itersym.c

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#include <../../nrnconf.h>
 
/**************************************************************************
**
** 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        "matrix.h"
#include        "matrix2.h"
#include    "sparse.h"
#include        "iter.h"
#include    <math.h>
 
static char rcsid[] = "itersym.c,v 1.1 1997/12/04 17:55:29 hines Exp";
 
 
#ifdef ANSI_C
VEC *spCHsolve(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.
   */
VEC  *iter_spcg(A,LLT,b,eps,x,limit,steps)
SPMAT   *A, *LLT;
VEC *b, *x;
double  eps;
int *steps, limit;
{   
   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;
  */
VEC  *iter_cg(ip)
ITER *ip;
{
   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;
   }
   
   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 */
void    iter_lanczos(ip,a,b,beta2,Q)
ITER    *ip;
VEC *a, *b;
Real    *beta2;
MAT *Q;
{
   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,(u_int)ip->k);    
   b = v_resize(b,(u_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;
   
}
 
/* iter_splanczos -- version that uses sparse matrix data structure */
void    iter_splanczos(A,m,x0,a,b,beta2,Q)
SPMAT   *A;
int     m;
VEC     *x0, *a, *b;
Real    *beta2;
MAT     *Q;
{   
   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 MAC
extern  double  frexp(), ldexp();
#endif
 
/* product -- returns the product of a long list of numbers
   -- answer stored in mant (mantissa) and expt (exponent) */
static  double  product(a,offset,expt)
VEC *a;
double  offset;
int *expt;
{
   Real mant, tmp_fctr;
   int  i, tmp_expt;
   
   if ( ! a )
     error(E_NULL,"product");
   
   mant = 1.0;
   *expt = 0;
   if ( offset == 0.0 )
     for ( i = 0; i < a->dim; i++ )
     {
    mant *= frexp(a->ve[i],&tmp_expt);
    *expt += tmp_expt;
    if ( ! (i % 10) )
    {
       mant = frexp(mant,&tmp_expt);
       *expt += tmp_expt;
    }
     }
   else
     for ( i = 0; i < a->dim; i++ )
     {
    tmp_fctr = a->ve[i] - offset;
    tmp_fctr += (tmp_fctr > 0.0 ) ? -MACHEPS*offset :
      MACHEPS*offset;
    mant *= frexp(tmp_fctr,&tmp_expt);
    *expt += tmp_expt;
    if ( ! (i % 10) )
    {
       mant = frexp(mant,&tmp_expt);
       *expt += tmp_expt;
    }
     }
   
   mant = frexp(mant,&tmp_expt);
   *expt += tmp_expt;
   
   return mant;
}
 
/* product2 -- returns the product of a long list of numbers
   -- answer stored in mant (mantissa) and expt (exponent) */
static  double  product2(a,k,expt)
VEC *a;
int k;  /* entry of a to leave out */
int *expt;
{
   Real mant, mu, tmp_fctr;
   int  i, tmp_expt;
   
   if ( ! a )
     error(E_NULL,"product2");
   if ( k < 0 || k >= a->dim )
     error(E_BOUNDS,"product2");
   
   mant = 1.0;
   *expt = 0;
   mu = a->ve[k];
   for ( i = 0; i < a->dim; i++ )
   {
      if ( i == k )
    continue;
      tmp_fctr = a->ve[i] - mu;
      tmp_fctr += ( tmp_fctr > 0.0 ) ? -MACHEPS*mu : MACHEPS*mu;
      mant *= frexp(tmp_fctr,&tmp_expt);
      *expt += tmp_expt;
      if ( ! (i % 10) )
      {
     mant = frexp(mant,&tmp_expt);
     *expt += tmp_expt;
      }
   }
   mant = frexp(mant,&tmp_expt);
   *expt += tmp_expt;
   
   return mant;
}
 
/* dbl_cmp -- comparison function to pass to qsort() */
static  int dbl_cmp(x,y)
Real    *x, *y;
{
   Real tmp;
   
   tmp = *x - *y;
   return (tmp > 0 ? 1 : tmp < 0 ? -1: 0);
}
 
/* iter_lanczos2 -- lanczos + error estimate for every e-val
   -- uses Cullum & Willoughby approach, Sparse Matrix Proc. 1978
   -- returns multiple e-vals where multiple e-vals may not exist
   -- returns evals vector */
VEC *iter_lanczos2(ip,evals,err_est)
ITER    *ip;            /* ITER structure */
VEC *evals;     /* eigenvalue vector */
VEC *err_est;   /* error estimates of eigenvalues */
{
   VEC      *a;
   static   VEC *b=VNULL, *a2=VNULL, *b2=VNULL;
   Real beta, pb_mant, det_mant, det_mant1, det_mant2;
   int  i, pb_expt, det_expt, det_expt1, det_expt2;
   
   if ( ! ip )
     error(E_NULL,"iter_lanczos2");
   if ( ! ip->Ax || ! ip->x )
     error(E_NULL,"iter_lanczos2");
   if ( ip->k <= 0 )
     error(E_RANGE,"iter_lanczos2");
   
   a = evals;
   a = v_resize(a,(u_int)ip->k);
   b = v_resize(b,(u_int)(ip->k-1));
   MEM_STAT_REG(b,TYPE_VEC);
   
   iter_lanczos(ip,a,b,&beta,MNULL);
   
   /* printf("# beta =%g\n",beta); */
   pb_mant = 0.0;
   if ( err_est )
   {
      pb_mant = product(b,(double)0.0,&pb_expt);
      /* printf("# pb_mant = %g, pb_expt = %d\n",pb_mant, pb_expt); */
   }
   
   /* printf("# diags =\n");    v_output(a); */
   /* printf("# off diags =\n");    v_output(b); */
   a2 = v_resize(a2,a->dim - 1);
   b2 = v_resize(b2,b->dim - 1);
   MEM_STAT_REG(a2,TYPE_VEC);
   MEM_STAT_REG(b2,TYPE_VEC);
   for ( i = 0; i < a2->dim - 1; i++ )
   {
      a2->ve[i] = a->ve[i+1];
      b2->ve[i] = b->ve[i+1];
   }
   a2->ve[a2->dim-1] = a->ve[a2->dim];
   
   trieig(a,b,MNULL);
   
   /* sort evals as a courtesy */
   qsort((void *)(a->ve),(int)(a->dim),sizeof(Real),(int (*)())dbl_cmp);
   
   /* error estimates */
   if ( err_est )
   {
      err_est = v_resize(err_est,(u_int)ip->k);
      
      trieig(a2,b2,MNULL);
      /* printf("# a =\n"); v_output(a); */
      /* printf("# a2 =\n");    v_output(a2); */
      
      for ( i = 0; i < a->dim; i++ )
      {
     det_mant1 = product2(a,i,&det_expt1);
     det_mant2 = product(a2,(double)a->ve[i],&det_expt2);
     /* printf("# det_mant1=%g, det_expt1=%d\n",
        det_mant1,det_expt1); */
     /* printf("# det_mant2=%g, det_expt2=%d\n",
        det_mant2,det_expt2); */
     if ( det_mant1 == 0.0 )
     {   /* multiple e-val of T */
        err_est->ve[i] = 0.0;
        continue;
     }
     else if ( det_mant2 == 0.0 )
     {
        err_est->ve[i] = HUGE;
        continue;
     }
     if ( (det_expt1 + det_expt2) % 2 )
       /* if odd... */
       det_mant = sqrt(2.0*fabs(det_mant1*det_mant2));
     else /* if even... */
       det_mant = sqrt(fabs(det_mant1*det_mant2));
     det_expt = (det_expt1+det_expt2)/2;
     err_est->ve[i] = fabs(beta*
                   ldexp(pb_mant/det_mant,pb_expt-det_expt));
      }
   }
   
   return a;
}
 
/* iter_splanczos2 -- version of iter_lanczos2() that uses sparse matrix data
   structure */
 
VEC    *iter_splanczos2(A,m,x0,evals,err_est)
SPMAT   *A;
int  m;
VEC *x0;        /* initial vector */
VEC *evals;     /* eigenvalue vector */
VEC *err_est;   /* error estimates of eigenvalues */
{   
   ITER *ip;
   VEC *a;
   
   ip = iter_get(0,0);
   ip->Ax = (Fun_Ax) sp_mv_mlt;
   ip->A_par = (void *) A;
   ip->x = x0;
   ip->k = m;
   a = iter_lanczos2(ip,evals,err_est); 
   ip->shared_x = ip->shared_b = TRUE;
   iter_free(ip);   /* release only ITER structure */
   return a;
}
 
 
 
 
/*
  Conjugate gradient method
  Another variant - mainly for testing
  */
 
VEC  *iter_cg1(ip)
ITER *ip;
{
   static VEC *r = VNULL, *p = VNULL, *q = VNULL, *z = VNULL;
   Real alpha;
   double 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);
   }
   
   if (ip->Bx) (ip->Bx)(ip->B_par,r,p);
   else v_copy(r,p);
   
   inner = in_prod(p,r);
   nres = sqrt(fabs(inner));
   if (ip->info) ip->info(ip,nres,r,p);
   if ( nres == 0.0) return ip->x;
   
   for ( ip->steps = 0; ip->steps <= ip->limit; ip->steps++ )
   {
      ip->Ax(ip->A_par,p,q);
      inner = in_prod(q,p);
      if (sqrt(fabs(inner)) <= MACHEPS*ip->init_res)
    error(E_BREAKDOWN,"iter_cg1");
 
      alpha = in_prod(p,r)/inner;
      v_mltadd(ip->x,p,alpha,ip->x);
      v_mltadd(r,q,-alpha,r);
      
      rr = r;
      if (ip->Bx) {
     ip->Bx(ip->B_par,r,z);
     rr = z;
      }
      
      nres = in_prod(r,rr);
      if (nres < 0.0) {
     warning(WARN_RES_LESS_0,"iter_cg");
     break;
      }
      nres = sqrt(fabs(nres));
      if (ip->info) ip->info(ip,nres,r,z);
      if (ip->steps == 0) ip->init_res = nres;
      if ( ip->stop_crit(ip,nres,r,z) ) break;
      
      alpha = -in_prod(rr,q)/inner;
      v_mltadd(rr,p,alpha,p);
      
   }
   
   return ip->x;
}