如何使用加速框架执行矩阵逆运算？ [英] How to perform matrix inverse operation using the accelerate framework?

问题描述

我想找到矩阵的逆。

我知道这首先涉及LU分解，然后进行反演步骤，但我无法通过搜索apple的来找到所需的函数。 10.7的文档！

I know this involves first LU factorisation then the inversion step but I cannot find the required function by searching apple's docs of 10.7!

这似乎是一个有用的帖子使用CBLAS / LAPACK在C中进行对称矩阵求逆，指出 sgetrf _ 和 sgetri _ 应该使用函数。但是搜索这些术语在Xcode文档中什么也没找到。

This seems like a useful post Symmetric Matrix Inversion in C using CBLAS/LAPACK, pointing out that the sgetrf_ and sgetri_ functions should be used. However searching these terms I find nothing in Xcode docs.

有人对这种矩阵运算有样板代码吗？

Does anybody have boiler plate code for this matrix operation?

推荐答案

Apple根本没有记录LAPACK代码，因为它们只是实现了 netlib.org 。很遗憾您无法从内置的Xcode文档中搜索这些函数名称，但是解决方案非常简单：只需在URL中指定函数名称，例如对于 dgetrf _（），请转到 http://www.netlib.org/clapack/what/double/dgetrf.c 。

Apple does not document the LAPACK code at all, I guess because they just implement the standard interface from netlib.org. It's a shame that you cannot search the these function names from the built-in Xcode docs, however the solution is fairly straight forward: just specify the function name in the URL e.g. for dgetrf_() go to, http://www.netlib.org/clapack/what/double/dgetrf.c.

要反转矩阵，需要两个LAPACK函数： dgetrf _（）执行LU分解，而 dgetri _（）获取上一个函数的输出并执行实际反演。

To invert a matrix two LAPACK function are need: dgetrf_(), which performs LU factorisation, and dgetri_() which takes the output of the previous function and does the actual inversion.

我使用Xcode创建了一个标准应用程序项目，添加了Accelerate Framework，创建了两个C文件：matinv.h，matinv.c并编辑了main.m文件以将其删除可可的东西：

I created a standard Application Project using Xcode, added the Accelerate Framework, create two C files: matinv.h, matinv.c and edited the main.m file to remove Cocoa things:

// main.m

#import "matinv.h"

int main(int argc, char *argv[])
{
    int N = 3;
    double A[N*N];
    A[0] = 1; A[1] = 1; A[2] = 7;
    A[3] = 1; A[4] = 2; A[5] = 1;
    A[6] = 1; A[7] = 1; A[8] = 3;
    matrix_invert(N, A);
    //        [ -1.25  -1.0  3.25 ]
    // A^-1 = [  0.5       1.0  -1.5  ]
    //        [  0.25   0.0 -0.25 ] 
    return 0;
}

现在是头文件，

//  matinv.h

int matrix_invert(int N, double *matrix);

然后是源文件，

int matrix_invert(int N, double *matrix) {

    int error=0;
    int *pivot = malloc(N*sizeof(int)); // LAPACK requires MIN(M,N), here M==N, so N will do fine.
    double *workspace = malloc(N*sizeof(double));

    /*  LU factorisation */
    dgetrf_(&N, &N, matrix, &N, pivot, &error);

    if (error != 0) {
        NSLog(@"Error 1");
        free(pivot);
        free(workspace);
        return error;
    }

    /*  matrix inversion */
    dgetri_(&N, matrix, &N, pivot, workspace, &N, &error);

    if (error != 0) {
        NSLog(@"Error 2");
        free(pivot);
        free(workspace);
        return error;
    }

    free(pivot);
    free(workspace);
    return error;
}

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