如何在对角线上为 MATLAB 矩阵赋值?

问题描述

假设我有一个 NxN 矩阵 A、一个由数字 1:N 的子集组成的索引向量 V 和一个值 K，我想这样做:

Suppose I have an NxN matrix A, an index vector V consisting of a subset of the numbers 1:N, and a value K, and I want to do this:

 for i = V
     A(i,i) = K
 end

有没有办法在一个带有矢量化的语句中做到这一点?

Is there a way to do this in one statement w/ vectorization?

例如A(某事) = K

语句 A(V,V) = K 不起作用，它分配了非对角元素，这不是我想要的.例如:

The statement A(V,V) = K will not work, it assigns off-diagonal elements, and this is not what I want. e.g.:

>> A = zeros(5);
>> V = [1 3 4];
>> A(V,V) = 1

A =

 1     0     1     1     0
 0     0     0     0     0
 1     0     1     1     0
 1     0     1     1     0
 0     0     0     0     0

推荐答案

我通常使用 眼睛:

A = magic(4)
A(logical(eye(size(A)))) = 99

A =
    99     2     3    13
     5    99    10     8
     9     7    99    12
     4    14    15    99

或者，您可以只创建线性索引列表，因为从一个对角线元素到下一个，需要 nRows+1 个步骤:

Alternatively, you can just create the list of linear indices, since from one diagonal element to the next, it takes nRows+1 steps:

[nRows,nCols] = size(A);
A(1:(nRows+1):nRows*nCols) = 101
A =
   101     2     3    13
     5   101    10     8
     9     7   101    12
     4    14    15   101

如果只想访问对角线元素的子集，则需要创建对角线索引列表:

If you only want to access a subset of diagonal elements, you need to create a list of diagonal indices:

subsetIdx = [1 3];
diagonalIdx = (subsetIdx-1) * (nRows + 1) + 1;
A(diagonalIdx) = 203
A =
   203     2     3    13
     5   101    10     8
     9     7   203    12
     4    14    15   101

或者，您可以使用 diag 创建逻辑索引数组(仅适用于方形数组)

Alternatively, you can create a logical index array using diag (works only for square arrays)

diagonalIdx = false(nRows,1);
diagonalIdx(subsetIdx) = true;
A(diag(diagonalIdx)) = -1
A =
    -1     2     3    13
     5   101    10     8
     9     7    -1    12
     4    14    15   101

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