学习在MATLAB中建立能带矩阵 [英] Learning to build band matrices in MATLAB

问题描述

我正在尝试使用

I am trying to build square band matrices using blkdiag or spdiags, but can't figure out how. I find the documentation for spdiags a bit confusing, and am not sure I can build these matrices in a simple call to blkdiag.

我想从两个参数构建一个方带矩阵:

I would like to build a square band matrix from two parameters:

• 乐队的宽度
• 矩阵大小

例如:

band_width = 2;
matrix size = 9;

结果:

[1 1 1 0 0 0 0 0 0]
[1 1 1 1 0 0 0 0 0]
[1 1 1 1 1 0 0 0 0]
[0 1 1 1 1 1 0 0 0]
[0 0 1 1 1 1 1 0 0]
[0 0 0 1 1 1 1 1 0]
[0 0 0 0 1 1 1 1 1]
[0 0 0 0 0 1 1 1 1]
[0 0 0 0 0 1 1 1 1]
[0 0 0 0 0 0 1 1 1]

推荐答案

一种复杂的单行创建卷积矩阵的方法是卷积:

A tricky one-line way to create a matrix like this is with convolution:

M = sign(conv2(eye(matrix_size),ones(band_width+1),'same'));

创建给定大小的身份矩阵，然后以2-D卷积和

An identity matrix is created of the given size, then convolved in 2-D with a square matrix of ones, then converted to zeroes and ones by taking the sign.

以上内容适合制作相对较小的非稀疏矩阵.对于较大的矩阵，卷积可能会变得昂贵，您可能希望将结果表示为而是使用稀疏矩阵.以下是使用 SPDIAGS 的常规方法:

The above is fine for making relatively small non-sparse matrices. For larger matrices the convolution may get expensive and you would probably want to represent the result as a sparse matrix instead. Here is how you can do this in a general way using SPDIAGS:

M = spdiags(ones(matrix_size,2*band_width+1),...
            -band_width:band_width,matrix_size,matrix_size);

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