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 matrix_solve_gauss_seidel_test():
matrix1 = gen_rand_matrix(100)
matrix2 = gen_sym_matrix(100)
matrix3 = gen_diagdom_matrix(100)
matrix4 = gen_diagdom_sym_matrix(100)
matrices = [matrix1, matrix2, matrix3, matrix4]
vector = [1] * len(matrix1)
for i in range(len(matrices)):
b = matrix_mult(matrices[i], convert_vec_mat(vector))
starttime = time.time()
solution = matrix_solve_gauss_seidel(matrices[i],
convert_vec_mat(b),
0.00001,
1000,
getIterCount=True)
print("Time: " + str(time.time() - starttime))
print("# of iterations: " + str(solution[1]))
print(solution[0])