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lis_solver_gpbicg.c
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lis_solver_gpbicg.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>
#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 Generalized Product type of BiConjugate Gradient *
********************************************************************
r(0) = b - Ax(0)
rtld(0) = r(0) or random
p(0) = M^-1 * r(0)
rho(0) = <rtld,r(0)>
t(-1) = (0,...,0)^T
w(-1) = (0,...,0)^T
********************************************************************
for k=1,2,...
ap(k-1) = A * p(k-1)
map(k-1)= M^-1 * ap(k-1)
tmpdot0 = <ap(k-1),rtld(0)>
alpha = rho(k-1) / tmpdot0
y(k-1) = t(k-2) - r(k-1) - alpha*w(k-2) + alpha*ap(k-1)
t(k-1) = r(k-1) - alpha*ap(k-1)
mt(k-1) = mr(k-1) - alpha*map(k-1)
amt(k-1)= A * mt(k-1)
tmpdot0 = <y(k-1),y(k-1)>
tmpdot1 = <amt(k-1),t(k-1)>
tmpdot2 = <y(k-1),t(k-1)>
tmpdot3 = <amt(k-1),y(k-1)>
tmpdot4 = <amt(k-1),amt(k-1)>
tmp = tmpdot4*tmpdot0-tmpdot3*tmpdot3
qsi = (tmpdot0*tmpdot1-tmpdot2*tmpdot3) / tmp
eta = (tmpdot4*tmpdot2-tmpdot3*tmpdot1) / tmp
u(k-1) = qsi*map(k-1) + eta*(mt(k-2) - mr(k-1) + beta*u(k-2))
z(k-1) = qsi*mr(k-1) + eta*z(k-2) - alpha*u(k-1)
x(k) = x(k-1) + alpha*p(k-1) + z(k-1)
r(k) = t(k-1) - eta*y(k-1) - qsi*amt(k-1)
mr(k) = M^-1 * r(k)
rho(k) = <rtld,r(k)>
beta = (rho(k) / rho(k-1)) * (alpha / qsi)
w(k) = amt(k) + beta*ap(k)
p(k) = mr(k) + beta*(p(k-1) - u(k-1))
********************************************************************/
#define NWORK 14
#undef __FUNC__
#define __FUNC__ "lis_gpbicg_check_params"
LIS_INT lis_gpbicg_check_params(LIS_SOLVER solver)
{
LIS_DEBUG_FUNC_IN;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
#undef __FUNC__
#define __FUNC__ "lis_gpbicg_malloc_work"
LIS_INT lis_gpbicg_malloc_work(LIS_SOLVER solver)
{
LIS_VECTOR *work;
LIS_INT i,j,worklen,err;
LIS_DEBUG_FUNC_IN;
worklen = NWORK;
work = (LIS_VECTOR *)lis_malloc( worklen*sizeof(LIS_VECTOR),"lis_gpbicg_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;
}
}
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_gpbicg"
LIS_INT lis_gpbicg(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r, rtld, mr, p, ap, map, t, mt_old, mt, amt, y, u, w, z;
LIS_SCALAR alpha, beta, rho, rho_old;
LIS_SCALAR qsi, eta;
LIS_SCALAR tmp, tmpdot[5];
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
LIS_DEBUG_FUNC_IN;
A = 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;
rtld = solver->work[0];
r = solver->work[1];
mr = solver->work[2];
p = solver->work[3];
ap = solver->work[4];
map = solver->work[5];
t = solver->work[6];
mt = solver->work[7];
amt = solver->work[8];
u = solver->work[9];
y = solver->work[10];
w = solver->work[11];
z = solver->work[12];
mt_old = solver->work[13];
/* 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);
times = lis_wtime();
lis_psolve(solver, r, p);
ptimes += lis_wtime()-times;
lis_vector_dot(rtld,r,&rho_old);
lis_vector_set_all(0,t);
lis_vector_set_all(0,w);
beta = 0.0;
for( iter=1; iter<=maxiter; iter++ )
{
/* ap(k-1) = A * p(k-1) */
/* map(k-1)= M^-1 * ap(k-1) */
/* tmpdot0 = <map(k-1),rtld(0)> */
LIS_MATVEC(A,p,ap);
times = lis_wtime();
lis_psolve(solver, ap, map);
ptimes += lis_wtime()-times;
lis_vector_dot(rtld,ap,&tmpdot[0]);
if( tmpdot[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho(k-1) / tmpdot0 */
/* y(k-1) = t(k-2) - r(k-1) - alpha*w(k-2) + alpha*ap(k-1) */
/* t(k-1) = r(k-1) - alpha*ap(k-1) */
alpha = rho_old / tmpdot[0];
lis_vector_axpyz(-1,w,ap,y);
lis_vector_xpay(t,alpha,y);
lis_vector_axpy(-1,r,y);
lis_vector_axpyz(-alpha,ap,r,t);
/* Early check for tolerance */
lis_solver_get_residual[conv](t,solver,&nrm2);
if( nrm2 <= tol )
{
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);
}
lis_vector_axpy(alpha,p,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* mt(k-1) = mr(k-1) - alpha*map(k-1) */
/* amt(k-1)= A * mt(k-1) */
/* tmpdot0 = <y(k-1),y(k-1)> */
/* tmpdot1 = <amt(k-1),t(k-1)> */
/* tmpdot2 = <y(k-1),t(k-1)> */
/* tmpdot3 = <amt(k-1),y(k-1)> */
/* tmpdot4 = <amt(k-1),amt(k-1)> */
/* tmp = tmpdot4*tmpdot0-tmpdot3*tmpdot3 */
/* qsi = (tmpdot0*tmpdot1-tmpdot2*tmpdot3) / tmp */
/* eta = (tmpdot4*tmpdot2-tmpdot3*tmpdot1) / tmp */
lis_vector_axpyz(-alpha,map,mr,mt);
LIS_MATVEC(A,mt,amt);
lis_vector_dot(y,y,&tmpdot[0]);
lis_vector_dot(amt,t,&tmpdot[1]);
lis_vector_dot(y,t,&tmpdot[2]);
lis_vector_dot(amt,y,&tmpdot[3]);
lis_vector_dot(amt,amt,&tmpdot[4]);
if(iter==1)
{
qsi = tmpdot[1] / tmpdot[4];
eta = 0.0;
}
else
{
tmp = tmpdot[4]*tmpdot[0] - tmpdot[3]*tmpdot[3];
qsi = (tmpdot[0]*tmpdot[1] - tmpdot[2]*tmpdot[3]) / tmp;
eta = (tmpdot[4]*tmpdot[2] - tmpdot[3]*tmpdot[1]) / tmp;
}
/* u(k-1) = qsi*map(k-1) + eta*(mt(k-2) - mr(k-1) + beta*u(k-2)) */
lis_vector_xpay(mt_old,beta,u);
lis_vector_axpy(-1,mr,u);
lis_vector_scale(eta,u);
lis_vector_axpy(qsi,map,u);
/* z(k-1) = qsi*mr(k-1) + eta*z(k-2) - alpha*u(k-1) */
lis_vector_scale(eta,z);
lis_vector_axpy(qsi,mr,z);
lis_vector_axpy(-alpha,u,z);
/* x(k) = x(k-1) + alpha*p(k-1) + z(k-1) */
lis_vector_axpy(alpha,p,x);
lis_vector_axpy(1,z,x);
/* r(k) = t(k-1) - eta*y(k-1) - qsi*amt(k-1) */
lis_vector_axpyz(-qsi,amt,t,r);
lis_vector_axpy(-eta,y,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;
}
/* mr(k) = M^-1 * r(k) */
/* rho(k) = <rtld,mr(k)> */
times = lis_wtime();
lis_psolve(solver, r, mr);
ptimes += lis_wtime()-times;
lis_vector_dot(rtld,r,&rho);
if( rho==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho(k) / rho(k-1)) * (alpha / qsi) */
beta = (rho / rho_old) * (alpha / qsi);
/* w(k) = amt(k) + beta*ap(k) */
/* p(k) = mr(k) + beta*(p(k-1) - u(k-1)) */
lis_vector_axpyz(beta,ap,amt,w);
lis_vector_axpy(-1,u,p);
lis_vector_xpay(mr,beta,p);
lis_vector_copy(mt,mt_old);
rho_old = rho;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
#if 0
#undef __FUNC__
#define __FUNC__ "lis_gpbicg"
LIS_INT lis_gpbicg(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r, rtld, rhat, p, ptld, phat;
LIS_VECTOR t, ttld, that, t0, t0hat;
LIS_VECTOR y, w, u, z;
LIS_SCALAR alpha, beta, rho, rho_old;
LIS_SCALAR qsi, eta;
LIS_SCALAR tmp, tmpdot[5];
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
LIS_DEBUG_FUNC_IN;
A = 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;
rtld = solver->work[0];
r = solver->work[1];
rhat = solver->work[2];
p = solver->work[3];
ptld = solver->work[4];
phat = solver->work[5];
t = solver->work[6];
ttld = solver->work[7];
that = solver->work[8];
t0 = solver->work[9];
t0hat = solver->work[10];
y = solver->work[11];
w = solver->work[12];
u = solver->work[13];
z = solver->work[14];
alpha = (LIS_SCALAR)1.0;
qsi = (LIS_SCALAR)1.0;
rho_old = (LIS_SCALAR)1.0;
/* 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_all(0,ttld);
lis_vector_set_all(0,ptld);
lis_vector_set_all(0,p);
lis_vector_set_all(0,u);
lis_vector_set_all(0,t);
lis_vector_set_all(0,t0);
for( iter=1; iter<=maxiter; iter++ )
{
/* rho = <rtld,r> */
lis_vector_dot(rtld,r,&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) * (alpha / qsi) */
beta = (rho / rho_old) * (alpha / qsi);
/* w = ttld + beta*ptld */
lis_vector_axpyz(beta,ptld,ttld,w);
/* rhat = M^-1 * r */
times = lis_wtime();
lis_psolve(solver, r, rhat);
ptimes += lis_wtime()-times;
/* p = rhat + beta*(p - u) */
lis_vector_axpy(-1,u,p);
lis_vector_xpay(rhat,beta,p);
/* ptld = A * p */
LIS_MATVEC(A,p,ptld);
/* tmpdot[0] = <rtld,ptld> */
lis_vector_dot(rtld,ptld,&tmpdot[0]);
/* test breakdown */
/* */
/* alpha = rho / tmpdot[0] */
alpha = rho / tmpdot[0];
/* y = t - r + alpha*(-w + ptld) */
lis_vector_axpyz(-1,w,ptld,y);
lis_vector_xpay(t,alpha,y);
lis_vector_axpy(-1,r,y);
/* t = r - alpha*ptld */
lis_vector_axpyz(-alpha,ptld,r,t);
/* Early check for tolerance */
lis_solver_get_residual[conv](t,solver,&nrm2);
if( nrm2 <= tol )
{
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);
}
lis_vector_axpy(alpha,p,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* that = M^-1 * t */
/* phat = M^-1 * ptld */
/* t0hat = M^-1 * t0 */
times = lis_wtime();
lis_psolve(solver, t, that);
lis_psolve(solver, ptld, phat);
lis_psolve(solver, t0, t0hat);
ptimes += lis_wtime()-times;
/* ttld = A * that */
LIS_MATVEC(A,that,ttld);
/* tmpdot[0] = <y,y> */
/* tmpdot[1] = <ttld,t> */
/* tmpdot[2] = <y,t> */
/* tmpdot[3] = <ttld,y> */
/* tmpdot[4] = <ttld,ttld> */
lis_vector_dot(y,y,&tmpdot[0]);
lis_vector_dot(ttld,t,&tmpdot[1]);
lis_vector_dot(y,t,&tmpdot[2]);
lis_vector_dot(ttld,y,&tmpdot[3]);
lis_vector_dot(ttld,ttld,&tmpdot[4]);
if(iter==1)
{
qsi = tmpdot[1] / tmpdot[4];
eta = 0.0;
}
else
{
tmp = tmpdot[4]*tmpdot[0] - tmpdot[3]*tmpdot[3];
qsi = (tmpdot[0]*tmpdot[1] - tmpdot[2]*tmpdot[3]) / tmp;
eta = (tmpdot[4]*tmpdot[2] - tmpdot[3]*tmpdot[1]) / tmp;
}
/* u = qsi*phat + eta*(t0hat - rhat + beta*u) */
lis_vector_xpay(t0hat,beta,u);
lis_vector_axpy(-1,rhat,u);
lis_vector_scale(eta,u);
lis_vector_axpy(qsi,phat,u);
/* z = qsi*rhat + eta*z - alpha*u */
lis_vector_scale(eta,z);
lis_vector_axpy(qsi,rhat,z);
lis_vector_axpy(-alpha,u,z);
/* x = x + alpha*p + z */
lis_vector_axpy(alpha,p,x);
lis_vector_axpy(1,z,x);
/* r = t - eta*y - qsi*ttld */
lis_vector_axpyz(-eta,y,t,r);
lis_vector_axpy(-qsi,ttld,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;
}
lis_vector_copy(t,t0);
rho_old = rho;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
#endif
#ifdef USE_QUAD_PRECISION
#undef __FUNC__
#define __FUNC__ "lis_gpbicg_quad"
LIS_INT lis_gpbicg_quad(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r, rtld, mr, p, ap, map, t, mt_old, mt, amt, y, u, w, z;
LIS_QUAD_PTR alpha, beta, rho, rho_old;
LIS_QUAD_PTR qsi, eta, one;
LIS_QUAD_PTR tmp, tmpdot[5];
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
LIS_DEBUG_FUNC_IN;
A = 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;
rtld = solver->work[0];
r = solver->work[1];
mr = solver->work[2];
p = solver->work[3];
ap = solver->work[4];
map = solver->work[5];
t = solver->work[6];
mt = solver->work[7];
amt = solver->work[8];
u = solver->work[9];
y = solver->work[10];
w = solver->work[11];
z = solver->work[12];
mt_old = solver->work[13];
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(qsi,4,1);
LIS_QUAD_SCALAR_MALLOC(eta,5,1);
LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[0],7,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[1],8,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[2],9,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[3],10,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[4],11,1);
LIS_QUAD_SCALAR_MALLOC(one,13,1);
/* 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);
times = lis_wtime();
lis_psolve(solver, r, p);
ptimes += lis_wtime()-times;
lis_vector_dotex_mmm(rtld,r,&rho_old);
lis_vector_set_allex_nm(0.0,t);
lis_vector_set_allex_nm(0.0,w);
one.hi[0] = -1.0;
one.lo[0] = 0.0;
for( iter=1; iter<=maxiter; iter++ )
{
/* ap(k-1) = A * p(k-1) */
/* map(k-1)= M^-1 * ap(k-1) */
/* tmpdot0 = <map(k-1),rtld(0)> */
LIS_MATVEC(A,p,ap);
times = lis_wtime();
lis_psolve(solver, ap, map);
ptimes += lis_wtime()-times;
lis_vector_dotex_mmm(rtld,ap,&tmpdot[0]);
if( tmpdot[0].hi[0]==0.0 && tmpdot[0].lo[0] )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho(k-1) / tmpdot0 */
/* y(k-1) = t(k-2) - r(k-1) - alpha*w(k-2) + alpha*ap(k-1) */
/* t(k-1) = r(k-1) - alpha*ap(k-1) */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho_old.hi,(LIS_QUAD *)tmpdot[0].hi);
lis_vector_axpyzex_mmmm(one,w,ap,y);
lis_vector_xpayex_mmm(t,alpha,y);
lis_vector_axpyex_mmm(one,r,y);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyzex_mmmm(alpha,ap,r,t);
/* Early check for tolerance */
lis_solver_get_residual[conv](t,solver,&nrm2);
if( nrm2 <= tol )
{
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);
}
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,p,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* mt(k-1) = mr(k-1) - alpha*map(k-1) */
/* amt(k-1)= A * mt(k-1) */
/* tmpdot0 = <y(k-1),y(k-1)> */
/* tmpdot1 = <amt(k-1),t(k-1)> */
/* tmpdot2 = <y(k-1),t(k-1)> */
/* tmpdot3 = <amt(k-1),y(k-1)> */
/* tmpdot4 = <amt(k-1),amt(k-1)> */
/* tmp = tmpdot4*tmpdot0-tmpdot3*tmpdot3 */
/* qsi = (tmpdot0*tmpdot1-tmpdot2*tmpdot3) / tmp */
/* eta = (tmpdot4*tmpdot2-tmpdot3*tmpdot1) / tmp */
lis_vector_axpyzex_mmmm(alpha,map,mr,mt);
LIS_MATVEC(A,mt,amt);
lis_vector_dotex_mmm(y,y,&tmpdot[0]);
lis_vector_dotex_mmm(amt,t,&tmpdot[1]);
lis_vector_dotex_mmm(y,t,&tmpdot[2]);
lis_vector_dotex_mmm(amt,y,&tmpdot[3]);
lis_vector_dotex_mmm(amt,amt,&tmpdot[4]);
if(iter==1)
{
lis_quad_div((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[1].hi,(LIS_QUAD *)tmpdot[4].hi);
eta.hi[0] = 0.0;
eta.lo[0] = 0.0;
}
else
{
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmpdot[4].hi,(LIS_QUAD *)tmpdot[0].hi);
lis_quad_sqr((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[3].hi);
lis_quad_sub((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)qsi.hi);
lis_quad_mul((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[0].hi,(LIS_QUAD *)tmpdot[1].hi);
lis_quad_mul((LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[2].hi,(LIS_QUAD *)tmpdot[3].hi);
lis_quad_sub((LIS_QUAD *)qsi.hi,(LIS_QUAD *)qsi.hi,(LIS_QUAD *)eta.hi);
lis_quad_div((LIS_QUAD *)qsi.hi,(LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmp.hi);
lis_quad_mul((LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[4].hi,(LIS_QUAD *)tmpdot[2].hi);
lis_quad_mul((LIS_QUAD *)tmpdot[0].hi,(LIS_QUAD *)tmpdot[3].hi,(LIS_QUAD *)tmpdot[1].hi);
lis_quad_sub((LIS_QUAD *)eta.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[0].hi);
lis_quad_div((LIS_QUAD *)eta.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)tmp.hi);
}
/* u(k-1) = qsi*map(k-1) + eta*(mt(k-2) - mr(k-1) + beta*u(k-2)) */
lis_vector_xpayex_mmm(mt_old,beta,u);
lis_vector_axpyex_mmm(one,mr,u);
lis_vector_scaleex_mm(eta,u);
lis_vector_axpyex_mmm(qsi,map,u);
/* z(k-1) = qsi*mr(k-1) + eta*z(k-2) - alpha*u(k-1) */
lis_vector_scaleex_mm(eta,z);
lis_vector_axpyex_mmm(qsi,mr,z);
lis_vector_axpyex_mmm(alpha,u,z);
/* x(k) = x(k-1) + alpha*p(k-1) + z(k-1) */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_quad_minus((LIS_QUAD *)one.hi);
lis_vector_axpyex_mmm(alpha,p,x);
lis_vector_axpyex_mmm(one,z,x);
lis_quad_minus((LIS_QUAD *)one.hi);
/* r(k) = t(k-1) - eta*y(k-1) - qsi*amt(k-1) */
lis_quad_minus((LIS_QUAD *)eta.hi);
lis_quad_minus((LIS_QUAD *)qsi.hi);
lis_vector_axpyzex_mmmm(qsi,amt,t,r);
lis_vector_axpyex_mmm(eta,y,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;
}
/* mr(k) = M^-1 * r(k) */
/* rho(k) = <rtld,mr(k)> */
times = lis_wtime();
lis_psolve(solver, r, mr);
ptimes += lis_wtime()-times;
lis_vector_dotex_mmm(rtld,r,&rho);
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(k) / rho(k-1)) * (alpha / qsi) */
lis_quad_minus((LIS_QUAD *)eta.hi);
lis_quad_minus((LIS_QUAD *)qsi.hi);
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)alpha.hi,(LIS_QUAD *)qsi.hi);
lis_quad_mul((LIS_QUAD *)beta.hi,(LIS_QUAD *)beta.hi,(LIS_QUAD *)tmp.hi);
/* w(k) = amt(k) + beta*ap(k) */
/* p(k) = mr(k) + beta*(p(k-1) - u(k-1)) */
lis_vector_axpyzex_mmmm(beta,ap,amt,w);
lis_vector_axpyex_mmm(one,u,p);
lis_vector_xpayex_mmm(mr,beta,p);
lis_vector_copyex_mm(mt,mt_old);
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_gpbicg_switch"
LIS_INT lis_gpbicg_switch(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r, rtld, mr, p, ap, map, t, mt_old, mt, amt, y, u, w, z;
LIS_QUAD_PTR alpha, beta, rho, rho_old;
LIS_QUAD_PTR qsi, eta, one;
LIS_QUAD_PTR tmp, tmpdot[5];
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;
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;
rtld = solver->work[0];
r = solver->work[1];
mr = solver->work[2];
p = solver->work[3];
ap = solver->work[4];
map = solver->work[5];
t = solver->work[6];
mt = solver->work[7];
amt = solver->work[8];
u = solver->work[9];
y = solver->work[10];
w = solver->work[11];
z = solver->work[12];
mt_old = solver->work[13];
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(qsi,4,1);
LIS_QUAD_SCALAR_MALLOC(eta,5,1);
LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[0],7,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[1],8,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[2],9,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[3],10,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[4],11,1);
LIS_QUAD_SCALAR_MALLOC(one,13,1);
one.hi[0] = -1.0;
one.lo[0] = 0.0;
r->precision = LIS_PRECISION_DEFAULT;
p->precision = LIS_PRECISION_DEFAULT;
mt->precision = LIS_PRECISION_DEFAULT;
ap->precision = LIS_PRECISION_DEFAULT;
/* 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);
times = lis_wtime();
lis_psolve(solver, r, p);
ptimes += lis_wtime()-times;
lis_vector_dot(rtld,r,&rho_old.hi[0]);
lis_vector_set_all(0,t);
lis_vector_set_all(0,w);
for( iter=1; iter<=maxiter2; iter++ )
{
/* ap(k-1) = A * p(k-1) */
/* map(k-1)= M^-1 * ap(k-1) */
/* tmpdot0 = <map(k-1),rtld(0)> */
LIS_MATVEC(A,p,ap);
times = lis_wtime();
lis_psolve(solver, ap, map);
ptimes += lis_wtime()-times;
lis_vector_dot(rtld,ap,&tmpdot[0].hi[0]);
if( tmpdot[0].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(k-1) / tmpdot0 */
/* y(k-1) = t(k-2) - r(k-1) - alpha*w(k-2) + alpha*ap(k-1) */
/* t(k-1) = r(k-1) - alpha*ap(k-1) */
alpha.hi[0] = rho_old.hi[0] / tmpdot[0].hi[0];
lis_vector_axpyz(-1,w,ap,y);
lis_vector_xpay(t,alpha.hi[0],y);
lis_vector_axpy(-1,r,y);
lis_vector_axpyz(-alpha.hi[0],ap,r,t);
/* Early check for tolerance */
lis_solver_get_residual[conv](t,solver,&nrm2);
if( nrm2 <= tol )
{
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);
}
lis_vector_axpy(alpha.hi[0],p,x);
solver->iter = iter;
solver->iter2 = iter;
solver->ptimes = ptimes;
break;
}
/* mt(k-1) = mr(k-1) - alpha*map(k-1) */
/* amt(k-1)= A * mt(k-1) */
/* tmpdot0 = <y(k-1),y(k-1)> */
/* tmpdot1 = <amt(k-1),t(k-1)> */
/* tmpdot2 = <y(k-1),t(k-1)> */
/* tmpdot3 = <amt(k-1),y(k-1)> */
/* tmpdot4 = <amt(k-1),amt(k-1)> */
/* tmp = tmpdot4*tmpdot0-tmpdot3*tmpdot3 */
/* qsi = (tmpdot0*tmpdot1-tmpdot2*tmpdot3) / tmp */
/* eta = (tmpdot4*tmpdot2-tmpdot3*tmpdot1) / tmp */
lis_vector_axpyz(-alpha.hi[0],map,mr,mt);
LIS_MATVEC(A,mt,amt);
lis_vector_dot(y,y,&tmpdot[0].hi[0]);
lis_vector_dot(amt,t,&tmpdot[1].hi[0]);
lis_vector_dot(y,t,&tmpdot[2].hi[0]);
lis_vector_dot(amt,y,&tmpdot[3].hi[0]);
lis_vector_dot(amt,amt,&tmpdot[4].hi[0]);
if(iter==1)
{
qsi.hi[0] = tmpdot[1].hi[0] / tmpdot[4].hi[0];
eta.hi[0] = 0.0;
}
else
{
tmp.hi[0] = tmpdot[4].hi[0]*tmpdot[0].hi[0] - tmpdot[3].hi[0]*tmpdot[3].hi[0];
qsi.hi[0] = (tmpdot[0].hi[0]*tmpdot[1].hi[0] - tmpdot[2].hi[0]*tmpdot[3].hi[0]) / tmp.hi[0];
eta.hi[0] = (tmpdot[4].hi[0]*tmpdot[2].hi[0] - tmpdot[3].hi[0]*tmpdot[1].hi[0]) / tmp.hi[0];
}
/* u(k-1) = qsi*map(k-1) + eta*(mt(k-2) - mr(k-1) + beta*u(k-2)) */
lis_vector_xpay(mt_old,beta.hi[0],u);
lis_vector_axpy(-1,mr,u);
lis_vector_scale(eta.hi[0],u);
lis_vector_axpy(qsi.hi[0],map,u);
/* z(k-1) = qsi*mr(k-1) + eta*z(k-2) - alpha*u(k-1) */
lis_vector_scale(eta.hi[0],z);
lis_vector_axpy(qsi.hi[0],mr,z);
lis_vector_axpy(-alpha.hi[0],u,z);
/* x(k) = x(k-1) + alpha*p(k-1) + z(k-1) */
lis_vector_axpy(alpha.hi[0],p,x);
lis_vector_axpy(1,z,x);
/* r(k) = t(k-1) - eta*y(k-1) - qsi*amt(k-1) */