コード例 #1
0
ファイル: lis_solver_gmres.c プロジェクト: rwl/lis
LIS_INT lis_gmres_switch(LIS_SOLVER solver)
{
	LIS_MATRIX A;
	LIS_VECTOR b,x;
	LIS_VECTOR r,s,z,*v;
	LIS_QUAD *h;
	LIS_SCALAR *hd;
	LIS_QUAD_PTR aa,bb,rr,a2,b2,t,one,tmp;
	LIS_QUAD_PTR rnorm;
	LIS_REAL bnrm2,nrm2,tol,tol2;
	LIS_INT iter,maxiter,n,output;
	LIS_INT iter2,maxiter2;
	double time,ptime;

	LIS_INT i,j,k,m;
	LIS_INT ii,i1,iiv,i1v,iih,jj;
	LIS_INT h_dim;
	LIS_INT cs,sn;

	LIS_DEBUG_FUNC_IN;

	A       = solver->A;
	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];
	tol      = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
	tol2     = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
	m        = solver->options[LIS_OPTIONS_RESTART];
	h_dim    = m+1;
	ptime    = 0.0;

	s       = solver->work[0];
	r       = solver->work[1];
	z       = solver->work[2];
	v       = &solver->work[3];

	LIS_QUAD_SCALAR_MALLOC(aa,0,1);
	LIS_QUAD_SCALAR_MALLOC(bb,1,1);
	LIS_QUAD_SCALAR_MALLOC(rr,2,1);
	LIS_QUAD_SCALAR_MALLOC(a2,3,1);
	LIS_QUAD_SCALAR_MALLOC(b2,4,1);
	LIS_QUAD_SCALAR_MALLOC(t,5,1);
	LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
	LIS_QUAD_SCALAR_MALLOC(one,7,1);
	LIS_QUAD_SCALAR_MALLOC(rnorm,8,1);

	h       = (LIS_QUAD *)lis_malloc( sizeof(LIS_QUAD)*(h_dim+1)*(h_dim+2),"lis_gmres_switch::h" );
	hd      = (LIS_SCALAR *)h;
	cs      = (m+1)*h_dim;
	sn      = (m+2)*h_dim;
	one.hi[0]   = 1.0;
	one.lo[0]   = 0.0;

	z->precision = LIS_PRECISION_DEFAULT;

	/* r = M^-1 * (b - A * x) */
	lis_matvec(A,x,z);
	lis_vector_xpay(b,-1.0,z);
	lis_psolve(solver,z,v[0]);

	/* Initial Residual */
	if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
	{
		lis_free(h);
		LIS_DEBUG_FUNC_OUT;
		return LIS_SUCCESS;
	}
	tol2     = solver->tol_switch;


	iter=0;
	while( iter<maxiter2 )
	{
		/* first column of V */
		/* v = r / ||r||_2 */
		lis_vector_nrm2(v[0],&rnorm.hi[0]);
		lis_vector_scale(1.0/rnorm.hi[0],v[0]);

		/* s = ||r||_2 e_1 */
		lis_vector_set_all(0,s);
		s->value[0] = rnorm.hi[0];

		i = 0;
		do
		{
			iter++;
			i++;
			ii  = i-1;
			i1  = i;
			iiv = i-1;
			i1v = i;
			iih = (i-1)*h_dim;


			/* z = M^-1 * v */
			time = lis_wtime();
			lis_psolve(solver,v[iiv],z);
			ptime += lis_wtime()-time;

			/* w = A * z */
			lis_matvec(A,z, v[i1v]);

			for(k=0;k<i;k++)
			{
				/* h[k,i]   = <w,v[k]>          */
				/* w        = w - h[k,i] * v[k] */
				lis_vector_dot(v[i1v],v[k],&t.hi[0]);
				hd[k+iih] = t.hi[0];
				lis_vector_axpy(-t.hi[0],v[k],v[i1v]);
			}
			/* h[i+1,i] = ||w||          */
			/* v[i+1]   = w / h[i+1,i]   */
			lis_vector_nrm2(v[i1v],&t.hi[0]);
			hd[i1+iih] = t.hi[0];
			lis_vector_scale(1.0/t.hi[0],v[i1v]);

			for(k=1;k<=ii;k++)
			{
				jj        = k-1;
				t.hi[0]   =  hd[jj+iih];
				aa.hi[0]  =  hd[jj+cs]*t.hi[0];
				aa.hi[0] +=  hd[jj+sn]*hd[k+iih];
				bb.hi[0]  = -hd[jj+sn]*t.hi[0];
				bb.hi[0] +=  hd[jj+cs]*hd[k+iih];
				hd[jj+iih] = aa.hi[0];
				hd[k+iih] = bb.hi[0];
			}
			aa.hi[0] = hd[ii+iih];
			bb.hi[0] = hd[i1+iih];
			a2.hi[0] = aa.hi[0]*aa.hi[0];
			b2.hi[0] = bb.hi[0]*bb.hi[0];
			rr.hi[0] = sqrt(a2.hi[0]+b2.hi[0]);
			if( rr.hi[0]==0.0 ) rr.hi[0]=1.0e-17;
			hd[ii+cs] = aa.hi[0]/rr.hi[0];
			hd[ii+sn] = bb.hi[0]/rr.hi[0];
			s->value[i1] = -hd[ii+sn]*s->value[ii];
			s->value[ii] =  hd[ii+cs]*s->value[ii];

			aa.hi[0]  =  hd[ii+cs]*hd[ii+iih];
			aa.hi[0] +=  hd[ii+sn]*hd[i1+iih];
			hd[ii+iih] = aa.hi[0];

			/* convergence check */
			nrm2 = fabs(s->value[i1])*bnrm2;

			if( output )
			{
				if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
				if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
			}

			if( tol2 >= nrm2 ) break;
		} while( i<m && iter <maxiter2 );

		/* Solve H * Y = S for upper Hessenberg matrix H */
		s->value[ii] = s->value[ii]/hd[ii+iih];
		for(k=1;k<=ii;k++)
		{
			jj = ii-k;
			t.hi[0]  = s->value[jj];
			for(j=jj+1;j<=ii;j++)
			{
				t.hi[0] -= hd[jj+j*h_dim]*s->value[j];
			}
			s->value[jj] = t.hi[0]/hd[jj+jj*h_dim];
		}
		/* z = z + y * v */
		for(k=0;k<n;k++)
		{
			z->value[k] = s->value[0]*v[0]->value[k];
		}
		for(j=1;j<=ii;j++)
		{
			lis_vector_axpy(s->value[j],v[j],z);
		}
		/* r = M^-1 * z */
		time = lis_wtime();
		lis_psolve(solver,z,r);
		ptime += lis_wtime()-time;

		/* x = x + r */
		lis_vector_axpy(1,r,x);

		if( tol2 >= nrm2 )
		{
			solver->iter       = iter;
			solver->iter2      = iter;
			solver->ptime      = ptime;
			break;
		}

		for(j=1;j<=i;j++)
		{
			jj = i1-j+1;
			s->value[jj-1] = -hd[jj-1+sn]*s->value[jj];
			s->value[jj]   =  hd[jj-1+cs]*s->value[jj];
		}

		for(j=0;j<=i1;j++)
		{
			t.hi[0] = s->value[j];
			if( j==0 ) t.hi[0] = t.hi[0]-1.0;
			lis_vector_axpy(t.hi[0],v[j],v[0]);
		}
	}

	/* Initial Residual */
	z->precision = LIS_PRECISION_QUAD;

	solver->options[LIS_OPTIONS_INITGUESS_ZEROS] = LIS_FALSE;
	lis_vector_copyex_mn(x,solver->xx);

	lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2);
	tol     = solver->tol;


	iter2=iter;
	while( iter2<maxiter )
	{
		/* first column of V */
		/* v = r / ||r||_2 */
		lis_vector_nrm2ex_mm(v[0],&rnorm);
		lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)one.hi,(LIS_QUAD *)rnorm.hi);
		lis_vector_scaleex_mm(tmp,v[0]);

		/* s = ||r||_2 e_1 */
		lis_vector_set_allex_nm(0.0,s);
		s->value[0]    = rnorm.hi[0];
		s->value_lo[0] = rnorm.lo[0];

		i = 0;
		do
		{
			iter2++;
			i++;
			ii  = i-1;
			i1  = i;
			iiv = i-1;
			i1v = i;
			iih = (i-1)*h_dim;


			/* z = M^-1 * v */
			time = lis_wtime();
			lis_psolve(solver,v[iiv],z);
			ptime += lis_wtime()-time;

			/* w = A * z */
			lis_matvec(A,z, v[i1v]);

			for(k=0;k<i;k++)
			{
				/* h[k,i]   = <w,v[k]>          */
				/* w        = w - h[k,i] * v[k] */
				lis_vector_dotex_mmm(v[i1v],v[k],&t);
				h[k+iih].hi = t.hi[0];
				h[k+iih].lo = t.lo[0];
				lis_quad_minus((LIS_QUAD *)t.hi);
				lis_vector_axpyex_mmm(t,v[k],v[i1v]);
			}
			/* h[i+1,i] = ||w||          */
			/* v[i+1]   = w / h[i+1,i]   */
			lis_vector_nrm2ex_mm(v[i1v],&t);
			h[i1+iih].hi = t.hi[0];
			h[i1+iih].lo = t.lo[0];
			lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)one.hi,(LIS_QUAD *)t.hi);
			lis_vector_scaleex_mm(tmp,v[i1v]);

			for(k=1;k<=ii;k++)
			{
				jj  = k-1;
				t.hi[0]   =  h[jj+iih].hi;
				t.lo[0]   =  h[jj+iih].lo;
				lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)t.hi);
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)&h[k+iih]);
				lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
				lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)t.hi);
				lis_quad_minus((LIS_QUAD *)bb.hi);
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)&h[k+iih]);
				lis_quad_add((LIS_QUAD *)bb.hi,(LIS_QUAD *)bb.hi,(LIS_QUAD *)tmp.hi);
				h[jj+iih].hi = aa.hi[0];
				h[jj+iih].lo = aa.lo[0];
				h[k+iih].hi = bb.hi[0];
				h[k+iih].lo = bb.lo[0];
			}
			aa.hi[0] = h[ii+iih].hi;
			aa.lo[0] = h[ii+iih].lo;
			bb.hi[0] = h[i1+iih].hi;
			bb.lo[0] = h[i1+iih].lo;
			lis_quad_sqr((LIS_QUAD *)a2.hi,(LIS_QUAD *)aa.hi);
			lis_quad_sqr((LIS_QUAD *)b2.hi,(LIS_QUAD *)bb.hi);
			lis_quad_add((LIS_QUAD *)rr.hi,(LIS_QUAD *)a2.hi,(LIS_QUAD *)b2.hi);
			lis_quad_sqrt((LIS_QUAD *)rr.hi,(LIS_QUAD *)rr.hi);
			lis_quad_div((LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)aa.hi,(LIS_QUAD *)rr.hi);
			lis_quad_div((LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)bb.hi,(LIS_QUAD *)rr.hi);
			tmp.hi[0] = s->value[ii];
			tmp.lo[0] = s->value_lo[ii];
			lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)tmp.hi);
			lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)tmp.hi);
			lis_quad_minus((LIS_QUAD *)aa.hi);
			s->value[i1] = aa.hi[0];
			s->value_lo[i1] = aa.lo[0];
			s->value[ii] = bb.hi[0];
			s->value_lo[ii] = bb.lo[0];

			lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)&h[ii+iih]);
			lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)&h[i1+iih]);
			lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
			h[ii+iih].hi = aa.hi[0];
			h[ii+iih].lo = aa.lo[0];

			/* convergence check */
			nrm2 = fabs(s->value[i1])*bnrm2;

			if( output )
			{
				if( output & LIS_PRINT_MEM ) solver->rhistory[iter2] = nrm2;
				if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
			}

			if( tol >= nrm2 ) break;
		} while( i<m && iter2 <maxiter );

		/* Solve H * Y = S for upper Hessenberg matrix H */
		tmp.hi[0] = s->value[ii];
		tmp.lo[0] = s->value_lo[ii];
		lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+iih]);
		s->value[ii] = tmp.hi[0];
		s->value_lo[ii] = tmp.lo[0];
		for(k=1;k<=ii;k++)
		{
			jj = ii-k;
			t.hi[0]  = s->value[jj];
			t.lo[0]  = s->value_lo[jj];
			for(j=jj+1;j<=ii;j++)
			{
				tmp.hi[0] = s->value[j];
				tmp.lo[0] = s->value_lo[j];
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+j*h_dim]);
				lis_quad_sub((LIS_QUAD *)t.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)tmp.hi);
			}
			lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)&h[jj+jj*h_dim]);
			s->value[jj] = tmp.hi[0];
			s->value_lo[jj] = tmp.lo[0];
		}
		/* z = z + y * v */
		for(k=0;k<n;k++)
		{
			aa.hi[0] = s->value[0];
			aa.lo[0] = s->value_lo[0];
			bb.hi[0] = v[0]->value[k];
			bb.lo[0] = v[0]->value_lo[k];
			lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)bb.hi);
			z->value[k] = tmp.hi[0];
			z->value_lo[k] = tmp.lo[0];
		}
		for(j=1;j<=ii;j++)
		{
			aa.hi[0] = s->value[j];
			aa.lo[0] = s->value_lo[j];
			lis_vector_axpyex_mmm(aa,v[j],z);
		}
		/* r = M^-1 * z */
		time = lis_wtime();
		lis_psolve(solver,z,r);
		ptime += lis_wtime()-time;

		/* x = x + r */
		lis_vector_axpyex_mmm(one,r,x);

		if( tol >= nrm2 )
		{
			solver->retcode    = LIS_SUCCESS;
			solver->iter       = iter2;
			solver->iter2      = iter;
			solver->resid      = nrm2;
			solver->ptime      = ptime;
			lis_free(h);
			LIS_DEBUG_FUNC_OUT;
			return LIS_SUCCESS;
		}

		for(j=1;j<=i;j++)
		{
			jj = i1-j+1;
			tmp.hi[0] = s->value[jj];
			tmp.lo[0] = s->value_lo[jj];
			lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj-1+sn]);
			lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj-1+cs]);
			lis_quad_minus((LIS_QUAD *)aa.hi);
			s->value[jj-1] = aa.hi[0];
			s->value_lo[jj-1] = aa.lo[0];
			s->value[jj] = bb.hi[0];
			s->value_lo[jj] = bb.lo[0];
		}

		for(j=0;j<=i1;j++)
		{
			t.hi[0] = s->value[j];
			t.lo[0] = s->value_lo[j];
			if( j==0 )
			{
				lis_quad_sub((LIS_QUAD *)t.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)one.hi);
			}
			lis_vector_axpyex_mmm(t,v[j],v[0]);
		}
	}

	solver->retcode   = LIS_MAXITER;
	solver->iter       = iter2+1;
	solver->iter2      = iter;
	solver->resid     = nrm2;
	lis_free(h);
	LIS_DEBUG_FUNC_OUT;
	return LIS_MAXITER;
}
コード例 #2
0
ファイル: lis_solver_gmres.c プロジェクト: rwl/lis
LIS_INT lis_fgmres_quad(LIS_SOLVER solver)
{
	LIS_MATRIX A;
	LIS_VECTOR b,x;
	LIS_VECTOR r,s,*z,*v;
	LIS_QUAD *h;
	LIS_QUAD_PTR aa,bb,rr,a2,b2,t,one,tmp;

	LIS_REAL bnrm2,nrm2,tol;
	LIS_INT iter,maxiter,n,output;
	double time,ptime;

	LIS_REAL rnorm;
	LIS_INT i,j,k,m;
	LIS_INT ii,i1,iiv,i1v,iih,jj;
	LIS_INT h_dim;
	LIS_INT cs,sn;

	LIS_DEBUG_FUNC_IN;

	A       = solver->A;
	b       = solver->b;
	x       = solver->x;
	n       = A->n;
	maxiter = solver->options[LIS_OPTIONS_MAXITER];
	output  = solver->options[LIS_OPTIONS_OUTPUT];
	m       = solver->options[LIS_OPTIONS_RESTART];
	h_dim   = m+1;
	ptime   = 0.0;

	s       = solver->work[0];
	r       = solver->work[1];
	z       = &solver->work[2];
	v       = &solver->work[m+2];

	h       = (LIS_QUAD *)lis_malloc( sizeof(LIS_QUAD)*(h_dim+1)*(h_dim+2),"lis_fgmres_quad::h" );
	cs      = (m+1)*h_dim;
	sn      = (m+2)*h_dim;

	LIS_QUAD_SCALAR_MALLOC(aa,0,1);
	LIS_QUAD_SCALAR_MALLOC(bb,1,1);
	LIS_QUAD_SCALAR_MALLOC(rr,2,1);
	LIS_QUAD_SCALAR_MALLOC(a2,3,1);
	LIS_QUAD_SCALAR_MALLOC(b2,4,1);
	LIS_QUAD_SCALAR_MALLOC(t,5,1);
	LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
	LIS_QUAD_SCALAR_MALLOC(one,7,1);

	one.hi[0]   = 1.0;
	one.lo[0]   = 0.0;

	/* Initial Residual */
	if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
	{
		lis_free(h);
		LIS_DEBUG_FUNC_OUT;
		return LIS_SUCCESS;
	}
	tol     = solver->tol;
	rnorm   = 1.0/bnrm2;


	iter=0;
	while( iter<maxiter )
	{
		/* first column of V */
		/* v = r / ||r||_2 */
		lis_vector_scaleex_nm(bnrm2,v[0]);

		/* s = ||r||_2 e_1 */
		lis_vector_set_allex_nm(0.0,s);
		s->value[0]    = rnorm;
		s->value_lo[0] = 0.0;

		i = 0;
		do
		{
			iter++;
			i++;
			ii  = i-1;
			i1  = i;
			iiv = i-1;
			i1v = i;
			iih = (i-1)*h_dim;


			/* z = M^-1 * v */
			time = lis_wtime();
			lis_psolve(solver,v[iiv],z[iiv]);
			ptime += lis_wtime()-time;

			/* w = A * z */
			lis_matvec(A,z[iiv], v[i1v]);

			for(k=0;k<i;k++)
			{
				/* h[k,i]   = <w,v[k]>          */
				/* w        = w - h[k,i] * v[k] */
				lis_vector_dotex_mmm(v[i1v],v[k],&t);
				h[k+iih].hi = t.hi[0];
				h[k+iih].lo = t.lo[0];
				lis_quad_minus((LIS_QUAD *)t.hi);
				lis_vector_axpyex_mmm(t,v[k],v[i1v]);
			}
			/* h[i+1,i] = ||w||          */
			/* v[i+1]   = w / h[i+1,i]   */
			lis_vector_nrm2ex_mm(v[i1v],&t);
			h[i1+iih].hi = t.hi[0];
			h[i1+iih].lo = t.lo[0];
			lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)one.hi,(LIS_QUAD *)t.hi);
			lis_vector_scaleex_mm(tmp,v[i1v]);

			for(k=1;k<=ii;k++)
			{
				jj  = k-1;
				t.hi[0]   =  h[jj+iih].hi;
				t.lo[0]   =  h[jj+iih].lo;
				lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)t.hi);
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)&h[k+iih]);
				lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
				lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)t.hi);
				lis_quad_minus((LIS_QUAD *)bb.hi);
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)&h[k+iih]);
				lis_quad_add((LIS_QUAD *)bb.hi,(LIS_QUAD *)bb.hi,(LIS_QUAD *)tmp.hi);
				h[jj+iih].hi = aa.hi[0];
				h[jj+iih].lo = aa.lo[0];
				h[k+iih].hi = bb.hi[0];
				h[k+iih].lo = bb.lo[0];
			}
			aa.hi[0] = h[ii+iih].hi;
			aa.lo[0] = h[ii+iih].lo;
			bb.hi[0] = h[i1+iih].hi;
			bb.lo[0] = h[i1+iih].lo;
			lis_quad_sqr((LIS_QUAD *)a2.hi,(LIS_QUAD *)aa.hi);
			lis_quad_sqr((LIS_QUAD *)b2.hi,(LIS_QUAD *)bb.hi);
			lis_quad_add((LIS_QUAD *)rr.hi,(LIS_QUAD *)a2.hi,(LIS_QUAD *)b2.hi);
			lis_quad_sqrt((LIS_QUAD *)rr.hi,(LIS_QUAD *)rr.hi);
			if( rr.hi[0]==0.0 )
			{
				rr.hi[0]=1.0e-17;
				rr.lo[0]=0.0;
			}
			lis_quad_div((LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)aa.hi,(LIS_QUAD *)rr.hi);
			lis_quad_div((LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)bb.hi,(LIS_QUAD *)rr.hi);
			tmp.hi[0] = s->value[ii];
			tmp.lo[0] = s->value_lo[ii];
			lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)tmp.hi);
			lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)tmp.hi);
			lis_quad_minus((LIS_QUAD *)aa.hi);
			s->value[i1] = aa.hi[0];
			s->value_lo[i1] = aa.lo[0];
			s->value[ii] = bb.hi[0];
			s->value_lo[ii] = bb.lo[0];

			lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)&h[ii+iih]);
			lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)&h[i1+iih]);
			lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
			h[ii+iih].hi = aa.hi[0];
			h[ii+iih].lo = aa.lo[0];

			/* convergence check */
			nrm2 = fabs(s->value[i1]);

			if( output )
			{
				if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
				if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
			}

			if( tol >= nrm2 ) break;
		} while( i<m && iter <maxiter );

		/* Solve H * Y = S for upper Hessenberg matrix H */
		tmp.hi[0] = s->value[ii];
		tmp.lo[0] = s->value_lo[ii];
		lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+iih]);
		s->value[ii] = tmp.hi[0];
		s->value_lo[ii] = tmp.lo[0];
		for(k=1;k<=ii;k++)
		{
			jj = ii-k;
			t.hi[0]  = s->value[jj];
			t.lo[0]  = s->value_lo[jj];
			for(j=jj+1;j<=ii;j++)
			{
				tmp.hi[0] = s->value[j];
				tmp.lo[0] = s->value_lo[j];
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+j*h_dim]);
				lis_quad_sub((LIS_QUAD *)t.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)tmp.hi);
			}
			lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)&h[jj+jj*h_dim]);
			s->value[jj] = tmp.hi[0];
			s->value_lo[jj] = tmp.lo[0];
		}
		/* x = x + y * z */
		for(j=0;j<=ii;j++)
		{
			aa.hi[0] = s->value[j];
			aa.lo[0] = s->value_lo[j];
			lis_vector_axpyex_mmm(aa,z[j],x);
		}

		if( tol >= nrm2 )
		{
			solver->retcode    = LIS_SUCCESS;
			solver->iter       = iter;
			solver->resid      = nrm2;
			solver->ptime      = ptime;
			lis_free(h);
			LIS_DEBUG_FUNC_OUT;
			return LIS_SUCCESS;
		}

		lis_matvec(A,x,v[0]);
		lis_vector_xpay(b,-1.0,v[0]);
		memset(v[0]->value_lo,0,n*sizeof(LIS_SCALAR));
		lis_vector_nrm2(v[0],&rnorm);
		bnrm2 = 1.0/rnorm;
	}

	solver->retcode   = LIS_MAXITER;
	solver->iter      = iter+1;
	solver->resid     = nrm2;
	lis_free(h);
	LIS_DEBUG_FUNC_OUT;
	return LIS_MAXITER;
}
コード例 #3
0
LIS_INT lis_gmres_quad(LIS_SOLVER solver)
{
	LIS_MATRIX A;
	LIS_PRECON M;
	LIS_VECTOR b,x;
	LIS_VECTOR r,s, z, *v;
	LIS_QUAD *h;
	LIS_QUAD_PTR aa,bb,rr,a2,b2,t,one,tmp;
	LIS_QUAD_PTR rnorm;

	LIS_REAL   bnrm2, nrm2, tol;
	LIS_INT iter,maxiter,n,output,conv;
	double times,ptimes;

	LIS_INT i,j,k,m;
	LIS_INT ii,i1,iiv,i1v,iih,i1h,jj;
	LIS_INT h_dim;
	LIS_INT cs,sn;

	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];
	m       = solver->options[LIS_OPTIONS_RESTART];
	conv    = solver->options[LIS_OPTIONS_CONV_COND];
	h_dim   = m+1;
	ptimes  = 0.0;

	s       = solver->work[0];
	r       = solver->work[1];
	z       = solver->work[2];
	v       = &solver->work[3];

	LIS_QUAD_SCALAR_MALLOC(aa,0,1);
	LIS_QUAD_SCALAR_MALLOC(bb,1,1);
	LIS_QUAD_SCALAR_MALLOC(rr,2,1);
	LIS_QUAD_SCALAR_MALLOC(a2,3,1);
	LIS_QUAD_SCALAR_MALLOC(b2,4,1);
	LIS_QUAD_SCALAR_MALLOC(t,5,1);
	LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
	LIS_QUAD_SCALAR_MALLOC(one,7,1);
	LIS_QUAD_SCALAR_MALLOC(rnorm,8,1);

	h       = (LIS_QUAD *)lis_malloc( sizeof(LIS_QUAD) * (h_dim+1) * (h_dim+2),"lis_gmres_quad::h" );
	cs      = (m+1)*h_dim;
	sn      = (m+2)*h_dim;
	one.hi[0]   = 1.0;
	one.lo[0]   = 0.0;

	/* Initial Residual */
	if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
	{
		lis_free(h);
		LIS_DEBUG_FUNC_OUT;
		return LIS_SUCCESS;
	}
	tol     = solver->tol;


	iter=0;
	while( iter<maxiter )
	{
		/* first column of V */
		/* v = r / ||r||_2 */
		lis_vector_nrm2ex_mm(v[0],&rnorm);
		lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)one.hi,(LIS_QUAD *)rnorm.hi);
		lis_vector_scaleex_mm(tmp,v[0]);

		/* s = ||r||_2 e_1 */
		lis_vector_set_allex_nm(0.0,s);
		s->value[0]    = rnorm.hi[0];
		s->value_lo[0] = rnorm.lo[0];

		i = 0;
		do
		{
			iter++;
			i++;
			ii  = i-1;
			i1  = i;
			iiv = i-1;
			i1v = i;
			iih = (i-1)*h_dim;
			i1h = i*h_dim;


			/* z = M^-1 v */
			times = lis_wtime();
			lis_psolve(solver, v[iiv], z);
			ptimes += lis_wtime()-times;

			/* v = Az */
			LIS_MATVEC(A,z, v[i1v]);

			for(k=0;k<i;k++)
			{
				/* h[k,i]   = <w,v[k]>       */
				/* w        = w - h[k,i]v[k] */
				lis_vector_dotex_mmm(v[i1v],v[k],&t);
				h[k + iih].hi = t.hi[0];
				h[k + iih].lo = t.lo[0];
				lis_quad_minus((LIS_QUAD *)t.hi);
				lis_vector_axpyex_mmm(t,v[k],v[i1v]);
			}
			/* h[i+1,i] = ||w||          */
			/* v[i+1]   = w / h[i+1,i]   */
			lis_vector_nrm2ex_mm(v[i1v],&t);
			h[i1 + iih].hi = t.hi[0];
			h[i1 + iih].lo = t.lo[0];
			lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)one.hi,(LIS_QUAD *)t.hi);
			lis_vector_scaleex_mm(tmp,v[i1v]);

			for(k=1;k<=ii;k++)
			{
				jj  = k-1;
				t.hi[0]   =  h[jj + iih].hi;
				t.lo[0]   =  h[jj + iih].lo;
				lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)t.hi);
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)&h[k+iih]);
				lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
				lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)t.hi);
				lis_quad_minus((LIS_QUAD *)bb.hi);
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)&h[k+iih]);
				lis_quad_add((LIS_QUAD *)bb.hi,(LIS_QUAD *)bb.hi,(LIS_QUAD *)tmp.hi);
				h[jj + iih].hi = aa.hi[0];
				h[jj + iih].lo = aa.lo[0];
				h[k  + iih].hi = bb.hi[0];
				h[k  + iih].lo = bb.lo[0];
			}
			aa.hi[0] = h[ii + iih].hi;
			aa.lo[0] = h[ii + iih].lo;
			bb.hi[0] = h[i1 + iih].hi;
			bb.lo[0] = h[i1 + iih].lo;
			lis_quad_sqr((LIS_QUAD *)a2.hi,(LIS_QUAD *)aa.hi);
			lis_quad_sqr((LIS_QUAD *)b2.hi,(LIS_QUAD *)bb.hi);
			lis_quad_add((LIS_QUAD *)rr.hi,(LIS_QUAD *)a2.hi,(LIS_QUAD *)b2.hi);
			lis_quad_sqrt((LIS_QUAD *)rr.hi,(LIS_QUAD *)rr.hi);
			if( rr.hi[0]==0.0 )
			{
				rr.hi[0]=1.0e-17;
				rr.lo[0]=0.0;
			}
			lis_quad_div((LIS_QUAD *)&h[ii + cs],(LIS_QUAD *)aa.hi,(LIS_QUAD *)rr.hi);
			lis_quad_div((LIS_QUAD *)&h[ii + sn],(LIS_QUAD *)bb.hi,(LIS_QUAD *)rr.hi);
			tmp.hi[0] = s->value[ii];
			tmp.lo[0] = s->value_lo[ii];
			lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii + sn],(LIS_QUAD *)tmp.hi);
			lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[ii + cs],(LIS_QUAD *)tmp.hi);
			lis_quad_minus((LIS_QUAD *)aa.hi);
			s->value[i1] = aa.hi[0];
			s->value_lo[i1] = aa.lo[0];
			s->value[ii] = bb.hi[0];
			s->value_lo[ii] = bb.lo[0];

			lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)&h[ii+iih]);
			lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)&h[i1+iih]);
			lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
			h[ii   + iih].hi = aa.hi[0];
			h[ii   + iih].lo = aa.lo[0];

			/* convergence check */
			nrm2 = fabs(s->value[i1]) * bnrm2;

			if( output )
			{
				if( output & LIS_PRINT_MEM ) solver->residual[iter] = nrm2;
				if( output & LIS_PRINT_OUT && A->my_rank==0 ) printf("iter: %5d  residual = %e\n", iter, nrm2);
			}

			if( tol >= nrm2 ) break;
		} while( i<m && iter <maxiter );

		/* Solve H*Y =S for upper triangular H */
		tmp.hi[0] = s->value[ii];
		tmp.lo[0] = s->value_lo[ii];
		lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii + iih]);
		s->value[ii] = tmp.hi[0];
		s->value_lo[ii] = tmp.lo[0];
		for(k=1;k<=ii;k++)
		{
			jj = ii-k;
			t.hi[0]  = s->value[jj];
			t.lo[0]  = s->value_lo[jj];
			for(j=jj+1;j<=ii;j++)
			{
				tmp.hi[0] = s->value[j];
				tmp.lo[0] = s->value_lo[j];
				lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj + j*h_dim]);
				lis_quad_sub((LIS_QUAD *)t.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)tmp.hi);
			}
			lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)&h[jj + jj*h_dim]);
			s->value[jj] = tmp.hi[0];
			s->value_lo[jj] = tmp.lo[0];
		}
		/* x = x + yv */
		for(k=0;k<n;k++)
		{
			aa.hi[0] = s->value[0];
			aa.lo[0] = s->value_lo[0];
			bb.hi[0] = v[0]->value[k];
			bb.lo[0] = v[0]->value_lo[k];
			lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)bb.hi);
			z->value[k] = tmp.hi[0];
			z->value_lo[k] = tmp.lo[0];
		}
		for(j=1;j<=ii;j++)
		{
			aa.hi[0] = s->value[j];
			aa.lo[0] = s->value_lo[j];
			lis_vector_axpyex_mmm(aa,v[j],z);
		}
		/* r = M^-1 z */
		times = lis_wtime();
		lis_psolve(solver, z, r);
		ptimes += lis_wtime()-times;

		/* x = x + r */
		lis_vector_axpyex_mmm(one,r,x);

		if( tol >= nrm2 )
		{
			solver->retcode    = LIS_SUCCESS;
			solver->iter       = iter;
			solver->iter2      = 0;
			solver->resid      = nrm2;
			solver->ptimes     = ptimes;
			lis_free(h);
			LIS_DEBUG_FUNC_OUT;
			return LIS_SUCCESS;
		}

		for(j=1;j<=i;j++)
		{
			jj = i1-j+1;
			tmp.hi[0] = s->value[jj];
			tmp.lo[0] = s->value_lo[jj];
			lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj-1 + sn]);
			lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj-1 + cs]);
			lis_quad_minus((LIS_QUAD *)aa.hi);
			s->value[jj-1] = aa.hi[0];
			s->value_lo[jj-1] = aa.lo[0];
			s->value[jj] = bb.hi[0];
			s->value_lo[jj] = bb.lo[0];
		}

		for(j=0;j<=i1;j++)
		{
			t.hi[0] = s->value[j];
			t.lo[0] = s->value_lo[j];
			if( j==0 )
			{
				lis_quad_sub((LIS_QUAD *)t.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)one.hi);
			}
			lis_vector_axpyex_mmm(t,v[j],v[0]);
		}
	}

	solver->retcode   = LIS_MAXITER;
	solver->iter      = iter+1;
	solver->iter2     = 0;
	solver->resid     = nrm2;
	lis_free(h);
	LIS_DEBUG_FUNC_OUT;
	return LIS_MAXITER;
}
コード例 #4
0
ファイル: lis_solver_bicgsafe.c プロジェクト: florianl/lis
LIS_INT lis_bicgsafe_switch(LIS_SOLVER solver)
{
	LIS_MATRIX A;
	LIS_VECTOR x;
	LIS_VECTOR r, rtld, rhat, p, ptld, phat;
	LIS_VECTOR t, ttld, that, t0, t0hat;
	LIS_VECTOR y, w, u, 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,output,conv;
	LIS_INT iter2,maxiter2;
	double time,ptime;


	LIS_DEBUG_FUNC_IN;

	A       = solver->A;
	x       = solver->x;
	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];
	ptime   = 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];

	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);

	rho_old.hi[0] = 1.0;
	rho_old.lo[0] = 0.0;
	alpha.hi[0] = 1.0;
	alpha.lo[0] = 0.0;
	qsi.hi[0] = 1.0;
	qsi.lo[0] = 0.0;
	one.hi[0] = -1.0;
	one.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, ttld);
	lis_vector_set_allex_nm(0.0, ptld);
	lis_vector_set_allex_nm(0.0, p);
	lis_vector_set_allex_nm(0.0, u);
	lis_vector_set_allex_nm(0.0, t);
	lis_vector_set_allex_nm(0.0, t0);

	for( iter=1; iter<=maxiter2; iter++ )
	{
		/* rho = <rtld,r> */
		lis_vector_dot(rtld,r,&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) * (alpha / qsi) */
		beta.hi[0] = (rho.hi[0] / rho_old.hi[0]) * (alpha.hi[0] / qsi.hi[0]);

		/* w = ttld + beta*ptld */
		lis_vector_axpyz(beta.hi[0],ptld,ttld,w);

		/* rhat = M^-1 * r */
		time = lis_wtime();
		lis_psolve(solver, r, rhat);
		ptime += lis_wtime()-time;

		/* p = rhat + beta*(p - u) */
		lis_vector_axpy(-1,u,p);
		lis_vector_xpay(rhat,beta.hi[0],p);
		
		/* ptld = A * p */
		lis_matvec(A,p,ptld);

		/* tmpdot[0] = <rtld,ptld> */
		lis_vector_dot(rtld,ptld,&tmpdot[0].hi[0]);
		/* test breakdown */
		/* */
		
		/* alpha = rho / tmpdot[0] */
		alpha.hi[0] = rho.hi[0] / tmpdot[0].hi[0];

		/* y = t - r + alpha*(-w + ptld) */
		lis_vector_axpyz(-1,w,ptld,y);
		lis_vector_xpay(t,alpha.hi[0],y);
		lis_vector_axpy(-1,r,y);

		/* t = r - alpha*ptld */
		lis_vector_axpyz(-alpha.hi[0],ptld,r,t);

		/* that  = M^-1 * t */
		/* phat  = M^-1 * ptld */
		/* t0hat = M^-1 * t0 */
		time = lis_wtime();
		lis_psolve(solver, t, that);
		lis_psolve(solver, ptld, phat);
		lis_psolve(solver, t0, t0hat);
		ptime += lis_wtime()-time;

		/* 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].hi[0]);
		lis_vector_dot(ttld,t,&tmpdot[1].hi[0]);
		lis_vector_dot(y,t,&tmpdot[2].hi[0]);
		lis_vector_dot(ttld,y,&tmpdot[3].hi[0]);
		lis_vector_dot(ttld,ttld,&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 = qsi*phat + eta*(t0hat - rhat + beta*u) */
		lis_vector_xpay(t0hat,beta.hi[0],u);
		lis_vector_axpy(-1,rhat,u);
		lis_vector_scale(eta.hi[0],u);
		lis_vector_axpy(qsi.hi[0],phat,u);

		/* z = qsi*rhat + eta*z - alpha*u */
		lis_vector_scale(eta.hi[0],z);
		lis_vector_axpy(qsi.hi[0],rhat,z);
		lis_vector_axpy(-alpha.hi[0],u,z);

		/* x = x + alpha*p + z */
		lis_vector_axpy(alpha.hi[0],p,x);
		lis_vector_axpy(1,z,x);
		
		/* r = t - eta*y - qsi*ttld */
		lis_vector_axpyz(-eta.hi[0],y,t,r);
		lis_vector_axpy(-qsi.hi[0],ttld,r);
		
		/* convergence check */
		lis_solver_get_residual[conv](r,solver,&nrm2);
		if( output )
		{
			if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
			if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
		}

		if( tol2 >= nrm2 )
		{
			solver->iter       = iter;
			solver->iter2      = iter;
			solver->ptime      = ptime;
			break;
		}

		lis_vector_copy(t,t0);
		rho_old.hi[0] = rho.hi[0];
	}

	r->precision = LIS_PRECISION_QUAD;
	p->precision = LIS_PRECISION_QUAD;
	t->precision = LIS_PRECISION_QUAD;
	t0->precision = LIS_PRECISION_QUAD;
	ptld->precision = LIS_PRECISION_QUAD;
	that->precision = LIS_PRECISION_QUAD;

	solver->options[LIS_OPTIONS_INITGUESS_ZEROS] = LIS_FALSE;
	lis_vector_copyex_mn(x,solver->xx);

	rho_old.hi[0] = 1.0;
	alpha.hi[0] = 1.0;
	qsi.hi[0] = 1.0;
	one.hi[0] = -1.0;

	/* Initial Residual */
	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, ttld);
	lis_vector_set_allex_nm(0.0, ptld);
	lis_vector_set_allex_nm(0.0, p);
	lis_vector_set_allex_nm(0.0, u);
	lis_vector_set_allex_nm(0.0, t);
	lis_vector_set_allex_nm(0.0, t0);

	for( iter2=iter+1; iter2<=maxiter; iter2++ )
	{
		/* rho = <rtld,r> */
		lis_vector_dotex_mmm(rtld,r,&rho);

		/* test breakdown */
		if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
		{
			solver->retcode   = LIS_BREAKDOWN;
			solver->iter      = iter2;
			solver->iter2     = iter;
			solver->resid     = nrm2;
			LIS_DEBUG_FUNC_OUT;
			return LIS_BREAKDOWN;
		}

		/* beta = (rho / rho_old) * (alpha / qsi) */
		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 = ttld + beta*ptld */
		lis_vector_axpyzex_mmmm(beta,ptld,ttld,w);

		/* rhat = M^-1 * r */
		time = lis_wtime();
		lis_psolve(solver, r, rhat);
		ptime += lis_wtime()-time;

		/* p = rhat + beta*(p - u) */
		lis_vector_axpyex_mmm(one,u,p);
		lis_vector_xpayex_mmm(rhat,beta,p);
		
		/* ptld = A * p */
		lis_matvec(A,p,ptld);

		/* tmpdot[0] = <rtld,ptld> */
		lis_vector_dotex_mmm(rtld,ptld,&tmpdot[0]);
		/* test breakdown */
		/* */
		
		/* alpha = rho / tmpdot[0] */
		lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot[0].hi);

		/* y = t - r + alpha*(-w + ptld) */
		lis_vector_axpyzex_mmmm(one,w,ptld,y);
		lis_vector_xpayex_mmm(t,alpha,y);
		lis_vector_axpyex_mmm(one,r,y);

		/* t = r - alpha*ptld */
		lis_quad_minus((LIS_QUAD *)alpha.hi);
		lis_vector_axpyzex_mmmm(alpha,ptld,r,t);

		/* that  = M^-1 * t */
		/* phat  = M^-1 * ptld */
		/* t0hat = M^-1 * t0 */
		time = lis_wtime();
		lis_psolve(solver, t, that);
		lis_psolve(solver, ptld, phat);
		lis_psolve(solver, t0, t0hat);
		ptime += lis_wtime()-time;

		/* 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_dotex_mmm(y,y,&tmpdot[0]);
		lis_vector_dotex_mmm(ttld,t,&tmpdot[1]);
		lis_vector_dotex_mmm(y,t,&tmpdot[2]);
		lis_vector_dotex_mmm(ttld,y,&tmpdot[3]);
		lis_vector_dotex_mmm(ttld,ttld,&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 = qsi*phat + eta*(t0hat - rhat + beta*u) */
		lis_vector_xpayex_mmm(t0hat,beta,u);
		lis_vector_axpyex_mmm(one,rhat,u);
		lis_vector_scaleex_mm(eta,u);
		lis_vector_axpyex_mmm(qsi,phat,u);

		/* z = qsi*rhat + eta*z - alpha*u */
		lis_vector_scaleex_mm(eta,z);
		lis_vector_axpyex_mmm(qsi,rhat,z);
		lis_vector_axpyex_mmm(alpha,u,z);

		/* x = x + alpha*p + z */
		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 = t - eta*y - qsi*ttld */
		lis_quad_minus((LIS_QUAD *)eta.hi);
		lis_quad_minus((LIS_QUAD *)qsi.hi);
		lis_vector_axpyzex_mmmm(eta,y,t,r);
		lis_vector_axpyex_mmm(qsi,ttld,r);
		lis_quad_minus((LIS_QUAD *)eta.hi);
		lis_quad_minus((LIS_QUAD *)qsi.hi);
		
		/* convergence check */
		lis_solver_get_residual[conv](r,solver,&nrm2);
		if( output )
		{
			if( output & LIS_PRINT_MEM ) solver->rhistory[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->ptime      = ptime;
			LIS_DEBUG_FUNC_OUT;
			return LIS_SUCCESS;
		}

		lis_vector_copyex_mm(t,t0);
		rho_old.hi[0] = rho.hi[0];
		rho_old.lo[0] = rho.lo[0];
	}
	solver->retcode   = LIS_MAXITER;
	solver->iter      = iter;
	solver->iter2     = iter2;
	solver->resid     = nrm2;
	LIS_DEBUG_FUNC_OUT;
	return LIS_MAXITER;
}
コード例 #5
0
ファイル: lis_solver_bicgsafe.c プロジェクト: florianl/lis
LIS_INT lis_bicgsafe_quad(LIS_SOLVER solver)
{
	LIS_MATRIX A;
	LIS_VECTOR x;
	LIS_VECTOR r, rtld, rhat, p, ptld;
	LIS_VECTOR t, ttld;
	LIS_VECTOR y, v, u, utld, z;
	LIS_QUAD_PTR alpha, beta, rho, rho_old;
	LIS_QUAD_PTR qsi, eta;
	LIS_QUAD_PTR tmp, tmpdot[5],one;
	LIS_REAL bnrm2, nrm2, tol;
	LIS_INT iter,maxiter,output,conv;
	double time,ptime;

	LIS_DEBUG_FUNC_IN;

	A       = solver->A;
	x       = solver->x;
	maxiter = solver->options[LIS_OPTIONS_MAXITER];
	output  = solver->options[LIS_OPTIONS_OUTPUT];
	conv    = solver->options[LIS_OPTIONS_CONV_COND];
	ptime   = 0.0;


	rtld    = solver->work[0];
	r       = solver->work[1];
	rhat    = solver->work[2];
	p       = solver->work[3];
	ptld    = solver->work[4];
	t       = solver->work[5];
	ttld    = solver->work[6];
	y       = solver->work[7];
	v       = solver->work[8];
	u       = solver->work[9];
	z       = solver->work[10];
	utld    = solver->work[11];

	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);

	rho_old.hi[0] = 1.0;
	rho_old.lo[0] = 0.0;
	alpha.hi[0] = 1.0;
	alpha.lo[0] = 0.0;
	qsi.hi[0] = 1.0;
	qsi.lo[0] = 0.0;
	one.hi[0] = -1.0;
	one.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,u);
	lis_vector_set_allex_nm(0.0,ptld);
	lis_vector_set_allex_nm(0.0,utld);
	
	for( iter=1; iter<=maxiter; iter++ )
	{
		/* rho = <rtld,r> */
		lis_vector_dotex_mmm(rtld,r,&rho);

		/* 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) * (alpha / qsi) */
		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);

		/* rhat = M^-1 * r */
		/* v    = A * rhat */
		time = lis_wtime();
		lis_psolve(solver, r, rhat);
		ptime += lis_wtime()-time;
		lis_matvec(A,rhat,v);

		/* p = rhat + beta*(p - u) */
		lis_vector_axpyex_mmm(one,u,p);
		lis_vector_xpayex_mmm(rhat,beta,p);
		
		/* ptld = v + beta*(ptld - utld) */
		lis_vector_axpyex_mmm(one,utld,ptld);
		lis_vector_xpayex_mmm(v,beta,ptld);

		/* tmpdot[0] = <rtld,ptld> */
		lis_vector_dotex_mmm(rtld,ptld,&tmpdot[0]);
		/* test breakdown */
		/* */
		
		/* alpha = rho / tmpdot[0] */
		lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot[0].hi);


		/* tmpdot[0] = <y,y>       */
		/* tmpdot[1] = <v,r>       */
		/* tmpdot[2] = <y,r>       */
		/* tmpdot[3] = <v,y>       */
		/* tmpdot[4] = <v,v>       */
		lis_vector_dotex_mmm(y,y,&tmpdot[0]);
		lis_vector_dotex_mmm(v,r,&tmpdot[1]);
		lis_vector_dotex_mmm(y,r,&tmpdot[2]);
		lis_vector_dotex_mmm(v,y,&tmpdot[3]);
		lis_vector_dotex_mmm(v,v,&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);
		}

		/* t = qsi*ptld + eta*y */
		lis_vector_copyex_mm(y,t);
		lis_vector_scaleex_mm(eta,t);
		lis_vector_axpyex_mmm(qsi,ptld,t);

		/* ttld  = M^-1 * t */
		time = lis_wtime();
		lis_psolve(solver, t, ttld);
		ptime += lis_wtime()-time;

		/* u    = ttld + eta*beta*u */
		/* utld = A * u             */
		lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)beta.hi);
		lis_vector_xpayex_mmm(ttld,tmp,u);
		lis_matvec(A,u,utld);

		/* z = qsi*rhat + eta*z - alpha*u */
		lis_vector_scaleex_mm(eta,z);
		lis_vector_axpyex_mmm(qsi,rhat,z);
		lis_quad_minus((LIS_QUAD *)alpha.hi);
		lis_vector_axpyex_mmm(alpha,u,z);

		/* y = qsi*v + eta*y - alpha*utld */
		lis_vector_scaleex_mm(eta,y);
		lis_vector_axpyex_mmm(qsi,v,y);
		lis_vector_axpyex_mmm(alpha,utld,y);
		lis_quad_minus((LIS_QUAD *)alpha.hi);

		/* x = x + alpha*p + z */
		lis_vector_axpyex_mmm(alpha,p,x);
		lis_quad_minus((LIS_QUAD *)one.hi);
		lis_vector_axpyex_mmm(one,z,x);
		lis_quad_minus((LIS_QUAD *)one.hi);
		
		/* r = r - alpha*ptld - y */
		lis_quad_minus((LIS_QUAD *)alpha.hi);
		lis_vector_axpyex_mmm(alpha,ptld,r);
		lis_quad_minus((LIS_QUAD *)alpha.hi);
		lis_vector_axpyex_mmm(one,y,r);
		
		/* convergence check */
		lis_solver_get_residual[conv](r,solver,&nrm2);
		if( output )
		{
			if( output & LIS_PRINT_MEM ) solver->rhistory[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->ptime      = ptime;
			LIS_DEBUG_FUNC_OUT;
			return LIS_SUCCESS;
		}

		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;
}
コード例 #6
0
ファイル: lis_solver_bicgsafe.c プロジェクト: florianl/lis
LIS_INT lis_bicrsafe_quad(LIS_SOLVER solver)
{
	LIS_MATRIX A;
	LIS_VECTOR x;
	LIS_VECTOR r, rtld, artld, mr, amr, p, ap, map;
	LIS_VECTOR y, my, u, au, 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,output,conv;
	double time,ptime;

	LIS_DEBUG_FUNC_IN;

	A       = solver->A;
	x       = solver->x;
	maxiter = solver->options[LIS_OPTIONS_MAXITER];
	output  = solver->options[LIS_OPTIONS_OUTPUT];
	conv    = solver->options[LIS_OPTIONS_CONV_COND];
	ptime   = 0.0;

	rtld    = solver->work[0];
	r       = solver->work[1];
	mr      = solver->work[2];
	amr     = solver->work[3];
	p       = solver->work[4];
	ap      = solver->work[5];
	map     = solver->work[6];
	my      = solver->work[7];
	y       = solver->work[8];
	u       = solver->work[9];
	z       = solver->work[10];
	au      = solver->work[11];
	artld   = solver->work[12];

	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);

	lis_matvect(A,rtld,artld);
	time = lis_wtime();
	lis_psolve(solver, r, mr);
	ptime += lis_wtime()-time;
	lis_matvec(A,mr,amr);
	lis_vector_dotex_mmm(rtld,amr,&rho_old);
	lis_vector_copyex_mm(amr,ap);
	lis_vector_copyex_mm(mr,p);
	one.hi[0] = -1.0;
	one.lo[0] = 0.0;

	
	for( iter=1; iter<=maxiter; iter++ )
	{
		/* map  = M^-1 * ap */
		time = lis_wtime();
		lis_psolve(solver, ap, map);
		ptime += lis_wtime()-time;

		/* tmpdot[0] = <artld,map> */
		/* alpha = rho_old / tmpdot[0] */
		lis_vector_dotex_mmm(artld,map,&tmpdot[0]);
		lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho_old.hi,(LIS_QUAD *)tmpdot[0].hi);


		/* tmpdot[0] = <y,y>           */
		/* tmpdot[1] = <amr,r>         */
		/* tmpdot[2] = <y,r>           */
		/* tmpdot[3] = <amr,y>         */
		/* tmpdot[4] = <amr,amr>       */
		lis_vector_dotex_mmm(y,y,&tmpdot[0]);
		lis_vector_dotex_mmm(amr,r,&tmpdot[1]);
		lis_vector_dotex_mmm(y,r,&tmpdot[2]);
		lis_vector_dotex_mmm(amr,y,&tmpdot[3]);
		lis_vector_dotex_mmm(amr,amr,&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    = qsi*map + eta*my + eta*beta*u */
		/* au   = A * u                         */
		lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)beta.hi);
		lis_vector_scaleex_mm(tmp,u);
		lis_vector_axpyex_mmm(qsi,map,u);
		lis_vector_axpyex_mmm(eta,my,u);
		lis_matvec(A,u,au);

		/* z = qsi*mr + eta*z - alpha*u */
		lis_vector_scaleex_mm(eta,z);
		lis_vector_axpyex_mmm(qsi,mr,z);
		lis_quad_minus((LIS_QUAD *)alpha.hi);
		lis_vector_axpyex_mmm(alpha,u,z);

		/* y  = qsi*amr + eta*y - alpha*au */
		/* my = M^-1 * y */
		lis_vector_scaleex_mm(eta,y);
		lis_vector_axpyex_mmm(qsi,amr,y);
		lis_vector_axpyex_mmm(alpha,au,y);
		time = lis_wtime();
		lis_psolve(solver, y, my);
		ptime += lis_wtime()-time;

		/* x = x + alpha*p + z */
		lis_quad_minus((LIS_QUAD *)alpha.hi);
		lis_vector_axpyex_mmm(alpha,p,x);
		lis_quad_minus((LIS_QUAD *)one.hi);
		lis_vector_axpyex_mmm(one,z,x);
		
		/* r = r - alpha*ap - y */
		lis_quad_minus((LIS_QUAD *)alpha.hi);
		lis_quad_minus((LIS_QUAD *)one.hi);
		lis_vector_axpyex_mmm(alpha,ap,r);
		lis_vector_axpyex_mmm(one,y,r);
		
		/* convergence check */
		lis_solver_get_residual[conv](r,solver,&nrm2);
		if( output )
		{
			if( output & LIS_PRINT_MEM ) solver->rhistory[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->ptime      = ptime;
			LIS_DEBUG_FUNC_OUT;
			return LIS_SUCCESS;
		}

		/* mr  = mr - alpha*map - my */
		/* amr = A * mr              */
		/* rho = <rtld,amr> */
		lis_vector_axpyex_mmm(alpha,map,mr);
		lis_vector_axpyex_mmm(one,my,mr);
		lis_matvec(A,mr,amr);
		lis_vector_dotex_mmm(rtld,amr,&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 / rho_old) * (alpha / qsi) */
		lis_quad_minus((LIS_QUAD *)alpha.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);


		/* p  = mr + beta*(p - u)    */
		/* ap = amr + beta*(ap - au) */
		lis_vector_axpyex_mmm(one,u,p);
		lis_vector_xpayex_mmm(mr,beta,p);
		lis_vector_axpyex_mmm(one,au,ap);
		lis_vector_xpayex_mmm(amr,beta,ap);

		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;
}