仅向矩阵的对角元素添加一个小值 [英] adding a small value to only the diagonal elements of a matrix

问题描述

我是matlab的新手，我正在尝试找出值非常小的矩阵逆.当我尝试找到逆时，我得到一个错误，说矩阵是奇异的.建议的解决方案之一是尝试向对角线元素添加一些元素.我知道我必须使用眼图和诊断方法，但是我无法提出正确的解决方案.

I am a newbie to matlab and I am trying to find out the inverse of matrix with very small values. When i try to find the inverse I get an error saying that the matrix is singular. One of the solutions suggested is to try and add some elements to the diagonal elements. I know i have to use eye and diag methods but I am not able come up the correct soltion.

任何评论都会有所帮助.

Any comments will be helpful.

推荐答案

如果您只想将身份矩阵或其倍数添加到 square 矩阵中，则可以进行

If you just want to add the identity matrix or a multiple of it to your square matrix, you can do

A_new = A_old + k*eye(size(A_old));

其中A_old是您的矩阵，k是一些乘数.如果您想为每个对角线元素添加不同的值，则可以执行类似的操作

where A_old is your matrix and k is some multiplier. If you want to add a different values to each diagonal element, you can do something like

A_new = A_old + diag(values);

其中values是一个向量，其元素数与矩阵A_old的列(或行)数一样.

where values is a vector with as many number of elements as the number of columns (or rows) of your matrix A_old.

如果您的矩阵很大，则将spdiags用作:

If your matrix is large, it will be more memory efficient to use spdiags as:

dim_A = size(A_old,1);
A_new = A_old + spdiags(values(:),0,dim_A,dim_A);

或像Amro的答案一样使用线性索引.

or use linear indexing like in Amro's answer.

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