|
|
!!$
|
|
|
!!$ Parallel Sparse BLAS version 3.4
|
|
|
!!$ (C) Copyright 2006, 2010, 2015
|
|
|
!!$ Salvatore Filippone University of Rome Tor Vergata
|
|
|
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
|
|
|
!!$
|
|
|
!!$ 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. The name of the PSBLAS group or the names of its contributors may
|
|
|
!!$ not be used to endorse or promote products derived from this
|
|
|
!!$ software without specific written permission.
|
|
|
!!$
|
|
|
!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
|
!!$ ``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 PSBLAS GROUP OR ITS CONTRIBUTORS
|
|
|
!!$ 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.
|
|
|
!!$
|
|
|
!!$
|
|
|
! File: psb_zgcr.f90
|
|
|
!!
|
|
|
!! Contributors: Ambra Abdullahi (UNITOV) and Pasqua D’Ambra (IAC-CNR)
|
|
|
!!
|
|
|
!!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
|
|
|
!!$ C C
|
|
|
!!$ C References: C
|
|
|
!!$ C [1] Duff, I., Marrone, M., Radicati, G., and Vittoli, C. C
|
|
|
!!$ C Level 3 basic linear algebra subprograms for sparse C
|
|
|
!!$ C matrices: a user level interface C
|
|
|
!!$ C ACM Trans. Math. Softw., 23(3), 379-401, 1997. C
|
|
|
!!$ C C
|
|
|
!!$ C C
|
|
|
!!$ C [2] S. Filippone, M. Colajanni C
|
|
|
!!$ C PSBLAS: A library for parallel linear algebra C
|
|
|
!!$ C computation on sparse matrices C
|
|
|
!!$ C ACM Trans. on Math. Softw., 26(4), 527-550, Dec. 2000. C
|
|
|
!!$ C C
|
|
|
!!$ C [3] M. Arioli, I. Duff, M. Ruiz C
|
|
|
!!$ C Stopping criteria for iterative solvers C
|
|
|
!!$ C SIAM J. Matrix Anal. Appl., Vol. 13, pp. 138-144, 1992 C
|
|
|
!!$ C C
|
|
|
!!$ C C
|
|
|
!!$ C [4] R. Barrett et al C
|
|
|
!!$ C Templates for the solution of linear systems C
|
|
|
!!$ C SIAM, 1993
|
|
|
!!$ C C
|
|
|
!!$ C [4] Notay, Yvan C
|
|
|
!!$ C Aggregation-based algebraic multigrid method C
|
|
|
!!$ C SIAM Journal on Scientific Computing 34, C
|
|
|
!!$ C pp. A2288-A2316, 2012 C
|
|
|
!!$ C C
|
|
|
!!$ C C
|
|
|
!!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
|
|
|
! File: psb_zgcr.f90
|
|
|
!
|
|
|
! Subroutine: psb_zgcr
|
|
|
! This subroutine implements the GCR method.
|
|
|
!
|
|
|
!
|
|
|
! Arguments:
|
|
|
!
|
|
|
! a - type(psb_zspmat_type) Input: sparse matrix containing A.
|
|
|
! prec - class(psb_zprec_type) Input: preconditioner
|
|
|
! b(:) - real Input: vector containing the
|
|
|
! right hand side B
|
|
|
! x(:) - real Input/Output: vector containing the
|
|
|
! initial guess and final solution X.
|
|
|
! eps - real Input: Stopping tolerance; the iteration is
|
|
|
! stopped when the error estimate |err| <= eps
|
|
|
! desc_a - type(psb_desc_type). Input: The communication descriptor.
|
|
|
! info - integer. Output: Return code
|
|
|
!
|
|
|
! itmax - integer(optional) Input: maximum number of iterations to be
|
|
|
! performed.
|
|
|
! iter - integer(optional) Output: how many iterations have been
|
|
|
! performed.
|
|
|
! performed.
|
|
|
! err - real (optional) Output: error estimate on exit. If the
|
|
|
! denominator of the estimate is exactly
|
|
|
! 0, it is changed into 1.
|
|
|
! itrace - integer(optional) Input: print an informational message
|
|
|
! with the error estimate every itrace
|
|
|
! iterations
|
|
|
! istop - integer(optional) Input: stopping criterion, or how
|
|
|
! to estimate the error.
|
|
|
! 1: err = |r|/(|a||x|+|b|); here the iteration is
|
|
|
! stopped when |r| <= eps * (|a||x|+|b|)
|
|
|
! 2: err = |r|/|b|; here the iteration is
|
|
|
! stopped when |r| <= eps * |b|
|
|
|
! where r is the (preconditioned, recursive
|
|
|
! estimate of) residual.
|
|
|
!
|
|
|
! irst - integer(optional) Input: restart parameter
|
|
|
!
|
|
|
|
|
|
subroutine psb_zgcr_vect(a,prec,b,x,eps,desc_a,info,&
|
|
|
& itmax,iter,err,itrace, irst, istop)
|
|
|
use psb_base_mod
|
|
|
use psb_prec_mod
|
|
|
use psb_z_krylov_conv_mod
|
|
|
use psb_krylov_mod
|
|
|
implicit none
|
|
|
|
|
|
|
|
|
type(psb_zspmat_type), intent(in) :: a
|
|
|
Type(psb_desc_type), Intent(in) :: desc_a
|
|
|
class(psb_zprec_type), intent(inout) :: prec
|
|
|
type(psb_z_vect_type), Intent(inout) :: b
|
|
|
type(psb_z_vect_type), Intent(inout) :: x
|
|
|
real(psb_dpk_), Intent(in) :: eps
|
|
|
integer(psb_ipk_), intent(out) :: info
|
|
|
integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, irst, istop
|
|
|
integer(psb_ipk_), Optional, Intent(out) :: iter
|
|
|
real(psb_dpk_), Optional, Intent(out) :: err
|
|
|
! = local data
|
|
|
complex(psb_dpk_), allocatable :: alpha(:), h(:,:)
|
|
|
type(psb_z_vect_type), allocatable :: z(:), c(:), c_scale(:)
|
|
|
type(psb_z_vect_type) :: r
|
|
|
|
|
|
real(psb_dpk_) :: r_norm, b_norm, a_norm, derr
|
|
|
integer(psb_ipk_) :: n_col, mglob, naux, err_act
|
|
|
integer(psb_ipk_) :: debug_level, debug_unit
|
|
|
integer(psb_ipk_) :: np, me, ictxt
|
|
|
integer(psb_ipk_) :: i, j, it, itx, istop_, itmax_, itrace_, nl, m, nrst
|
|
|
complex(psb_dpk_) :: hjj
|
|
|
complex(psb_dpk_), allocatable, target :: aux(:)
|
|
|
character(len=20) :: name
|
|
|
type(psb_itconv_type) :: stopdat
|
|
|
character(len=*), parameter :: methdname='GCR'
|
|
|
integer(psb_ipk_) ::int_err(5)
|
|
|
info = psb_success_
|
|
|
name = 'psb_zgcr'
|
|
|
call psb_erractionsave(err_act)
|
|
|
debug_unit = psb_get_debug_unit()
|
|
|
debug_level = psb_get_debug_level()
|
|
|
|
|
|
ictxt = desc_a%get_context()
|
|
|
|
|
|
call psb_info(ictxt, me, np)
|
|
|
if (.not.allocated(b%v)) then
|
|
|
info = psb_err_invalid_vect_state_
|
|
|
call psb_errpush(info,name)
|
|
|
goto 9999
|
|
|
endif
|
|
|
if (.not.allocated(x%v)) then
|
|
|
info = psb_err_invalid_vect_state_
|
|
|
call psb_errpush(info,name)
|
|
|
goto 9999
|
|
|
endif
|
|
|
|
|
|
mglob = desc_a%get_global_rows()
|
|
|
n_col = desc_a%get_local_cols()
|
|
|
|
|
|
if (present(istop)) then
|
|
|
istop_ = istop
|
|
|
else
|
|
|
istop_ = 2
|
|
|
endif
|
|
|
|
|
|
!
|
|
|
! ISTOP_ = 1: Normwise backward error, infinity norm
|
|
|
! ISTOP_ = 2: ||r||/||b||, 2-norm
|
|
|
!
|
|
|
|
|
|
if ((istop_ < 1 ).or.(istop_ > 2 ) ) then
|
|
|
info=psb_err_invalid_istop_
|
|
|
int_err(1)=istop_
|
|
|
err=info
|
|
|
call psb_errpush(info,name,i_err=int_err)
|
|
|
goto 9999
|
|
|
endif
|
|
|
|
|
|
|
|
|
call psb_chkvect(mglob,ione,x%get_nrows(),ione,ione,desc_a,info)
|
|
|
if (info == psb_success_)&
|
|
|
& call psb_chkvect(mglob,ione,b%get_nrows(),ione,ione,desc_a,info)
|
|
|
if(info /= psb_success_) then
|
|
|
info=psb_err_from_subroutine_
|
|
|
call psb_errpush(info,name,a_err='psb_chkvect on X/B')
|
|
|
goto 9999
|
|
|
end if
|
|
|
|
|
|
if (present(itmax)) then
|
|
|
itmax_ = itmax
|
|
|
else
|
|
|
itmax_ = 1000
|
|
|
endif
|
|
|
|
|
|
if (present(itrace)) then
|
|
|
itrace_ = itrace
|
|
|
else
|
|
|
itrace_ = 0
|
|
|
end if
|
|
|
|
|
|
if (present(irst)) then
|
|
|
nl = irst
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
& ' present: irst: ',irst,nl
|
|
|
else
|
|
|
nl = 10
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
|
& ' not present: irst: ',irst,nl
|
|
|
endif
|
|
|
|
|
|
if (nl <=0 ) then
|
|
|
info=psb_err_invalid_istop_
|
|
|
int_err(1)=nl
|
|
|
err=info
|
|
|
call psb_errpush(info,name,i_err=int_err)
|
|
|
goto 9999
|
|
|
endif
|
|
|
|
|
|
naux=4*n_col
|
|
|
allocate(aux(naux),h(nl+1,nl+1),&
|
|
|
&c_scale(nl+1),c(nl+1),z(nl+1), alpha(nl+1), stat=info)
|
|
|
|
|
|
h = zzero
|
|
|
if (info /= psb_success_) then
|
|
|
info=psb_err_from_subroutine_non_
|
|
|
call psb_errpush(info,name)
|
|
|
goto 9999
|
|
|
end if
|
|
|
|
|
|
call psb_geasb(r, desc_a,info, scratch=.true.,mold=x%v)
|
|
|
|
|
|
do i =1,nl+1
|
|
|
call psb_geasb(c(i), desc_a,info, scratch=.true.,mold=x%v)
|
|
|
call psb_geasb(z(i), desc_a,info, scratch=.true.,mold=x%v)
|
|
|
call psb_geasb(c_scale(i), desc_a,info, scratch=.true.,mold=x%v)
|
|
|
end do
|
|
|
|
|
|
itx = 0
|
|
|
|
|
|
nrst = -1
|
|
|
call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
|
|
|
restart: do
|
|
|
if (itx>= itmax_) exit restart
|
|
|
h = zzero
|
|
|
|
|
|
it = 0
|
|
|
! compute r0 = b-ax0
|
|
|
|
|
|
if (info /= psb_success_) then
|
|
|
info=psb_err_from_subroutine_non_
|
|
|
call psb_errpush(info,name)
|
|
|
goto 9999
|
|
|
end if
|
|
|
|
|
|
|
|
|
call psb_geaxpby(zone, b, zzero, r, desc_a, info)
|
|
|
call psb_spmm(-zone,a,x,zone,r,desc_a,info,work=aux)
|
|
|
if (info /= psb_success_) then
|
|
|
info=psb_err_from_subroutine_non_
|
|
|
call psb_errpush(info,name)
|
|
|
goto 9999
|
|
|
end if
|
|
|
|
|
|
if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart
|
|
|
|
|
|
nrst = nrst + 1
|
|
|
|
|
|
iteration: do
|
|
|
|
|
|
itx = itx + 1
|
|
|
it = it + 1
|
|
|
j = it
|
|
|
!Apply preconditioner
|
|
|
call prec%apply(r,z(j),desc_a,info,work=aux)
|
|
|
|
|
|
call psb_spmm(zone,a,z(j),zzero,c(1),desc_a,info,work=aux)
|
|
|
do i =1, j - 1
|
|
|
|
|
|
h(i,j) = psb_gedot(c_scale(i), c(i), desc_a, info)
|
|
|
|
|
|
call psb_geaxpby(zone, c(i), zzero, c(i+1), desc_a, info)
|
|
|
call psb_geaxpby(-h(i,j), c_scale(i), zone, c(i+1), desc_a, info)
|
|
|
end do
|
|
|
|
|
|
h(j,j) = psb_norm2(c(j), desc_a, info)
|
|
|
hjj = zone/h(j,j)
|
|
|
call psb_geaxpby(hjj, c(j), zzero, c_scale(j), desc_a, info)
|
|
|
|
|
|
alpha(j) = psb_gedot(c_scale(j), r, desc_a, info)
|
|
|
|
|
|
!Update residual
|
|
|
call psb_geaxpby(zone, r, zzero, r, desc_a, info)
|
|
|
call psb_geaxpby(-alpha(j), c_scale(j), zone, r, desc_a, info)
|
|
|
|
|
|
if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart
|
|
|
|
|
|
if (j >= irst) exit iteration
|
|
|
|
|
|
|
|
|
end do iteration
|
|
|
|
|
|
m = j
|
|
|
|
|
|
!Compute solution
|
|
|
|
|
|
call ztrsm('l','u','n','n',m,1,zone,h,size(h,1),alpha,size(alpha,1))
|
|
|
|
|
|
if (nrst == 0 ) then
|
|
|
call x%set(zzero)
|
|
|
endif
|
|
|
do i=1,m
|
|
|
call psb_geaxpby(alpha(i), z(i), zone, x, desc_a, info)
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
end do restart
|
|
|
m = j
|
|
|
!Compute solution
|
|
|
call ztrsm('l','u','n','n',m,1,zone,h,size(h,1),alpha,size(alpha,1))
|
|
|
call x%set(zzero)
|
|
|
do i=1,m
|
|
|
call psb_geaxpby(alpha(i), z(i), zone, x, desc_a, info)
|
|
|
enddo
|
|
|
|
|
|
iter = j
|
|
|
|
|
|
call psb_end_conv(methdname,itx,desc_a,stopdat,info,derr,iter)
|
|
|
if (present(err)) err = derr
|
|
|
|
|
|
if (info == psb_success_) call psb_gefree(r,desc_a,info)
|
|
|
|
|
|
do j = 1,m
|
|
|
if (info == psb_success_) call psb_gefree(z(j),desc_a,info)
|
|
|
if (info == psb_success_) call psb_gefree(c_scale(j),desc_a,info)
|
|
|
enddo
|
|
|
|
|
|
do i =1,nl+1
|
|
|
if (info == psb_success_) call psb_gefree(c(i),desc_a,info)
|
|
|
end do
|
|
|
|
|
|
if (info == psb_success_) deallocate(aux,h,c_scale,z,c,alpha,stat=info)
|
|
|
if (info /= psb_success_) then
|
|
|
info=psb_err_from_subroutine_non_
|
|
|
call psb_errpush(info,name)
|
|
|
goto 9999
|
|
|
end if
|
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
return
|
|
|
|
|
|
9999 continue
|
|
|
call psb_erractionrestore(err_act)
|
|
|
if (err_act.eq.psb_act_abort_) then
|
|
|
call psb_error()
|
|
|
return
|
|
|
end if
|
|
|
|
|
|
return
|
|
|
end subroutine psb_zgcr_vect
|
|
|
|
|
|
|