paso/src/FGMRES.c

/* $Id:$ */

/*******************************************************
 *
 *       Copyright 2008 by University of Queensland
 *
 *                http://esscc.uq.edu.au
 *        Primary Business: Queensland, Australia
 *  Licensed under the Open Software License version 3.0
 *     http://www.opensource.org/licenses/osl-3.0.php
 *
 *******************************************************/
/*
*  Purpose
*  =======
*
*  FGMRES solves the non-linear system f0+J_0*d=0 
*  where f0=F(x0), J_0 is the jacobian of F at x0.
*
*  Convergence test: norm(f0+J_0*d)<=tolerance*norm(f0)
*
*  Arguments
*  =========
*
*   Paso_Function * F   evaluation of F (including any preconditioner)
*
*   x0                  (input) current point
*
*   f0                  (input) function F at current point x0
*
*   d                   (output) solution of f0+J0*d=0 with accuracy tolerance
*
*   iter                (input/output)
*                       On input, the maximum num_iterations to be performed.
*                       On output, actual number of num_iterations performed.
*   tolerance           (input/output) 
*                        On input, the allowable convergence measure for norm(f0+J0*d)/norm(f0)
*                        On output, the final value for norm(f0+J0*d)
*  return value
*
*         =SOLVER_NO_ERROR: Successful exit. approximate solution returned.
*         =SOLVER_MAXNUM_ITER_REACHED
*         =SOLVER_INPUT_ERROR Illegal parameter:
*         =SOLVER_BREAKDOWN: bad luck!
*         =SOLVER_MEMORY_ERROR : no memory available
*
*  ==============================================================
*/

#include "Common.h"
#include "Solver.h"
#include "Util.h"
#ifdef _OPENMP
#include <omp.h>
#endif

err_t Paso_Solver_NLGMRES(
    Paso_Function * F,
    const double* f0,
    const double* x0,
    double * x,
    dim_t *iter,
    double* tolerance,
    Paso_Performance* pp) 
{
  double static RENORMALIZATION_CONST=0.001;
  dim_t l=(*iter)+1, iter_max=*iter,k=0,n=F->local_n,i,j;
  double rel_tol=*tolerance, abs_tol, normf0, normv, normv2, hh, hr, nu, norm_of_residual=0.;
  bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE;
  double *h=NULL, **v=NULL, *c=NULL,*s=NULL,*g=NULL, *work=NULL;
  err_t Status=SOLVER_NO_ERROR;

  /*     Test the input parameters. */
  if (n < 0 || iter_max<=0 || l<1 || rel_tol<0) {
    return SOLVER_INPUT_ERROR;
  }
  Paso_zeroes(n,x);
  /*     
   *  allocate memory: 
   */
  h=TMPMEMALLOC(l*l,double);
  v=TMPMEMALLOC(iter_max,double*);
  c=TMPMEMALLOC(l,double);
  s=TMPMEMALLOC(l,double);
  g=TMPMEMALLOC(l,double);
  work=TMPMEMALLOC(n,double);

  if (h==NULL || v ==NULL || c== NULL || s == NULL || g== NULL || work==NULL) {
     Status=SOLVER_MEMORY_ERROR;
  } else {
     for (i=0;i<iter_max;i++) v[i]=NULL;
     for (i=0;i<iter_max;i++) {
       v[i]=TMPMEMALLOC(n,double);
       if (v[i]==NULL) {
          Status=SOLVER_MEMORY_ERROR;
          break;
       }
     }
  }
  if ( Status ==SOLVER_NO_ERROR ) {
     /*     
      *  the show begins:
      */
      normf0=Paso_l2(n,f0,F->mpi_info);
      k=0;
      convergeFlag=(ABS(normf0)<=0);
      if (! convergeFlag) {
          abs_tol=rel_tol*normf0;
          Paso_zeroes(n,v[0]);
          Paso_Update(n,1.,v[0],-1./normf0,f0);
          g[0]=normf0;
          while(! (breakFlag || maxIterFlag || convergeFlag)) {
               k++;
               /*
               *      call directional derivative function
               */
               Paso_FunctionDerivative(v[k],v[k-1],F,f0,x0,work);
               normv=Paso_l2(n,v[k],F->mpi_info);
               /*
                * Modified Gram-Schmidt
                */
                for (j=0;j<k;j++){
                   hh=Paso_InnerProduct(n,v[j],v[k],F->mpi_info);
                   Paso_Update(n,1.,v[k],(-hh),v[j]);
                   h[INDEX2(j,k-1,l)]=hh;
                }
                normv2=Paso_l2(n,v[k],F->mpi_info);
                h[INDEX2(k,k-1,l)]=normv2;
                /*
                 * reorthogonalize
                 */
                if (! (normv + RENORMALIZATION_CONST*normv2 > normv)) {
                     for (j=0;j<k;j++){
                         hr=Paso_InnerProduct(n,v[j],v[k],F->mpi_info);
                     h[INDEX2(j,k-1,l)]+=hr;
                         Paso_Update(n,1.,v[k],(-hr),v[j]);
                     }
                     normv2=Paso_l2(n,v[k],F->mpi_info);
                     h[INDEX2(k,k-1,l)]=normv2;
                 }
                /* 
                 *   watch out for happy breakdown
                 */
                if(normv2 > 0.) {
                   Paso_Update(n,1./normv2,v[k],0.,v[k]);
                } 
                /*
                 *   Form and store the information for the new Givens rotation
                 */
                ApplyGivensRotations(k,&h[INDEX2(0,k-1,l)],c,s);
                /*
                 *  Don't divide by zero if solution has  been found
                 */
                g[k]=0;
                nu=sqrt(h[INDEX2(k-1,k-1,l)]*h[INDEX2(k-1,k-1,l)]+h[INDEX2(k,k-1,l)]*h[INDEX2(k,k-1,l)]);
                if (nu>0) {
                    c[k-1]=h[INDEX2(k-1,k-1,l)]/nu;
                    s[k-1]=-h[k,k-1]/nu;
                    h[INDEX2(k-1,k-1,l)]=c[k-1]*h[INDEX2(k-1,k-1,l)]-s[k-1]*h[k,k-1];
                    h[INDEX2(k,k-1,l)]=0;
                    ApplyGivensRotations(2,&(g[k-1]),&(c[k-1]),&(s[k-1]));
                }
                norm_of_residual=abs(g[k]);
                maxIterFlag = (k>=iter_max);
                convergeFlag = (abs(g[k]) <= abs_tol);
printf("FGMRES step %d: error %e (tol=%e)\n",k,fabs(g[k]),abs_tol);
          }
      }
      /*
       * all done and ready for the forward substitution:
      */
      
      for (i=0;i<k;i++) {
           for (j=0;j<i;j++) {
              g[i]-=h[INDEX2(j,i,l)]*g[j];
           }
           g[i]/=h[INDEX2(i,i,l)];
           Paso_Update(n,1.,x,g[i],v[i]);
      }
 }
 /*     
  *  clean up:
  */
  if ( v !=NULL) {
    for (i=0;i<iter_max;i++) TMPMEMFREE(v);
  }
  TMPMEMFREE(h);
  TMPMEMFREE(v);
  TMPMEMFREE(c);
  TMPMEMFREE(s);
  TMPMEMFREE(g);
  TMPMEMFREE(work);
  *iter=k;
  *tolerance=norm_of_residual;
  return Status;
}

1	/* $Id:$ */
2
3	/*******************************************************
4	*
5	* Copyright 2008 by University of Queensland
6	*
7	* http://esscc.uq.edu.au
8	* Primary Business: Queensland, Australia
9	* Licensed under the Open Software License version 3.0
10	* http://www.opensource.org/licenses/osl-3.0.php
11	*
12	*******************************************************/
13	/*
14	* Purpose
15	* =======
16	*
17	* FGMRES solves the non-linear system f0+J_0*d=0
18	* where f0=F(x0), J_0 is the jacobian of F at x0.
19	*
20	* Convergence test: norm(f0+J_0d)<=tolerancenorm(f0)
21	*
22	* Arguments
23	* =========
24	*
25	* Paso_Function * F evaluation of F (including any preconditioner)
26	*
27	* x0 (input) current point
28	*
29	* f0 (input) function F at current point x0
30	*
31	* d (output) solution of f0+J0*d=0 with accuracy tolerance
32	*
33	* iter (input/output)
34	* On input, the maximum num_iterations to be performed.
35	* On output, actual number of num_iterations performed.
36	* tolerance (input/output)
37	* On input, the allowable convergence measure for norm(f0+J0*d)/norm(f0)
38	* On output, the final value for norm(f0+J0*d)
39	* return value
40	*
41	* =SOLVER_NO_ERROR: Successful exit. approximate solution returned.
42	* =SOLVER_MAXNUM_ITER_REACHED
43	* =SOLVER_INPUT_ERROR Illegal parameter:
44	* =SOLVER_BREAKDOWN: bad luck!
45	* =SOLVER_MEMORY_ERROR : no memory available
46	*
47	* ==============================================================
48	*/
49
50	#include "Common.h"
51	#include "Solver.h"
52	#include "Util.h"
53	#ifdef _OPENMP
54	#include <omp.h>
55	#endif
56
57	err_t Paso_Solver_NLGMRES(
58	Paso_Function * F,
59	const double* f0,
60	const double* x0,
61	double * x,
62	dim_t *iter,
63	double* tolerance,
64	Paso_Performance* pp)
65	{
66	double static RENORMALIZATION_CONST=0.001;
67	dim_t l=(iter)+1, iter_max=iter,k=0,n=F->local_n,i,j;
68	double rel_tol=*tolerance, abs_tol, normf0, normv, normv2, hh, hr, nu, norm_of_residual=0.;
69	bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE;
70	double h=NULL, v=NULL, c=NULL,s=NULL,g=NULL, *work=NULL;
71	err_t Status=SOLVER_NO_ERROR;
72
73	/* Test the input parameters. */
74	if (n < 0 \|\| iter_max<=0 \|\| l<1 \|\| rel_tol<0) {
75	return SOLVER_INPUT_ERROR;
76	}
77	Paso_zeroes(n,x);
78	/*
79	* allocate memory:
80	*/
81	h=TMPMEMALLOC(l*l,double);
82	v=TMPMEMALLOC(iter_max,double*);
83	c=TMPMEMALLOC(l,double);
84	s=TMPMEMALLOC(l,double);
85	g=TMPMEMALLOC(l,double);
86	work=TMPMEMALLOC(n,double);
87
88	if (h==NULL \|\| v ==NULL \|\| c== NULL \|\| s == NULL \|\| g== NULL \|\| work==NULL) {
89	Status=SOLVER_MEMORY_ERROR;
90	} else {
91	for (i=0;i<iter_max;i++) v[i]=NULL;
92	for (i=0;i<iter_max;i++) {
93	v[i]=TMPMEMALLOC(n,double);
94	if (v[i]==NULL) {
95	Status=SOLVER_MEMORY_ERROR;
96	break;
97	}
98	}
99	}
100	if ( Status ==SOLVER_NO_ERROR ) {
101	/*
102	* the show begins:
103	*/
104	normf0=Paso_l2(n,f0,F->mpi_info);
105	k=0;
106	convergeFlag=(ABS(normf0)<=0);
107	if (! convergeFlag) {
108	abs_tol=rel_tol*normf0;
109	Paso_zeroes(n,v[0]);
110	Paso_Update(n,1.,v[0],-1./normf0,f0);
111	g[0]=normf0;
112	while(! (breakFlag \|\| maxIterFlag \|\| convergeFlag)) {
113	k++;
114	/*
115	* call directional derivative function
116	*/
117	Paso_FunctionDerivative(v[k],v[k-1],F,f0,x0,work);
118	normv=Paso_l2(n,v[k],F->mpi_info);
119	/*
120	* Modified Gram-Schmidt
121	*/
122	for (j=0;j<k;j++){
123	hh=Paso_InnerProduct(n,v[j],v[k],F->mpi_info);
124	Paso_Update(n,1.,v[k],(-hh),v[j]);
125	h[INDEX2(j,k-1,l)]=hh;
126	}
127	normv2=Paso_l2(n,v[k],F->mpi_info);
128	h[INDEX2(k,k-1,l)]=normv2;
129	/*
130	* reorthogonalize
131	*/
132	if (! (normv + RENORMALIZATION_CONST*normv2 > normv)) {
133	for (j=0;j<k;j++){
134	hr=Paso_InnerProduct(n,v[j],v[k],F->mpi_info);
135	h[INDEX2(j,k-1,l)]+=hr;
136	Paso_Update(n,1.,v[k],(-hr),v[j]);
137	}
138	normv2=Paso_l2(n,v[k],F->mpi_info);
139	h[INDEX2(k,k-1,l)]=normv2;
140	}
141	/*
142	* watch out for happy breakdown
143	*/
144	if(normv2 > 0.) {
145	Paso_Update(n,1./normv2,v[k],0.,v[k]);
146	}
147	/*
148	* Form and store the information for the new Givens rotation
149	*/
150	ApplyGivensRotations(k,&h[INDEX2(0,k-1,l)],c,s);
151	/*
152	* Don't divide by zero if solution has been found
153	*/
154	g[k]=0;
155	nu=sqrt(h[INDEX2(k-1,k-1,l)]h[INDEX2(k-1,k-1,l)]+h[INDEX2(k,k-1,l)]h[INDEX2(k,k-1,l)]);
156	if (nu>0) {
157	c[k-1]=h[INDEX2(k-1,k-1,l)]/nu;
158	s[k-1]=-h[k,k-1]/nu;
159	h[INDEX2(k-1,k-1,l)]=c[k-1]h[INDEX2(k-1,k-1,l)]-s[k-1]h[k,k-1];
160	h[INDEX2(k,k-1,l)]=0;
161	ApplyGivensRotations(2,&(g[k-1]),&(c[k-1]),&(s[k-1]));
162	}
163	norm_of_residual=abs(g[k]);
164	maxIterFlag = (k>=iter_max);
165	convergeFlag = (abs(g[k]) <= abs_tol);
166	printf("FGMRES step %d: error %e (tol=%e)\n",k,fabs(g[k]),abs_tol);
167	}
168	}
169	/*
170	* all done and ready for the forward substitution:
171	*/
172
173	for (i=0;i<k;i++) {
174	for (j=0;j<i;j++) {
175	g[i]-=h[INDEX2(j,i,l)]*g[j];
176	}
177	g[i]/=h[INDEX2(i,i,l)];
178	Paso_Update(n,1.,x,g[i],v[i]);
179	}
180	}
181	/*
182	* clean up:
183	*/
184	if ( v !=NULL) {
185	for (i=0;i<iter_max;i++) TMPMEMFREE(v);
186	}
187	TMPMEMFREE(h);
188	TMPMEMFREE(v);
189	TMPMEMFREE(c);
190	TMPMEMFREE(s);
191	TMPMEMFREE(g);
192	TMPMEMFREE(work);
193	*iter=k;
194	*tolerance=norm_of_residual;
195	return Status;
196	}
197