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//----------------------------------------------------------------------------
// Anti-Grain Geometry - Version 2.3
// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
//
// Permission to copy, use, modify, sell and distribute this software
// is granted provided this copyright notice appears in all copies.
// This software is provided "as is" without express or implied
// warranty, and with no claim as to its suitability for any purpose.
//
//----------------------------------------------------------------------------
// Contact: mcseem@antigrain.com
// mcseemagg@yahoo.com
// http://www.antigrain.com
//----------------------------------------------------------------------------
//
// Solving simultaneous equations
//
//----------------------------------------------------------------------------
#ifndef AGG_SIMUL_EQ_INCLUDED
#define AGG_SIMUL_EQ_INCLUDED
#include <math.h>
#include "agg_basics.h"
namespace agg
{
//=============================================================swap_arrays
template<class T> void swap_arrays(T* a1, T* a2, unsigned n)
{
unsigned i;
for(i = 0; i < n; i++)
{
T tmp = *a1;
*a1++ = *a2;
*a2++ = tmp;
}
}
//============================================================matrix_pivot
template<unsigned Rows, unsigned Cols>
struct matrix_pivot
{
static int pivot(double m[Rows][Cols], unsigned row)
{
int k = int(row);
double max_val, tmp;
max_val = -1.0;
unsigned i;
for(i = row; i < Rows; i++)
{
if((tmp = fabs(m[i][row])) > max_val && tmp != 0.0)
{
max_val = tmp;
k = i;
}
}
if(m[k][row] == 0.0)
{
return -1;
}
if(k != int(row))
{
swap_arrays(m[k], m[row], Cols);
return k;
}
return 0;
}
};
//===============================================================simul_eq
template<unsigned Size, unsigned RightCols>
struct simul_eq
{
static bool solve(const double left[Size][Size],
const double right[Size][RightCols],
double result[Size][RightCols])
{
unsigned i, j, k;
double a1;
double tmp[Size][Size + RightCols];
for(i = 0; i < Size; i++)
{
for(j = 0; j < Size; j++)
{
tmp[i][j] = left[i][j];
}
for(j = 0; j < RightCols; j++)
{
tmp[i][Size + j] = right[i][j];
}
}
for(k = 0; k < Size; k++)
{
if(matrix_pivot<Size, Size + RightCols>::pivot(tmp, k) < 0)
{
return false; // Singularity....
}
a1 = tmp[k][k];
for(j = k; j < Size + RightCols; j++)
{
tmp[k][j] /= a1;
}
for(i = k + 1; i < Size; i++)
{
a1 = tmp[i][k];
for (j = k; j < Size + RightCols; j++)
{
tmp[i][j] -= a1 * tmp[k][j];
}
}
}
for(k = 0; k < RightCols; k++)
{
int m;
for(m = int(Size - 1); m >= 0; m--)
{
result[m][k] = tmp[m][Size + k];
for(j = m + 1; j < Size; j++)
{
result[m][k] -= tmp[m][j] * result[j][k];
}
}
}
return true;
}
};
}
#endif
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