Detailed description

As it is already reported previously, SVD of version 2.3 and later is slower than SVD of version 2.2.
#4313
#7563
#7917

Below, I will report the benchmark result.

OpenCV 2.2 use LAPACK, so its SVD was fast, but OpenCV 2.3 use own implementation, and so its SVD is slow. OpenCV's SVD is implemented in lapack.cpp's JacobiSVDImpl_. I looked at this code, but I could not understand. I just guess that the speed of this function becomes slow when there are zero singular values. In order to check my hypothesis, two benchmark tests are done below: One with the matrix filled with the value "one," and the other with the matrix filled with random numbers.

System information (version)

• OpenCV => 3.1 or 2.2
• Operating System / Platform => Windows 64 Bit
• Compiler => Visual Studio 2015

Steps to reproduce

const int ROW = 2000;
const int COL = 2000;
Mat mat = Mat::ones(ROW, COL, CV_64F);
int64 start = getTickCount();
cout << "start = " << start << endl;
SVD svd(mat);
int64 end = getTickCount();
cout << "end = " << end << endl;
int calctime = (int)((end - start) * 1000 / getTickFrequency());
cout << "duration = " << calctime << " [msec]" << endl << endl;
cout << "W = " << endl << svd.w.rowRange(Range(0, 9)) << endl;

For random matrix, following code is used for mat.

RNG gen(getTickCount());
Mat mat(ROW, COL, CV_64F);
gen.fill(mat, RNG::UNIFORM, 0.0, 1.0);

Benchmark result: random

Benchmark result: ones