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376 lines
10 KiB
C++
376 lines
10 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) 2009-2011, 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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namespace cv { namespace hal {
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/****************************************************************************************\
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* LU & Cholesky implementation for small matrices *
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\****************************************************************************************/
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template<typename _Tp> static inline int
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LUImpl(_Tp* A, size_t astep, int m, _Tp* b, size_t bstep, int n, _Tp eps)
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{
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int i, j, k, p = 1;
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astep /= sizeof(A[0]);
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bstep /= sizeof(b[0]);
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for( i = 0; i < m; i++ )
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{
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k = i;
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for( j = i+1; j < m; j++ )
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if( std::abs(A[j*astep + i]) > std::abs(A[k*astep + i]) )
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k = j;
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if( std::abs(A[k*astep + i]) < eps )
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return 0;
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if( k != i )
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{
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for( j = i; j < m; j++ )
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std::swap(A[i*astep + j], A[k*astep + j]);
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if( b )
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for( j = 0; j < n; j++ )
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std::swap(b[i*bstep + j], b[k*bstep + j]);
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p = -p;
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}
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_Tp d = -1/A[i*astep + i];
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for( j = i+1; j < m; j++ )
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{
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_Tp alpha = A[j*astep + i]*d;
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for( k = i+1; k < m; k++ )
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A[j*astep + k] += alpha*A[i*astep + k];
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if( b )
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for( k = 0; k < n; k++ )
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b[j*bstep + k] += alpha*b[i*bstep + k];
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}
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}
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if( b )
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{
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for( i = m-1; i >= 0; i-- )
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for( j = 0; j < n; j++ )
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{
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_Tp s = b[i*bstep + j];
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for( k = i+1; k < m; k++ )
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s -= A[i*astep + k]*b[k*bstep + j];
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b[i*bstep + j] = s/A[i*astep + i];
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}
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}
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return p;
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}
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int LU32f(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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int output;
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CALL_HAL_RET(LU32f, cv_hal_LU32f, output, A, astep, m, b, bstep, n)
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output = LUImpl(A, astep, m, b, bstep, n, FLT_EPSILON*10);
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return output;
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}
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int LU64f(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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int output;
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CALL_HAL_RET(LU64f, cv_hal_LU64f, output, A, astep, m, b, bstep, n)
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output = LUImpl(A, astep, m, b, bstep, n, DBL_EPSILON*100);
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return output;
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}
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template<typename _Tp> static inline bool
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CholImpl(_Tp* A, size_t astep, int m, _Tp* b, size_t bstep, int n)
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{
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_Tp* L = A;
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int i, j, k;
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double s;
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astep /= sizeof(A[0]);
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bstep /= sizeof(b[0]);
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for( i = 0; i < m; i++ )
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{
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for( j = 0; j < i; j++ )
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{
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s = A[i*astep + j];
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for( k = 0; k < j; k++ )
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s -= L[i*astep + k]*L[j*astep + k];
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L[i*astep + j] = (_Tp)(s*L[j*astep + j]);
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}
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s = A[i*astep + i];
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for( k = 0; k < j; k++ )
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{
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double t = L[i*astep + k];
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s -= t*t;
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}
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if( s < std::numeric_limits<_Tp>::epsilon() )
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return false;
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L[i*astep + i] = (_Tp)(1./std::sqrt(s));
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}
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if (!b)
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{
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for( i = 0; i < m; i++ )
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L[i*astep + i]=1/L[i*astep + i];
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return true;
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}
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// LLt x = b
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// 1: L y = b
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// 2. Lt x = y
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/*
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[ L00 ] y0 b0
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[ L10 L11 ] y1 = b1
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[ L20 L21 L22 ] y2 b2
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[ L30 L31 L32 L33 ] y3 b3
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[ L00 L10 L20 L30 ] x0 y0
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[ L11 L21 L31 ] x1 = y1
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[ L22 L32 ] x2 y2
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[ L33 ] x3 y3
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*/
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for( i = 0; i < m; i++ )
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{
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for( j = 0; j < n; j++ )
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{
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s = b[i*bstep + j];
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for( k = 0; k < i; k++ )
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s -= L[i*astep + k]*b[k*bstep + j];
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b[i*bstep + j] = (_Tp)(s*L[i*astep + i]);
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}
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}
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for( i = m-1; i >= 0; i-- )
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{
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for( j = 0; j < n; j++ )
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{
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s = b[i*bstep + j];
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for( k = m-1; k > i; k-- )
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s -= L[k*astep + i]*b[k*bstep + j];
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b[i*bstep + j] = (_Tp)(s*L[i*astep + i]);
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}
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}
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for( i = 0; i < m; i++ )
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L[i*astep + i]=1/L[i*astep + i];
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return true;
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}
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bool Cholesky32f(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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bool output;
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CALL_HAL_RET(Cholesky32f, cv_hal_Cholesky32f, output, A, astep, m, b, bstep, n)
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return CholImpl(A, astep, m, b, bstep, n);
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}
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bool Cholesky64f(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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bool output;
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CALL_HAL_RET(Cholesky64f, cv_hal_Cholesky64f, output, A, astep, m, b, bstep, n)
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return CholImpl(A, astep, m, b, bstep, n);
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}
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template<typename _Tp> inline static int
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sign(_Tp x)
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{
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if (x >= (_Tp)0)
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return 1;
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else
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return -1;
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}
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template<typename _Tp> static inline int
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QRImpl(_Tp* A, size_t astep, int m, int n, int k, _Tp* b, size_t bstep, _Tp* hFactors, _Tp eps)
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{
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astep /= sizeof(_Tp);
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bstep /= sizeof(_Tp);
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cv::AutoBuffer<_Tp> buffer;
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size_t buf_size = m ? m + n : hFactors != NULL;
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buffer.allocate(buf_size);
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_Tp* vl = buffer;
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if (hFactors == NULL)
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hFactors = vl + m;
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for (int l = 0; l < n; l++)
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{
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//generate vl
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int vlSize = m - l;
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_Tp vlNorm = (_Tp)0;
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for (int i = 0; i < vlSize; i++)
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{
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vl[i] = A[(l + i)*astep + l];
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vlNorm += vl[i] * vl[i];
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}
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_Tp tmpV = vl[0];
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vl[0] = vl[0] + sign(vl[0])*std::sqrt(vlNorm);
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vlNorm = std::sqrt(vlNorm + vl[0] * vl[0] - tmpV*tmpV);
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for (int i = 0; i < vlSize; i++)
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{
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vl[i] /= vlNorm;
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}
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//multiply A_l*vl
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for (int j = l; j < n; j++)
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{
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_Tp v_lA = (_Tp)0;
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for (int i = l; i < m; i++)
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{
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v_lA += vl[i - l] * A[i*astep + j];
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}
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for (int i = l; i < m; i++)
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{
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A[i*astep + j] -= 2 * vl[i - l] * v_lA;
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}
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}
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//save vl and factors
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hFactors[l] = vl[0] * vl[0];
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for (int i = 1; i < vlSize; i++)
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{
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A[(l + i)*astep + l] = vl[i] / vl[0];
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}
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}
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if (b)
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{
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//generate new rhs
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for (int l = 0; l < n; l++)
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{
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//unpack vl
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vl[0] = (_Tp)1;
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for (int j = 1; j < m - l; j++)
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{
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vl[j] = A[(j + l)*astep + l];
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}
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//h_l*x
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for (int j = 0; j < k; j++)
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{
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_Tp v_lB = (_Tp)0;
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for (int i = l; i < m; i++)
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v_lB += vl[i - l] * b[i*bstep + j];
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for (int i = l; i < m; i++)
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b[i*bstep + j] -= 2 * vl[i - l] * v_lB * hFactors[l];
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}
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}
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//do back substitution
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for (int i = n - 1; i >= 0; i--)
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{
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for (int j = n - 1; j > i; j--)
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{
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for (int p = 0; p < k; p++)
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b[i*bstep + p] -= b[j*bstep + p] * A[i*astep + j];
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}
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if (std::abs(A[i*astep + i]) < eps)
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return 0;
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for (int p = 0; p < k; p++)
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b[i*bstep + p] /= A[i*astep + i];
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}
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}
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return 1;
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}
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int QR32f(float* A, size_t astep, int m, int n, int k, float* b, size_t bstep, float* hFactors)
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{
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CV_INSTRUMENT_REGION()
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int output;
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CALL_HAL_RET(QR32f, cv_hal_QR32f, output, A, astep, m, n, k, b, bstep, hFactors);
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output = QRImpl(A, astep, m, n, k, b, bstep, hFactors, FLT_EPSILON * 10);
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return output;
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}
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int QR64f(double* A, size_t astep, int m, int n, int k, double* b, size_t bstep, double* hFactors)
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{
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CV_INSTRUMENT_REGION()
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int output;
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CALL_HAL_RET(QR64f, cv_hal_QR64f, output, A, astep, m, n, k, b, bstep, hFactors)
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output = QRImpl(A, astep, m, n, k, b, bstep, hFactors, DBL_EPSILON * 100);
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return output;
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}
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//=============================================================================
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// for compatibility with 3.0
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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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return LUImpl(A, astep, m, b, bstep, n, FLT_EPSILON*10);
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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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return LUImpl(A, astep, m, b, bstep, n, DBL_EPSILON*100);
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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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return CholImpl(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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return CholImpl(A, astep, m, b, bstep, n);
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}
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}}
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