在矩阵的逆最快方法 [英] Fastest method in inverse of matrix

问题描述

我要处理与反逻辑功能和功能很多照片。对于code，以快速度可以运行任何一个建议中的3反演方法快速的方法？

 双cvInvert（常量CvArr * SRC，CvArr * DST，诠释方法= CV_LU）
 

• CV_LU高斯消元法具有最佳的支点元素选择
• CV_SVD奇异值分解（SVD）方法
• CV_SVD_SYM SVD方法对称正定义的矩阵。

解决方案

在OpenCV2.x，有一个所谓的新界面垫:: INV（INT方法）来计算一矩阵的逆。请参见参考。

  

C ++：MatExpr垫:: INV（INT方法= DECOMP_LU）常量

     

参数：          方法 -

 矩阵求逆方法。可能的值如下：
        DECOMP_LU是LU分解。基质必须是非奇异的。
        DECOMP_CHOLESKY是乔里斯基LL ^​​ T分解仅供对称正定矩阵。这种类型的两倍左右，比卢在大型矩阵更快。
        DECOMP_SVD是SVD分解。如果矩阵是奇异的，甚至非正方形，伪反演计算。
 

我与各该方法的试验中，它表明DECOMP_CHOLESKY是最快的测试的情况下，和卢给出类似的结果。

 的#include＆LT; opencv2 /核心/ core.hpp＆GT;
＃包括＆LT; opencv2 /一下HighGUI / highgui.hpp＆GT;
＃包括＆LT; opencv2 / imgproc / imgproc.hpp＆GT;
＃包括＆LT;的iostream＆GT;

INT主要（无效）
{
    CV ::垫IMG1 = CV :: imread（2.png）;
    CV ::垫IMG2，IMG3，IMG;
    CV :: cvtColor（IMG1，IMG2，CV_BGR2GRAY）;
    img2.convertTo（IMG3，CV_32FC1）;
    CV ::调整（IMG3，IMG，CV ::尺寸（200,200））;

    双频率= CV :: getTickFrequency（）;

    双T1 = 0.0，T2 = 0.0;
    T1 =（双）CV ::的GetTickCount（）;
    CV ::垫M4 = img.inv（CV :: DECOMP_LU）;
    T2 =（CV ::的GetTickCount（） -  T1）/频率;
    性病::法院＆LT;＆LT; 卢：＆LT;＆LT; T2＆LT;＆LT;的std :: ENDL;

    T1 =（双）CV ::的GetTickCount（）;
    CV ::垫M5 = img.inv（CV :: DECOMP_SVD）;
    T2 =（CV ::的GetTickCount（） -  T1）/频率;
    性病::法院＆LT;＆LT; DECOMP_SVD：＆其中;＆其中; T2＆LT;＆LT;的std :: ENDL;

    T1 =（双）CV ::的GetTickCount（）;
    CV ::垫M6 = img.inv（CV :: DECOMP_CHOLESKY）;
    T2 =（CV ::的GetTickCount（） -  T1）/频率;
    性病::法院＆LT;＆LT; DECOMP_CHOLESKY：＆其中;＆其中; T2＆LT;＆LT;的std :: ENDL;

    CV :: waitKey（0）;
}
 

下面是运行resutls：

  

LU：0.000423759

     

DECOMP_SVD：0.0583525

     

DECOMP_CHOLESKY：9.3453e-05

I want to process Images with Inverse function and lot of functions. For code to run fastly can any one suggest fast method among the 3 inversion methods ?

double cvInvert(const CvArr* src, CvArr* dst, int method=CV_LU)

• CV_LU Gaussian elimination with optimal pivot element chosen
• CV_SVD Singular value decomposition (SVD) method
• CV_SVD_SYM SVD method for a symmetric positively-defined matrix.

解决方案

In OpenCV2.x, there's a new interface called Mat::inv(int method) to compute the inverse of a matrix. See reference.

C++: MatExpr Mat::inv(int method=DECOMP_LU) const

Parameters: method –

   Matrix inversion method. Possible values are the following:
        DECOMP_LU is the LU decomposition. The matrix must be non-singular.
        DECOMP_CHOLESKY is the Cholesky LL^T decomposition for symmetrical positively defined matrices only. This type is about twice faster than LU on big matrices.
        DECOMP_SVD is the SVD decomposition. If the matrix is singular or even non-square, the pseudo inversion is computed.

I made a test with each of the method, it shows that DECOMP_CHOLESKY is the fastest for the test case, and LU gives the similar result.

#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <iostream>

int main(void)
{
    cv::Mat img1 = cv::imread("2.png");
    cv::Mat img2, img3, img;
    cv::cvtColor(img1, img2, CV_BGR2GRAY);
    img2.convertTo(img3, CV_32FC1);
    cv::resize(img3, img, cv::Size(200,200));

    double freq = cv::getTickFrequency();

    double t1 = 0.0, t2 = 0.0;
    t1 = (double)cv::getTickCount();
    cv::Mat m4 = img.inv(cv::DECOMP_LU);
    t2 = (cv::getTickCount()-t1)/freq;
    std::cout << "LU:" << t2 << std::endl;

    t1 = (double)cv::getTickCount();
    cv::Mat m5 = img.inv(cv::DECOMP_SVD);
    t2 = (cv::getTickCount()-t1)/freq;
    std::cout << "DECOMP_SVD:" << t2 << std::endl;

    t1 = (double)cv::getTickCount();
    cv::Mat m6 = img.inv(cv::DECOMP_CHOLESKY);
    t2 = (cv::getTickCount()-t1)/freq;
    std::cout << "DECOMP_CHOLESKY:" << t2 << std::endl;

    cv::waitKey(0);
}

Here is the running resutls:

LU:0.000423759

DECOMP_SVD:0.0583525

DECOMP_CHOLESKY:9.3453e-05

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