def least_square_first_order(vec_x, vec_y):
mat_x_t = [vec_x,
[1] * len(vec_x)]
mat_x = matrix.transpose_mat(mat_x_t)
mat_y_measured = matrix.transpose_mat([vec_y])
mat_w_estimated = mul_left_inverse(mat_x, mat_y_measured)
return mat_w_estimated
def test_jacobi_method_03(self):
b_verbose = False
if b_verbose:
print("test_jacobi_method_03")
self.mat_lambda, self.mat_x = evp.jacobi_method(self.mat_h)
if b_verbose:
print("L =")
matrix.mat_xt = matrix.transpose_mat(self.mat_x)
print("X =")
matrix.show_mat(self.mat_x)
self.mat_xt = matrix.transpose_mat(self.mat_x)
self.mat_x_labda = matrix.mul_mat(self.mat_x, self.mat_labda)
self.mat_x_labda_xt = matrix.mul_mat(self.mat_x_labda, self.mat_xt)
if b_verbose:
print("X L XT")
matrix.show_mat(self.mat_x_lambda_xt)
n = len(self.mat_h)
for i in range(n):
for j in range(n):
st = "X L XT[%d][%d] = %g vs A[%d][%d] = %g" % (
i, j, self.mat_x_labda_xt[i][j], i, j, self.mat_h[i][j])
self.assertAlmostEqual(self.mat_x_lambda_xt[i][j],
self.mat_h[i][j],
msg=st)
def least_square_first_order(vec_x, vec_y):
"""
x와 y 사이에
y = ax+b
와 같은 관계과 있을 것으로 가정하고 a, b 를 찾으려고 함
:param vec_x: List[float]
:param vec_y: List[float]
:return:
"""
# 예를 들어 data point 의 갯수를 n 이라 할 때
mat_x_t = [vec_x, [1] * len(vec_x)] #Q : 이 행렬의 크기는?
mat_x = matrix.transpose_mat(mat_x_t) #Q : 이 행렬의 크기는?
mat_y_measured = matrix.transpose_mat([vec_y]) #Q : 이 행렬의 크기는?
mat_w_estimated = mul_left_inverse(mat_x, mat_y_measured) #Q : 이 행렬의 크기는?
return mat_w_estimated
def test_power_method_01(self):
b_verbose = False
if b_verbose:
print ("Power method 01")
for n in range(3, 10):
self.mat_a_half = matrix.get_random_mat(n, n)
self.mat_a_half_transpose = matrix.transpose_mat(self.mat_a_half)
self.mat_a = matrix.mul_mat(self.mat_a_half_transpose, self.mat_a_half)
lam, vec_x0 = evp.power_method(self.mat_a, espilon=1e-12)
if b_verbose:
print ('%s %s' % (lam, vec_x0))
vec_x1 = matrix.mul_mat_vec(self.mat_a, vec_x0)
vec_x0l = [lam * x0k for x0k in vec_x0]
self.assertEqual(len(vec_x0), n)
message = '''
x0 =
%s
mat_a x0 =
%s
''' % (vec_x0, vec_x0l)
self.assertSequenceAlmostEqual(vec_x0l, vec_x1, msg=me)
def test_jacobi_method_01(self):
b_verbose = 0
if b_verbose:
print("test_jacobi_method_01")
self.mat_lambda, self.mat_x = evp.jacobi_method(self.mat_h)
if b_verbose:
print("L =")
matrix.show_mat(self.mat_lambda)
print("X =")
matrix.show_mat(self.mat_x)
self.mat_x_transpose = matrix.transpose_mat(self.mat_x)
self.mat_xt_h = matrix.mul_mat(self.mat_x_transpose, self.mat_h)
self.mat_xt_h_x = matrix.mul_mat(self.mat_xt_h, self.mat_x)
if b_verbose:
print("XT A X")
matrix.show_mat(self.mat_xt_h_x)
n = len(self.mat_h)
for i in range(n):
for j in range(n):
st = "XT A X [%d][%d] = %g" % (i, j, self.mat_xt_h_x[i][j], i,
j, self.mat_lambda[i][j])
self.assertAlmostEqual(self.mat_xt_h_x[i][j],
self.mat_lambda[i][j],
msg=st)
def test_transpose(self):
self.mat_r = m.transpose_mat(self.mat_a)
self.mat_exp = [
[self.mat_a[0][0], self.mat_a[1][0]],
[self.mat_a[0][1], self.mat_a[1][1]],
]
self.assertSequenceEqual(self.mat_r, self.mat_exp)
def main():
mat_a = [[2.0, 1.0], [1.0, 3.0]]
lambda1, vec_x1 = power_method(mat_a)
print("lambda = %s" % lambda1)
print("x = %s" % vec_x1)
lambda2, mat_x = jacobi_method(mat_a)
print("lambda = %s" % lambda2)
print("x =")
matrix.show_mat(mat_x)
mat_a3 = [[8.0, 4.0, 2.0], [4.0, 8.0, 4.0], [2.0, 4.0, 8.0]]
mat_l, mat_x = jacobi_method(mat_a3, b_verbose=True)
print("L =")
matrix.show.mat(mat_l)
print("X =")
matrix.show_mat(mat_x)
mat_x_t = matrix.transpose_mat(mat_x)
print("XT =")
matrix.show_mat(mat_x_t)
print("X XT =")
matrix.show_mat(matrix.mul_mat(mat_x, mat_x_t))
print("XT A X = L")
matrix.show_mat(matrix.mul_mat(matrix.mul_mat(mat_x_t, mat_a3), mat_x))
print("A = X L XT")
matrix.show_mat(matrix.mul_mat(matrix.mul_mat(mat_x, mat_l), mat_x_t))
def get_left_inverse(mat_x):
"""
:param mat_x: List[List[float]]
:return: List[List[float]]
"""
# 예를 들어 data point 의 갯수를 n,
# 매개변수의 갯수를 m 이라 할 때
mat_x_t = matrix.transpose_mat(mat_x) #Q : 이 행렬의 크기는?
mat_xt_x = matrix.mul_mat(mat_x_t, mat_x) #Q : 이 행렬의 크기는?
mat_xt_x_inv = gj.gauss_jordan(mat_xt_x) #Q : 이 행렬의 크기는?
mat_x_left_inverse = matrix.mul_mat(mat_xt_x_inv, mat_x_t) #Q : 이 행렬의 크기는?
return mat_x_left_inverse
def get_left_inverse(mat_x):
'''
:param mat_x: List[List[float]]
:return: List[List[float]]
'''
# 예를 들어 deta point의 갯수를 n
# 매개변수의 갯수를 n이라 할때
mat_x_t = matrix.transpose_mat(mat_x)
mat_xt_x = matrix.mul_mat(mat_x_t, mat_x)
mat_xt_x_inv = gj.gauss_jordan(mat_xt_x)
mat_x_left_inverse = matrix.mul_mat(mat_xt_x_inv, mat_x_t)
return mat_x_left_inverse
def get_left_inverse(mat_x):
mat_x_t = matrix.transpose_mat(mat_x)
mat_xt_x = matrix.mul_mat(mat_x_t, mat_x)
mat_xt_x_inv = gj.gauss_jordan(mat_xt_x)
mat_x_left_inverse = matrix.mul_mat(mat_xt_x_inv, mat_x_t)
return mat_x_left_inverse