def matrix_solve_LU(matrix, vector):
temp_list = matrix_LU_factor(matrix)
matrix_l = temp_list[0]
matrix_u = temp_list[1]
solution_y = matrix_solve_lower_tri(matrix_l, vector)
solution_x = matrix_solve_upper_tri(matrix_u, solution_y)
return solution_x
def matrix_solve_least_square_normal(matrix,vector):
vector = [[vector[i]] for i in range(len(vector))]
matrix_A_At = matrix_mult(matrix_transpose(matrix),matrix)
vector_At_b = matrix_mult(matrix_transpose(matrix),vector)
matrix_G = matrix_cholesky_fac(matrix_A_At)
vector_y = matrix_solve_lower_tri(matrix_G,matrix_transpose(vector_At_b)[0])
vector_x = matrix_solve_upper_tri(matrix_transpose(matrix_G),vector_y)
return vector_x
def matrix_solve_least_squares_QR(matrix,vector):
(matrix_Q, matrix_R) = matrix_QR_factorization_mod(matrix)
print(matrix_Q)
print(matrix_R)
matrix_Qtb = matrix_mult(matrix_transpose(matrix_Q), convert_vec_mat(vector))
print(matrix_Qtb)
solution = matrix_solve_upper_tri(matrix_R, convert_vec_mat(matrix_Qtb))
print(solution)
return solution
def matrix_solve_LU_scaled_partial_pivoting(matrix, vector):
n = len(matrix)
LU = matrix_LU_factor_scaled_partial_pivoting(matrix)
U = [[(LU[i][j] if (i <= j) else 0.0) for j in range(n)] for i in range(n)]
L = [[(LU[i][j] if (i > j) else (1.0 if (i == j) else 0.0))
for j in range(n)] for i in range(n)]
solution_y = matrix_solve_lower_tri(L, vector)
solution_x = matrix_solve_upper_tri(U, solution_y)
return solution_x
def matrix_solve(matrix, vector):
n = len(matrix)
solution = [0] * len(vector)
for i in range(n):
matrix[i].append(vector[i])
ref_matrix = matrix_ref(matrix)
for i in range(n):
solution[i] = ref_matrix[i][-1]
del ref_matrix[i][-1]
solution = matrix_solve_upper_tri(ref_matrix, solution)
return solution
def matrix_solve_least_squares_QR_householder(matrix, vector):
(matrix_Q, matrix_R) = matrix_QR_factorization_householder(matrix)
matrix_Qtb = matrix_mult(matrix_transpose(matrix_Q),
convert_vec_mat(vector))
solution = matrix_solve_upper_tri(matrix_R, convert_vec_mat(matrix_Qtb))
return solution
def matrix_solve_QR_factorization(matrix, vector):
(matrix_Q, matrix_R) = matrix_QR_factorization(matrix)
matrix_Qtb = matrix_mult(matrix_transpose(matrix_Q),
convert_vec_mat(vector))
solution = matrix_solve_upper_tri(matrix_R, convert_vec_mat(matrix_Qtb))
return solution