def hilbert_matrix_steepest_descent_test():
selection = [
4,
8,
16,
32,
64,
128,
]
hilbert_matrix = []
solution = []
# Create the hilbert matrices and their corresponding Q factorization matrix.
for n in selection:
hilbert_matrix.append([[1 / (1 + i + j) for i in range(n)]
for j in range(n)]) # Hilbert Matrix generator
b = [sum([1 / (1 + i + j) for i in range(n)])
for j in range(n)] #the solution should be a vector of 1s.
solution.append(
matrix_solve_steepest_descent(hilbert_matrix[-1], b, 0.0001,
10000))
print("Absolute error for " + str(n) + "x" + str(n) + ": " +
str(abs_error_2norm([1] * n, solution[-1])))
print(solution[-1])
def steepest_descent_conjugate_gradient_compare():
n=100;
random_matrix = gen_diagdom_sym_matrix(n)
b = convert_vec_mat(matrix_mult(random_matrix,[[1]] * n)) #the solution should be a vector of 1s.
(solution1,iterCount1) = matrix_solve_steepest_descent(random_matrix,b,0.0001,10000,True)
(solution2, iterCount2) = matrix_solve_conjugate_gradient(random_matrix, b, 0.0001, 10000, True)
print("Steepest Descent " + str(n) + "x" + str(n) + ": Absolute Error=" + str(abs_error_2norm([1] * n,solution1)) + " Iteration Count=" + str(iterCount1))
print("Conjugate Gradient " + str(n) + "x" + str(n) + ": Absolute Error=" + str(abs_error_2norm([1] * n,solution2)) + " Iteration Count=" + str(iterCount2))
def steepest_descent_conjugate_gradient_gauss_seidel_compare():
n=100;
random_matrix = gen_diagdom_sym_matrix(n)
b = convert_vec_mat(matrix_mult(random_matrix,[[1]] * n)) #the solution should be a vector of 1s.
start_time = time.time()
(solution1,iterCount1) = matrix_solve_steepest_descent(random_matrix,b,0.00000000001,10000,True)
time1 = time.time() - start_time
start_time = time.time()
(solution2, iterCount2) = matrix_solve_conjugate_gradient(random_matrix, b, 0.00000000001, 10000, True)
time2 = time.time() - start_time
start_time = time.time()
(solution3, iterCount3) = matrix_solve_gauss_seidel(random_matrix, b, 0.00000000001, 10000, True)
time3 = time.time() - start_time
print("Steepest Descent " + str(n) + "x" + str(n) + ": Absolute Error=" + str(abs_error_2norm([1] * n,solution1)) + " Iteration Count=" + str(iterCount1) + " time=" + str(time1))
print("Conjugate Gradient " + str(n) + "x" + str(n) + ": Absolute Error=" + str(abs_error_2norm([1] * n,solution2)) + " Iteration Count=" + str(iterCount2) + " time=" + str(time2))
print("Gauss Seidel " + str(n) + "x" + str(n) + ": Absolute Error=" + str(abs_error_2norm([1] * n,solution3)) + " Iteration Count=" + str(iterCount3) + " time=" + str(time3))
def hilbert_matrix_steepest_descent_test():
selection = [4, 8, 16, 32]
hilbert_matrix = []
solution = []
# Create the hilbert matrices and their corresponding Q factorization matrix.
for n in selection:
hilbert_matrix.append([[1 / (1 + i + j) for i in range(n)]
for j in range(n)]) # Hilbert Matrix generator
solution.append(
matrix_solve_steepest_descent(hilbert_matrix[-1], [1] * n, 0.0001,
10000))
for i in range(0, len(selection)): # 4, 6, 8, 10
#print(matrix_mult(hilbert_matrix[i],convert_vec_mat(solution[i])))
print("Absolute error for " + str(selection[i]) + "x" +
str(selection[i]) + ": " + str(
abs_error_2norm([1] * selection[i],
convert_vec_mat(
matrix_mult(hilbert_matrix[i],
convert_vec_mat(
solution[i]))))))
print(solution[i])