在Matlab中与矩阵索引的向量相混淆 [英] Got confused with a vector indexed by a matrix, in Matlab

问题描述

以下代码在Matlab中运行:

The following codes runs in Matlab:

a = [1 2 3 4]
b = [ 1 2 3; 1 2 3; 1 2 3]
a(b)

a(b)的结果是一个矩阵:

The result of a(b) is a matrix:

[ 1 2 3; 1 2 3; 1 2 3]

有人可以解释这里发生了什么吗?为什么向量可以被矩阵索引，如何解释结果?

Can anyone explain what happened here? Why a vector can be indexed by a matrix, how to interpret the result?

推荐答案

这是您正在执行的非常标准的MATLAB操作.当您有一个向量或矩阵时，可以提供另一个向量或矩阵以访问特定的值.在MATLAB中访问值不仅限于单个索引(即A(1), A(2)等).

That's a very standard MATLAB operation that you're doing. When you have a vector or a matrix, you can provide another vector or matrix in order to access specific values. Accessing values in MATLAB is not just limited to single indices (i.e. A(1), A(2) and so on).

例如，您拥有的向量为a = [1 2 3 4].当您尝试使用b访问向量时，您实际上所做的是查找.输出的大小基本上与b相同，并且您正在执行的操作是创建一个包含3行的矩阵，并且每个元素都访问第一个，第二个和第三个元素.您不仅可以对向量执行此操作，而且还可以对矩阵执行此操作.

For example, what you have there is a vector of a = [1 2 3 4]. When you try to use b to access the vector, what you are essentially doing is a lookup. The output is basically the same size as b, and what you are doing is creating a matrix where there are 3 rows, and each element accesses the first, second and third element. Not only can you do this for a vector, but you can do this for a matrix as well.

请记住，对矩阵执行此操作时，您将以列主格式访问元素.例如，假设我们有这个矩阵:

Bear in mind that when you're doing this for a matrix, you access the elements in column major format. For example, supposing we had this matrix:

 A = [1 2
      3 4
      5 6
      7 8]

A(1)将为1，A(2)将为3，A(3)将为5，依此类推.您将从第一列开始，并且增加的索引将遍历第一列.达到第5个索引后，它会跳到下一列.因此A(5)为2，A(6)为4，依此类推.

A(1) would be 1, A(2) would be 3, A(3) would be 5 and so on. You would start with the first column, and increasing indices will traverse down the first column. Once you hit the 5th index, it skips over to the next column. So A(5) would be 2, A(6) would be 4 and so on.

这里有一些例子可以加深您的理解.让我们定义一个矩阵A:

Here are some examples to further your understanding. Let's define a matrix A such that:

 A = [5 1 3
      7 8 0
      4 6 2]

以下是一些MATLAB代码，可增强您对这种索引的理解:

Here is some MATLAB code to strengthen your understanding for this kind of indexing:

 A = [5 1 3; 7 8 0; 4 6 2]; % 3 x 3 matrix
 B = [1 2 3 4];
 C = A(B); % C should give [5 7 4 1]
 D = [5 6 7; 1 2 3; 4 5 6];
 E = A(D); % E should give [8 6 3; 5 7 4; 1 8 6]
 F = [9 8; 7 6; 1 2];
 G = A(F); % G should give [2 0; 3 6; 5 7]

这样，当您以这种方式访问​​元素时，输出就是您指定为参数的向量或矩阵的大小.

As such, the output when you access elements this way is whatever the size of the vector or matrix that you specify as the argument.

为了完整起见，让我们对向量进行此操作:

In order to be complete, let's do this for a vector:

 V = [-1 9 7 3 0 5]; % A 6 x 1 vector
 B = [1 2 3 4];
 C = V(B); % C should give [-1 9 7 3]
 D = [1 3 5 2];
 E = V(D); % E should give [-1 7 0 9]
 F = [1 2; 4 5; 6 3];
 G = V(F); % G should give [-1 9; 3 0; 5 7]

注意::您必须确保没有提供会超出访问范围的索引.例如，如果您尝试在示例中指定索引5，则会给您一个错误.此外，如果在我的示例中尝试大于9的任何操作，这也会给您带来错误.该3 x 3矩阵中有9个元素，因此，将列主索引指定为大于9的任何值都会给您带来超出范围的错误.

NB: You have to make sure that you are not providing indexes that would make the accessing out of bounds. For example if you tried to specify the index of 5 in your example, it would give you an error. Also, if you tried anything bigger than 9 in my example, it would also give you an error. There are 9 elements in that 3 x 3 matrix, so specifying a column major index of anything bigger than 9 will give you an out of bounds error.

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