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#include "precomp.hpp"
#ifdef HAVE_VECLIB
#include <vecLib/clapack.h>
typedef __CLPK_integer integer;
typedef __CLPK_real real;
#else
#include "clapack.h"
#endif
#undef abs
#undef max
#undef min
namespace cv
{
/****************************************************************************************\
* LU & Cholesky implementation for small matrices *
\****************************************************************************************/
template<typename _Tp> static inline int LUImpl(_Tp* A, int m, _Tp* b, int n)
{
int i, j, k, p = 1;
for( i = 0; i < m; i++ )
{
k = i;
for( j = i+1; j < m; j++ )
if( std::abs(A[j*m + i]) > std::abs(A[k*m + i]) )
k = j;
if( std::abs(A[k*m + i]) < std::numeric_limits<_Tp>::epsilon() )
return 0;
if( k != i )
{
for( j = i; j < m; j++ )
std::swap(A[i*m + j], A[k*m + j]);
if( b )
for( j = 0; j < n; j++ )
std::swap(b[i*n + j], b[k*n + j]);
p = -p;
}
_Tp d = -1/A[i*m + i];
for( j = i+1; j < m; j++ )
{
_Tp alpha = A[j*m + i]*d;
for( k = i+1; k < m; k++ )
A[j*m + k] += alpha*A[i*m + k];
if( b )
for( k = 0; k < n; k++ )
b[j*n + k] += alpha*b[i*n + k];
}
A[i*m + i] = -d;
}
if( b )
{
for( i = m-1; i >= 0; i-- )
for( j = 0; j < n; j++ )
{
_Tp s = b[i*n + j];
for( k = i+1; k < m; k++ )
s -= A[i*m + k]*b[k*n + j];
b[i*n + j] = s*A[i*m + i];
}
}
return p;
}
int LU(float* A, int m, float* b, int n)
{
return LUImpl(A, m, b, n);
}
int LU(double* A, int m, double* b, int n)
{
return LUImpl(A, m, b, n);
}
template<typename _Tp> static inline bool CholImpl(_Tp* A, int m, _Tp* b, int n)
{
_Tp* L = A;
int i, j, k;
double s;
for( i = 0; i < m; i++ )
{
for( j = 0; j < i; j++ )
{
s = A[i*m + j];
for( k = 0; k < j; k++ )
s -= L[i*m + k]*L[j*m + k];
L[i*m + j] = (_Tp)(s*L[j*m + j]);
}
s = A[i*m + i];
for( k = 0; k < j; k++ )
{
double t = L[i*m + k];
s -= t*t;
}
if( s < std::numeric_limits<_Tp>::epsilon() )
return 0;
L[i*m + i] = (_Tp)(1./std::sqrt(s));
}
if( !b )
return false;
// 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*n + j];
for( k = 0; k < i; k++ )
s -= L[i*m + k]*b[k*n + j];
b[i*n + j] = (_Tp)(s*L[i*m + i]);
}
}
for( i = m-1; i >= 0; i-- )
{
for( j = 0; j < n; j++ )
{
s = b[i*n + j];
for( k = m-1; k > i; k-- )
s -= L[k*m + i]*b[k*n + j];
b[i*n + j] = (_Tp)(s*L[i*m + i]);
}
}
return true;
}
bool Cholesky(float* A, int m, float* b, int n)
{
return CholImpl(A, m, b, n);
}
bool Cholesky(double* A, int m, double* b, int n)
{
return CholImpl(A, m, b, n);
}
/****************************************************************************************\
* Determinant of the matrix *
\****************************************************************************************/
#define det2(m) (m(0,0)*m(1,1) - m(0,1)*m(1,0))
#define det3(m) (m(0,0)*(m(1,1)*m(2,2) - m(1,2)*m(2,1)) - \
m(0,1)*(m(1,0)*m(2,2) - m(1,2)*m(2,0)) + \
m(0,2)*(m(1,0)*m(2,1) - m(1,1)*m(2,0)))
double determinant( const Mat& mat )
{
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( rows <= 10 )
{
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, rows, 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, rows, 0, 0);
if( result )
{
for( int i = 0; i < rows; i++ )
result *= ((const double*)(a.data + a.step*i))[i];
result = 1./result;
}
}
}
}
else
{
integer i, n = rows, *ipiv, info=0, sign = 0;
size_t bufSize = n*n*sizeof(double) + (n+1)*sizeof(ipiv[0]);
AutoBuffer<uchar> buffer(bufSize);
Mat a(n, n, CV_64F, (uchar*)buffer);
mat.convertTo(a, CV_64F);
ipiv = (integer*)cvAlignPtr(a.data + a.step*a.rows, sizeof(integer));
dgetrf_(&n, &n, (double*)a.data, &n, ipiv, &info);
assert(info >= 0);
if( info == 0 )
{
result = 1;
for( i = 0; i < n; i++ )
{
result *= ((double*)a.data)[i*(n+1)];
sign ^= ipiv[i] != i+1;
}
result *= sign ? -1 : 1;
}
}
#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 invert( const Mat& src, Mat& dst, int method )
{
double result = 0;
int type = src.type();
CV_Assert( method == DECOMP_LU || method == DECOMP_CHOLESKY || method == DECOMP_SVD );
if( method == DECOMP_SVD )
{
int n = std::min(src.rows, src.cols);
SVD svd(src);
svd.backSubst(Mat(), dst);
return type == CV_32F ?
(((float*)svd.w.data)[0] >= FLT_EPSILON ?
((float*)svd.w.data)[n-1]/((float*)svd.w.data)[0] : 0) :
(((double*)svd.w.data)[0] >= DBL_EPSILON ?
((double*)svd.w.data)[n-1]/((double*)svd.w.data)[0] : 0);
}
CV_Assert( src.rows == src.cols && (type == CV_32F || type == CV_64F));
dst.create( src.rows, src.cols, type );
if( src.rows <= 3 )
{
uchar* srcdata = src.data;
uchar* dstdata = dst.data;
size_t srcstep = src.step;
size_t dststep = dst.step;
if( src.rows == 2 )
{
if( type == CV_32FC1 )
{
double d = det2(Sf);
if( d != 0. )
{
double t0, t1;
result = d;
d = 1./d;
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. )
{
double t0, t1;
result = d;
d = 1./d;
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( src.rows == 3 )
{
if( type == CV_32FC1 )
{
double d = det3(Sf);
if( d != 0. )
{
float t[9];
result = d;
d = 1./d;
t[0] = (float)((Sf(1,1) * Sf(2,2) - Sf(1,2) * Sf(2,1)) * d);
t[1] = (float)((Sf(0,2) * Sf(2,1) - Sf(0,1) * Sf(2,2)) * d);
t[2] = (float)((Sf(0,1) * Sf(1,2) - Sf(0,2) * Sf(1,1)) * d);
t[3] = (float)((Sf(1,2) * Sf(2,0) - Sf(1,0) * Sf(2,2)) * d);
t[4] = (float)((Sf(0,0) * Sf(2,2) - Sf(0,2) * Sf(2,0)) * d);
t[5] = (float)((Sf(0,2) * Sf(1,0) - Sf(0,0) * Sf(1,2)) * d);
t[6] = (float)((Sf(1,0) * Sf(2,1) - Sf(1,1) * Sf(2,0)) * d);
t[7] = (float)((Sf(0,1) * Sf(2,0) - Sf(0,0) * Sf(2,1)) * d);
t[8] = (float)((Sf(0,0) * Sf(1,1) - Sf(0,1) * Sf(1,0)) * d);
Df(0,0) = t[0]; Df(0,1) = t[1]; Df(0,2) = t[2];
Df(1,0) = t[3]; Df(1,1) = t[4]; Df(1,2) = t[5];
Df(2,0) = t[6]; Df(2,1) = t[7]; Df(2,2) = t[8];
}
}
else
{
double d = det3(Sd);
if( d != 0. )
{
double t[9];
result = d;
d = 1./d;
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( src.rows == 1 );
if( type == CV_32FC1 )
{
double d = Sf(0,0);
if( d != 0. )
{
result = d;
Df(0,0) = (float)(1./d);
}
}
else
{
double d = Sd(0,0);
if( d != 0. )
{
result = d;
Dd(0,0) = 1./d;
}
}
}
return result;
}
if( dst.cols <= 10 )
{
int n = dst.cols, elem_size = CV_ELEM_SIZE(type);
AutoBuffer<uchar> buf(n*n*2*elem_size);
Mat src1(n, n, type, (uchar*)buf);
Mat dst1(n, n, type, dst.isContinuous() ? dst.data : src1.data + n*n*elem_size);
src.copyTo(src1);
setIdentity(dst1);
if( method == DECOMP_LU && type == CV_32F )
result = LU((float*)src1.data, n, (float*)dst1.data, n);
else if( method == DECOMP_LU && type == CV_64F )
result = LU((double*)src1.data, n, (double*)dst1.data, n);
else if( method == DECOMP_CHOLESKY && type == CV_32F )
result = Cholesky((float*)src1.data, n, (float*)dst1.data, n);
else
result = Cholesky((double*)src1.data, n, (double*)dst1.data, n);
dst1.copyTo(dst);
result = std::abs(result);
}
else
{
integer n = dst.cols, lwork=-1, lda = n, piv1=0, info=0;
int t_size = type == CV_32F ? n*n*sizeof(double) : 0;
int buf_size = t_size;
AutoBuffer<uchar> buf;
if( method == DECOMP_LU )
{
double work1 = 0;
dgetri_(&n, (double*)dst.data, &lda, &piv1, &work1, &lwork, &info);
lwork = cvRound(work1);
buf_size += (int)(n*sizeof(integer) + (lwork + 1)*sizeof(double));
buf.allocate(buf_size);
uchar* buffer = (uchar*)buf;
Mat arr = dst;
if( type == CV_32F )
{
arr = Mat(n, n, CV_64F, buffer);
src.convertTo(arr, CV_64F);
buffer += t_size;
}
else
{
src.copyTo(arr);
lda = (integer)(arr.step/sizeof(double));
}
dgetrf_(&n, &n, (double*)arr.data, &lda, (integer*)buffer, &info);
if(info==0)
dgetri_(&n, (double*)arr.data, &lda, (integer*)buffer,
(double*)cvAlignPtr(buffer + n*sizeof(integer), sizeof(double)),
&lwork, &info);
if(info==0 && arr.data != dst.data)
arr.convertTo(dst, dst.type());
}
else if( method == DECOMP_CHOLESKY )
{
Mat arr = dst;
if( type == CV_32F )
{
buf.allocate(buf_size);
arr = Mat(n, n, CV_64F, (uchar*)buf);
src.convertTo(arr, CV_64F);
}
else
{
src.copyTo(arr);
lda = (integer)(arr.step/sizeof(double));
}
char L[] = {'L', '\0'};
dpotrf_(L, &n, (double*)arr.data, &lda, &info);
if(info==0)
dpotri_(L, &n, (double*)arr.data, &lda, &info);
if(info==0)
{
completeSymm(arr);
if( arr.data != dst.data )
arr.convertTo(dst, dst.type());
}
}
result = info == 0;
}
if( !result )
dst = Scalar(0);
return result;
}
/****************************************************************************************\
* Solving a linear system *
\****************************************************************************************/
bool solve( const Mat& src, const Mat& _src2, Mat& dst, int method )
{
bool result = true;
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) &&
src.rows <= 3 && src.rows == src.cols && _src2.cols == 1 )
{
dst.create( src.cols, _src2.cols, src.type() );
#define bf(y) ((float*)(bdata + y*src2step))[0]
#define bd(y) ((double*)(bdata + y*src2step))[0]
uchar* srcdata = src.data;
uchar* bdata = _src2.data;
uchar* dstdata = dst.data;
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. )
{
float t;
d = 1./d;
t = (float)((bf(0)*Sf(1,1) - bf(1)*Sf(0,1))*d);
Df(1,0) = (float)((bf(1)*Sf(0,0) - bf(0)*Sf(1,0))*d);
Df(0,0) = 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)*(Sf(1,1)*Sf(2,2) - Sf(1,2)*Sf(2,1)) -
Sf(0,1)*(bf(1)*Sf(2,2) - Sf(1,2)*bf(2)) +
Sf(0,2)*(bf(1)*Sf(2,1) - Sf(1,1)*bf(2))));
t[1] = (float)(d*
(Sf(0,0)*(bf(1)*Sf(2,2) - Sf(1,2)*bf(2)) -
bf(0)*(Sf(1,0)*Sf(2,2) - Sf(1,2)*Sf(2,0)) +
Sf(0,2)*(Sf(1,0)*bf(2) - bf(1)*Sf(2,0))));
t[2] = (float)(d*
(Sf(0,0)*(Sf(1,1)*bf(2) - bf(1)*Sf(2,1)) -
Sf(0,1)*(Sf(1,0)*bf(2) - bf(1)*Sf(2,0)) +
bf(0)*(Sf(1,0)*Sf(2,1) - 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;
}
double rcond=-1, s1=0, work1=0, *work=0, *s=0;
float frcond=-1, fs1=0, fwork1=0, *fwork=0, *fs=0;
integer m = src.rows, m_ = m, n = src.cols, mn = std::max(m,n),
nm = std::min(m, n), nb = _src2.cols, lwork=-1, liwork=0, iwork1=0,
lda = m, ldx = mn, info=0, rank=0, *iwork=0;
int elem_size = CV_ELEM_SIZE(type);
bool copy_rhs=false;
int buf_size=0;
AutoBuffer<uchar> buffer;
uchar* ptr;
char N[] = {'N', '\0'}, L[] = {'L', '\0'};
Mat src2 = _src2;
dst.create( src.cols, src2.cols, src.type() );
if( m <= n )
is_normal = false;
else if( is_normal )
m_ = n;
buf_size += (is_normal ? n*n : m*n)*elem_size;
if( m_ != n || nb > 1 || !dst.isContinuous() )
{
copy_rhs = true;
if( is_normal )
buf_size += n*nb*elem_size;
else
buf_size += mn*nb*elem_size;
}
if( method == DECOMP_SVD || method == DECOMP_EIG )
{
integer nlvl = cvRound(std::log(std::max(std::min(m_,n)/25., 1.))/CV_LOG2) + 1;
liwork = std::min(m_,n)*(3*std::max(nlvl,(integer)0) + 11);
if( type == CV_32F )
sgelsd_(&m_, &n, &nb, (float*)src.data, &lda, (float*)dst.data, &ldx,
&fs1, &frcond, &rank, &fwork1, &lwork, &iwork1, &info);
else
dgelsd_(&m_, &n, &nb, (double*)src.data, &lda, (double*)dst.data, &ldx,
&s1, &rcond, &rank, &work1, &lwork, &iwork1, &info );
buf_size += nm*elem_size + (liwork + 1)*sizeof(integer);
}
else if( method == DECOMP_QR )
{
if( type == CV_32F )
sgels_(N, &m_, &n, &nb, (float*)src.data, &lda,
(float*)dst.data, &ldx, &fwork1, &lwork, &info );
else
dgels_(N, &m_, &n, &nb, (double*)src.data, &lda,
(double*)dst.data, &ldx, &work1, &lwork, &info );
}
else if( method == DECOMP_LU )
{
buf_size += (n+1)*sizeof(integer);
}
else if( method == DECOMP_CHOLESKY )
;
else
CV_Error( CV_StsBadArg, "Unknown method" );
assert(info == 0);
lwork = cvRound(type == CV_32F ? (double)fwork1 : work1);
buf_size += lwork*elem_size;
buffer.allocate(buf_size);
ptr = (uchar*)buffer;
Mat at(n, m_, type, ptr);
ptr += n*m_*elem_size;
if( method == DECOMP_CHOLESKY || method == DECOMP_EIG )
src.copyTo(at);
else if( !is_normal )
transpose(src, at);
else
mulTransposed(src, at, true);
Mat xt;
if( !is_normal )
{
if( copy_rhs )
{
Mat temp(nb, mn, type, ptr);
ptr += nb*mn*elem_size;
Mat bt = temp.colRange(0, m);
xt = temp.colRange(0, n);
transpose(src2, bt);
}
else
{
src2.copyTo(dst);
xt = Mat(1, n, type, dst.data);
}
}
else
{
if( copy_rhs )
{
xt = Mat(nb, n, type, ptr);
ptr += nb*n*elem_size;
}
else
xt = Mat(1, n, type, dst.data);
// (a'*b)' = b'*a
gemm( src2, src, 1, Mat(), 0, xt, GEMM_1_T );
}
lda = (int)(at.step ? at.step/elem_size : at.cols);
ldx = (int)(xt.step ? xt.step/elem_size : (!is_normal && copy_rhs ? mn : n));
if( method == DECOMP_SVD || method == DECOMP_EIG )
{
if( type == CV_32F )
{
fs = (float*)ptr;
ptr += nm*elem_size;
fwork = (float*)ptr;
ptr += lwork*elem_size;
iwork = (integer*)cvAlignPtr(ptr, sizeof(integer));
sgelsd_(&m_, &n, &nb, (float*)at.data, &lda, (float*)xt.data, &ldx,
fs, &frcond, &rank, fwork, &lwork, iwork, &info);
}
else
{
s = (double*)ptr;
ptr += nm*elem_size;
work = (double*)ptr;
ptr += lwork*elem_size;
iwork = (integer*)cvAlignPtr(ptr, sizeof(integer));
dgelsd_(&m_, &n, &nb, (double*)at.data, &lda, (double*)xt.data, &ldx,
s, &rcond, &rank, work, &lwork, iwork, &info);
}
}
else if( method == CV_QR )
{
if( type == CV_32F )
{
fwork = (float*)ptr;
sgels_(N, &m_, &n, &nb, (float*)at.data, &lda,
(float*)xt.data, &ldx, fwork, &lwork, &info);
}
else
{
work = (double*)ptr;
dgels_(N, &m_, &n, &nb, (double*)at.data, &lda,
(double*)xt.data, &ldx, work, &lwork, &info);
}
}
else if( method == CV_CHOLESKY || (method == CV_LU && is_normal) )
{
if( type == CV_32F )
{
spotrf_(L, &n, (float*)at.data, &lda, &info);
if(info==0)
spotrs_(L, &n, &nb, (float*)at.data, &lda, (float*)xt.data, &ldx, &info);
}
else
{
dpotrf_(L, &n, (double*)at.data, &lda, &info);
if(info==0)
dpotrs_(L, &n, &nb, (double*)at.data, &lda, (double*)xt.data, &ldx, &info);
}
}
else if( method == CV_LU )
{
iwork = (integer*)cvAlignPtr(ptr, sizeof(integer));
if( type == CV_32F )
sgesv_(&n, &nb, (float*)at.data, &lda, iwork, (float*)xt.data, &ldx, &info );
else
dgesv_(&n, &nb, (double*)at.data, &lda, iwork, (double*)xt.data, &ldx, &info );
}
else
assert(0);
result = info == 0;
if( !result )
dst = Scalar(0);
else if( xt.data != dst.data )
transpose( xt, dst );
return result;
}
/////////////////// finding eigenvalues and eigenvectors of a symmetric matrix ///////////////
template<typename Real> static inline Real hypot(Real a, Real b)
{
a = std::abs(a);
b = std::abs(b);
Real f;
if( a > b )
{
f = b/a;
return a*std::sqrt(1 + f*f);
}
if( b == 0 )
return 0;
f = a/b;
return b*std::sqrt(1 + f*f);
}
template<typename Real> bool jacobi(const Mat& _S0, Mat& _e, Mat& matE, bool computeEvects, Real eps)
{
int n = _S0.cols, i, j, k, m;
if( computeEvects )
matE = Mat::eye(n, n, _S0.type());
int iters, maxIters = n*n*30;
AutoBuffer<uchar> buf(n*2*sizeof(int) + (n*n+n*2+1)*sizeof(Real));
Real* S = alignPtr((Real*)(uchar*)buf, sizeof(Real));
Real* maxSR = S + n*n;
Real* maxSC = maxSR + n;
int* indR = (int*)(maxSC + n);
int* indC = indR + n;
Mat matS(_S0.size(), _S0.type(), S);
_S0.copyTo(matS);
Real mv;
Real* E = (Real*)matE.data;
Real* e = (Real*)_e.data;
int Sstep = (int)(matS.step/sizeof(Real));
int estep = _e.rows == 1 ? 1 : (int)(_e.step/sizeof(Real));
int Estep = (int)(matE.step/sizeof(Real));
for( k = 0; k < n; k++ )
{
e[k*estep] = S[(Sstep + 1)*k];
if( k < n - 1 )
{
for( m = k+1, mv = std::abs(S[Sstep*k + m]), i = k+2; i < n; i++ )
{
Real v = std::abs(S[Sstep*k+i]);
if( mv < v )
mv = v, m = i;
}
maxSR[k] = mv;
indR[k] = m;
}
if( k > 0 )
{
for( m = 0, mv = std::abs(S[k]), i = 1; i < k; i++ )
{
Real v = std::abs(S[Sstep*i+k]);
if( mv < v )
mv = v, m = i;
}
maxSC[k] = mv;
indC[k] = m;
}
}
for( iters = 0; iters < maxIters; iters++ )
{
// find index (k,l) of pivot p
for( k = 0, mv = maxSR[0], i = 1; i < n-1; i++ )
{
Real v = maxSR[i];
if( mv < v )
mv = v, k = i;
}
int l = indR[k];
for( i = 1; i < n; i++ )
{
Real v = maxSC[i];
if( mv < v )
mv = v, k = indC[i], l = i;
}
Real p = S[Sstep*k + l];
if( std::abs(p) <= eps )
break;
Real y = Real((e[estep*l] - e[estep*k])*0.5);
Real t = std::abs(y) + hypot(p, y);
Real s = hypot(p, t);
Real c = t/s;
s = p/s; t = (p/t)*p;
if( y < 0 )
s = -s, t = -t;
S[Sstep*k + l] = 0;
e[estep*k] -= t;
e[estep*l] += t;
Real 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(S[Sstep*i+k], S[Sstep*i+l]);
for( i = k+1; i < l; i++ )
rotate(S[Sstep*k+i], S[Sstep*i+l]);
for( i = l+1; i < n; i++ )
rotate(S[Sstep*k+i], S[Sstep*l+i]);
// rotate eigenvectors
if( computeEvects )
for( i = 0; i < n; i++ )
rotate(E[Estep*k+i], E[Estep*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(S[Sstep*idx + m]), i = idx+2; i < n; i++ )
{
Real v = std::abs(S[Sstep*idx+i]);
if( mv < v )
mv = v, m = i;
}
maxSR[idx] = mv;
indR[idx] = m;
}
if( idx > 0 )
{
for( m = 0, mv = std::abs(S[idx]), i = 1; i < idx; i++ )
{
Real v = std::abs(S[Sstep*i+idx]);
if( mv < v )
mv = v, m = i;
}
maxSC[idx] = mv;
indC[idx] = m;
}
}
}
// sort eigenvalues & eigenvectors
for( k = 0; k < n-1; k++ )
{
m = k;
for( i = k+1; i < n; i++ )
{
if( e[estep*m] < e[estep*i] )
m = i;
}
if( k != m )
{
std::swap(e[estep*m], e[estep*k]);
if( computeEvects )
for( i = 0; i < n; i++ )
std::swap(E[Estep*m + i], E[Estep*k + i]);
}
}
return true;
}
static bool eigen( const Mat& src, Mat& evals, Mat& evects, bool computeEvects,
int lowindex, int highindex )
{
int type = src.type();
integer n = src.rows;
// If a range is selected both limits are needed.
CV_Assert( ( lowindex >= 0 && highindex >= 0 ) ||
( lowindex < 0 && highindex < 0 ) );
// lapack sorts from lowest to highest so we flip
integer il = n - highindex;
integer iu = n - lowindex;
CV_Assert( src.rows == src.cols );
CV_Assert (type == CV_32F || type == CV_64F);
// allow for 1xn eigenvalue matrix too
if( !(evals.rows == 1 && evals.cols == n && evals.type() == type) )
evals.create(n, 1, type);
if( n <= 20 )
{
if( type == CV_32F )
return jacobi<float>(src, evals, evects, computeEvects, FLT_EPSILON);
else
return jacobi<double>(src, evals, evects, computeEvects, DBL_EPSILON);
}
bool result;
integer m=0, lda, ldv=n, lwork=-1, iwork1=0, liwork=-1, idummy=0, info=0;
integer *isupport, *iwork;
char job[] = { computeEvects ? 'V' : 'N', '\0' };
char range[2] = "I";
range[0] = (il < n + 1) ? 'I' : 'A';
char L[] = {'L', '\0'};
uchar* work;
AutoBuffer<uchar> buf;
int elem_size = (int)src.elemSize();
lda = (int)(src.step/elem_size);
if( computeEvects )
{
evects.create(n, n, type);
ldv = (int)(evects.step/elem_size);
}
bool copy_evals = !evals.isContinuous();
if( type == CV_32FC1 )
{
float work1 = 0, dummy = 0, abstol = 0, *s;
ssyevr_(job, range, L, &n, (float*)src.data, &lda, &dummy, &dummy, &il, &iu,
&abstol, &m, (float*)evals.data, (float*)evects.data, &ldv,
&idummy, &work1, &lwork, &iwork1, &liwork, &info );
assert( info == 0 );
lwork = cvRound(work1);
liwork = iwork1;
buf.allocate((lwork + n*n + (copy_evals ? n : 0))*elem_size +
(liwork+2*n+1)*sizeof(integer));
Mat a(n, n, type, (uchar*)buf);
src.copyTo(a);
lda = (integer)a.step1();
work = a.data + n*n*elem_size;
if( copy_evals )
s = (float*)(work + lwork*elem_size);
else
s = (float*)evals.data;
iwork = (integer*)cvAlignPtr(work + (lwork + (copy_evals ? n : 0))*elem_size, sizeof(integer));
isupport = iwork + liwork;
ssyevr_(job, range, L, &n, (float*)a.data, &lda, &dummy, &dummy,
&il, &iu, &abstol, &m, s, (float*)evects.data,
&ldv, isupport, (float*)work, &lwork, iwork, &liwork, &info );
result = info == 0;
}
else
{
double work1 = 0, dummy = 0, abstol = 0, *s;
dsyevr_(job, range, L, &n, (double*)src.data, &lda, &dummy, &dummy, &il, &iu,
&abstol, &m, (double*)evals.data, (double*)evects.data, &ldv,
&idummy, &work1, &lwork, &iwork1, &liwork, &info );
assert( info == 0 );
lwork = cvRound(work1);
liwork = iwork1;
buf.allocate((lwork + n*n + (copy_evals ? n : 0))*elem_size +
(liwork+2*n+1)*sizeof(integer));
Mat a(n, n, type, (uchar*)buf);
src.copyTo(a);
lda = (integer)a.step1();
work = a.data + n*n*elem_size;
if( copy_evals )
s = (double*)(work + lwork*elem_size);
else
s = (double*)evals.data;
iwork = (integer*)cvAlignPtr(work + (lwork + (copy_evals ? n : 0))*elem_size, sizeof(integer));
isupport = iwork + liwork;
dsyevr_(job, range, L, &n, (double*)a.data, &lda, &dummy, &dummy,
&il, &iu, &abstol, &m, s, (double*)evects.data,
&ldv, isupport, (double*)work, &lwork, iwork, &liwork, &info );
result = info == 0;
}
if( copy_evals )
Mat(evals.rows, evals.cols, type, work + lwork*elem_size).copyTo(evals);
if( il < n + 1 && n > 20 ) {
int nVV = iu - il + 1;
if( computeEvects ) {
Mat flipme = evects.rowRange(0, nVV);
flip(flipme, flipme, 0);
flipme = evals.rowRange(0, nVV);
flip(flipme, flipme, 0);
}
} else {
flip(evals, evals, evals.rows > 1 ? 0 : 1);
if( computeEvects )
flip(evects, evects, 0);
}
return result;
}
bool eigen( const Mat& src, Mat& evals, int lowindex, int highindex )
{
Mat evects;
return eigen(src, evals, evects, false, lowindex, highindex);
}
bool eigen( const Mat& src, Mat& evals, Mat& evects, int lowindex,
int highindex )
{
return eigen(src, evals, evects, true, lowindex, highindex);
}
/* 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];
for( j = 0; 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;
}
for( ; j < n; j++ )
y[j] = (T3)(y[j] + s*x[j]);
}
}
template<typename T> static void
SVBkSb( int m, int n, const T* w, int incw,
const T* u, int ldu, int uT,
const T* v, int ldv, int 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( 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 _SVDcompute( const Mat& a, Mat& w, Mat* u, Mat* vt, int flags )
{
integer m = a.rows, n = a.cols, mn = std::max(m, n), nm = std::min(m, n);
int type = a.type(), elem_size = (int)a.elemSize();
bool compute_uv = u && vt;
if( flags & SVD::NO_UV )
{
if(u) u->release();
if(vt) vt->release();
u = vt = 0;
compute_uv = false;
}
if( compute_uv )
{
u->create( (int)m, (int)((flags & SVD::FULL_UV) ? m : nm), type );
vt->create( (int)((flags & SVD::FULL_UV) ? n : nm), n, type );
}
w.create(nm, 1, type);
Mat _a = a;
int a_ofs = 0, work_ofs=0, iwork_ofs=0, buf_size = 0;
bool temp_a = false;
double u1=0, v1=0, work1=0;
float uf1=0, vf1=0, workf1=0;
integer lda, ldu, ldv, lwork=-1, iwork1=0, info=0;
char mode[] = {compute_uv ? 'S' : 'N', '\0'};
if( m != n && compute_uv && (flags & SVD::FULL_UV) )
mode[0] = 'A';
if( !(flags & SVD::MODIFY_A) )
{
if( mode[0] == 'N' || mode[0] == 'A' )
temp_a = true;
else if( compute_uv && (a.size() == vt->size() || a.size() == u->size()) && mode[0] == 'S' )
mode[0] = 'O';
}
lda = a.cols;
ldv = ldu = mn;
if( type == CV_32F )
{
sgesdd_(mode, &n, &m, (float*)a.data, &lda, (float*)w.data,
&vf1, &ldv, &uf1, &ldu, &workf1, &lwork, &iwork1, &info );
lwork = cvRound(workf1);
}
else
{
dgesdd_(mode, &n, &m, (double*)a.data, &lda, (double*)w.data,
&v1, &ldv, &u1, &ldu, &work1, &lwork, &iwork1, &info );
lwork = cvRound(work1);
}
assert(info == 0);
if( temp_a )
{
a_ofs = buf_size;
buf_size += n*m*elem_size;
}
work_ofs = buf_size;
buf_size += lwork*elem_size;
buf_size = cvAlign(buf_size, sizeof(integer));
iwork_ofs = buf_size;
buf_size += 8*nm*sizeof(integer);
AutoBuffer<uchar> buf(buf_size);
uchar* buffer = (uchar*)buf;
if( temp_a )
{
_a = Mat(a.rows, a.cols, type, buffer );
a.copyTo(_a);
}
if( !(flags & SVD::MODIFY_A) && !temp_a )
{
if( compute_uv && a.size() == vt->size() )
{
a.copyTo(*vt);
_a = *vt;
}
else if( compute_uv && a.size() == u->size() )
{
a.copyTo(*u);
_a = *u;
}
}
if( compute_uv )
{
ldv = (int)(vt->step ? vt->step/elem_size : vt->cols);
ldu = (int)(u->step ? u->step/elem_size : u->cols);
}
lda = (int)(_a.step ? _a.step/elem_size : _a.cols);
if( type == CV_32F )
{
sgesdd_(mode, &n, &m, (float*)_a.data, &lda, (float*)w.data,
vt ? (float*)vt->data : (float*)&v1, &ldv, u ? (float*)u->data : (float*)&u1, &ldu,
(float*)(buffer + work_ofs), &lwork, (integer*)(buffer + iwork_ofs), &info );
}
else
{
dgesdd_(mode, &n, &m, (double*)_a.data, &lda, (double*)w.data,
vt ? (double*)vt->data : &v1, &ldv, u ? (double*)u->data : &u1, &ldu,
(double*)(buffer + work_ofs), &lwork, (integer*)(buffer + iwork_ofs), &info );
}
CV_Assert(info >= 0);
if(info != 0)
{
*u = Scalar(0.);
*vt = Scalar(0.);
w = Scalar(0.);
}
}
void SVD::compute( const Mat& a, Mat& w, Mat& u, Mat& vt, int flags )
{
_SVDcompute(a, w, &u, &vt, flags);
}
void SVD::compute( const Mat& a, Mat& w, int flags )
{
_SVDcompute(a, w, 0, 0, flags);
}
void SVD::backSubst( const Mat& w, const Mat& u, const Mat& vt, const Mat& rhs, Mat& dst )
{
int type = w.type(), esz = (int)w.elemSize();
int m = u.rows, n = vt.cols, nb = rhs.data ? rhs.cols : m;
AutoBuffer<double> buffer(nb);
CV_Assert( u.data && vt.data && w.data );
if( rhs.data )
CV_Assert( rhs.type() == type && rhs.rows == m );
dst.create( n, nb, type );
if( type == CV_32F )
SVBkSb(m, n, (float*)w.data, 1, (float*)u.data, (int)(u.step/esz), false,
(float*)vt.data, (int)(vt.step/esz), true, (float*)rhs.data, (int)(rhs.step/esz),
nb, (float*)dst.data, (int)(dst.step/esz), buffer, 10*FLT_EPSILON );
else if( type == CV_64F )
SVBkSb(m, n, (double*)w.data, 1, (double*)u.data, (int)(u.step/esz), false,
(double*)vt.data, (int)(vt.step/esz), true, (double*)rhs.data, (int)(rhs.step/esz),
nb, (double*)dst.data, (int)(dst.step/esz), buffer, 2*DBL_EPSILON );
else
CV_Error( CV_StsUnsupportedFormat, "" );
}
SVD& SVD::operator ()(const Mat& a, int flags)
{
_SVDcompute(a, w, &u, &vt, flags);
return *this;
}
void SVD::backSubst( const Mat& rhs, Mat& dst ) const
{
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::Mat(mat));
}
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 || method == CV_SVD_SYM ? cv::DECOMP_SVD : 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 );
return cv::solve( A, b, x, method == CV_CHOLESKY ? cv::DECOMP_CHOLESKY :
method == CV_SVD || method == CV_SVD_SYM ? cv::DECOMP_SVD :
A.rows > A.cols ? cv::DECOMP_QR : cv::DECOMP_LU );
}
CV_IMPL void
cvEigenVV( CvArr* srcarr, CvArr* evectsarr, CvArr* evalsarr, double,
int lowindex, int highindex)
{
cv::Mat src = cv::cvarrToMat(srcarr), evals = cv::cvarrToMat(evalsarr);
if( evectsarr )
{
cv::Mat evects = cv::cvarrToMat(evectsarr);
eigen(src, evals, evects, lowindex, highindex);
}
else
eigen(src, evals, lowindex, highindex);
}
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.data );
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.data )
{
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.data )
{
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);
int type = w.type();
bool uT = (flags & CV_SVD_U_T) != 0, vT = (flags & CV_SVD_V_T) != 0;
int m = !uT ? u.rows : u.cols;
int n = vT ? v.cols : v.rows;
int nm = std::min(n, m), nb;
int esz = (int)w.elemSize();
int incw = w.size() == cv::Size(nm, 1) ? 1 : (int)(w.step/esz) + (w.cols > 1 && w.rows > 1);
CV_Assert( type == u.type() && type == v.type() &&
type == dst.type() && dst.rows == n &&
(!uT ? u.cols : u.rows) >= nm && (vT ? v.rows : v.cols) >= nm &&
(w.size() == cv::Size(nm, 1) || w.size() == cv::Size(1, nm) ||
w.size() == cv::Size(nm, nm) || w.size() == cv::Size(n, m)));
if( rhsarr )
{
rhs = cv::cvarrToMat(rhsarr);
nb = rhs.cols;
CV_Assert( type == rhs.type() );
}
else
nb = m;
CV_Assert( dst.cols == nb );
cv::AutoBuffer<double> buffer(nb);
if( type == CV_32F )
cv::SVBkSb(m, n, (float*)w.data, incw, (float*)u.data, (int)(u.step/esz), uT,
(float*)v.data, (int)(v.step/esz), vT, (float*)rhs.data, (int)(rhs.step/esz),
nb, (float*)dst.data, (int)(dst.step/esz), buffer, 2*FLT_EPSILON );
else
cv::SVBkSb(m, n, (double*)w.data, incw, (double*)u.data, (int)(u.step/esz), uT,
(double*)v.data, (int)(v.step/esz), vT, (double*)rhs.data, (int)(rhs.step/esz),
nb, (double*)dst.data, (int)(dst.step/esz), buffer, 2*DBL_EPSILON );
}