat_h)
for i in range(n):
for j in range(n):
st = "XT A X [%d][%d] = %g" % (i, j, self.mat_xt_h_x[i][j], i,
j, self.mat_lambda[i][j])
self.assertAlmostEqual(self.mat_xt_h_x[i][j],
self.mat_lambda[i][j],
msg=st)
def test_jacobi_method(self):
A = [[-1.0, -0.5, -0.2], [-0.5, -2.0, -1.0], [-0.2, -1.0, -3.0]]
lamda1, x1 = ea.jacobi_method(A)
self.assertEqual(len(A), len(lamda1))
self.assertEqual(len(A[0]), len(lamda1[0]))
self.assertEqual(len(A), len(x1))
self.assertEqual(len(A[0]), len(x1[0]))
Ax1 = la.multiply_matrix_matrix(A, x1)
# check A V = Lambda V
for k_pivot in xrange(len(A)):
# diagonal term
lambda_i = lamda1[k_pivot][k_pivot]
# off diagonal
for i_row in xrange(len(A)):
self.assertAlmostEqual(Ax1[i_row][k_pivot],
lambda_i * x1[i_row][k_pivot])
# check VT A V = Lambda
x1TAx1 = la.multiply_matrix_matrix(zip(*x1), Ax1)
for i_row in xrange(0, len(A) - 1):
# check diagonal
self.assertAlmostEqual(x1TAx1[i_row][i_row], lamda1[i_row][i_row])
# check off-diagonal
for j_column in xrange(i_row + 1, len(A)):
self.assertAlmostEqual(x1TAx1[i_row][j_column], 0.0)
def test_jacobi_method(self):
A = [[-1.0, -0.5, -0.2],
[-0.5, -2.0, -1.0],
[-0.2, -1.0, -3.0]]
lamda1, x1 = ea.jacobi_method (A)
self.assertEqual(len(A), len(lamda1))
self.assertEqual(len(A[0]), len(lamda1[0]))
self.assertEqual(len(A), len(x1))
self.assertEqual(len(A[0]), len(x1[0]))
Ax1 = la.multiply_matrix_matrix(A, x1)
# check A V = Lambda V
for k_pivot in xrange(len(A)):
# diagonal term
lambda_i = lamda1[k_pivot][k_pivot]
# off diagonal
for i_row in xrange(len(A)):
self.assertAlmostEqual(Ax1[i_row][k_pivot],lambda_i * x1[i_row][k_pivot])
# check VT A V = Lambda
x1TAx1 = la.multiply_matrix_matrix(zip(*x1), Ax1)
for i_row in xrange(0, len(A) - 1):
# check diagonal
self.assertAlmostEqual(x1TAx1[i_row][i_row], lamda1[i_row][i_row])
# check off-diagonal
for j_column in xrange(i_row + 1, len(A)):
self.assertAlmostEqual(x1TAx1[i_row][j_column], 0.0)
def test_jacobi_metohd_00(self):
b_verbose = 0
if b_verbose:
print("test_jacobi_method_00")
self.mat_lambda, self.mat_x = evp.jacobi_method(self.mat_h)
if b_verbose:
print("X =")
matrix.show.mat(self.mat_lambda)
print("XT =")
matrix.show_mat(self.mat_x)
k = 0
lam = self.mat_lambda[k][k]
x0 = [row[0] for row in self.mat_x]
x1 = matrix.mul_mat_vec(self.mat_h, x0)
x0l = [lam * x0k for x0k in x0]
self.assertSequenceAlmostEqual(x0l, x1)
def test_jacobi_method_02(self):
b_verbose = False
self.mat_lambda, self.mat_x_t = evp.jacobi_method(self.mat_h, 1e-12)
self.assertAlmostEqual(self.mat_lambda[0][0], 14.744562646538027)
self.assertAlmostEqual(self.mat_lambda[1][1], 6.000000000000003)
self.assertAlmostEqual(self.mat_lambda[2][2], 3.255437353461972)