Toeplitz矩阵的Toeplitz矩阵 [英] Toeplitz matrix of toeplitz matrix

问题描述

我想创建一个toeplitz矩阵的toeplitz矩阵. H1，H2和H3已经是Toeplitz矩阵.我的结果应如下所示: H1 0 0 H2 H1 0 H3 H2 H1 0 H3 H2 0 0 H3

I want to create a toeplitz matrix of toeplitz matrix. H1, H2 and H3 are toeplitz matrices already. My result should look like that: H1 0 0 H2 H1 0 H3 H2 H1 0 H3 H2 0 0 H3

现有的toeplitz函数仅接受向量，因此我不能将其用于矩阵.目前，我正在使用vstack创建第一列，然后创建第二列，等等，然后使用hstack合并所有列.这需要花费很多精力，因为我必须在某些位置专门添加np.zeros矩阵.我想不出一种更好的方法来连接numpy数组，因为该函数只有几个函数，而这些函数都不适合我的问题.

The existing toeplitz-function only accepts vector, so I can't use it for matrix. Currently I'm using vstack to create the first column, then second column etc. and then I use hstackto merge all columns. This takes a lot of effort, since I have to specifically add np.zeros matrices at certain places. I can't think of a better way to concatenate numpy arrays, since there are only a few functions for that and none of them really fits my problem.

推荐答案

代替对vstack和hstack的嵌套调用，预分配最终数组然后使用嵌套循环填充将更有效.数组.最初，您可以使用更高维的数组来保持代码的干净.

Instead of nested calls to vstack and hstack, it will be more efficient to preallocate the final array, and then use a nested loop to fill in the array. You can initially use a higher dimensional array to keep the code clean.

例如，该脚本

import numpy as np

H1 = np.array([[11, 11], [11, 11]])
H2 = np.array([[22, 22], [22, 22]])
H3 = np.array([[33, 33], [33, 33]])

inputs = (H1, H2, H3)

# This assumes all the arrays in `inputs` have the same shape,
# and that the data type of all the arrays is the same as H1.dtype.
nh = len(inputs)
nrows = 2*nh - 1
m, n = H1.shape
# T is a 4D array.  For a given i and j, T[i, :, j, :] is a 2D array
# with shape (m, n).  T can be intepreted as a 2D array of 2D arrays. 
T = np.zeros((nrows, m, nh, n), dtype=H1.dtype)
for i, H in enumerate(inputs):
    for j in range(nh):
        T[i + j, :, j, :] = H

# Partially flatten the 4D array to a 2D array that has the desired
# block structure.
T.shape = (nrows*m, nh*n)

print(T)

打印

[[11 11  0  0  0  0]
 [11 11  0  0  0  0]
 [22 22 11 11  0  0]
 [22 22 11 11  0  0]
 [33 33 22 22 11 11]
 [33 33 22 22 11 11]
 [ 0  0 33 33 22 22]
 [ 0  0 33 33 22 22]
 [ 0  0  0  0 33 33]
 [ 0  0  0  0 33 33]]

(请注意，结果不是Toeplitz矩阵；它是阻止Toeplitz矩阵.)

(Note that the result is not a Toeplitz matrix; it is a block Toeplitz matrix.)

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