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147 lines
3.9 KiB
147 lines
3.9 KiB
//---------------------------------------------------------------------------- |
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// Anti-Grain Geometry - Version 2.4 |
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// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com) |
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// |
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// Permission to copy, use, modify, sell and distribute this software |
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// is granted provided this copyright notice appears in all copies. |
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// This software is provided "as is" without express or implied |
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// warranty, and with no claim as to its suitability for any purpose. |
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// |
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//---------------------------------------------------------------------------- |
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// Contact: mcseem@antigrain.com |
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// mcseemagg@yahoo.com |
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// http://www.antigrain.com |
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//---------------------------------------------------------------------------- |
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// |
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// Solving simultaneous equations |
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// |
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//---------------------------------------------------------------------------- |
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#ifndef AGG_SIMUL_EQ_INCLUDED |
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#define AGG_SIMUL_EQ_INCLUDED |
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#include <cmath> |
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#include "agg_basics.h" |
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namespace agg |
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{ |
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//=============================================================swap_arrays |
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template<class T> void swap_arrays(T* a1, T* a2, unsigned n) |
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{ |
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unsigned i; |
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for(i = 0; i < n; i++) |
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{ |
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T tmp = *a1; |
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*a1++ = *a2; |
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*a2++ = tmp; |
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} |
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} |
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//============================================================matrix_pivot |
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template<unsigned Rows, unsigned Cols> |
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struct matrix_pivot |
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{ |
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static int pivot(double m[Rows][Cols], unsigned row) |
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{ |
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int k = int(row); |
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double max_val, tmp; |
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max_val = -1.0; |
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unsigned i; |
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for(i = row; i < Rows; i++) |
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{ |
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if((tmp = std::fabs(m[i][row])) > max_val && tmp != 0.0) |
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{ |
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max_val = tmp; |
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k = i; |
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} |
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} |
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if(m[k][row] == 0.0) |
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{ |
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return -1; |
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} |
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if(k != int(row)) |
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{ |
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swap_arrays(m[k], m[row], Cols); |
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return k; |
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} |
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return 0; |
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} |
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}; |
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//===============================================================simul_eq |
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template<unsigned Size, unsigned RightCols> |
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struct simul_eq |
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{ |
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static bool solve(const double left[Size][Size], |
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const double right[Size][RightCols], |
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double result[Size][RightCols]) |
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{ |
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unsigned i, j, k; |
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double a1; |
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double tmp[Size][Size + RightCols]; |
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for(i = 0; i < Size; i++) |
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{ |
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for(j = 0; j < Size; j++) |
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{ |
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tmp[i][j] = left[i][j]; |
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} |
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for(j = 0; j < RightCols; j++) |
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{ |
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tmp[i][Size + j] = right[i][j]; |
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} |
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} |
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for(k = 0; k < Size; k++) |
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{ |
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if(matrix_pivot<Size, Size + RightCols>::pivot(tmp, k) < 0) |
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{ |
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return false; // Singularity.... |
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} |
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a1 = tmp[k][k]; |
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for(j = k; j < Size + RightCols; j++) |
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{ |
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tmp[k][j] /= a1; |
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} |
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for(i = k + 1; i < Size; i++) |
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{ |
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a1 = tmp[i][k]; |
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for (j = k; j < Size + RightCols; j++) |
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{ |
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tmp[i][j] -= a1 * tmp[k][j]; |
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} |
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} |
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} |
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for(k = 0; k < RightCols; k++) |
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{ |
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int m; |
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for(m = int(Size - 1); m >= 0; m--) |
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{ |
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result[m][k] = tmp[m][Size + k]; |
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for(j = m + 1; j < Size; j++) |
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{ |
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result[m][k] -= tmp[m][j] * result[j][k]; |
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} |
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} |
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} |
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return true; |
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} |
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}; |
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} |
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#endif
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