python 矩阵 将所有列向量合并成一个向量 将虚数矩阵转化为实数矩阵

有M✖️N 维度的矩阵，将它转化为MN✖️1的矩阵

import numpy as np
from numpy import squeeze

M, N = 4, 3
h_mat = np.random.randn(M, N)
h_new = squeeze(h_mat.T.reshape(-1, 1))
print(h_new, h_mat, h_new.shape, h_mat.shape)

[-1.06950402  0.57459646  0.41926508  3.20023608 -0.8934199  -1.48817502
 -1.46684445  1.04572083 -0.2769263   0.83589263  0.34593235  0.34324631] 
 [[-1.06950402 -0.8934199  -0.2769263 ]
 [ 0.57459646 -1.48817502  0.83589263]
 [ 0.41926508 -1.46684445  0.34593235]
 [ 3.20023608  1.04572083  0.34324631]] 
 (12,) (4, 3)

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将虚数矩阵转化为实数矩阵

这里m为N*1维矩阵

from numpy import real, imag
import numpy as np


mat = np.array([1, 2, 3, -1, -2, -3]) + 1j * np.array([1, 1, 1, 2, 2, 2])
real_mat = squeeze(real(mat).reshape(-1, 1))
img_mat = squeeze(imag(mat).reshape(-1, 1))
all_mat = np.hstack((real_mat, img_mat))
print(mat, "\n", all_mat, "\n", all_mat.shape)

vec_size = int(len(all_mat)/2)
real_part = all_mat[:vec_size,]
img_part = all_mat[vec_size:,]
recon_mat = real_part + 1j * img_part
np.array_equal(mat, recon_mat)

输出：

[ 1.+1.j  2.+1.j  3.+1.j -1.+2.j -2.+2.j -3.+2.j] 
 [ 1.  2.  3. -1. -2. -3.  1.  1.  1.  2.  2.  2.] 
 (12,)
True

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两个类似的，一个负号的区别

import numpy as np
from numpy import real,imag
mat = np.array([1, 2, 3, -1, -2, -3]) + 1j * np.array([1, 1, 1, 2, 2, 2]).reshape(-1,1)
mat = mat * mat.T
real_mat = real(mat)
img_mat = imag(mat)
up = np.hstack((real_mat, -img_mat))
down = np.hstack((img_mat, real_mat))
all_mat = np.vstack((up, down))
print(all_mat)
#%%
mat_size = int(all_mat.shape[0]/2)
real_part = all_mat[:mat_size,:mat_size]
img_part = all_mat[mat_size:,:mat_size]
final_mat = real_part + 1j * img_part
np.array_equal(final_mat, mat)