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1835 lines (1593 loc) · 55.2 KB
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/*M///////////////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
// By downloading, copying, installing or using the software you agree to this license.
// If you do not agree to this license, do not download, install,
// copy or use the software.
//
//
// License Agreement
// For Open Source Computer Vision Library
//
// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * The name of the copyright holders may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
// the use of this software, even if advised of the possibility of such damage.
//
//M*/
#include "precomp.hpp"
#if defined _M_IX86 && defined _MSC_VER && _MSC_VER < 1700
#pragma float_control(precise, on)
#endif
namespace cv
{
/****************************************************************************************\
* LU & Cholesky implementation for small matrices *
\****************************************************************************************/
template<typename _Tp> static inline int
LUImpl(_Tp* A, size_t astep, int m, _Tp* b, size_t bstep, int n)
{
int i, j, k, p = 1;
astep /= sizeof(A[0]);
bstep /= sizeof(b[0]);
for( i = 0; i < m; i++ )
{
k = i;
for( j = i+1; j < m; j++ )
if( std::abs(A[j*astep + i]) > std::abs(A[k*astep + i]) )
k = j;
if( std::abs(A[k*astep + i]) < std::numeric_limits<_Tp>::epsilon() )
return 0;
if( k != i )
{
for( j = i; j < m; j++ )
std::swap(A[i*astep + j], A[k*astep + j]);
if( b )
for( j = 0; j < n; j++ )
std::swap(b[i*bstep + j], b[k*bstep + j]);
p = -p;
}
_Tp d = -1/A[i*astep + i];
for( j = i+1; j < m; j++ )
{
_Tp alpha = A[j*astep + i]*d;
for( k = i+1; k < m; k++ )
A[j*astep + k] += alpha*A[i*astep + k];
if( b )
for( k = 0; k < n; k++ )
b[j*bstep + k] += alpha*b[i*bstep + k];
}
A[i*astep + i] = -d;
}
if( b )
{
for( i = m-1; i >= 0; i-- )
for( j = 0; j < n; j++ )
{
_Tp s = b[i*bstep + j];
for( k = i+1; k < m; k++ )
s -= A[i*astep + k]*b[k*bstep + j];
b[i*bstep + j] = s*A[i*astep + i];
}
}
return p;
}
int LU(float* A, size_t astep, int m, float* b, size_t bstep, int n)
{
return LUImpl(A, astep, m, b, bstep, n);
}
int LU(double* A, size_t astep, int m, double* b, size_t bstep, int n)
{
return LUImpl(A, astep, m, b, bstep, n);
}
template<typename _Tp> static inline bool
CholImpl(_Tp* A, size_t astep, int m, _Tp* b, size_t bstep, int n)
{
_Tp* L = A;
int i, j, k;
double s;
astep /= sizeof(A[0]);
bstep /= sizeof(b[0]);
for( i = 0; i < m; i++ )
{
for( j = 0; j < i; j++ )
{
s = A[i*astep + j];
for( k = 0; k < j; k++ )
s -= L[i*astep + k]*L[j*astep + k];
L[i*astep + j] = (_Tp)(s*L[j*astep + j]);
}
s = A[i*astep + i];
for( k = 0; k < j; k++ )
{
double t = L[i*astep + k];
s -= t*t;
}
if( s < std::numeric_limits<_Tp>::epsilon() )
return false;
L[i*astep + i] = (_Tp)(1./std::sqrt(s));
}
if( !b )
return true;
// LLt x = b
// 1: L y = b
// 2. Lt x = y
/*
[ L00 ] y0 b0
[ L10 L11 ] y1 = b1
[ L20 L21 L22 ] y2 b2
[ L30 L31 L32 L33 ] y3 b3
[ L00 L10 L20 L30 ] x0 y0
[ L11 L21 L31 ] x1 = y1
[ L22 L32 ] x2 y2
[ L33 ] x3 y3
*/
for( i = 0; i < m; i++ )
{
for( j = 0; j < n; j++ )
{
s = b[i*bstep + j];
for( k = 0; k < i; k++ )
s -= L[i*astep + k]*b[k*bstep + j];
b[i*bstep + j] = (_Tp)(s*L[i*astep + i]);
}
}
for( i = m-1; i >= 0; i-- )
{
for( j = 0; j < n; j++ )
{
s = b[i*bstep + j];
for( k = m-1; k > i; k-- )
s -= L[k*astep + i]*b[k*bstep + j];
b[i*bstep + j] = (_Tp)(s*L[i*astep + i]);
}
}
return true;
}
bool Cholesky(float* A, size_t astep, int m, float* b, size_t bstep, int n)
{
return CholImpl(A, astep, m, b, bstep, n);
}
bool Cholesky(double* A, size_t astep, int m, double* b, size_t bstep, int n)
{
return CholImpl(A, astep, m, b, bstep, n);
}
template<typename _Tp> static inline _Tp hypot(_Tp a, _Tp b)
{
a = std::abs(a);
b = std::abs(b);
if( a > b )
{
b /= a;
return a*std::sqrt(1 + b*b);
}
if( b > 0 )
{
a /= b;
return b*std::sqrt(1 + a*a);
}
return 0;
}
template<typename _Tp> bool
JacobiImpl_( _Tp* A, size_t astep, _Tp* W, _Tp* V, size_t vstep, int n, uchar* buf )
{
const _Tp eps = std::numeric_limits<_Tp>::epsilon();
int i, j, k, m;
astep /= sizeof(A[0]);
if( V )
{
vstep /= sizeof(V[0]);
for( i = 0; i < n; i++ )
{
for( j = 0; j < n; j++ )
V[i*vstep + j] = (_Tp)0;
V[i*vstep + i] = (_Tp)1;
}
}
int iters, maxIters = n*n*30;
int* indR = (int*)alignPtr(buf, sizeof(int));
int* indC = indR + n;
_Tp mv = (_Tp)0;
for( k = 0; k < n; k++ )
{
W[k] = A[(astep + 1)*k];
if( k < n - 1 )
{
for( m = k+1, mv = std::abs(A[astep*k + m]), i = k+2; i < n; i++ )
{
_Tp val = std::abs(A[astep*k+i]);
if( mv < val )
mv = val, m = i;
}
indR[k] = m;
}
if( k > 0 )
{
for( m = 0, mv = std::abs(A[k]), i = 1; i < k; i++ )
{
_Tp val = std::abs(A[astep*i+k]);
if( mv < val )
mv = val, m = i;
}
indC[k] = m;
}
}
if( n > 1 ) for( iters = 0; iters < maxIters; iters++ )
{
// find index (k,l) of pivot p
for( k = 0, mv = std::abs(A[indR[0]]), i = 1; i < n-1; i++ )
{
_Tp val = std::abs(A[astep*i + indR[i]]);
if( mv < val )
mv = val, k = i;
}
int l = indR[k];
for( i = 1; i < n; i++ )
{
_Tp val = std::abs(A[astep*indC[i] + i]);
if( mv < val )
mv = val, k = indC[i], l = i;
}
_Tp p = A[astep*k + l];
if( std::abs(p) <= eps )
break;
_Tp y = (_Tp)((W[l] - W[k])*0.5);
_Tp t = std::abs(y) + hypot(p, y);
_Tp s = hypot(p, t);
_Tp c = t/s;
s = p/s; t = (p/t)*p;
if( y < 0 )
s = -s, t = -t;
A[astep*k + l] = 0;
W[k] -= t;
W[l] += t;
_Tp a0, b0;
#undef rotate
#define rotate(v0, v1) a0 = v0, b0 = v1, v0 = a0*c - b0*s, v1 = a0*s + b0*c
// rotate rows and columns k and l
for( i = 0; i < k; i++ )
rotate(A[astep*i+k], A[astep*i+l]);
for( i = k+1; i < l; i++ )
rotate(A[astep*k+i], A[astep*i+l]);
for( i = l+1; i < n; i++ )
rotate(A[astep*k+i], A[astep*l+i]);
// rotate eigenvectors
if( V )
for( i = 0; i < n; i++ )
rotate(V[vstep*k+i], V[vstep*l+i]);
#undef rotate
for( j = 0; j < 2; j++ )
{
int idx = j == 0 ? k : l;
if( idx < n - 1 )
{
for( m = idx+1, mv = std::abs(A[astep*idx + m]), i = idx+2; i < n; i++ )
{
_Tp val = std::abs(A[astep*idx+i]);
if( mv < val )
mv = val, m = i;
}
indR[idx] = m;
}
if( idx > 0 )
{
for( m = 0, mv = std::abs(A[idx]), i = 1; i < idx; i++ )
{
_Tp val = std::abs(A[astep*i+idx]);
if( mv < val )
mv = val, m = i;
}
indC[idx] = m;
}
}
}
// sort eigenvalues & eigenvectors
for( k = 0; k < n-1; k++ )
{
m = k;
for( i = k+1; i < n; i++ )
{
if( W[m] < W[i] )
m = i;
}
if( k != m )
{
std::swap(W[m], W[k]);
if( V )
for( i = 0; i < n; i++ )
std::swap(V[vstep*m + i], V[vstep*k + i]);
}
}
return true;
}
static bool Jacobi( float* S, size_t sstep, float* e, float* E, size_t estep, int n, uchar* buf )
{
return JacobiImpl_(S, sstep, e, E, estep, n, buf);
}
static bool Jacobi( double* S, size_t sstep, double* e, double* E, size_t estep, int n, uchar* buf )
{
return JacobiImpl_(S, sstep, e, E, estep, n, buf);
}
template<typename T> struct VBLAS
{
int dot(const T*, const T*, int, T*) const { return 0; }
int givens(T*, T*, int, T, T) const { return 0; }
int givensx(T*, T*, int, T, T, T*, T*) const { return 0; }
};
#if CV_SSE2
template<> inline int VBLAS<float>::dot(const float* a, const float* b, int n, float* result) const
{
if( n < 8 )
return 0;
int k = 0;
__m128 s0 = _mm_setzero_ps(), s1 = _mm_setzero_ps();
for( ; k <= n - 8; k += 8 )
{
__m128 a0 = _mm_load_ps(a + k), a1 = _mm_load_ps(a + k + 4);
__m128 b0 = _mm_load_ps(b + k), b1 = _mm_load_ps(b + k + 4);
s0 = _mm_add_ps(s0, _mm_mul_ps(a0, b0));
s1 = _mm_add_ps(s1, _mm_mul_ps(a1, b1));
}
s0 = _mm_add_ps(s0, s1);
float sbuf[4];
_mm_storeu_ps(sbuf, s0);
*result = sbuf[0] + sbuf[1] + sbuf[2] + sbuf[3];
return k;
}
template<> inline int VBLAS<float>::givens(float* a, float* b, int n, float c, float s) const
{
if( n < 4 )
return 0;
int k = 0;
__m128 c4 = _mm_set1_ps(c), s4 = _mm_set1_ps(s);
for( ; k <= n - 4; k += 4 )
{
__m128 a0 = _mm_load_ps(a + k);
__m128 b0 = _mm_load_ps(b + k);
__m128 t0 = _mm_add_ps(_mm_mul_ps(a0, c4), _mm_mul_ps(b0, s4));
__m128 t1 = _mm_sub_ps(_mm_mul_ps(b0, c4), _mm_mul_ps(a0, s4));
_mm_store_ps(a + k, t0);
_mm_store_ps(b + k, t1);
}
return k;
}
template<> inline int VBLAS<float>::givensx(float* a, float* b, int n, float c, float s,
float* anorm, float* bnorm) const
{
if( n < 4 )
return 0;
int k = 0;
__m128 c4 = _mm_set1_ps(c), s4 = _mm_set1_ps(s);
__m128 sa = _mm_setzero_ps(), sb = _mm_setzero_ps();
for( ; k <= n - 4; k += 4 )
{
__m128 a0 = _mm_load_ps(a + k);
__m128 b0 = _mm_load_ps(b + k);
__m128 t0 = _mm_add_ps(_mm_mul_ps(a0, c4), _mm_mul_ps(b0, s4));
__m128 t1 = _mm_sub_ps(_mm_mul_ps(b0, c4), _mm_mul_ps(a0, s4));
_mm_store_ps(a + k, t0);
_mm_store_ps(b + k, t1);
sa = _mm_add_ps(sa, _mm_mul_ps(t0, t0));
sb = _mm_add_ps(sb, _mm_mul_ps(t1, t1));
}
float abuf[4], bbuf[4];
_mm_storeu_ps(abuf, sa);
_mm_storeu_ps(bbuf, sb);
*anorm = abuf[0] + abuf[1] + abuf[2] + abuf[3];
*bnorm = bbuf[0] + bbuf[1] + bbuf[2] + bbuf[3];
return k;
}
template<> inline int VBLAS<double>::dot(const double* a, const double* b, int n, double* result) const
{
if( n < 4 )
return 0;
int k = 0;
__m128d s0 = _mm_setzero_pd(), s1 = _mm_setzero_pd();
for( ; k <= n - 4; k += 4 )
{
__m128d a0 = _mm_load_pd(a + k), a1 = _mm_load_pd(a + k + 2);
__m128d b0 = _mm_load_pd(b + k), b1 = _mm_load_pd(b + k + 2);
s0 = _mm_add_pd(s0, _mm_mul_pd(a0, b0));
s1 = _mm_add_pd(s1, _mm_mul_pd(a1, b1));
}
s0 = _mm_add_pd(s0, s1);
double sbuf[2];
_mm_storeu_pd(sbuf, s0);
*result = sbuf[0] + sbuf[1];
return k;
}
template<> inline int VBLAS<double>::givens(double* a, double* b, int n, double c, double s) const
{
int k = 0;
__m128d c2 = _mm_set1_pd(c), s2 = _mm_set1_pd(s);
for( ; k <= n - 2; k += 2 )
{
__m128d a0 = _mm_load_pd(a + k);
__m128d b0 = _mm_load_pd(b + k);
__m128d t0 = _mm_add_pd(_mm_mul_pd(a0, c2), _mm_mul_pd(b0, s2));
__m128d t1 = _mm_sub_pd(_mm_mul_pd(b0, c2), _mm_mul_pd(a0, s2));
_mm_store_pd(a + k, t0);
_mm_store_pd(b + k, t1);
}
return k;
}
template<> inline int VBLAS<double>::givensx(double* a, double* b, int n, double c, double s,
double* anorm, double* bnorm) const
{
int k = 0;
__m128d c2 = _mm_set1_pd(c), s2 = _mm_set1_pd(s);
__m128d sa = _mm_setzero_pd(), sb = _mm_setzero_pd();
for( ; k <= n - 2; k += 2 )
{
__m128d a0 = _mm_load_pd(a + k);
__m128d b0 = _mm_load_pd(b + k);
__m128d t0 = _mm_add_pd(_mm_mul_pd(a0, c2), _mm_mul_pd(b0, s2));
__m128d t1 = _mm_sub_pd(_mm_mul_pd(b0, c2), _mm_mul_pd(a0, s2));
_mm_store_pd(a + k, t0);
_mm_store_pd(b + k, t1);
sa = _mm_add_pd(sa, _mm_mul_pd(t0, t0));
sb = _mm_add_pd(sb, _mm_mul_pd(t1, t1));
}
double abuf[2], bbuf[2];
_mm_storeu_pd(abuf, sa);
_mm_storeu_pd(bbuf, sb);
*anorm = abuf[0] + abuf[1];
*bnorm = bbuf[0] + bbuf[1];
return k;
}
#endif
template<typename _Tp> void
JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* _W, _Tp* Vt, size_t vstep,
int m, int n, int n1, double minval, _Tp eps)
{
VBLAS<_Tp> vblas;
AutoBuffer<double> Wbuf(n);
double* W = Wbuf;
int i, j, k, iter, max_iter = std::max(m, 30);
_Tp c, s;
double sd;
astep /= sizeof(At[0]);
vstep /= sizeof(Vt[0]);
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] = sd;
if( Vt )
{
for( k = 0; k < n; k++ )
Vt[i*vstep + k] = 0;
Vt[i*vstep + i] = 1;
}
}
for( iter = 0; iter < max_iter; iter++ )
{
bool changed = false;
for( i = 0; i < n-1; i++ )
for( j = i+1; j < n; j++ )
{
_Tp *Ai = At + i*astep, *Aj = At + j*astep;
double a = W[i], p = 0, b = W[j];
for( k = 0; k < m; k++ )
p += (double)Ai[k]*Aj[k];
if( std::abs(p) <= eps*std::sqrt((double)a*b) )
continue;
p *= 2;
double beta = a - b, gamma = hypot((double)p, beta);
if( beta < 0 )
{
double delta = (gamma - beta)*0.5;
s = (_Tp)std::sqrt(delta/gamma);
c = (_Tp)(p/(gamma*s*2));
}
else
{
c = (_Tp)std::sqrt((gamma + beta)/(gamma*2));
s = (_Tp)(p/(gamma*c*2));
}
a = b = 0;
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;
while( sd <= minval )
{
// 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)(1/sd);
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)
{
JacobiSVDImpl_(At, astep, W, Vt, vstep, m, n, !Vt ? 0 : n1 < 0 ? n : n1, FLT_MIN, FLT_EPSILON*2);
}
static void JacobiSVD(double* At, size_t astep, double* W, double* Vt, size_t vstep, int m, int n, int n1=-1)
{
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, j;
for( i = 0; i < m; i++, x += dx, y += dy )
{
T2 s = a[i*inca];
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 )
{
Mat mat = _mat.getMat();
double result = 0;
int type = mat.type(), rows = mat.rows;
size_t step = mat.step;
const uchar* m = mat.data;
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 = LU((float*)a.data, a.step, rows, 0, 0, 0);
if( result )
{
for( int i = 0; i < rows; i++ )
result *= ((const float*)(a.data + a.step*i))[i];
result = 1./result;
}
}
}
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 = LU((double*)a.data, a.step, rows, 0, 0, 0);
if( result )
{
for( int i = 0; i < rows; i++ )
result *= ((const double*)(a.data + a.step*i))[i];
result = 1./result;
}
}
}
#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 )
{
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.data + m*nm*esz);
Mat vt(nm, n, type, w.data + nm*esz);
SVD::compute(src, w, u, vt);
SVD::backSubst(w, u, vt, Mat(), _dst);
return type == CV_32F ?
(((float*)w.data)[0] >= FLT_EPSILON ?
((float*)w.data)[n-1]/((float*)w.data)[0] : 0) :
(((double*)w.data)[0] >= DBL_EPSILON ?
((double*)w.data)[n-1]/((double*)w.data)[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.data + n*n*esz);
Mat vt(n, n, type, w.data + n*esz);
eigen(src, w, vt);
transpose(vt, u);
SVD::backSubst(w, u, vt, Mat(), _dst);
return type == CV_32F ?
(((float*)w.data)[0] >= FLT_EPSILON ?
((float*)w.data)[n-1]/((float*)w.data)[0] : 0) :
(((double*)w.data)[0] >= DBL_EPSILON ?
((double*)w.data)[n-1]/((double*)w.data)[0] : 0);
}
CV_Assert( method == DECOMP_LU || method == DECOMP_CHOLESKY );
_dst.create( n, n, type );
Mat dst = _dst.getMat();
if( n <= 3 )
{
uchar* srcdata = src.data;
uchar* dstdata = dst.data;
size_t srcstep = src.step;
size_t dststep = dst.step;
if( n == 2 )
{
if( type == CV_32FC1 )
{
double d = det2(Sf);
if( d != 0. )
{