Matlab中的扩展块对角矩阵 [英] Extended block diagonal matrix in Matlab

问题描述

我知道要在Matlab中生成块对角矩阵，命令blkdiag会生成这样的矩阵:

I know that to generate a block-diagonal matrix in Matlab the command blkdiag generates such a matrix:

现在，我面临着生成相同的块对角矩阵的问题，但是在上对角线上还有矩阵元素B_1，B_2，...，B_{n-1}，其他地方为零:

Now I am faced with generating the same block-diagonal matrix, but with also matrix elements B_1, B_2,..., B_{n-1} on the upper diagonal, zeros elsewhere:

• 我想这可以用循环进行硬编码，但是我想找到一个更优雅的解决方案.有关如何实施此类操作的任何想法?

P.S.我 diag 命令，该命令使用返回第k个对角线.我需要一些东西来写矩阵，> 0和块矩阵，不仅是元素.

P.S. I diag command, that using diag(A,k) returns the kth diagonal. I need something for writing in the matrix, for k>0, and for block matrices, not only elements.

推荐答案

文件交换上有一个提交可以做到这一点: (阻止)tri-diagonal矩阵.

There is a submission on the File Exchange that can do this: (Block) tri-diagonal matrices.

您为函数提供了三个3D阵列，该3D阵列的每一层代表一个主，次对角或超对角线的块. (这意味着这些块必须具有相同的大小.)结果将是一个稀疏矩阵，因此在内存方面应该相当有效.

You provide the function with three 3D-arrays, each layer of the 3D array represents a block of the main, sub- or superdiagonal. (Which means that the blocks will have to be of the same size.) The result will be a sparse matrix, so it should be rather efficient in terms of memory.

用法示例为:

As = bsxfun(@times,ones(3),permute(1:3,[3,1,2]));
Bs = bsxfun(@times,ones(3),permute(10:11,[3,1,2]));
M = blktridiag(As, zeros(size(Bs)), Bs);

其中full(M)为您提供:

 1     1     1    10    10    10     0     0     0
 1     1     1    10    10    10     0     0     0
 1     1     1    10    10    10     0     0     0
 0     0     0     2     2     2    11    11    11
 0     0     0     2     2     2    11    11    11
 0     0     0     2     2     2    11    11    11
 0     0     0     0     0     0     3     3     3
 0     0     0     0     0     0     3     3     3
 0     0     0     0     0     0     3     3     3

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