def jacobi_method(mat_a, epsilon=1e-9, b_verbose=False):
n = len(mat_a)
mat_a0 = matrix.alloc_mat(n, n)
for i in range(n):
for j in range(n):
mat_a0[i][j] = mat_a[i][j]
mat_x = matrix.get_identity_matrix(n)
#############################
while True:
abs_ars, ars, r, s = find_r_s(mat_a0, n)
if abs_ars < epsilon:
break
if b_verbose:
print("ars = %s" % ars)
print("r, s = (%g, %g)" % (r, s))
arr = mat_a0[r][r]
ass = mat_a0[s][s]
theta_rad = calc_theta(ars, arr, ass)
if b_verbose:
print("theta = %s (deg)" % (theta_rad * 180 / math.pi))
cos = math.cos(theta_rad)
sin = math.sin(theta_rad)
for k in range(n):
if k == r:
pass
elif k == s:
pass
else:
akr = mat_a0[k][r]
aks = mat_a0[k][s]
mat_a0[r][k] = akr * cos + aks * sin
mat_a0[s][k] = aks * cos - akr * sin
mat_a0[k][r] = mat_a0[r][k]
mat_a0[k][s] = mat_a0[s][k]
xkr = mat_x[k][r]
xks = mat_x[k][s]
mat_x[k][r] = xkr * cos + xks * sin
mat_x[k][s] = xks * cos - xkr * sin
mat_a0[r][
r] = arr * cos * cos + 2.0 * ars * sin * cos + ass * sin * sin
mat_a0[s][
s] = arr * sin * sin - 2.0 * ars * sin * cos + ass * cos * cos
mat_a0[r][s] = mat_a0[s][r] = 0.0
if b_verbose:
print("mat_a0")
matrix.show_mat(mat_a0)
print("mat_x")
matrix.show_mat(mat_x)
return mat_a0, mat_x
def gauss_elimination(mat_a, b):
"""
1차 다원 연립 방정식 Ax = b에서 x를 구함
A : 계수행렬
b : 상수벡터
:param mat_a:
:param b:
:return:
"""
m_row, n_col = matrix.shape(mat_a)
mat_a_vec_b = matrix.alloc_mat(m_row, n_col + 1)
for i in range(m_row):
for j in range(n_col):
mat_a_vec_b[i][j] = mat_a[i][j]
mat_a_vec_b[i][-1] = b[i]
upper_triangle(mat_a_vec_b)
x = back_substitution(mat_a_vec_b)
del mat_a_vec_b[:]
del mat_a_vec_b
return x
def generate_mat_ai(mat_a):
m_row, n_col = matrix.shape(mat_a)
mat_ai = matrix.alloc_mat(m_row, n_col + m_row)
for i_pivot in range(m_row):
for j_col in range(n_col):
mat_ai[i_pivot][j_col] = mat_a[i_pivot][j_col]
mat_ai[i_pivot][n_col + i_pivot] = 1.0
return mat_ai
def initialize_jacobi_method(mat_a):
remove_all_figure_files()
n = len(mat_a)
mat_a0 = matrix.alloc_mat(n, n)
for i in range(n):
for j in range(n):
mat_a0[i][j] = mat_a[i][j]
mat_x = matrix.get_identity_matrix(n)
counter = 0
return mat_a0, mat_x, n, counter
def initialize_jacobi_method(mat_a:Matrix, b_plot:bool=False) -> Tuple[Matrix, Matrix, int, int]:
if b_plot:
matshow.remove_all_figure_files()
n = len(mat_a)
mat_a0 = matrix.alloc_mat(n, n)
for i in range(n):
for j in range(n):
mat_a0[i][j] = mat_a[i][j]
mat_x = matrix.get_identity_matrix(n)
counter = 0
return mat_a0, mat_x, n, counter
def gauss_elimination(mat_a, b):
m_row, n_col = matrix.shape(mat_a)
mat_a_vec_b = matrix.alloc_mat(m_row, n_col + 1)
for i in range(m_row):
for j in range(n_col):
mat_a_vec_b[i][j] = mat_a[i][j]
mat_a_vec_b[i][-1] = b[i]
upper_triangle(mat_a_vec_b)
x = back_substitution(mat_a_vec_b)
del mat_a_vec_b[:]
del mat_a_vec_b
return x
def gauss_jordan(mat_a):
mat_ai = generate_mat_ai(mat_a)
for i_pivot in range(len(mat_ai)):
matrix.row_mul_scalar(mat_ai, i_pivot, 1.0 / mat_ai[i_pivot][i_pivot])
for j_row in range(len(mat_ai)):
if i_pivot != j_row:
matrix.row_mul_add(mat_ai, j_row, i_pivot,
-mat_ai[j_row][i_pivot])
inv_mat = matrix.alloc_mat(
len(mat_ai),
len(mat_ai),
)
for i in range(len(mat_ai)):
for j in range(len(mat_ai)):
inv_mat[i][j] = mat_ai[i][len(mat_ai) + j]
del mat_ai[:]
del mat_ai
return inv_mat