itersym.c

C语言版本的矩阵库

/**************************************************************************
**
** Copyright (C) 1993 David E. Stewart & Zbigniew Leyk, all rights reserved.
**
**			     Meschach Library
** 
** This Meschach Library is provided "as is" without any express 
** or implied warranty of any kind with respect to this software. 
** In particular the authors shall not be liable for any direct, 
** indirect, special, incidental or consequential damages arising 
** in any way from use of the software.
** 
** Everyone is granted permission to copy, modify and redistribute this
** Meschach Library, provided:
**  1.  All copies contain this copyright notice.
**  2.  All modified copies shall carry a notice stating who
**      made the last modification and the date of such modification.
**  3.  No charge is made for this software or works derived from it.  
**      This clause shall not be construed as constraining other software
**      distributed on the same medium as this software, nor is a
**      distribution fee considered a charge.
**
***************************************************************************/


/* itersym.c 17/09/93 */


/* 
  ITERATIVE METHODS - implementation of several iterative methods;
  see also iter0.c
  */

#include        <stdio.h>
#include	<math.h>
#include        "matrix.h"
#include        "matrix2.h"
#include	"sparse.h"
#include        "iter.h"

static char rcsid[] = "$Id: itersym.c,v 1.2 1995/01/30 14:55:54 des Exp $";


#ifdef ANSI_C
VEC	*spCHsolve(const SPMAT *,VEC *,VEC *);
VEC	*trieig(VEC *,VEC *,MAT *);
#else
VEC	*spCHsolve();
VEC	*trieig();
#endif



/* iter_spcg -- a simple interface to iter_cg() which uses sparse matrix
   data structures
   -- assumes that LLT contains the Cholesky factorisation of the
   actual preconditioner;
   use always as follows:
   x = iter_spcg(A,LLT,b,eps,x,limit,steps);
   or 
   x = iter_spcg(A,LLT,b,eps,VNULL,limit,steps);
   In the second case the solution vector is created.
   */
#ifndef ANSI_C
VEC  *iter_spcg(A,LLT,b,eps,x,limit,steps)
SPMAT	*A, *LLT;
VEC	*b, *x;
double	eps;
int *steps, limit;
#else
VEC  *iter_spcg(SPMAT *A, SPMAT *LLT, VEC *b, double eps, VEC *x,
		int limit, int *steps)
#endif
{	
   ITER *ip;
   
   ip = iter_get(0,0);
   ip->Ax = (Fun_Ax) sp_mv_mlt;
   ip->A_par = (void *)A;
   ip->Bx = (Fun_Ax) spCHsolve;
   ip->B_par = (void *)LLT;
   ip->info = (Fun_info) NULL;
   ip->b = b;
   ip->eps = eps;
   ip->limit = limit;
   ip->x = x;
   iter_cg(ip);
   x = ip->x;
   if (steps) *steps = ip->steps;
   ip->shared_x = ip->shared_b = TRUE;
   iter_free(ip);   /* release only ITER structure */
   return x;		
}

/* 
  Conjugate gradients method;
  */
#ifndef ANSI_C
VEC  *iter_cg(ip)
ITER *ip;
#else
VEC  *iter_cg(ITER *ip)
#endif
{
   STATIC VEC *r = VNULL, *p = VNULL, *q = VNULL, *z = VNULL;
   Real	alpha, beta, inner, old_inner, nres;
   VEC *rr;   /* rr == r or rr == z */
   
   if (ip == INULL)
     error(E_NULL,"iter_cg");
   if (!ip->Ax || !ip->b)
     error(E_NULL,"iter_cg");
   if ( ip->x == ip->b )
     error(E_INSITU,"iter_cg");
   if (!ip->stop_crit)
     error(E_NULL,"iter_cg");
   
   if ( ip->eps <= 0.0 )
     ip->eps = MACHEPS;
   
   r = v_resize(r,ip->b->dim);
   p = v_resize(p,ip->b->dim);
   q = v_resize(q,ip->b->dim);
   
   MEM_STAT_REG(r,TYPE_VEC);
   MEM_STAT_REG(p,TYPE_VEC);
   MEM_STAT_REG(q,TYPE_VEC);
   
   if (ip->Bx != (Fun_Ax)NULL) {
      z = v_resize(z,ip->b->dim);
      MEM_STAT_REG(z,TYPE_VEC);
      rr = z;
   }
   else rr = r;
   
   if (ip->x != VNULL) {
      if (ip->x->dim != ip->b->dim)
	error(E_SIZES,"iter_cg");
      ip->Ax(ip->A_par,ip->x,p);    		/* p = A*x */
      v_sub(ip->b,p,r);		 		/* r = b - A*x */
   }
   else {  /* ip->x == 0 */
      ip->x = v_get(ip->b->dim);
      ip->shared_x = FALSE;
      v_copy(ip->b,r);
   }
   
   old_inner = 0.0;
   for ( ip->steps = 0; ip->steps <= ip->limit; ip->steps++ )
   {
      if ( ip->Bx )
	(ip->Bx)(ip->B_par,r,rr);		/* rr = B*r */
      
      inner = in_prod(rr,r);
      nres = sqrt(fabs(inner));
      if (ip->info) ip->info(ip,nres,r,rr);
      if (ip->steps == 0) ip->init_res = nres;
      if ( ip->stop_crit(ip,nres,r,rr) ) break;
      
      if ( ip->steps )	/* if ( ip->steps > 0 ) ... */
      {
	 beta = inner/old_inner;
	 p = v_mltadd(rr,p,beta,p);
      }
      else		/* if ( ip->steps == 0 ) ... */
      {
	 beta = 0.0;
	 p = v_copy(rr,p);
	 old_inner = 0.0;
      }
      (ip->Ax)(ip->A_par,p,q);     /* q = A*p */
      alpha = in_prod(p,q);
      if (sqrt(fabs(alpha)) <= MACHEPS*ip->init_res) 
	error(E_BREAKDOWN,"iter_cg");
      alpha = inner/alpha;
      v_mltadd(ip->x,p,alpha,ip->x);
      v_mltadd(r,q,-alpha,r);
      old_inner = inner;
   }

#ifdef	THREADSAFE
   V_FREE(r);   V_FREE(p);   V_FREE(q);   V_FREE(z);
#endif

   return ip->x;
}



/* iter_lanczos -- raw lanczos algorithm -- no re-orthogonalisation
   -- creates T matrix of size == m,
   but no larger than before beta_k == 0
   -- uses passed routine to do matrix-vector multiplies */
#ifndef ANSI_C
void	iter_lanczos(ip,a,b,beta2,Q)
ITER    *ip;
VEC	*a, *b;
Real	*beta2;
MAT	*Q;
#else
void	iter_lanczos(ITER *ip, VEC *a, VEC *b, Real *beta2, MAT *Q)
#endif
{
   int	j;
   STATIC VEC	*v = VNULL, *w = VNULL, *tmp = VNULL;
   Real	alpha, beta, c;
   
   if ( ! ip )
     error(E_NULL,"iter_lanczos");
   if ( ! ip->Ax || ! ip->x || ! a || ! b )
     error(E_NULL,"iter_lanczos");
   if ( ip->k <= 0 )
     error(E_BOUNDS,"iter_lanczos");
   if ( Q && ( Q->n < ip->x->dim || Q->m < ip->k ) )
     error(E_SIZES,"iter_lanczos");
   
   a = v_resize(a,(unsigned int)ip->k);	
   b = v_resize(b,(unsigned int)(ip->k-1));
   v = v_resize(v,ip->x->dim);
   w = v_resize(w,ip->x->dim);
   tmp = v_resize(tmp,ip->x->dim);
   MEM_STAT_REG(v,TYPE_VEC);
   MEM_STAT_REG(w,TYPE_VEC);
   MEM_STAT_REG(tmp,TYPE_VEC);
   
   beta = 1.0;
   v_zero(a);
   v_zero(b);
   if (Q) m_zero(Q);
   
   /* normalise x as w */
   c = v_norm2(ip->x);
   if (c <= MACHEPS) { /* ip->x == 0 */
      *beta2 = 0.0;
      return;
   }
   else 
     sv_mlt(1.0/c,ip->x,w);
   
   (ip->Ax)(ip->A_par,w,v);
   
   for ( j = 0; j < ip->k; j++ )
   {
      /* store w in Q if Q not NULL */
      if ( Q ) set_row(Q,j,w);
      
      alpha = in_prod(w,v);
      a->ve[j] = alpha;
      v_mltadd(v,w,-alpha,v);
      beta = v_norm2(v);
      if ( beta == 0.0 )
      {
	 *beta2 = 0.0;
	 return;
      }
      
      if ( j < ip->k-1 )
	b->ve[j] = beta;
      v_copy(w,tmp);
      sv_mlt(1/beta,v,w);
      sv_mlt(-beta,tmp,v);
      (ip->Ax)(ip->A_par,w,tmp);
      v_add(v,tmp,v);
   }
   *beta2 = beta;

#ifdef	THREADSAFE
   V_FREE(v);   V_FREE(w);   V_FREE(tmp);
#endif
}

/* iter_splanczos -- version that uses sparse matrix data structure */
#ifndef ANSI_C
void    iter_splanczos(A,m,x0,a,b,beta2,Q)
SPMAT	*A;
int     m;
VEC     *x0, *a, *b;
Real    *beta2;
MAT     *Q;
#else
void    iter_splanczos(SPMAT *A, int m, VEC *x0, 
		       VEC *a, VEC *b, Real *beta2, MAT *Q)
#endif
{	
   ITER *ip;
   
   ip = iter_get(0,0);
   ip->shared_x = ip->shared_b = TRUE;
   ip->Ax = (Fun_Ax) sp_mv_mlt;
   ip->A_par = (void *) A;
   ip->x = x0;
   ip->k = m;
   iter_lanczos(ip,a,b,beta2,Q);	
   iter_free(ip);   /* release only ITER structure */
}


#ifndef ANSI_C
extern	double	frexp(), ldexp();
#else
extern	double	frexp(double num, int *exponent),
  ldexp(double num, int exponent);
#endif

/* product -- returns the product of a long list of numbers
   -- answer stored in mant (mantissa) and expt (exponent) */
#ifndef ANSI_C
static	double	product(a,offset,expt)
VEC	*a;
double	offset;
int	*expt;
#else
static	double	product(VEC *a, double offset, int *expt)
#endif
{
   Real	mant, tmp_fctr;
   int	i, tmp_expt;
   
   if ( ! a )
     error(E_NULL,"product");
   
   mant = 1.0;
   *expt = 0;
   if ( offset == 0.0 )