问题描述
我有一个矩阵 B ，我想通过获得尺寸为.(L + k)* m 的矩阵 C L * n L 和 k 是输入值. B0，B1，...，Bk 的大小为 m ，大小为 n .
I have a matrix B and I want to obtain a matrix C of dimension (L+k)*m by L*n. L and k are input values. B0 , B1 , ... , Bk has size m by n.
例如:
如果我有一个矩阵 B = [1 1;1 1;1 1] ，其中 B0 = [1 1] ， B1 = [1 1] 和 B2 = [1 1] ，以及每个尺寸为 1 乘以 2 的 B0，B1，B2 ，其中 k = 2 和 L =4 .
If I have a matrix B = [1 1 ; 1 1 ; 1 1] with B0 = [1 1], B1 = [1 1] and B2 = [1 1], and each B0 , B1 , B2 of dimension 1 by 2 with k = 2 and L = 4.
则获得的矩阵 C 由 C = [1 1 0 0 0 0 0 0;1 1 1 1 0 0 0 0;1 1 1 1 1 1 0 0 00 0 1 1 1 1 1 1;0 0 0 0 1 1 1 1;0 0 0 0 0 0 1 1] 和尺寸 6 通过 8 .
Then the matrix C obtained is given by C = [1 1 0 0 0 0 0 0 ; 1 1 1 1 0 0 0 0 ; 1 1 1 1 1 1 0 0 ; 0 0 1 1 1 1 1 1 ; 0 0 0 0 1 1 1 1 ; 0 0 0 0 0 0 1 1] and of dimension6 by 8.
我想针对任何大小的矩阵 B 概括我的程序.
I would like to generalize my program for any size matrix B.
我的程序解决了 B = [1 1;1 1;1 1] ，其中 m = 1 ， n = 2 ， k = 2 和 L = 4 .
My program solves the problem for B = [1 1 ; 1 1 ; 1 1] with m = 1 , n = 2 , k = 2 and L = 4.
我的代码:
clc;
clear;
k = 2;
L = 4;
B = [1 1 ; 1 1 ; 1 1];
B0 = [1 1];
B1 = [1 1];
B2 = [1 1];
m = size(B0,1);
n = size(B0,2);
c = [B ; zeros(size(B))];
C = zeros((L+k)*m,L*n);
for i = 1:L
C(:,2*i-1:2*i) = circshift(c,i-1,1);
end
结果: C =
1 1 0 0 0 0 0 0
1 1 1 1 0 0 0 0
1 1 1 1 1 1 0 0
0 0 1 1 1 1 1 1
0 0 0 0 1 1 1 1
0 0 0 0 0 0 1 1
对于任何给定的矩阵 B 和 k 和 L 的任何值，我都难以归纳.
I have difficulties to generalize for any given matrix B and for any value of k and L.
有什么建议吗?
推荐答案
B = [1 2 3; 4 5 6; 7 8 9; 100 110 120; 130 140 150; 160 170 180]; % input
L = 4; % input
k = 2; % input
m = size(B,1)/(k+1); % obtain m
n = size(B,2); % obtain n
C = zeros((L-1)*m+1, (L-1)*n+1); % initiallize result
C(1:((L-1)*m+1)*n+m:end) = 1; % each 1 marks the upper-left corner for a copy of B
C = conv2(C, B); % insert copies of B, extending size
倒数第二行使用 linear索引.最后一行适用二维卷积.在此示例中的结果是
The second-to-last line uses linear indexing. The last line applies two-dimensional convolution. The result in this example is
B =
1 2 3
4 5 6
7 8 9
100 110 120
130 140 150
160 170 180
C =
1 2 3 0 0 0 0 0 0 0 0 0
4 5 6 0 0 0 0 0 0 0 0 0
7 8 9 1 2 3 0 0 0 0 0 0
100 110 120 4 5 6 0 0 0 0 0 0
130 140 150 7 8 9 1 2 3 0 0 0
160 170 180 100 110 120 4 5 6 0 0 0
0 0 0 130 140 150 7 8 9 1 2 3
0 0 0 160 170 180 100 110 120 4 5 6
0 0 0 0 0 0 130 140 150 7 8 9
0 0 0 0 0 0 160 170 180 100 110 120
0 0 0 0 0 0 0 0 0 130 140 150
0 0 0 0 0 0 0 0 0 160 170 180
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