mirror of
https://github.com/opencv/opencv.git
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1762 lines
54 KiB
C++
1762 lines
54 KiB
C++
/*M///////////////////////////////////////////////////////////////////////////////////////
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//
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// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
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//
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// By downloading, copying, installing or using the software you agree to this license.
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// If you do not agree to this license, do not download, install,
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// copy or use the software.
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//
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//
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// License Agreement
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// For Open Source Computer Vision Library
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//
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// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
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// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
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// Third party copyrights are property of their respective owners.
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//
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// Redistribution and use in source and binary forms, with or without modification,
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// are permitted provided that the following conditions are met:
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//
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// * Redistribution's of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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//
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// * Redistribution's in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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//
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// * The name of the copyright holders may not be used to endorse or promote products
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// derived from this software without specific prior written permission.
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//
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// This software is provided by the copyright holders and contributors "as is" and
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// any express or implied warranties, including, but not limited to, the implied
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// warranties of merchantability and fitness for a particular purpose are disclaimed.
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// In no event shall the Intel Corporation or contributors be liable for any direct,
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// indirect, incidental, special, exemplary, or consequential damages
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// (including, but not limited to, procurement of substitute goods or services;
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// loss of use, data, or profits; or business interruption) however caused
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// and on any theory of liability, whether in contract, strict liability,
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// or tort (including negligence or otherwise) arising in any way out of
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// the use of this software, even if advised of the possibility of such damage.
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//
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//M*/
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#include "precomp.hpp"
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#include <limits>
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#if defined _M_IX86 && defined _MSC_VER && _MSC_VER < 1700
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#pragma float_control(precise, on)
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#endif
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namespace cv
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{
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int LU(float* A, size_t astep, int m, float* b, size_t bstep, int n)
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{
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CV_INSTRUMENT_REGION()
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return hal::LU32f(A, astep, m, b, bstep, n);
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}
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int LU(double* A, size_t astep, int m, double* b, size_t bstep, int n)
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{
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CV_INSTRUMENT_REGION()
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return hal::LU64f(A, astep, m, b, bstep, n);
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}
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bool Cholesky(float* A, size_t astep, int m, float* b, size_t bstep, int n)
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{
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CV_INSTRUMENT_REGION()
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return hal::Cholesky32f(A, astep, m, b, bstep, n);
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}
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bool Cholesky(double* A, size_t astep, int m, double* b, size_t bstep, int n)
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{
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CV_INSTRUMENT_REGION()
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return hal::Cholesky64f(A, astep, m, b, bstep, n);
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}
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template<typename _Tp> static inline _Tp hypot(_Tp a, _Tp b)
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{
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a = std::abs(a);
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b = std::abs(b);
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if( a > b )
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{
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b /= a;
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return a*std::sqrt(1 + b*b);
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}
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if( b > 0 )
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{
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a /= b;
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return b*std::sqrt(1 + a*a);
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}
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return 0;
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}
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template<typename _Tp> bool
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JacobiImpl_( _Tp* A, size_t astep, _Tp* W, _Tp* V, size_t vstep, int n, uchar* buf )
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{
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const _Tp eps = std::numeric_limits<_Tp>::epsilon();
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int i, j, k, m;
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astep /= sizeof(A[0]);
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if( V )
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{
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vstep /= sizeof(V[0]);
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for( i = 0; i < n; i++ )
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{
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for( j = 0; j < n; j++ )
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V[i*vstep + j] = (_Tp)0;
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V[i*vstep + i] = (_Tp)1;
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}
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}
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int iters, maxIters = n*n*30;
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int* indR = (int*)alignPtr(buf, sizeof(int));
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int* indC = indR + n;
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_Tp mv = (_Tp)0;
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for( k = 0; k < n; k++ )
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{
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W[k] = A[(astep + 1)*k];
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if( k < n - 1 )
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{
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for( m = k+1, mv = std::abs(A[astep*k + m]), i = k+2; i < n; i++ )
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{
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_Tp val = std::abs(A[astep*k+i]);
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if( mv < val )
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mv = val, m = i;
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}
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indR[k] = m;
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}
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if( k > 0 )
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{
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for( m = 0, mv = std::abs(A[k]), i = 1; i < k; i++ )
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{
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_Tp val = std::abs(A[astep*i+k]);
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if( mv < val )
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mv = val, m = i;
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}
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indC[k] = m;
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}
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}
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if( n > 1 ) for( iters = 0; iters < maxIters; iters++ )
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{
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// find index (k,l) of pivot p
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for( k = 0, mv = std::abs(A[indR[0]]), i = 1; i < n-1; i++ )
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{
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_Tp val = std::abs(A[astep*i + indR[i]]);
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if( mv < val )
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mv = val, k = i;
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}
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int l = indR[k];
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for( i = 1; i < n; i++ )
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{
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_Tp val = std::abs(A[astep*indC[i] + i]);
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if( mv < val )
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mv = val, k = indC[i], l = i;
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}
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_Tp p = A[astep*k + l];
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if( std::abs(p) <= eps )
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break;
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_Tp y = (_Tp)((W[l] - W[k])*0.5);
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_Tp t = std::abs(y) + hypot(p, y);
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_Tp s = hypot(p, t);
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_Tp c = t/s;
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s = p/s; t = (p/t)*p;
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if( y < 0 )
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s = -s, t = -t;
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A[astep*k + l] = 0;
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W[k] -= t;
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W[l] += t;
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_Tp a0, b0;
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#undef rotate
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#define rotate(v0, v1) a0 = v0, b0 = v1, v0 = a0*c - b0*s, v1 = a0*s + b0*c
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// rotate rows and columns k and l
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for( i = 0; i < k; i++ )
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rotate(A[astep*i+k], A[astep*i+l]);
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for( i = k+1; i < l; i++ )
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rotate(A[astep*k+i], A[astep*i+l]);
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for( i = l+1; i < n; i++ )
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rotate(A[astep*k+i], A[astep*l+i]);
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// rotate eigenvectors
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if( V )
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for( i = 0; i < n; i++ )
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rotate(V[vstep*k+i], V[vstep*l+i]);
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#undef rotate
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for( j = 0; j < 2; j++ )
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{
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int idx = j == 0 ? k : l;
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if( idx < n - 1 )
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{
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for( m = idx+1, mv = std::abs(A[astep*idx + m]), i = idx+2; i < n; i++ )
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{
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_Tp val = std::abs(A[astep*idx+i]);
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if( mv < val )
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mv = val, m = i;
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}
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indR[idx] = m;
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}
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if( idx > 0 )
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{
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for( m = 0, mv = std::abs(A[idx]), i = 1; i < idx; i++ )
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{
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_Tp val = std::abs(A[astep*i+idx]);
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if( mv < val )
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mv = val, m = i;
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}
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indC[idx] = m;
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}
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}
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}
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// sort eigenvalues & eigenvectors
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for( k = 0; k < n-1; k++ )
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{
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m = k;
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for( i = k+1; i < n; i++ )
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{
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if( W[m] < W[i] )
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m = i;
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}
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if( k != m )
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{
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std::swap(W[m], W[k]);
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if( V )
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for( i = 0; i < n; i++ )
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std::swap(V[vstep*m + i], V[vstep*k + i]);
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}
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}
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return true;
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}
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static bool Jacobi( float* S, size_t sstep, float* e, float* E, size_t estep, int n, uchar* buf )
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{
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return JacobiImpl_(S, sstep, e, E, estep, n, buf);
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}
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static bool Jacobi( double* S, size_t sstep, double* e, double* E, size_t estep, int n, uchar* buf )
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{
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return JacobiImpl_(S, sstep, e, E, estep, n, buf);
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}
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template<typename T> struct VBLAS
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{
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int dot(const T*, const T*, int, T*) const { return 0; }
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int givens(T*, T*, int, T, T) const { return 0; }
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int givensx(T*, T*, int, T, T, T*, T*) const { return 0; }
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};
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#if CV_SSE2
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template<> inline int VBLAS<float>::dot(const float* a, const float* b, int n, float* result) const
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{
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if( n < 8 )
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return 0;
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int k = 0;
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__m128 s0 = _mm_setzero_ps(), s1 = _mm_setzero_ps();
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for( ; k <= n - 8; k += 8 )
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{
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__m128 a0 = _mm_load_ps(a + k), a1 = _mm_load_ps(a + k + 4);
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__m128 b0 = _mm_load_ps(b + k), b1 = _mm_load_ps(b + k + 4);
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s0 = _mm_add_ps(s0, _mm_mul_ps(a0, b0));
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s1 = _mm_add_ps(s1, _mm_mul_ps(a1, b1));
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}
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s0 = _mm_add_ps(s0, s1);
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float sbuf[4];
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_mm_storeu_ps(sbuf, s0);
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*result = sbuf[0] + sbuf[1] + sbuf[2] + sbuf[3];
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return k;
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}
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template<> inline int VBLAS<float>::givens(float* a, float* b, int n, float c, float s) const
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{
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if( n < 4 )
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return 0;
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int k = 0;
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__m128 c4 = _mm_set1_ps(c), s4 = _mm_set1_ps(s);
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for( ; k <= n - 4; k += 4 )
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{
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__m128 a0 = _mm_load_ps(a + k);
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__m128 b0 = _mm_load_ps(b + k);
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__m128 t0 = _mm_add_ps(_mm_mul_ps(a0, c4), _mm_mul_ps(b0, s4));
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__m128 t1 = _mm_sub_ps(_mm_mul_ps(b0, c4), _mm_mul_ps(a0, s4));
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_mm_store_ps(a + k, t0);
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_mm_store_ps(b + k, t1);
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}
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return k;
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}
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template<> inline int VBLAS<float>::givensx(float* a, float* b, int n, float c, float s,
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float* anorm, float* bnorm) const
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{
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if( n < 4 )
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return 0;
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int k = 0;
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__m128 c4 = _mm_set1_ps(c), s4 = _mm_set1_ps(s);
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__m128 sa = _mm_setzero_ps(), sb = _mm_setzero_ps();
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for( ; k <= n - 4; k += 4 )
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{
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__m128 a0 = _mm_load_ps(a + k);
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__m128 b0 = _mm_load_ps(b + k);
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__m128 t0 = _mm_add_ps(_mm_mul_ps(a0, c4), _mm_mul_ps(b0, s4));
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__m128 t1 = _mm_sub_ps(_mm_mul_ps(b0, c4), _mm_mul_ps(a0, s4));
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_mm_store_ps(a + k, t0);
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_mm_store_ps(b + k, t1);
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sa = _mm_add_ps(sa, _mm_mul_ps(t0, t0));
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sb = _mm_add_ps(sb, _mm_mul_ps(t1, t1));
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}
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float abuf[4], bbuf[4];
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_mm_storeu_ps(abuf, sa);
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_mm_storeu_ps(bbuf, sb);
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*anorm = abuf[0] + abuf[1] + abuf[2] + abuf[3];
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*bnorm = bbuf[0] + bbuf[1] + bbuf[2] + bbuf[3];
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return k;
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}
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template<> inline int VBLAS<double>::dot(const double* a, const double* b, int n, double* result) const
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{
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if( n < 4 )
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return 0;
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int k = 0;
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__m128d s0 = _mm_setzero_pd(), s1 = _mm_setzero_pd();
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for( ; k <= n - 4; k += 4 )
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{
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__m128d a0 = _mm_load_pd(a + k), a1 = _mm_load_pd(a + k + 2);
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__m128d b0 = _mm_load_pd(b + k), b1 = _mm_load_pd(b + k + 2);
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s0 = _mm_add_pd(s0, _mm_mul_pd(a0, b0));
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s1 = _mm_add_pd(s1, _mm_mul_pd(a1, b1));
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}
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s0 = _mm_add_pd(s0, s1);
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double sbuf[2];
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_mm_storeu_pd(sbuf, s0);
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*result = sbuf[0] + sbuf[1];
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return k;
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}
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template<> inline int VBLAS<double>::givens(double* a, double* b, int n, double c, double s) const
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{
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int k = 0;
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__m128d c2 = _mm_set1_pd(c), s2 = _mm_set1_pd(s);
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for( ; k <= n - 2; k += 2 )
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{
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__m128d a0 = _mm_load_pd(a + k);
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__m128d b0 = _mm_load_pd(b + k);
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__m128d t0 = _mm_add_pd(_mm_mul_pd(a0, c2), _mm_mul_pd(b0, s2));
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__m128d t1 = _mm_sub_pd(_mm_mul_pd(b0, c2), _mm_mul_pd(a0, s2));
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_mm_store_pd(a + k, t0);
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_mm_store_pd(b + k, t1);
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}
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return k;
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}
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template<> inline int VBLAS<double>::givensx(double* a, double* b, int n, double c, double s,
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double* anorm, double* bnorm) const
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{
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int k = 0;
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__m128d c2 = _mm_set1_pd(c), s2 = _mm_set1_pd(s);
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__m128d sa = _mm_setzero_pd(), sb = _mm_setzero_pd();
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for( ; k <= n - 2; k += 2 )
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{
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__m128d a0 = _mm_load_pd(a + k);
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__m128d b0 = _mm_load_pd(b + k);
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__m128d t0 = _mm_add_pd(_mm_mul_pd(a0, c2), _mm_mul_pd(b0, s2));
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__m128d t1 = _mm_sub_pd(_mm_mul_pd(b0, c2), _mm_mul_pd(a0, s2));
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_mm_store_pd(a + k, t0);
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_mm_store_pd(b + k, t1);
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sa = _mm_add_pd(sa, _mm_mul_pd(t0, t0));
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sb = _mm_add_pd(sb, _mm_mul_pd(t1, t1));
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}
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double abuf[2], bbuf[2];
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_mm_storeu_pd(abuf, sa);
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_mm_storeu_pd(bbuf, sb);
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*anorm = abuf[0] + abuf[1];
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*bnorm = bbuf[0] + bbuf[1];
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return k;
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}
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#endif
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template<typename _Tp> void
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JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* _W, _Tp* Vt, size_t vstep,
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int m, int n, int n1, double minval, _Tp eps)
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{
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VBLAS<_Tp> vblas;
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AutoBuffer<double> Wbuf(n);
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double* W = Wbuf;
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int i, j, k, iter, max_iter = std::max(m, 30);
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_Tp c, s;
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double sd;
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astep /= sizeof(At[0]);
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vstep /= sizeof(Vt[0]);
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for( i = 0; i < n; i++ )
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{
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for( k = 0, sd = 0; k < m; k++ )
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{
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_Tp t = At[i*astep + k];
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sd += (double)t*t;
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}
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W[i] = sd;
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if( Vt )
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{
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for( k = 0; k < n; k++ )
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Vt[i*vstep + k] = 0;
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Vt[i*vstep + i] = 1;
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}
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}
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for( iter = 0; iter < max_iter; iter++ )
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{
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bool changed = false;
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for( i = 0; i < n-1; i++ )
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for( j = i+1; j < n; j++ )
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{
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_Tp *Ai = At + i*astep, *Aj = At + j*astep;
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double a = W[i], p = 0, b = W[j];
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for( k = 0; k < m; k++ )
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p += (double)Ai[k]*Aj[k];
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if( std::abs(p) <= eps*std::sqrt((double)a*b) )
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continue;
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p *= 2;
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double beta = a - b, gamma = hypot((double)p, beta);
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if( beta < 0 )
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{
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double delta = (gamma - beta)*0.5;
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s = (_Tp)std::sqrt(delta/gamma);
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c = (_Tp)(p/(gamma*s*2));
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}
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else
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{
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c = (_Tp)std::sqrt((gamma + beta)/(gamma*2));
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s = (_Tp)(p/(gamma*c*2));
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}
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a = b = 0;
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|
for( k = 0; k < m; k++ )
|
|
{
|
|
_Tp t0 = c*Ai[k] + s*Aj[k];
|
|
_Tp t1 = -s*Ai[k] + c*Aj[k];
|
|
Ai[k] = t0; Aj[k] = t1;
|
|
|
|
a += (double)t0*t0; b += (double)t1*t1;
|
|
}
|
|
W[i] = a; W[j] = b;
|
|
|
|
changed = true;
|
|
|
|
if( Vt )
|
|
{
|
|
_Tp *Vi = Vt + i*vstep, *Vj = Vt + j*vstep;
|
|
k = vblas.givens(Vi, Vj, n, c, s);
|
|
|
|
for( ; k < n; k++ )
|
|
{
|
|
_Tp t0 = c*Vi[k] + s*Vj[k];
|
|
_Tp t1 = -s*Vi[k] + c*Vj[k];
|
|
Vi[k] = t0; Vj[k] = t1;
|
|
}
|
|
}
|
|
}
|
|
if( !changed )
|
|
break;
|
|
}
|
|
|
|
for( i = 0; i < n; i++ )
|
|
{
|
|
for( k = 0, sd = 0; k < m; k++ )
|
|
{
|
|
_Tp t = At[i*astep + k];
|
|
sd += (double)t*t;
|
|
}
|
|
W[i] = std::sqrt(sd);
|
|
}
|
|
|
|
for( i = 0; i < n-1; i++ )
|
|
{
|
|
j = i;
|
|
for( k = i+1; k < n; k++ )
|
|
{
|
|
if( W[j] < W[k] )
|
|
j = k;
|
|
}
|
|
if( i != j )
|
|
{
|
|
std::swap(W[i], W[j]);
|
|
if( Vt )
|
|
{
|
|
for( k = 0; k < m; k++ )
|
|
std::swap(At[i*astep + k], At[j*astep + k]);
|
|
|
|
for( k = 0; k < n; k++ )
|
|
std::swap(Vt[i*vstep + k], Vt[j*vstep + k]);
|
|
}
|
|
}
|
|
}
|
|
|
|
for( i = 0; i < n; i++ )
|
|
_W[i] = (_Tp)W[i];
|
|
|
|
if( !Vt )
|
|
return;
|
|
|
|
RNG rng(0x12345678);
|
|
for( i = 0; i < n1; i++ )
|
|
{
|
|
sd = i < n ? W[i] : 0;
|
|
|
|
for( int ii = 0; ii < 100 && sd <= minval; ii++ )
|
|
{
|
|
// if we got a zero singular value, then in order to get the corresponding left singular vector
|
|
// we generate a random vector, project it to the previously computed left singular vectors,
|
|
// subtract the projection and normalize the difference.
|
|
const _Tp val0 = (_Tp)(1./m);
|
|
for( k = 0; k < m; k++ )
|
|
{
|
|
_Tp val = (rng.next() & 256) != 0 ? val0 : -val0;
|
|
At[i*astep + k] = val;
|
|
}
|
|
for( iter = 0; iter < 2; iter++ )
|
|
{
|
|
for( j = 0; j < i; j++ )
|
|
{
|
|
sd = 0;
|
|
for( k = 0; k < m; k++ )
|
|
sd += At[i*astep + k]*At[j*astep + k];
|
|
_Tp asum = 0;
|
|
for( k = 0; k < m; k++ )
|
|
{
|
|
_Tp t = (_Tp)(At[i*astep + k] - sd*At[j*astep + k]);
|
|
At[i*astep + k] = t;
|
|
asum += std::abs(t);
|
|
}
|
|
asum = asum > eps*100 ? 1/asum : 0;
|
|
for( k = 0; k < m; k++ )
|
|
At[i*astep + k] *= asum;
|
|
}
|
|
}
|
|
sd = 0;
|
|
for( k = 0; k < m; k++ )
|
|
{
|
|
_Tp t = At[i*astep + k];
|
|
sd += (double)t*t;
|
|
}
|
|
sd = std::sqrt(sd);
|
|
}
|
|
|
|
s = (_Tp)(sd > minval ? 1/sd : 0.);
|
|
for( k = 0; k < m; k++ )
|
|
At[i*astep + k] *= s;
|
|
}
|
|
}
|
|
|
|
|
|
static void JacobiSVD(float* At, size_t astep, float* W, float* Vt, size_t vstep, int m, int n, int n1=-1)
|
|
{
|
|
hal::SVD32f(At, astep, W, NULL, astep, Vt, vstep, m, n, n1);
|
|
}
|
|
|
|
static void JacobiSVD(double* At, size_t astep, double* W, double* Vt, size_t vstep, int m, int n, int n1=-1)
|
|
{
|
|
hal::SVD64f(At, astep, W, NULL, astep, Vt, vstep, m, n, n1);
|
|
}
|
|
|
|
template <typename fptype> static inline int
|
|
decodeSVDParameters(const fptype* U, const fptype* Vt, int m, int n, int n1)
|
|
{
|
|
int halSVDFlag = 0;
|
|
if(Vt == NULL)
|
|
halSVDFlag = CV_HAL_SVD_NO_UV;
|
|
else if(n1 <= 0 || n1 == n)
|
|
{
|
|
halSVDFlag = CV_HAL_SVD_SHORT_UV;
|
|
if(U == NULL)
|
|
halSVDFlag |= CV_HAL_SVD_MODIFY_A;
|
|
}
|
|
else if(n1 == m)
|
|
{
|
|
halSVDFlag = CV_HAL_SVD_FULL_UV;
|
|
if(U == NULL)
|
|
halSVDFlag |= CV_HAL_SVD_MODIFY_A;
|
|
}
|
|
return halSVDFlag;
|
|
}
|
|
|
|
void hal::SVD32f(float* At, size_t astep, float* W, float* U, size_t ustep, float* Vt, size_t vstep, int m, int n, int n1)
|
|
{
|
|
CALL_HAL(SVD32f, cv_hal_SVD32f, At, astep, W, U, ustep, Vt, vstep, m, n, decodeSVDParameters(U, Vt, m, n, n1))
|
|
JacobiSVDImpl_(At, astep, W, Vt, vstep, m, n, !Vt ? 0 : n1 < 0 ? n : n1, FLT_MIN, FLT_EPSILON*2);
|
|
}
|
|
|
|
void hal::SVD64f(double* At, size_t astep, double* W, double* U, size_t ustep, double* Vt, size_t vstep, int m, int n, int n1)
|
|
{
|
|
CALL_HAL(SVD64f, cv_hal_SVD64f, At, astep, W, U, ustep, Vt, vstep, m, n, decodeSVDParameters(U, Vt, m, n, n1))
|
|
JacobiSVDImpl_(At, astep, W, Vt, vstep, m, n, !Vt ? 0 : n1 < 0 ? n : n1, DBL_MIN, DBL_EPSILON*10);
|
|
}
|
|
|
|
/* y[0:m,0:n] += diag(a[0:1,0:m]) * x[0:m,0:n] */
|
|
template<typename T1, typename T2, typename T3> static void
|
|
MatrAXPY( int m, int n, const T1* x, int dx,
|
|
const T2* a, int inca, T3* y, int dy )
|
|
{
|
|
int i;
|
|
for( i = 0; i < m; i++, x += dx, y += dy )
|
|
{
|
|
T2 s = a[i*inca];
|
|
int j = 0;
|
|
#if CV_ENABLE_UNROLLED
|
|
for(; j <= n - 4; j += 4 )
|
|
{
|
|
T3 t0 = (T3)(y[j] + s*x[j]);
|
|
T3 t1 = (T3)(y[j+1] + s*x[j+1]);
|
|
y[j] = t0;
|
|
y[j+1] = t1;
|
|
t0 = (T3)(y[j+2] + s*x[j+2]);
|
|
t1 = (T3)(y[j+3] + s*x[j+3]);
|
|
y[j+2] = t0;
|
|
y[j+3] = t1;
|
|
}
|
|
#endif
|
|
for( ; j < n; j++ )
|
|
y[j] = (T3)(y[j] + s*x[j]);
|
|
}
|
|
}
|
|
|
|
template<typename T> static void
|
|
SVBkSbImpl_( int m, int n, const T* w, int incw,
|
|
const T* u, int ldu, bool uT,
|
|
const T* v, int ldv, bool vT,
|
|
const T* b, int ldb, int nb,
|
|
T* x, int ldx, double* buffer, T eps )
|
|
{
|
|
double threshold = 0;
|
|
int udelta0 = uT ? ldu : 1, udelta1 = uT ? 1 : ldu;
|
|
int vdelta0 = vT ? ldv : 1, vdelta1 = vT ? 1 : ldv;
|
|
int i, j, nm = std::min(m, n);
|
|
|
|
if( !b )
|
|
nb = m;
|
|
|
|
for( i = 0; i < n; i++ )
|
|
for( j = 0; j < nb; j++ )
|
|
x[i*ldx + j] = 0;
|
|
|
|
for( i = 0; i < nm; i++ )
|
|
threshold += w[i*incw];
|
|
threshold *= eps;
|
|
|
|
// v * inv(w) * uT * b
|
|
for( i = 0; i < nm; i++, u += udelta0, v += vdelta0 )
|
|
{
|
|
double wi = w[i*incw];
|
|
if( (double)std::abs(wi) <= threshold )
|
|
continue;
|
|
wi = 1/wi;
|
|
|
|
if( nb == 1 )
|
|
{
|
|
double s = 0;
|
|
if( b )
|
|
for( j = 0; j < m; j++ )
|
|
s += u[j*udelta1]*b[j*ldb];
|
|
else
|
|
s = u[0];
|
|
s *= wi;
|
|
|
|
for( j = 0; j < n; j++ )
|
|
x[j*ldx] = (T)(x[j*ldx] + s*v[j*vdelta1]);
|
|
}
|
|
else
|
|
{
|
|
if( b )
|
|
{
|
|
for( j = 0; j < nb; j++ )
|
|
buffer[j] = 0;
|
|
MatrAXPY( m, nb, b, ldb, u, udelta1, buffer, 0 );
|
|
for( j = 0; j < nb; j++ )
|
|
buffer[j] *= wi;
|
|
}
|
|
else
|
|
{
|
|
for( j = 0; j < nb; j++ )
|
|
buffer[j] = u[j*udelta1]*wi;
|
|
}
|
|
MatrAXPY( n, nb, buffer, 0, v, vdelta1, x, ldx );
|
|
}
|
|
}
|
|
}
|
|
|
|
static void
|
|
SVBkSb( int m, int n, const float* w, size_t wstep,
|
|
const float* u, size_t ustep, bool uT,
|
|
const float* v, size_t vstep, bool vT,
|
|
const float* b, size_t bstep, int nb,
|
|
float* x, size_t xstep, uchar* buffer )
|
|
{
|
|
SVBkSbImpl_(m, n, w, wstep ? (int)(wstep/sizeof(w[0])) : 1,
|
|
u, (int)(ustep/sizeof(u[0])), uT,
|
|
v, (int)(vstep/sizeof(v[0])), vT,
|
|
b, (int)(bstep/sizeof(b[0])), nb,
|
|
x, (int)(xstep/sizeof(x[0])),
|
|
(double*)alignPtr(buffer, sizeof(double)), (float)(DBL_EPSILON*2) );
|
|
}
|
|
|
|
static void
|
|
SVBkSb( int m, int n, const double* w, size_t wstep,
|
|
const double* u, size_t ustep, bool uT,
|
|
const double* v, size_t vstep, bool vT,
|
|
const double* b, size_t bstep, int nb,
|
|
double* x, size_t xstep, uchar* buffer )
|
|
{
|
|
SVBkSbImpl_(m, n, w, wstep ? (int)(wstep/sizeof(w[0])) : 1,
|
|
u, (int)(ustep/sizeof(u[0])), uT,
|
|
v, (int)(vstep/sizeof(v[0])), vT,
|
|
b, (int)(bstep/sizeof(b[0])), nb,
|
|
x, (int)(xstep/sizeof(x[0])),
|
|
(double*)alignPtr(buffer, sizeof(double)), DBL_EPSILON*2 );
|
|
}
|
|
|
|
}
|
|
|
|
/****************************************************************************************\
|
|
* Determinant of the matrix *
|
|
\****************************************************************************************/
|
|
|
|
#define det2(m) ((double)m(0,0)*m(1,1) - (double)m(0,1)*m(1,0))
|
|
#define det3(m) (m(0,0)*((double)m(1,1)*m(2,2) - (double)m(1,2)*m(2,1)) - \
|
|
m(0,1)*((double)m(1,0)*m(2,2) - (double)m(1,2)*m(2,0)) + \
|
|
m(0,2)*((double)m(1,0)*m(2,1) - (double)m(1,1)*m(2,0)))
|
|
|
|
double cv::determinant( InputArray _mat )
|
|
{
|
|
CV_INSTRUMENT_REGION()
|
|
|
|
Mat mat = _mat.getMat();
|
|
double result = 0;
|
|
int type = mat.type(), rows = mat.rows;
|
|
size_t step = mat.step;
|
|
const uchar* m = mat.ptr();
|
|
|
|
CV_Assert( !mat.empty() );
|
|
CV_Assert( mat.rows == mat.cols && (type == CV_32F || type == CV_64F));
|
|
|
|
#define Mf(y, x) ((float*)(m + y*step))[x]
|
|
#define Md(y, x) ((double*)(m + y*step))[x]
|
|
|
|
if( type == CV_32F )
|
|
{
|
|
if( rows == 2 )
|
|
result = det2(Mf);
|
|
else if( rows == 3 )
|
|
result = det3(Mf);
|
|
else if( rows == 1 )
|
|
result = Mf(0,0);
|
|
else
|
|
{
|
|
size_t bufSize = rows*rows*sizeof(float);
|
|
AutoBuffer<uchar> buffer(bufSize);
|
|
Mat a(rows, rows, CV_32F, (uchar*)buffer);
|
|
mat.copyTo(a);
|
|
|
|
result = hal::LU32f(a.ptr<float>(), a.step, rows, 0, 0, 0);
|
|
if( result )
|
|
{
|
|
for( int i = 0; i < rows; i++ )
|
|
result *= a.at<float>(i,i);
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if( rows == 2 )
|
|
result = det2(Md);
|
|
else if( rows == 3 )
|
|
result = det3(Md);
|
|
else if( rows == 1 )
|
|
result = Md(0,0);
|
|
else
|
|
{
|
|
size_t bufSize = rows*rows*sizeof(double);
|
|
AutoBuffer<uchar> buffer(bufSize);
|
|
Mat a(rows, rows, CV_64F, (uchar*)buffer);
|
|
mat.copyTo(a);
|
|
|
|
result = hal::LU64f(a.ptr<double>(), a.step, rows, 0, 0, 0);
|
|
if( result )
|
|
{
|
|
for( int i = 0; i < rows; i++ )
|
|
result *= a.at<double>(i,i);
|
|
}
|
|
}
|
|
}
|
|
|
|
#undef Mf
|
|
#undef Md
|
|
|
|
return result;
|
|
}
|
|
|
|
/****************************************************************************************\
|
|
* Inverse (or pseudo-inverse) of a matrix *
|
|
\****************************************************************************************/
|
|
|
|
#define Sf( y, x ) ((float*)(srcdata + y*srcstep))[x]
|
|
#define Sd( y, x ) ((double*)(srcdata + y*srcstep))[x]
|
|
#define Df( y, x ) ((float*)(dstdata + y*dststep))[x]
|
|
#define Dd( y, x ) ((double*)(dstdata + y*dststep))[x]
|
|
|
|
double cv::invert( InputArray _src, OutputArray _dst, int method )
|
|
{
|
|
CV_INSTRUMENT_REGION()
|
|
|
|
bool result = false;
|
|
Mat src = _src.getMat();
|
|
int type = src.type();
|
|
|
|
CV_Assert(type == CV_32F || type == CV_64F);
|
|
|
|
size_t esz = CV_ELEM_SIZE(type);
|
|
int m = src.rows, n = src.cols;
|
|
|
|
if( method == DECOMP_SVD )
|
|
{
|
|
int nm = std::min(m, n);
|
|
|
|
AutoBuffer<uchar> _buf((m*nm + nm + nm*n)*esz + sizeof(double));
|
|
uchar* buf = alignPtr((uchar*)_buf, (int)esz);
|
|
Mat u(m, nm, type, buf);
|
|
Mat w(nm, 1, type, u.ptr() + m*nm*esz);
|
|
Mat vt(nm, n, type, w.ptr() + nm*esz);
|
|
|
|
SVD::compute(src, w, u, vt);
|
|
SVD::backSubst(w, u, vt, Mat(), _dst);
|
|
return type == CV_32F ?
|
|
(w.ptr<float>()[0] >= FLT_EPSILON ?
|
|
w.ptr<float>()[n-1]/w.ptr<float>()[0] : 0) :
|
|
(w.ptr<double>()[0] >= DBL_EPSILON ?
|
|
w.ptr<double>()[n-1]/w.ptr<double>()[0] : 0);
|
|
}
|
|
|
|
CV_Assert( m == n );
|
|
|
|
if( method == DECOMP_EIG )
|
|
{
|
|
AutoBuffer<uchar> _buf((n*n*2 + n)*esz + sizeof(double));
|
|
uchar* buf = alignPtr((uchar*)_buf, (int)esz);
|
|
Mat u(n, n, type, buf);
|
|
Mat w(n, 1, type, u.ptr() + n*n*esz);
|
|
Mat vt(n, n, type, w.ptr() + n*esz);
|
|
|
|
eigen(src, w, vt);
|
|
transpose(vt, u);
|
|
SVD::backSubst(w, u, vt, Mat(), _dst);
|
|
return type == CV_32F ?
|
|
(w.ptr<float>()[0] >= FLT_EPSILON ?
|
|
w.ptr<float>()[n-1]/w.ptr<float>()[0] : 0) :
|
|
(w.ptr<double>()[0] >= DBL_EPSILON ?
|
|
w.ptr<double>()[n-1]/w.ptr<double>()[0] : 0);
|
|
}
|
|
|
|
CV_Assert( method == DECOMP_LU || method == DECOMP_CHOLESKY );
|
|
|
|
_dst.create( n, n, type );
|
|
Mat dst = _dst.getMat();
|
|
|
|
if( n <= 3 )
|
|
{
|
|
const uchar* srcdata = src.ptr();
|
|
uchar* dstdata = dst.ptr();
|
|
size_t srcstep = src.step;
|
|
size_t dststep = dst.step;
|
|
|
|
if( n == 2 )
|
|
{
|
|
if( type == CV_32FC1 )
|
|
{
|
|
double d = det2(Sf);
|
|
if( d != 0. )
|
|
{
|
|
result = true;
|
|
d = 1./d;
|
|
|
|
#if CV_SSE2
|
|
if(USE_SSE2)
|
|
{
|
|
__m128 zero = _mm_setzero_ps();
|
|
__m128 t0 = _mm_loadl_pi(zero, (const __m64*)srcdata); //t0 = sf(0,0) sf(0,1)
|
|
__m128 t1 = _mm_loadh_pi(zero, (const __m64*)(srcdata+srcstep)); //t1 = sf(1,0) sf(1,1)
|
|
__m128 s0 = _mm_or_ps(t0, t1);
|
|
__m128 det =_mm_set1_ps((float)d);
|
|
s0 = _mm_mul_ps(s0, det);
|
|
static const uchar CV_DECL_ALIGNED(16) inv[16] = {0,0,0,0,0,0,0,0x80,0,0,0,0x80,0,0,0,0};
|
|
__m128 pattern = _mm_load_ps((const float*)inv);
|
|
s0 = _mm_xor_ps(s0, pattern);//==-1*s0
|
|
s0 = _mm_shuffle_ps(s0, s0, _MM_SHUFFLE(0,2,1,3));
|
|
_mm_storel_pi((__m64*)dstdata, s0);
|
|
_mm_storeh_pi((__m64*)((float*)(dstdata+dststep)), s0);
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
double t0, t1;
|
|
t0 = Sf(0,0)*d;
|
|
t1 = Sf(1,1)*d;
|
|
Df(1,1) = (float)t0;
|
|
Df(0,0) = (float)t1;
|
|
t0 = -Sf(0,1)*d;
|
|
t1 = -Sf(1,0)*d;
|
|
Df(0,1) = (float)t0;
|
|
Df(1,0) = (float)t1;
|
|
}
|
|
|
|
}
|
|
}
|
|
else
|
|
{
|
|
double d = det2(Sd);
|
|
if( d != 0. )
|
|
{
|
|
result = true;
|
|
d = 1./d;
|
|
#if CV_SSE2
|
|
if(USE_SSE2)
|
|
{
|
|
__m128d s0 = _mm_loadu_pd((const double*)srcdata); //s0 = sf(0,0) sf(0,1)
|
|
__m128d s1 = _mm_loadu_pd ((const double*)(srcdata+srcstep));//s1 = sf(1,0) sf(1,1)
|
|
__m128d sm = _mm_unpacklo_pd(s0, _mm_load_sd((const double*)(srcdata+srcstep)+1)); //sm = sf(0,0) sf(1,1) - main diagonal
|
|
__m128d ss = _mm_shuffle_pd(s0, s1, _MM_SHUFFLE2(0,1)); //ss = sf(0,1) sf(1,0) - secondary diagonal
|
|
__m128d det = _mm_load1_pd((const double*)&d);
|
|
sm = _mm_mul_pd(sm, det);
|
|
|
|
static const uchar CV_DECL_ALIGNED(16) inv[8] = {0,0,0,0,0,0,0,0x80};
|
|
__m128d pattern = _mm_load1_pd((double*)inv);
|
|
ss = _mm_mul_pd(ss, det);
|
|
ss = _mm_xor_pd(ss, pattern);//==-1*ss
|
|
|
|
s0 = _mm_shuffle_pd(sm, ss, _MM_SHUFFLE2(0,1));
|
|
s1 = _mm_shuffle_pd(ss, sm, _MM_SHUFFLE2(0,1));
|
|
_mm_storeu_pd((double*)dstdata, s0);
|
|
_mm_storeu_pd((double*)(dstdata+dststep), s1);
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
double t0, t1;
|
|
t0 = Sd(0,0)*d;
|
|
t1 = Sd(1,1)*d;
|
|
Dd(1,1) = t0;
|
|
Dd(0,0) = t1;
|
|
t0 = -Sd(0,1)*d;
|
|
t1 = -Sd(1,0)*d;
|
|
Dd(0,1) = t0;
|
|
Dd(1,0) = t1;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
else if( n == 3 )
|
|
{
|
|
if( type == CV_32FC1 )
|
|
{
|
|
double d = det3(Sf);
|
|
|
|
if( d != 0. )
|
|
{
|
|
double t[12];
|
|
|
|
result = true;
|
|
d = 1./d;
|
|
t[0] = (((double)Sf(1,1) * Sf(2,2) - (double)Sf(1,2) * Sf(2,1)) * d);
|
|
t[1] = (((double)Sf(0,2) * Sf(2,1) - (double)Sf(0,1) * Sf(2,2)) * d);
|
|
t[2] = (((double)Sf(0,1) * Sf(1,2) - (double)Sf(0,2) * Sf(1,1)) * d);
|
|
|
|
t[3] = (((double)Sf(1,2) * Sf(2,0) - (double)Sf(1,0) * Sf(2,2)) * d);
|
|
t[4] = (((double)Sf(0,0) * Sf(2,2) - (double)Sf(0,2) * Sf(2,0)) * d);
|
|
t[5] = (((double)Sf(0,2) * Sf(1,0) - (double)Sf(0,0) * Sf(1,2)) * d);
|
|
|
|
t[6] = (((double)Sf(1,0) * Sf(2,1) - (double)Sf(1,1) * Sf(2,0)) * d);
|
|
t[7] = (((double)Sf(0,1) * Sf(2,0) - (double)Sf(0,0) * Sf(2,1)) * d);
|
|
t[8] = (((double)Sf(0,0) * Sf(1,1) - (double)Sf(0,1) * Sf(1,0)) * d);
|
|
|
|
Df(0,0) = (float)t[0]; Df(0,1) = (float)t[1]; Df(0,2) = (float)t[2];
|
|
Df(1,0) = (float)t[3]; Df(1,1) = (float)t[4]; Df(1,2) = (float)t[5];
|
|
Df(2,0) = (float)t[6]; Df(2,1) = (float)t[7]; Df(2,2) = (float)t[8];
|
|
}
|
|
}
|
|
else
|
|
{
|
|
double d = det3(Sd);
|
|
if( d != 0. )
|
|
{
|
|
result = true;
|
|
d = 1./d;
|
|
double t[9];
|
|
|
|
t[0] = (Sd(1,1) * Sd(2,2) - Sd(1,2) * Sd(2,1)) * d;
|
|
t[1] = (Sd(0,2) * Sd(2,1) - Sd(0,1) * Sd(2,2)) * d;
|
|
t[2] = (Sd(0,1) * Sd(1,2) - Sd(0,2) * Sd(1,1)) * d;
|
|
|
|
t[3] = (Sd(1,2) * Sd(2,0) - Sd(1,0) * Sd(2,2)) * d;
|
|
t[4] = (Sd(0,0) * Sd(2,2) - Sd(0,2) * Sd(2,0)) * d;
|
|
t[5] = (Sd(0,2) * Sd(1,0) - Sd(0,0) * Sd(1,2)) * d;
|
|
|
|
t[6] = (Sd(1,0) * Sd(2,1) - Sd(1,1) * Sd(2,0)) * d;
|
|
t[7] = (Sd(0,1) * Sd(2,0) - Sd(0,0) * Sd(2,1)) * d;
|
|
t[8] = (Sd(0,0) * Sd(1,1) - Sd(0,1) * Sd(1,0)) * d;
|
|
|
|
Dd(0,0) = t[0]; Dd(0,1) = t[1]; Dd(0,2) = t[2];
|
|
Dd(1,0) = t[3]; Dd(1,1) = t[4]; Dd(1,2) = t[5];
|
|
Dd(2,0) = t[6]; Dd(2,1) = t[7]; Dd(2,2) = t[8];
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
assert( n == 1 );
|
|
|
|
if( type == CV_32FC1 )
|
|
{
|
|
double d = Sf(0,0);
|
|
if( d != 0. )
|
|
{
|
|
result = true;
|
|
Df(0,0) = (float)(1./d);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
double d = Sd(0,0);
|
|
if( d != 0. )
|
|
{
|
|
result = true;
|
|
Dd(0,0) = 1./d;
|
|
}
|
|
}
|
|
}
|
|
if( !result )
|
|
dst = Scalar(0);
|
|
return result;
|
|
}
|
|
|
|
int elem_size = CV_ELEM_SIZE(type);
|
|
AutoBuffer<uchar> buf(n*n*elem_size);
|
|
Mat src1(n, n, type, (uchar*)buf);
|
|
src.copyTo(src1);
|
|
setIdentity(dst);
|
|
|
|
if( method == DECOMP_LU && type == CV_32F )
|
|
result = hal::LU32f(src1.ptr<float>(), src1.step, n, dst.ptr<float>(), dst.step, n) != 0;
|
|
else if( method == DECOMP_LU && type == CV_64F )
|
|
result = hal::LU64f(src1.ptr<double>(), src1.step, n, dst.ptr<double>(), dst.step, n) != 0;
|
|
else if( method == DECOMP_CHOLESKY && type == CV_32F )
|
|
result = hal::Cholesky32f(src1.ptr<float>(), src1.step, n, dst.ptr<float>(), dst.step, n);
|
|
else
|
|
result = hal::Cholesky64f(src1.ptr<double>(), src1.step, n, dst.ptr<double>(), dst.step, n);
|
|
|
|
if( !result )
|
|
dst = Scalar(0);
|
|
|
|
return result;
|
|
}
|
|
|
|
|
|
|
|
/****************************************************************************************\
|
|
* Solving a linear system *
|
|
\****************************************************************************************/
|
|
|
|
bool cv::solve( InputArray _src, InputArray _src2arg, OutputArray _dst, int method )
|
|
{
|
|
CV_INSTRUMENT_REGION()
|
|
|
|
bool result = true;
|
|
Mat src = _src.getMat(), _src2 = _src2arg.getMat();
|
|
int type = src.type();
|
|
bool is_normal = (method & DECOMP_NORMAL) != 0;
|
|
|
|
CV_Assert( type == _src2.type() && (type == CV_32F || type == CV_64F) );
|
|
|
|
method &= ~DECOMP_NORMAL;
|
|
CV_Assert( (method != DECOMP_LU && method != DECOMP_CHOLESKY) ||
|
|
is_normal || src.rows == src.cols );
|
|
|
|
// check case of a single equation and small matrix
|
|
if( (method == DECOMP_LU || method == DECOMP_CHOLESKY) && !is_normal &&
|
|
src.rows <= 3 && src.rows == src.cols && _src2.cols == 1 )
|
|
{
|
|
_dst.create( src.cols, _src2.cols, src.type() );
|
|
Mat dst = _dst.getMat();
|
|
|
|
#define bf(y) ((float*)(bdata + y*src2step))[0]
|
|
#define bd(y) ((double*)(bdata + y*src2step))[0]
|
|
|
|
const uchar* srcdata = src.ptr();
|
|
const uchar* bdata = _src2.ptr();
|
|
uchar* dstdata = dst.ptr();
|
|
size_t srcstep = src.step;
|
|
size_t src2step = _src2.step;
|
|
size_t dststep = dst.step;
|
|
|
|
if( src.rows == 2 )
|
|
{
|
|
if( type == CV_32FC1 )
|
|
{
|
|
double d = det2(Sf);
|
|
if( d != 0. )
|
|
{
|
|
double t;
|
|
d = 1./d;
|
|
t = (float)(((double)bf(0)*Sf(1,1) - (double)bf(1)*Sf(0,1))*d);
|
|
Df(1,0) = (float)(((double)bf(1)*Sf(0,0) - (double)bf(0)*Sf(1,0))*d);
|
|
Df(0,0) = (float)t;
|
|
}
|
|
else
|
|
result = false;
|
|
}
|
|
else
|
|
{
|
|
double d = det2(Sd);
|
|
if( d != 0. )
|
|
{
|
|
double t;
|
|
d = 1./d;
|
|
t = (bd(0)*Sd(1,1) - bd(1)*Sd(0,1))*d;
|
|
Dd(1,0) = (bd(1)*Sd(0,0) - bd(0)*Sd(1,0))*d;
|
|
Dd(0,0) = t;
|
|
}
|
|
else
|
|
result = false;
|
|
}
|
|
}
|
|
else if( src.rows == 3 )
|
|
{
|
|
if( type == CV_32FC1 )
|
|
{
|
|
double d = det3(Sf);
|
|
if( d != 0. )
|
|
{
|
|
float t[3];
|
|
d = 1./d;
|
|
|
|
t[0] = (float)(d*
|
|
(bf(0)*((double)Sf(1,1)*Sf(2,2) - (double)Sf(1,2)*Sf(2,1)) -
|
|
Sf(0,1)*((double)bf(1)*Sf(2,2) - (double)Sf(1,2)*bf(2)) +
|
|
Sf(0,2)*((double)bf(1)*Sf(2,1) - (double)Sf(1,1)*bf(2))));
|
|
|
|
t[1] = (float)(d*
|
|
(Sf(0,0)*(double)(bf(1)*Sf(2,2) - (double)Sf(1,2)*bf(2)) -
|
|
bf(0)*((double)Sf(1,0)*Sf(2,2) - (double)Sf(1,2)*Sf(2,0)) +
|
|
Sf(0,2)*((double)Sf(1,0)*bf(2) - (double)bf(1)*Sf(2,0))));
|
|
|
|
t[2] = (float)(d*
|
|
(Sf(0,0)*((double)Sf(1,1)*bf(2) - (double)bf(1)*Sf(2,1)) -
|
|
Sf(0,1)*((double)Sf(1,0)*bf(2) - (double)bf(1)*Sf(2,0)) +
|
|
bf(0)*((double)Sf(1,0)*Sf(2,1) - (double)Sf(1,1)*Sf(2,0))));
|
|
|
|
Df(0,0) = t[0];
|
|
Df(1,0) = t[1];
|
|
Df(2,0) = t[2];
|
|
}
|
|
else
|
|
result = false;
|
|
}
|
|
else
|
|
{
|
|
double d = det3(Sd);
|
|
if( d != 0. )
|
|
{
|
|
double t[9];
|
|
|
|
d = 1./d;
|
|
|
|
t[0] = ((Sd(1,1) * Sd(2,2) - Sd(1,2) * Sd(2,1))*bd(0) +
|
|
(Sd(0,2) * Sd(2,1) - Sd(0,1) * Sd(2,2))*bd(1) +
|
|
(Sd(0,1) * Sd(1,2) - Sd(0,2) * Sd(1,1))*bd(2))*d;
|
|
|
|
t[1] = ((Sd(1,2) * Sd(2,0) - Sd(1,0) * Sd(2,2))*bd(0) +
|
|
(Sd(0,0) * Sd(2,2) - Sd(0,2) * Sd(2,0))*bd(1) +
|
|
(Sd(0,2) * Sd(1,0) - Sd(0,0) * Sd(1,2))*bd(2))*d;
|
|
|
|
t[2] = ((Sd(1,0) * Sd(2,1) - Sd(1,1) * Sd(2,0))*bd(0) +
|
|
(Sd(0,1) * Sd(2,0) - Sd(0,0) * Sd(2,1))*bd(1) +
|
|
(Sd(0,0) * Sd(1,1) - Sd(0,1) * Sd(1,0))*bd(2))*d;
|
|
|
|
Dd(0,0) = t[0];
|
|
Dd(1,0) = t[1];
|
|
Dd(2,0) = t[2];
|
|
}
|
|
else
|
|
result = false;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
assert( src.rows == 1 );
|
|
|
|
if( type == CV_32FC1 )
|
|
{
|
|
double d = Sf(0,0);
|
|
if( d != 0. )
|
|
Df(0,0) = (float)(bf(0)/d);
|
|
else
|
|
result = false;
|
|
}
|
|
else
|
|
{
|
|
double d = Sd(0,0);
|
|
if( d != 0. )
|
|
Dd(0,0) = (bd(0)/d);
|
|
else
|
|
result = false;
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
|
|
int m = src.rows, m_ = m, n = src.cols, nb = _src2.cols;
|
|
size_t esz = CV_ELEM_SIZE(type), bufsize = 0;
|
|
size_t vstep = alignSize(n*esz, 16);
|
|
size_t astep = method == DECOMP_SVD && !is_normal ? alignSize(m*esz, 16) : vstep;
|
|
AutoBuffer<uchar> buffer;
|
|
|
|
Mat src2 = _src2;
|
|
_dst.create( src.cols, src2.cols, src.type() );
|
|
Mat dst = _dst.getMat();
|
|
|
|
if( m < n )
|
|
CV_Error(CV_StsBadArg, "The function can not solve under-determined linear systems" );
|
|
|
|
if( m == n )
|
|
is_normal = false;
|
|
else if( is_normal )
|
|
{
|
|
m_ = n;
|
|
if( method == DECOMP_SVD )
|
|
method = DECOMP_EIG;
|
|
}
|
|
|
|
size_t asize = astep*(method == DECOMP_SVD || is_normal ? n : m);
|
|
bufsize += asize + 32;
|
|
|
|
if( is_normal )
|
|
bufsize += n*nb*esz;
|
|
if( method == DECOMP_SVD || method == DECOMP_EIG )
|
|
bufsize += n*5*esz + n*vstep + nb*sizeof(double) + 32;
|
|
|
|
buffer.allocate(bufsize);
|
|
uchar* ptr = alignPtr((uchar*)buffer, 16);
|
|
|
|
Mat a(m_, n, type, ptr, astep);
|
|
|
|
if( is_normal )
|
|
mulTransposed(src, a, true);
|
|
else if( method != DECOMP_SVD )
|
|
src.copyTo(a);
|
|
else
|
|
{
|
|
a = Mat(n, m_, type, ptr, astep);
|
|
transpose(src, a);
|
|
}
|
|
ptr += asize;
|
|
|
|
if( !is_normal )
|
|
{
|
|
if( method == DECOMP_LU || method == DECOMP_CHOLESKY )
|
|
src2.copyTo(dst);
|
|
}
|
|
else
|
|
{
|
|
// a'*b
|
|
if( method == DECOMP_LU || method == DECOMP_CHOLESKY )
|
|
gemm( src, src2, 1, Mat(), 0, dst, GEMM_1_T );
|
|
else
|
|
{
|
|
Mat tmp(n, nb, type, ptr);
|
|
ptr += n*nb*esz;
|
|
gemm( src, src2, 1, Mat(), 0, tmp, GEMM_1_T );
|
|
src2 = tmp;
|
|
}
|
|
}
|
|
|
|
if( method == DECOMP_LU )
|
|
{
|
|
if( type == CV_32F )
|
|
result = hal::LU32f(a.ptr<float>(), a.step, n, dst.ptr<float>(), dst.step, nb) != 0;
|
|
else
|
|
result = hal::LU64f(a.ptr<double>(), a.step, n, dst.ptr<double>(), dst.step, nb) != 0;
|
|
}
|
|
else if( method == DECOMP_CHOLESKY )
|
|
{
|
|
if( type == CV_32F )
|
|
result = hal::Cholesky32f(a.ptr<float>(), a.step, n, dst.ptr<float>(), dst.step, nb);
|
|
else
|
|
result = hal::Cholesky64f(a.ptr<double>(), a.step, n, dst.ptr<double>(), dst.step, nb);
|
|
}
|
|
else if( method == DECOMP_QR )
|
|
{
|
|
Mat rhsMat;
|
|
if( is_normal || m == n )
|
|
{
|
|
src2.copyTo(dst);
|
|
rhsMat = dst;
|
|
}
|
|
else
|
|
{
|
|
rhsMat = Mat(m, nb, type);
|
|
src2.copyTo(rhsMat);
|
|
}
|
|
|
|
if( type == CV_32F )
|
|
result = hal::QR32f(a.ptr<float>(), a.step, a.rows, a.cols, rhsMat.cols, rhsMat.ptr<float>(), rhsMat.step, NULL) != 0;
|
|
else
|
|
result = hal::QR64f(a.ptr<double>(), a.step, a.rows, a.cols, rhsMat.cols, rhsMat.ptr<double>(), rhsMat.step, NULL) != 0;
|
|
|
|
if (rhsMat.rows != dst.rows)
|
|
rhsMat.rowRange(0, dst.rows).copyTo(dst);
|
|
}
|
|
else
|
|
{
|
|
ptr = alignPtr(ptr, 16);
|
|
Mat v(n, n, type, ptr, vstep), w(n, 1, type, ptr + vstep*n), u;
|
|
ptr += n*(vstep + esz);
|
|
|
|
if( method == DECOMP_EIG )
|
|
{
|
|
if( type == CV_32F )
|
|
Jacobi(a.ptr<float>(), a.step, w.ptr<float>(), v.ptr<float>(), v.step, n, ptr);
|
|
else
|
|
Jacobi(a.ptr<double>(), a.step, w.ptr<double>(), v.ptr<double>(), v.step, n, ptr);
|
|
u = v;
|
|
}
|
|
else
|
|
{
|
|
if( type == CV_32F )
|
|
JacobiSVD(a.ptr<float>(), a.step, w.ptr<float>(), v.ptr<float>(), v.step, m_, n);
|
|
else
|
|
JacobiSVD(a.ptr<double>(), a.step, w.ptr<double>(), v.ptr<double>(), v.step, m_, n);
|
|
u = a;
|
|
}
|
|
|
|
if( type == CV_32F )
|
|
{
|
|
SVBkSb(m_, n, w.ptr<float>(), 0, u.ptr<float>(), u.step, true,
|
|
v.ptr<float>(), v.step, true, src2.ptr<float>(),
|
|
src2.step, nb, dst.ptr<float>(), dst.step, ptr);
|
|
}
|
|
else
|
|
{
|
|
SVBkSb(m_, n, w.ptr<double>(), 0, u.ptr<double>(), u.step, true,
|
|
v.ptr<double>(), v.step, true, src2.ptr<double>(),
|
|
src2.step, nb, dst.ptr<double>(), dst.step, ptr);
|
|
}
|
|
result = true;
|
|
}
|
|
|
|
if( !result )
|
|
dst = Scalar(0);
|
|
|
|
return result;
|
|
}
|
|
|
|
|
|
/////////////////// finding eigenvalues and eigenvectors of a symmetric matrix ///////////////
|
|
|
|
bool cv::eigen( InputArray _src, OutputArray _evals, OutputArray _evects )
|
|
{
|
|
CV_INSTRUMENT_REGION()
|
|
|
|
Mat src = _src.getMat();
|
|
int type = src.type();
|
|
int n = src.rows;
|
|
|
|
CV_Assert( src.rows == src.cols );
|
|
CV_Assert (type == CV_32F || type == CV_64F);
|
|
|
|
Mat v;
|
|
if( _evects.needed() )
|
|
{
|
|
_evects.create(n, n, type);
|
|
v = _evects.getMat();
|
|
}
|
|
|
|
size_t elemSize = src.elemSize(), astep = alignSize(n*elemSize, 16);
|
|
AutoBuffer<uchar> buf(n*astep + n*5*elemSize + 32);
|
|
uchar* ptr = alignPtr((uchar*)buf, 16);
|
|
Mat a(n, n, type, ptr, astep), w(n, 1, type, ptr + astep*n);
|
|
ptr += astep*n + elemSize*n;
|
|
src.copyTo(a);
|
|
bool ok = type == CV_32F ?
|
|
Jacobi(a.ptr<float>(), a.step, w.ptr<float>(), v.ptr<float>(), v.step, n, ptr) :
|
|
Jacobi(a.ptr<double>(), a.step, w.ptr<double>(), v.ptr<double>(), v.step, n, ptr);
|
|
|
|
w.copyTo(_evals);
|
|
return ok;
|
|
}
|
|
|
|
namespace cv
|
|
{
|
|
|
|
static void _SVDcompute( InputArray _aarr, OutputArray _w,
|
|
OutputArray _u, OutputArray _vt, int flags )
|
|
{
|
|
Mat src = _aarr.getMat();
|
|
int m = src.rows, n = src.cols;
|
|
int type = src.type();
|
|
bool compute_uv = _u.needed() || _vt.needed();
|
|
bool full_uv = (flags & SVD::FULL_UV) != 0;
|
|
|
|
CV_Assert( type == CV_32F || type == CV_64F );
|
|
|
|
if( flags & SVD::NO_UV )
|
|
{
|
|
_u.release();
|
|
_vt.release();
|
|
compute_uv = full_uv = false;
|
|
}
|
|
|
|
bool at = false;
|
|
if( m < n )
|
|
{
|
|
std::swap(m, n);
|
|
at = true;
|
|
}
|
|
|
|
int urows = full_uv ? m : n;
|
|
size_t esz = src.elemSize(), astep = alignSize(m*esz, 16), vstep = alignSize(n*esz, 16);
|
|
AutoBuffer<uchar> _buf(urows*astep + n*vstep + n*esz + 32);
|
|
uchar* buf = alignPtr((uchar*)_buf, 16);
|
|
Mat temp_a(n, m, type, buf, astep);
|
|
Mat temp_w(n, 1, type, buf + urows*astep);
|
|
Mat temp_u(urows, m, type, buf, astep), temp_v;
|
|
|
|
if( compute_uv )
|
|
temp_v = Mat(n, n, type, alignPtr(buf + urows*astep + n*esz, 16), vstep);
|
|
|
|
if( urows > n )
|
|
temp_u = Scalar::all(0);
|
|
|
|
if( !at )
|
|
transpose(src, temp_a);
|
|
else
|
|
src.copyTo(temp_a);
|
|
|
|
if( type == CV_32F )
|
|
{
|
|
JacobiSVD(temp_a.ptr<float>(), temp_u.step, temp_w.ptr<float>(),
|
|
temp_v.ptr<float>(), temp_v.step, m, n, compute_uv ? urows : 0);
|
|
}
|
|
else
|
|
{
|
|
JacobiSVD(temp_a.ptr<double>(), temp_u.step, temp_w.ptr<double>(),
|
|
temp_v.ptr<double>(), temp_v.step, m, n, compute_uv ? urows : 0);
|
|
}
|
|
temp_w.copyTo(_w);
|
|
if( compute_uv )
|
|
{
|
|
if( !at )
|
|
{
|
|
if( _u.needed() )
|
|
transpose(temp_u, _u);
|
|
if( _vt.needed() )
|
|
temp_v.copyTo(_vt);
|
|
}
|
|
else
|
|
{
|
|
if( _u.needed() )
|
|
transpose(temp_v, _u);
|
|
if( _vt.needed() )
|
|
temp_u.copyTo(_vt);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void SVD::compute( InputArray a, OutputArray w, OutputArray u, OutputArray vt, int flags )
|
|
{
|
|
CV_INSTRUMENT_REGION()
|
|
|
|
_SVDcompute(a, w, u, vt, flags);
|
|
}
|
|
|
|
void SVD::compute( InputArray a, OutputArray w, int flags )
|
|
{
|
|
CV_INSTRUMENT_REGION()
|
|
|
|
_SVDcompute(a, w, noArray(), noArray(), flags);
|
|
}
|
|
|
|
void SVD::backSubst( InputArray _w, InputArray _u, InputArray _vt,
|
|
InputArray _rhs, OutputArray _dst )
|
|
{
|
|
Mat w = _w.getMat(), u = _u.getMat(), vt = _vt.getMat(), rhs = _rhs.getMat();
|
|
int type = w.type(), esz = (int)w.elemSize();
|
|
int m = u.rows, n = vt.cols, nb = rhs.data ? rhs.cols : m, nm = std::min(m, n);
|
|
size_t wstep = w.rows == 1 ? (size_t)esz : w.cols == 1 ? (size_t)w.step : (size_t)w.step + esz;
|
|
AutoBuffer<uchar> buffer(nb*sizeof(double) + 16);
|
|
CV_Assert( w.type() == u.type() && u.type() == vt.type() && u.data && vt.data && w.data );
|
|
CV_Assert( u.cols >= nm && vt.rows >= nm &&
|
|
(w.size() == Size(nm, 1) || w.size() == Size(1, nm) || w.size() == Size(vt.rows, u.cols)) );
|
|
CV_Assert( rhs.data == 0 || (rhs.type() == type && rhs.rows == m) );
|
|
|
|
_dst.create( n, nb, type );
|
|
Mat dst = _dst.getMat();
|
|
if( type == CV_32F )
|
|
SVBkSb(m, n, w.ptr<float>(), wstep, u.ptr<float>(), u.step, false,
|
|
vt.ptr<float>(), vt.step, true, rhs.ptr<float>(), rhs.step, nb,
|
|
dst.ptr<float>(), dst.step, buffer);
|
|
else if( type == CV_64F )
|
|
SVBkSb(m, n, w.ptr<double>(), wstep, u.ptr<double>(), u.step, false,
|
|
vt.ptr<double>(), vt.step, true, rhs.ptr<double>(), rhs.step, nb,
|
|
dst.ptr<double>(), dst.step, buffer);
|
|
else
|
|
CV_Error( CV_StsUnsupportedFormat, "" );
|
|
}
|
|
|
|
|
|
SVD& SVD::operator ()(InputArray a, int flags)
|
|
{
|
|
_SVDcompute(a, w, u, vt, flags);
|
|
return *this;
|
|
}
|
|
|
|
|
|
void SVD::backSubst( InputArray rhs, OutputArray dst ) const
|
|
{
|
|
backSubst( w, u, vt, rhs, dst );
|
|
}
|
|
|
|
}
|
|
|
|
|
|
void cv::SVDecomp(InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags)
|
|
{
|
|
CV_INSTRUMENT_REGION()
|
|
|
|
SVD::compute(src, w, u, vt, flags);
|
|
}
|
|
|
|
void cv::SVBackSubst(InputArray w, InputArray u, InputArray vt, InputArray rhs, OutputArray dst)
|
|
{
|
|
CV_INSTRUMENT_REGION()
|
|
|
|
SVD::backSubst(w, u, vt, rhs, dst);
|
|
}
|
|
|
|
|
|
CV_IMPL double
|
|
cvDet( const CvArr* arr )
|
|
{
|
|
if( CV_IS_MAT(arr) && ((CvMat*)arr)->rows <= 3 )
|
|
{
|
|
CvMat* mat = (CvMat*)arr;
|
|
int type = CV_MAT_TYPE(mat->type);
|
|
int rows = mat->rows;
|
|
uchar* m = mat->data.ptr;
|
|
int step = mat->step;
|
|
CV_Assert( rows == mat->cols );
|
|
|
|
#define Mf(y, x) ((float*)(m + y*step))[x]
|
|
#define Md(y, x) ((double*)(m + y*step))[x]
|
|
|
|
if( type == CV_32F )
|
|
{
|
|
if( rows == 2 )
|
|
return det2(Mf);
|
|
if( rows == 3 )
|
|
return det3(Mf);
|
|
}
|
|
else if( type == CV_64F )
|
|
{
|
|
if( rows == 2 )
|
|
return det2(Md);
|
|
if( rows == 3 )
|
|
return det3(Md);
|
|
}
|
|
}
|
|
return cv::determinant(cv::cvarrToMat(arr));
|
|
}
|
|
|
|
|
|
CV_IMPL double
|
|
cvInvert( const CvArr* srcarr, CvArr* dstarr, int method )
|
|
{
|
|
cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr);
|
|
|
|
CV_Assert( src.type() == dst.type() && src.rows == dst.cols && src.cols == dst.rows );
|
|
return cv::invert( src, dst, method == CV_CHOLESKY ? cv::DECOMP_CHOLESKY :
|
|
method == CV_SVD ? cv::DECOMP_SVD :
|
|
method == CV_SVD_SYM ? cv::DECOMP_EIG : cv::DECOMP_LU );
|
|
}
|
|
|
|
|
|
CV_IMPL int
|
|
cvSolve( const CvArr* Aarr, const CvArr* barr, CvArr* xarr, int method )
|
|
{
|
|
cv::Mat A = cv::cvarrToMat(Aarr), b = cv::cvarrToMat(barr), x = cv::cvarrToMat(xarr);
|
|
|
|
CV_Assert( A.type() == x.type() && A.cols == x.rows && x.cols == b.cols );
|
|
bool is_normal = (method & CV_NORMAL) != 0;
|
|
method &= ~CV_NORMAL;
|
|
return cv::solve( A, b, x, (method == CV_CHOLESKY ? cv::DECOMP_CHOLESKY :
|
|
method == CV_SVD ? cv::DECOMP_SVD :
|
|
method == CV_SVD_SYM ? cv::DECOMP_EIG :
|
|
A.rows > A.cols ? cv::DECOMP_QR : cv::DECOMP_LU) + (is_normal ? cv::DECOMP_NORMAL : 0) );
|
|
}
|
|
|
|
|
|
CV_IMPL void
|
|
cvEigenVV( CvArr* srcarr, CvArr* evectsarr, CvArr* evalsarr, double,
|
|
int, int )
|
|
{
|
|
cv::Mat src = cv::cvarrToMat(srcarr), evals0 = cv::cvarrToMat(evalsarr), evals = evals0;
|
|
if( evectsarr )
|
|
{
|
|
cv::Mat evects0 = cv::cvarrToMat(evectsarr), evects = evects0;
|
|
eigen(src, evals, evects);
|
|
if( evects0.data != evects.data )
|
|
{
|
|
const uchar* p = evects0.ptr();
|
|
evects.convertTo(evects0, evects0.type());
|
|
CV_Assert( p == evects0.ptr() );
|
|
}
|
|
}
|
|
else
|
|
eigen(src, evals);
|
|
if( evals0.data != evals.data )
|
|
{
|
|
const uchar* p = evals0.ptr();
|
|
if( evals0.size() == evals.size() )
|
|
evals.convertTo(evals0, evals0.type());
|
|
else if( evals0.type() == evals.type() )
|
|
cv::transpose(evals, evals0);
|
|
else
|
|
cv::Mat(evals.t()).convertTo(evals0, evals0.type());
|
|
CV_Assert( p == evals0.ptr() );
|
|
}
|
|
}
|
|
|
|
|
|
CV_IMPL void
|
|
cvSVD( CvArr* aarr, CvArr* warr, CvArr* uarr, CvArr* varr, int flags )
|
|
{
|
|
cv::Mat a = cv::cvarrToMat(aarr), w = cv::cvarrToMat(warr), u, v;
|
|
int m = a.rows, n = a.cols, type = a.type(), mn = std::max(m, n), nm = std::min(m, n);
|
|
|
|
CV_Assert( w.type() == type &&
|
|
(w.size() == cv::Size(nm,1) || w.size() == cv::Size(1, nm) ||
|
|
w.size() == cv::Size(nm, nm) || w.size() == cv::Size(n, m)) );
|
|
|
|
cv::SVD svd;
|
|
|
|
if( w.size() == cv::Size(nm, 1) )
|
|
svd.w = cv::Mat(nm, 1, type, w.ptr() );
|
|
else if( w.isContinuous() )
|
|
svd.w = w;
|
|
|
|
if( uarr )
|
|
{
|
|
u = cv::cvarrToMat(uarr);
|
|
CV_Assert( u.type() == type );
|
|
svd.u = u;
|
|
}
|
|
|
|
if( varr )
|
|
{
|
|
v = cv::cvarrToMat(varr);
|
|
CV_Assert( v.type() == type );
|
|
svd.vt = v;
|
|
}
|
|
|
|
svd(a, ((flags & CV_SVD_MODIFY_A) ? cv::SVD::MODIFY_A : 0) |
|
|
((!svd.u.data && !svd.vt.data) ? cv::SVD::NO_UV : 0) |
|
|
((m != n && (svd.u.size() == cv::Size(mn, mn) ||
|
|
svd.vt.size() == cv::Size(mn, mn))) ? cv::SVD::FULL_UV : 0));
|
|
|
|
if( !u.empty() )
|
|
{
|
|
if( flags & CV_SVD_U_T )
|
|
cv::transpose( svd.u, u );
|
|
else if( u.data != svd.u.data )
|
|
{
|
|
CV_Assert( u.size() == svd.u.size() );
|
|
svd.u.copyTo(u);
|
|
}
|
|
}
|
|
|
|
if( !v.empty() )
|
|
{
|
|
if( !(flags & CV_SVD_V_T) )
|
|
cv::transpose( svd.vt, v );
|
|
else if( v.data != svd.vt.data )
|
|
{
|
|
CV_Assert( v.size() == svd.vt.size() );
|
|
svd.vt.copyTo(v);
|
|
}
|
|
}
|
|
|
|
if( w.data != svd.w.data )
|
|
{
|
|
if( w.size() == svd.w.size() )
|
|
svd.w.copyTo(w);
|
|
else
|
|
{
|
|
w = cv::Scalar(0);
|
|
cv::Mat wd = w.diag();
|
|
svd.w.copyTo(wd);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
CV_IMPL void
|
|
cvSVBkSb( const CvArr* warr, const CvArr* uarr,
|
|
const CvArr* varr, const CvArr* rhsarr,
|
|
CvArr* dstarr, int flags )
|
|
{
|
|
cv::Mat w = cv::cvarrToMat(warr), u = cv::cvarrToMat(uarr),
|
|
v = cv::cvarrToMat(varr), rhs,
|
|
dst = cv::cvarrToMat(dstarr), dst0 = dst;
|
|
if( flags & CV_SVD_U_T )
|
|
{
|
|
cv::Mat tmp;
|
|
transpose(u, tmp);
|
|
u = tmp;
|
|
}
|
|
if( !(flags & CV_SVD_V_T) )
|
|
{
|
|
cv::Mat tmp;
|
|
transpose(v, tmp);
|
|
v = tmp;
|
|
}
|
|
if( rhsarr )
|
|
rhs = cv::cvarrToMat(rhsarr);
|
|
|
|
cv::SVD::backSubst(w, u, v, rhs, dst);
|
|
CV_Assert( dst.data == dst0.data );
|
|
}
|