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lis_solver_bicg.c
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lis_solver_bicg.c
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/* Copyright (C) The Scalable Software Infrastructure Project. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. Neither the name of the project nor the names of its contributors
may be used to endorse or promote products derived from this software
without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE SCALABLE SOFTWARE INFRASTRUCTURE PROJECT
``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE SCALABLE SOFTWARE INFRASTRUCTURE
PROJECT BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/
#ifdef HAVE_CONFIG_H
#include "lis_config.h"
#else
#ifdef HAVE_CONFIG_WIN_H
#include "lis_config_win.h"
#endif
#endif
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#ifdef HAVE_MALLOC_H
#include <malloc.h>
#endif
#include <string.h>
#include <stdarg.h>
#ifdef _OPENMP
#include <omp.h>
#endif
#ifdef USE_MPI
#include <mpi.h>
#endif
#include "lislib.h"
/*****************************************
* Preconditioned BiConjugate Gradient *
*****************************************
r(0) = b - Ax(0)
rtld(0) = r(0) or random
rho(-1) = 1
p(0) = (0,...,0)^T
ptld(0) = (0,...,0)^T
*****************************************
for k=1,2,...
z(k-1) = M^-1 * r(k-1)
ztld(k-1) = M^-T * rtld(k-1)
rho(k-1) = <z(k-1),rtld(k-1)>
beta = rho(k-1) / rho(k-2)
p(k) = z(k-1) + beta*p(k-1)
ptld(k) = ztld(k-1) + beta*ptld(k-1)
q(k) = A * p(k)
qtld(k) = A^T * ptld(k)
tmpdot1 = <ptld(k),q(k)>
alpha = rho(k-1) / tmpdot1
x(k) = x(k-1) + alpha*p(k)
r(k) = r(k-1) - alpha*q(k)
rtld(k) = rtld(k-1) - alpha*qtld(k)
*****************************************/
#define NWORK 6
#undef __FUNC__
#define __FUNC__ "lis_bicg_check_params"
LIS_INT lis_bicg_check_params(LIS_SOLVER solver)
{
LIS_DEBUG_FUNC_IN;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
#undef __FUNC__
#define __FUNC__ "lis_bicg_malloc_work"
LIS_INT lis_bicg_malloc_work(LIS_SOLVER solver)
{
LIS_VECTOR *work;
LIS_INT i,j,worklen,err;
LIS_DEBUG_FUNC_IN;
/*
err = lis_matrix_convert(solver->A,&solver->At,LIS_MATRIX_CCS);
if( err ) return err;
*/
// suifengls: allocate extra vectors: 3 = Ones + sumA + sumAt, 5 = ckpX + ckpP + ckpPt + ckpR + ckpRt
worklen = NWORK + 3 + 5;
work = (LIS_VECTOR *)lis_malloc( worklen*sizeof(LIS_VECTOR),"lis_bicg_malloc_work::work" );
if( work==NULL )
{
LIS_SETERR_MEM(worklen*sizeof(LIS_VECTOR));
return LIS_ERR_OUT_OF_MEMORY;
}
if( solver->precision==LIS_PRECISION_DEFAULT )
{
for(i=0;i<worklen;i++)
{
err = lis_vector_duplicate(solver->A,&work[i]);
if( err ) break;
}
}
else
{
for(i=0;i<worklen;i++)
{
err = lis_vector_duplicateex(LIS_PRECISION_QUAD,solver->A,&work[i]);
if( err ) break;
memset(work[i]->value_lo,0,solver->A->np*sizeof(LIS_SCALAR));
}
}
if( i<worklen )
{
for(j=0;j<i;j++) lis_vector_destroy(work[j]);
lis_free(work);
return err;
}
solver->worklen = worklen;
solver->work = work;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
#undef __FUNC__
#define __FUNC__ "lis_bicg"
LIS_INT lis_bicg(LIS_SOLVER solver)
{
LIS_MATRIX A,At;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, z,ztld,p, ptld, q, qtld;
LIS_SCALAR alpha, beta, rho, rho_old, tmpdot1;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
// suifengls: ft-defined variables
int rank;
const LIS_INT CHECK_ITER = 15;
const LIS_INT ERROR_ITER = 43;
const LIS_INT CHKPT_ITER = 15;
const LIS_SCALAR eps = 1e-10;
LIS_INT flag = 0;
LIS_SCALAR rerrX, rerrR, rerrRt;
LIS_INT localN, globalN;
LIS_VECTOR sumA, sumAt, Ones;
LIS_SCALAR cksA, cksAt, cksR, cksRt, cksZ, cksZt, cksP, cksPt, cksQ, cksQt, cksX, checksum;
// suifengls: checkpointing variable
LIS_VECTOR ckpX, ckpP, ckpPt, ckpR, ckpRt;
LIS_SCALAR ckprho = 0.0, ckpx, ckpp, ckppt, ckpr, ckprt;
LIS_INT ckpiter = 0;
LIS_DEBUG_FUNC_IN;
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
A = solver->A;
At = solver->A;
M = solver->precon;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
ptimes = 0.0;
r = solver->work[0];
rtld = solver->work[1];
z = solver->work[2];
ztld = solver->work[3];
p = solver->work[4];
ptld = solver->work[5];
q = solver->work[2];
qtld = solver->work[3];
rho_old = (LIS_SCALAR)1.0;
// suifengls: assign checksum vectors
Ones = solver->work[6];
sumA = solver->work[7];
sumAt = solver->work[8];
// suifengls: assign ckp vecotrs
ckpX = solver->work[9];
ckpP = solver->work[10];
ckpPt = solver->work[11];
ckpR = solver->work[12];
ckpRt = solver->work[13];
// suifengls: get global size of A
lis_matrix_get_size(A, &localN, &globalN);
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_all(0, p);
lis_vector_set_all(0, ptld);
// suifengls: initialize all checksum
// checksum of A
lis_vector_set_all(1.0, Ones);
lis_matvec(A, Ones, sumAt);
lis_matvect(At, Ones, sumA);
lis_vector_dot(Ones, sumA, &cksA);
cksAt = cksA;
lis_vector_axpy(-cksA/(globalN+1), Ones, sumA);
lis_vector_axpy(-cksAt/(globalN+1), Ones, sumAt);
lis_vector_dot(Ones, sumA, &cksA);
lis_vector_dot(Ones, sumAt, &cksAt);
// checksum of others
cksZ = 0.0, cksZt = 0.0, cksP = 0.0, cksPt = 0.0, cksQ = 0.0, cksQt = 0.0, checksum = 0.0;
lis_vector_dot(Ones, x, &cksX);
lis_vector_dot(Ones, r, &cksR);
lis_vector_dot(Ones, rtld, &cksRt);
flag = 0;
for( iter=1; iter<=maxiter; iter++ )
{
/* z = M^-1 * r */
/* ztld = M^-T * rtld */
times = lis_wtime();
lis_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
ptimes += lis_wtime()-times;
// suifengls: checksum Z and Ztld
lis_vector_dot(Ones, z, &cksZ);
lis_vector_dot(Ones, ztld, &cksZt);
/* rho = <z,rtld> */
lis_vector_dot(z,rtld,&rho);
/* printf("rho = %e\n",rho);*/
/* test breakdown */
if( rho==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
beta = rho / rho_old;
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* q = A * p */
/* qtld = A^T * ptld */
lis_vector_xpay(z,beta,p);
// suifengls: checksum P
cksP = cksZ + beta * cksP;
LIS_MATVEC(A,p,q);
// suifengls: checksum Q
lis_vector_dot(p, sumA, &cksQ);
cksQ = cksQ + cksP * cksA;
lis_vector_xpay(ztld,beta,ptld);
// suifengls: checksum Ptld
cksPt = cksZt + beta * cksPt;
LIS_MATVECT(At,ptld,qtld);
// suifengls: checksum Qtld
lis_vector_dot(ptld, sumAt, &cksQt);
cksQt = cksQt + cksPt * cksAt;
// suifengls: introduce an error
if(!rank && iter == ERROR_ITER)
{
printf("========== Introducing an error at iteration %d ==========\n", iter);
lis_vector_set_value(LIS_INS_VALUE, 0, 16, z);
}
/* tmpdot1 = <ptld,q> */
lis_vector_dot(ptld,q,&tmpdot1);
/* printf("tmpdot1 = %e\n",tmpdot1);*/
/* test breakdown */
if( tmpdot1==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
alpha = rho / tmpdot1;
/* x = x + alpha*p */
lis_vector_axpy(alpha,p,x);
// suifengls: checksum X
cksX = cksX + alpha * cksP;
/* r = r - alpha*q */
lis_vector_axpy(-alpha,q,r);
// suifengls: checksum R
cksR = cksR - alpha * cksQ;
/* rtld = rtld - alpha*qtld */
lis_vector_axpy(-alpha,qtld,rtld);
// suifengls: checksum Rtld
cksRt = cksRt - alpha * cksQt;
rho_old = rho;
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
// suifengls: checking, checkpointing, recovering
if(nrm2 <= tol || iter % CHECK_ITER == 0)
{
// suifengls: checking cksX
lis_vector_dot(Ones, x, &checksum);
rerrX = fabs(checksum - cksX)/fabs(cksX);
if(rerrX > eps && !flag)
{
flag = 1; // error detected
if(!rank)
printf("========== Error deteced in X: %e at iteration %d ==========\n", rerrX, iter);
}
// suifengls: checking cksR
lis_vector_dot(Ones, r, &checksum);
rerrR = fabs(checksum - cksR)/fabs(cksR);
if((fabs(cksR) > eps && fabs(checksum) > eps) && rerrR > eps && !flag)
{
flag = 1; // error detected
if(!rank)
printf("========== Error deteced in R: %e at iteration %d ==========\n", rerrR, iter);
}
// suifengls: checking cksRt
lis_vector_dot(Ones, rtld, &checksum);
rerrRt = fabs(checksum - cksRt)/fabs(cksRt);
if((fabs(cksRt) > eps && fabs(checksum) > eps) && rerrRt > eps && !flag)
{
flag = 1; // error detected
if(!rank)
printf("========== Error deteced in Rtld: %e at iteration %d ==========\n", rerrRt, iter);
}
// suifengls: checkpointing and recovery
if(!flag && nrm2 > tol) // checkpointing
{
if(!rank)
printf("========== Checkpointing at iteration %d ==========\n", iter);
ckpiter = iter;
ckprho = rho_old;
lis_vector_copy(r, ckpR);
ckpr = cksR;
lis_vector_copy(rtld, ckpRt);
ckprt = cksRt;
lis_vector_copy(p, ckpP);
ckpp = cksP;
lis_vector_copy(ptld, ckpPt);
ckppt = cksPt;
lis_vector_copy(x, ckpX);
ckpx = cksX;
}
else if(flag) // error detected, recovery
{
if(!rank)
printf("========== Rollback at iteration %d ==========\n", ckpiter);
//iter = ckpiter;
rho_old = ckprho;
lis_vector_copy(ckpR, r);
cksR = ckpr;
lis_vector_copy(ckpRt, rtld);
cksRt = ckprt;
lis_vector_copy(ckpP, p);
cksP = ckpp;
lis_vector_copy(ckpPt, ptld);
cksPt = ckppt;
lis_vector_copy(ckpX, x);
cksX = ckpx;
flag = 0;
}
}
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
#ifdef USE_QUAD_PRECISION
#undef __FUNC__
#define __FUNC__ "lis_bicg_quad"
LIS_INT lis_bicg_quad(LIS_SOLVER solver)
{
LIS_MATRIX A,At;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, z,ztld,p, ptld, q, qtld;
LIS_QUAD_PTR alpha, beta, rho, rho_old, tmpdot1;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
LIS_DEBUG_FUNC_IN;
A = solver->A;
At = solver->A;
M = solver->precon;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
ptimes = 0.0;
r = solver->work[0];
rtld = solver->work[1];
z = solver->work[2];
ztld = solver->work[3];
p = solver->work[4];
ptld = solver->work[5];
q = solver->work[2];
qtld = solver->work[3];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot1,4,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, ptld);
for( iter=1; iter<=maxiter; iter++ )
{
/* z = M^-1 * r */
/* ztld = M^-T * rtld */
times = lis_wtime();
lis_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
ptimes += lis_wtime()-times;
/* rho = <z,rtld> */
lis_vector_dotex_mmm(z,rtld,&rho);
/* printf("rho = %e %e\n",rho.hi[0],rho.lo[0]);*/
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
/* printf("beta = %e %e\n",beta.hi[0],beta.lo[0]);*/
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* q = A * p */
/* qtld = A^T * ptld */
lis_vector_xpayex_mmm(z,beta,p);
LIS_MATVEC(A,p,q);
lis_vector_xpayex_mmm(ztld,beta,ptld);
LIS_MATVECT(At,ptld,qtld);
/* tmpdot1 = <ptld,q> */
lis_vector_dotex_mmm(ptld,q,&tmpdot1);
/* printf("tmpdot1 = %e %e\n",tmpdot1.hi[0],tmpdot1.lo[0]);*/
/* test breakdown */
if( tmpdot1.hi[0]==0.0 && tmpdot1.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot1.hi);
/* printf("alpha = %e %e\n",alpha.hi[0],alpha.lo[0]);*/
/* x = x + alpha*p */
lis_vector_axpyex_mmm(alpha,p,x);
/* r = r - alpha*q */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,q,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol > nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* rtld = rtld - alpha*qtld */
lis_vector_axpyex_mmm(alpha,qtld,rtld);
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
#undef __FUNC__
#define __FUNC__ "lis_bicg_switch"
LIS_INT lis_bicg_switch(LIS_SOLVER solver)
{
LIS_MATRIX A,At;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, z,ztld,p, ptld, q, qtld;
LIS_QUAD_PTR alpha, beta, rho, rho_old, tmpdot1;
LIS_REAL bnrm2, nrm2, tol, tol2;
LIS_INT iter,maxiter,n,output,conv;
LIS_INT iter2,maxiter2;
double times,ptimes;
LIS_DEBUG_FUNC_IN;
A = solver->A;
At = solver->A;
M = solver->precon;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
maxiter2 = solver->options[LIS_OPTIONS_SWITCH_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol2 = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
ptimes = 0.0;
r = solver->work[0];
rtld = solver->work[1];
z = solver->work[2];
ztld = solver->work[3];
p = solver->work[4];
ptld = solver->work[5];
q = solver->work[2];
qtld = solver->work[3];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot1,4,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol2 = solver->tol_switch;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, ptld);
r->precision = LIS_PRECISION_DEFAULT;
rtld->precision = LIS_PRECISION_DEFAULT;
p->precision = LIS_PRECISION_DEFAULT;
ptld->precision = LIS_PRECISION_DEFAULT;
for( iter=1; iter<=maxiter2; iter++ )
{
/* z = M^-1 * r */
/* ztld = M^-T * rtld */
times = lis_wtime();
lis_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
ptimes += lis_wtime()-times;
/* rho = <z,rtld> */
lis_vector_dot(z,rtld,&rho.hi[0]);
/* test breakdown */
if( rho.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
beta.hi[0] = rho.hi[0] / rho_old.hi[0];
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* q = A * p */
/* qtld = A^T * ptld */
lis_vector_xpay(z,beta.hi[0],p);
LIS_MATVEC(A,p,q);
lis_vector_xpay(ztld,beta.hi[0],ptld);
LIS_MATVECT(At,ptld,qtld);
/* tmpdot1 = <ptld,q> */
lis_vector_dot(ptld,q,&tmpdot1.hi[0]);
/* test breakdown */
if( tmpdot1.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
alpha.hi[0] = rho.hi[0] / tmpdot1.hi[0];
/* x = x + alpha*p */
lis_vector_axpy(alpha.hi[0],p,x);
/* r = r - alpha*q */
lis_vector_axpy(-alpha.hi[0],q,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( nrm2 <= tol2 )
{
solver->iter = iter;
solver->iter2 = iter;
solver->ptimes = ptimes;
break;
}
/* rtld = rtld - alpha*qtld */
lis_vector_axpy(-alpha.hi[0],qtld,rtld);
rho_old.hi[0] = rho.hi[0];
}
r->precision = LIS_PRECISION_QUAD;
rtld->precision = LIS_PRECISION_QUAD;
p->precision = LIS_PRECISION_QUAD;
ptld->precision = LIS_PRECISION_QUAD;
/* solver->precon->precon_type = 0;*/
solver->options[LIS_OPTIONS_INITGUESS_ZEROS] = LIS_FALSE;
lis_vector_copyex_mn(x,solver->xx);
rho_old.hi[0] = 1.0;
lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2);
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, ptld);
for( iter2=iter+1; iter2<=maxiter; iter2++ )
{
/* z = M^-1 * r */
/* ztld = M^-T * rtld */
times = lis_wtime();
lis_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
/* memset(z->value_lo,0,n*sizeof(LIS_SCALAR));
memset(ztld->value_lo,0,n*sizeof(LIS_SCALAR));*/
ptimes += lis_wtime()-times;
/* rho = <z,rtld> */
lis_vector_dotex_mmm(z,rtld,&rho);
/* printf("rho = %e %e\n",rho.hi[0],rho.lo[0]);*/
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* q = A * p */
/* qtld = A^T * ptld */
lis_vector_xpayex_mmm(z,beta,p);
LIS_MATVEC(A,p,q);
lis_vector_xpayex_mmm(ztld,beta,ptld);
LIS_MATVECT(At,ptld,qtld);
/* tmpdot1 = <ptld,q> */
lis_vector_dotex_mmm(ptld,q,&tmpdot1);
/* test breakdown */
if( tmpdot1.hi[0]==0.0 && tmpdot1.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot1.hi);
/* x = x + alpha*p */
lis_vector_axpyex_mmm(alpha,p,x);
/* r = r - alpha*q */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,q,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter2] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol > nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* rtld = rtld - alpha*qtld */
lis_vector_axpyex_mmm(alpha,qtld,rtld);
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
#endif
/*****************************************
* Preconditioned BiConjugate Residual *
*****************************************
r(0) = b - Ax(0)
rtld(0) = r(0) or random
z(0) = M^-1 * r(0)
ztld(0) = M^-1 * rtld(0)
p(0) = z(0)
ptld(0) = ztld(0)
ap(0) = A * z(0)
rho(0) = <ap(0),ztld(0)>
*****************************************
for k=1,2,...
aptld(k-1) = A^T * ptld(k-1)
map(k-1) = M^-1 * ap(k-1)
tmpdot1 = <map(k-1),aptld(k-1)>
alpha = rho(k-1) / tmpdot1
x(k) = x(k-1) + alpha*ap(k-1)
r(k) = r(k-1) - alpha*ap(k-1)
rtld(k) = rtld(k-1) - alpha*aptld(k-1)
z(k) = z(k-1) - alpha * map(k-1)
ztld(k) = M^-T * rtld(k-1)
az(k) = A * z(k)
rho(k) = <az(k),ztld(k)>
beta = rho(k) / rho(k-1)
p(k) = z(k) + beta*p(k-1)
ptld(k) = ztld(k) + beta*ptld(k-1)
ap(k) = az(k) + beta*ap(k-1)
*****************************************/
#undef NWORK
#define NWORK 10
#undef __FUNC__
#define __FUNC__ "lis_bicr_check_params"
LIS_INT lis_bicr_check_params(LIS_SOLVER solver)
{
LIS_DEBUG_FUNC_IN;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
#undef __FUNC__
#define __FUNC__ "lis_bicr_malloc_work"
LIS_INT lis_bicr_malloc_work(LIS_SOLVER solver)
{
LIS_VECTOR *work;
LIS_INT i,j,worklen,err;
LIS_DEBUG_FUNC_IN;
/*
err = lis_matrix_convert(solver->A,&solver->At,LIS_MATRIX_CCS);
if( err ) return err;
*/
worklen = NWORK;
work = (LIS_VECTOR *)lis_malloc( worklen*sizeof(LIS_VECTOR),"lis_bicg_malloc_work::work" );
if( work==NULL )
{
LIS_SETERR_MEM(worklen*sizeof(LIS_VECTOR));
return LIS_ERR_OUT_OF_MEMORY;
}
if( solver->precision==LIS_PRECISION_DEFAULT )
{
for(i=0;i<worklen;i++)
{
err = lis_vector_duplicate(solver->A,&work[i]);
if( err ) break;
}
}
else
{
for(i=0;i<worklen;i++)
{
err = lis_vector_duplicateex(LIS_PRECISION_QUAD,solver->A,&work[i]);
if( err ) break;
memset(work[i]->value_lo,0,solver->A->np*sizeof(LIS_SCALAR));
}
}
if( i<worklen )
{
for(j=0;j<i;j++) lis_vector_destroy(work[j]);
lis_free(work);
return err;
}
solver->worklen = worklen;
solver->work = work;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
#undef __FUNC__
#define __FUNC__ "lis_bicr"
LIS_INT lis_bicr(LIS_SOLVER solver)
{
LIS_MATRIX A,At;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, z,ztld,p, ptld, ap, map, az, aptld;
LIS_SCALAR alpha, beta, rho, rho_old, tmpdot1;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
LIS_DEBUG_FUNC_IN;
A = solver->A;
At = solver->A;
M = solver->precon;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
ptimes = 0.0;
r = solver->work[0];
rtld = solver->work[1];
z = solver->work[2];
ztld = solver->work[3];
p = solver->work[4];
ptld = solver->work[5];
ap = solver->work[6];
az = solver->work[7];
map = solver->work[8];
aptld = solver->work[9];
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
lis_vector_copy(z,p);
lis_vector_copy(ztld,ptld);
LIS_MATVEC(A,z,ap);
lis_vector_dot(ap,ztld,&rho_old);
for( iter=1; iter<=maxiter; iter++ )
{
/* aptld = A^T * ptld */
/* map = M^-1 * ap */
LIS_MATVECT(A,ptld,aptld);
times = lis_wtime();
lis_psolve(solver, ap, map);
ptimes += lis_wtime()-times;