text: /*
   * Copyright (c) 2007 - 2020 Joseph Gaeddert
   *
   * Permission is hereby granted, free of charge, to any person obtaining a copy
   * of this software and associated documentation files (the "Software"), to deal
   * in the Software without restriction, including without limitation the rights
   * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   * copies of the Software, and to permit persons to whom the Software is
   * furnished to do so, subject to the following conditions:
   *
   * The above copyright notice and this permission notice shall be included in
   * all copies or substantial portions of the Software.
   *
   * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
   * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
   * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
   * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
   * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
   * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
   * THE SOFTWARE.
   */
  
  //
  // Solve linear system of equations
  //
  
  #include <string.h>
  
  #include "liquid.internal.h"
  
  // solve linear system of n equations: Ax = b
  //  _A      :   system matrix [size: _n x _n]
  //  _n      :   system size
  //  _b      :   equality vector [size: _n x 1]
  //  _x      :   solution vector [size: _n x 1]
  //  _opts   :   options (ignored for now)
  int MATRIX(_linsolve)(T *          _A,
                        unsigned int _n,
                        T *          _b,
                        T *          _x,
                        void *       _opts)
  {
  #if 0
      T A_inv[_n*_n];
      memmove(A_inv, _A, _n*_n*sizeof(T));
      MATRIX(_inv)(A_inv,_n,_n);
  
      MATRIX(_mul)(A_inv, _n, _n,
                   _b,    _n,  1,
                   _x,    _n,  1);
  #else
      unsigned int r;
      unsigned int c;
  
      // compute augmented matrix M [size: _n x _n+1] as
      // T:
      //  A11 A12 A13 ... A1n b1
      //  A21 A22 A23 ... A2n b2
      //  A31 A32 A33 ... A3n b3
      //  ...
      //  An1 An2 An3 ... Ann bn
      T M[_n*_n + _n];    // allocate array
      unsigned int m=0;   // output matrix index counter
      unsigned int a=0;   // input matrix index counter
      for (r=0; r<_n; r++) {
          for (c=0; c<_n; c++)
              M[m++] = _A[a++];
  
          M[m++] = _b[r];
      }
  
      // run Gauss-Jordan elimination on M
      // T:
      //  1   0   0   ... 0   x1
      //  0   1   0   ... 0   x2
      //  0   0   1   ... 0   x3
      //  ...
      //  0   0   0   ... 1   xn
      MATRIX(_gjelim)(M, _n, _n+1);
  
      // copy result from right-most column of M
      for (r=0; r<_n; r++)
          _x[r] = M[(_n+1)*(r+1)-1];
  #endif
      return LIQUID_OK;
  }
  
  