3 个矩阵相乘求和 [英] multiplication of 3 matrices in a sum

问题描述

我想计算:

result = SUM (c=0,N) { V_ck * U_lc * S_c }

但是我的 2D 矩阵被索引为 1D 并存储为列主.

But my 2D matrices are indexed as 1D and stored as column major.

我正在尝试:

float *A,*B;

int M,N;


A = (float *) malloc( M * N * sizeof(float) );
B = (float *) malloc( M * sizeof(float) );


float *S = (float *)malloc( N * sizeof( float) ); 
float *U = (float *)malloc( M * M * sizeof( float) ); 
float *V = (float *)malloc( N * N  * sizeof( float) ); 

float * result = (float *) malloc( M * N * sizeof(float) );

float thesum=0;

for (int k=0; k < M ; k++) {

      for (int l=0 ; l < N; l++) {

        for ( int c=0; c < N; c++) {

        thesum += V[ k+c*N ] * S[c] * U[l*M + k];
        result[ k+l*M ]=thesum;

                }
        }

        }

我有一个大错误，我认为在上面，因为我需要另一个循环?为了首先正确地进行乘法，然后使用:

I have one big mistake ,I think in the above,because I need another loop ? in order to do properly the multiplication first and then use the:

for ( int c=0; c

求和的循环，对吧?

然后，我是否必须创建一个数组来保存乘法值，然后使用这个数组来保存求和值?

And then, do I have to create an array which will hold the multiplication values and then use this array to hold the summation values?

如果我使用 2D 表示法，我会简单地使用 U[l][k] 等等.

If I were using 2D notation , I would simple use U[l][k] and so on.

但现在，我对如何应用适当的索引感到困惑.

But now,I am confused about how to apply the appropriate indices.

我希望有人解释我应该如何处理这个问题.

And I want someone to explain me how should I proceed with this.

推荐答案

如果我使用 2D 表示法，我会简单地使用 U[l][k] 等等.

If I were using 2D notation , I would simple use U[l][k] and so on.

因此，添加该抽象层 - 不要让其他一切变得复杂.你有:

So, add that layer of abstraction - don't let everything else get complicated. You have:

A = (float *) malloc( M * N * sizeof(float) );

至少，您可以使用:

float& at(float* p, int rows, int col, int row) { return p[rows * col + row]; }

(根据口味重新排列参数)

(reorder arguments to taste)

然后你可以说:

at(A, M, col, row)

(或类似的 - 我不会发誓我把所有的行/列名称都弄对了 - 但恕我直言，你应该使用 Rows 和 Columns 而不是 M 和 N，所以我不会为此大吃一惊.)

(Or similar - I wouldn't swear I got all the rows/column names right - but IMHO you should have used Rows and Columns instead of M and N so I'm not going to bust a gut over it.)

如果你想更高级一点，在 C++ 中，你可以将分配包装在一个存储指针和 #rows/columns 的类中，然后重载 float&operator()(int col, int row) 和 const float&operator()(int col, int row) const (或者只是 float operator()(int col, int row) const 如果您不关心获取地址的能力数组条目).

If you want to get a little fancier, in C++ you can wrap the allocations in a class that stores the pointer and #rows/columns, then overloads float& operator()(int col, int row) and const float& operator()(int col, int row) const (or just float operator()(int col, int row) const if you don't care about ability to take the address of the array entry).

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