def test_solve_lower_triangular(self):
l = array([[3, 0, 0], [6, 4, 0], [8, 2, 4]], dtype=numpy.double)
b = array([3, 26, 42], dtype=numpy.double)
x = solve_lower_triangular(l, b)
print "x=", x
x_actual = scipy_solve(l, b)
print 'x_actual=', x_actual
def test_gauss_seidel(self):
# create random sdd matrix
A = randn(37,37) + 37*numpy.diag(numpy.ones(37))
b = randn(37)
y_actual = scipy_solve(A,b)
y,_ = gauss_seidel(A,b)
error = norm(y - y_actual)
self.assertLess(error, 1e-4)
def test_jacobi_epsilon(self):
# create random sdd matrix
A = randn(37,37) + 37*numpy.diag(numpy.ones(37))
b = randn(37)
epsilon=1e-12
y_actual = scipy_solve(A,b)
y,_ = jacobi(A,b)
error = norm(y - y_actual)
self.assertLess(error, 1e-8)
def test_jacobi_highn(self):
A, b = five_diagonal_system(20)
xactual = scipy_solve(A,b)
x, n = jacobi(A,b)
error = norm(xactual - x)
self.assertLess(error,1e-7)
A, b = five_diagonal_system(40)
xactual = scipy_solve(A,b)
x, n = jacobi(A,b,epsilon=1e-12)
error = norm(xactual - x)
self.assertLess(error,1e-7)
A, b = five_diagonal_system(8)
xactual = scipy_solve(A,b)
x, n = jacobi(A,b,epsilon=1e-3)
error = norm(xactual - x)
self.assertLess(error,1e-2)
def test_gauss_hign(self):
A, b = five_diagonal_system(20)
xactual = scipy_solve(A,b)
x, n = gauss_seidel(A,b)
error = norm(xactual - x)
self.assertLess(error,1e-7)
A, b = five_diagonal_system(40)
xactual = scipy_solve(A,b)
x, n = gauss_seidel(A,b)
error = norm(xactual - x)
self.assertLess(error,1e-7)
A, b = five_diagonal_system(8)
xactual = scipy_solve(A,b)
x, n = gauss_seidel(A,b,epsilon=1e-3)
error = norm(xactual - x)
self.assertLess(error,1e-2)
A, b = five_diagonal_system(80)
xactual = scipy_solve(A,b)
x, n = gauss_seidel(A,b,epsilon=1e-12)
error = norm(xactual - x)
self.assertLess(error,1e-7)
def scipy_solve_test():
x = scipy_solve(A, b)
def test_gauss(self):
A, b = five_diagonal_system(3)
xactual = scipy_solve(A,b)
x, n = gauss_seidel(A,b)
error = norm(xactual - x)
self.assertLess(error,1e-8)
def test_jacobi(self):
A, b = five_diagonal_system(3)
xactual = scipy_solve(A,b)
x, n = jacobi(A,b)
error = norm(xactual - x)
self.assertLess(error,1e-8)