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#include "precomp.hpp"
namespace cv { namespace hal {
/****************************************************************************************\
* 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, _Tp eps)
{
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]) < eps )
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, FLT_EPSILON*10);
}
int LU(double* A, size_t astep, int m, double* b, size_t bstep, int n)
{
return LUImpl(A, astep, m, b, bstep, n, DBL_EPSILON*100);
}
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);
}
}}