Make a program that is able to solve a system of equations using the
Gauss-Seidel method.\
"""
redact_ex(EXERCISE_07, 7)
a = np.array([[1, 2, -1], [2, 4, 5], [3, -1, -2]], dtype=float)
b = np.array([[2], [25], [-5]], dtype=float)
a = a.reshape(len(a), len(a))
b = b.reshape(len(b), 1)
ab = np.concatenate((a, b), axis=1)
print("Matrix of coefficients A (given):", a, sep='\n\n', end='\n\n')
print("Vector of independent terms B (given):", b, sep='\n\n', end='\n\n')
print("Expanded matrix (AB):", ab, sep='\n\n', end='\n\n')
sols = gauss_seidel_solve(ab)
print("Obtained solutions:", sols, sep='\n\n', end='\n\n')
sols = deprox_arr(sols)
print("Fixed solutions:", sols, sep='\n\n', end='\n\n')
osols = check_sys_sols(sols, ab)
if osols is None:
print("Obtained solutions were incorrect.")
quit()
print("Ordered solutions:", osols, sep='\n\n', end='\n\n')
print("i.e.:",
*("x_{i} = {sol_i}".format(i=i + 1, sol_i=osols[i])
for i in range(len(osols))),
sep='\n')
from package import redact_ex
from package import \
jacobi_eigenfind, \
deprox_num, \
deprox_arr
EXERCISE_01 = """\
Make a program that is able to compute the eigenvalues and eigenvectors of a
simetrical matrix using the Jacobi method.\
"""
redact_ex(EXERCISE_01, 1)
import numpy as np
mat = np.array([[3, -1, 0], [-1, 2, -1], [0, -1, 3]], dtype=float)
mat = mat.reshape(len(mat), len(mat))
d, v = jacobi_eigenfind(mat)
print("Matrix (M):", mat, sep='\n', end='\n\n')
print("Obtained eigencouples (\u03BB, v):",
*[(deprox_num(d[i,i]), deprox_arr(v[:,i])) \
for i in range(d.shape[0])], sep = '\n')