matrix.h

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/* -----------------------------------------------------------------------------------------
  $Id: matrix.h 486 2006-07-07 21:07:52Z svacek $
  $Author: svacek $
   ----------------------------------------------------------------------------------------- */
#include <malloc.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "wlog.h"
#include "vector.h"
#include "constants.h"
#ifndef __MAT_SVH
#define __MAT_SVH
/* ------------------------------------------------------------------------------- */
/*@{*/
/** \defgroup MATRIX_OPS Matrix Operations */
/** \ingroup LINEAR_ALGEBRA */
/** Structure matrix : definition of full matrix 
     @todo Should be replaced with BLAS/CGNS tools 
*/
/* -------------------------------------------------------------------------- */
typedef struct 
{
  double **a;
  long n,m;
} matrix;
/* ------------------------------------------------------------------------------- */

/*
  function construct()
  function construct_transpose()
  function construct_multiply()
  function destruct()
  - provede alokaci/dealokaci matice A dle rozmeru nebo okopirovanim 
    jine matice(pripadne transponovanim resp. nasobenim)
  function construct_mtransf()
  function construct_mtransfinv()
  
   out - je matice transformace referencniho trojuhelniku na troj. ABC (ia,ib,ic - indexy vrcholu)
    (L1,L2,L3)=MTransf*(1,x,y)   
    MTransfInv*(L1,L2,L3)=(1,x,y)
    kde L1,L2,L3 jsou barycentricke souradnice, x,y jsou souradnice bodu v trojuhelniku ABC.
 */
void construct_mat(matrix *A,long n,long m);                                     /**< Construct matrix A of order n X m */
void construct_mat_copy(matrix *A,const matrix B);                               /**< Construct copy of matrix B and puts it into B */
void construct_mat_transpose(matrix *out,const matrix in);                       /**< Makes transport of in and puts it into out  */
void construct_mat_multiply(matrix *out,const matrix A,const matrix B);          /**< Construct Matrix Multiplication out:=A*B */
void mat_transf(matrix out,long ia,long ib,long ic,double *_x,double *_y);       
/**< Creates the transformation matrix from the element ABC onto the reference triangle. 
 *
 *  Let \f$ A =(x_{i_a},y_{i_a}), B =(x_{i_b},y_{i_b}), C =(x_{i_c},y_{i_c}), \f$.
 *
 *  Let us denote it \f$\bf M\f$ the matrix of linear transformation
 *
 *  from the reference triangle \f$ \hat{T}\f$ onto triangle \f$ T=\triangle ABC\f$.
 *
 *  we can write it in the baricentric coordinates as 
 *
 * \f$ F_{T}(\lambda_1,\lambda_2,\lambda_3) = 
 *     \bf b + \bf M \cdot (\lambda_1,\lambda_2,\lambda_3)^T
 *  \f$
 *
 *  The computed matrix out is then \f$ \bf M^{-1} \f$.
 */
void mat_transfinv(matrix out,long ia,long ib,long ic,double *_x,double *_y);
/**< Creates the transformation matrix from  the reference triangle onto the element ABC. 
 *
 * Let \f$ A =(x_{i_a},y_{i_a}), B =(x_{i_b},y_{i_b}), C =(x_{i_c},y_{i_c}), \f$, then 
 *  the matrix out (let us denote it \f$\bf M\f$ the matrix of linear transformation
 *  from the reference triangle \f$ \hat{T}\f$ onto triangle \f$ T=\triangle ABC\f$, i.e.
 *  we can write it in the baricentric coordinates as 
 *
 * \f$ F_{T}(\lambda_1,\lambda_2,\lambda_3) = 
 *     \bf b + \bf M \cdot (\lambda_1,\lambda_2,\lambda_3)^T
 *  \f$
 *
 *  The computed matrix is then \f$ \bf M \f$, i.e.
 *  \f$ M= \left( \begin{array}{rrr} 1 1 1 \\ x_{i_a} x_{i_b} x_{i_c} \\ y_{i_a} y_{i_b} y_{i_c} \end{array} \right)\f$
 */

void destruct_mat(matrix *A);
/* 
   function vypis() - vypis fmatrix do souboru
 */
void save_mat(const matrix which,char *filename);
/*
  function transpose()
  provede transponovani matice do jiz alokovane matice odpovidajicich rozmeru
 */
void transpose_mat(matrix *out,const matrix in);
/*
  function multiply()
  maticove nasobeni resp. nasobeni skalarem
 */
void matrix_multiply_mat(matrix *out,const matrix A,const matrix B);
void multiply_mat(matrix M,const double beta);
/* 
   function add/subtract()
   A:= A+B/A-B 
   function multiply_rows()
   A[i]:=A[i]*v[i] nasobeni radku matice 
 */
void zeroize_mat(matrix A);
void add_mat(matrix A,const matrix B);
void subtract_mat(matrix A,const matrix B);
void multiply_mat_rows(matrix A,const vector v);
/*
  function multiply()
  out:=A*v (out jiz ma byt alokovano na odpovidajici velikost!)
  resp. out:=v*A
 */
void matrix_reziduum(vector out,const matrix A,const vector v);
void matrix_multiply_right(vector out,const matrix A,const vector v);
void matrix_multiply_left(vector out,const vector v,const matrix A);
/*
  function solve()

  GJ eliminacni algoritmus pro reseni soustavy linarnich rovnic
  sol:=A\b (sol jiz alokovano!)

  function Rsolve()
  
  out:=R\b, pouze prvnich k-radek je brano v uvahu, R - horni trojuhelnikova matice(predpoklad)
 */
void solve_mat(vector sol,const matrix A,const vector b);
void upper_solve_mat(vector out,const matrix R,const vector b,long k);
void ludcmp(matrix out);
void lusolve(vector sol,const matrix out,const vector rhs);
/*@}*/
/* -------------------------------------------------------------------------- */
#endif

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