Merge branch 'development' into remap-coarse
sfilippone
17 hours ago
commit
4315a2b395
@ -0,0 +1,511 @@
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!
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! Parallel Sparse BLAS version 3.5
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! (C) Copyright 2006-2018
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! Salvatore Filippone
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! Alfredo Buttari
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!
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! Redistribution and use in source and binary forms, with or without
|
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! modification, are permitted provided that the following conditions
|
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! 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 prior written permission.
|
||||
!
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||||
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
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! ``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
|
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! 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.
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||||
!
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!
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! File: psb_cminres.f90
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! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
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! C C
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||||
! 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
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||||
! C matrices: a user level interface C
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||||
! C ACM Trans. Math. Softw., 23(3), 379-401, 1997. C
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||||
! 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
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||||
! C ACM Trans. on Math. Softw., 26(4), 527-550, Dec. 2000. C
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||||
! C C
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! C [3] M. Arioli, I. Duff, M. Ruiz C
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! C Stopping criteria for iterative solvers C
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! C SIAM J. Matrix Anal. Appl., Vol. 13, pp. 138-144, 1992 C
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||||
! C C
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||||
! C C
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||||
! C [4] R. Barrett et al C
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! C Templates for the solution of linear systems C
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||||
! C SIAM, 1993
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||||
! C C
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||||
! C C
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! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
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! File: psb_cminres.f90
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!
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! Subroutine: psb_cminres
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! This subroutine implements the MINRES method.
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!
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!
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! Arguments:
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!
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! a - type(psb_cspmat_type) Input: sparse matrix containing A.
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! prec - class(psb_cprec_type) Input: preconditioner
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! b(:) - complex Input: vector containing the
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! right hand side B
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! x(:) - complex Input/Output: vector containing the
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! initial guess and final solution X.
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! eps - real Input: Stopping tolerance; the iteration is
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! stopped when the error estimate |err| <= eps
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! desc_a - type(psb_desc_type). Input: The communication descriptor.
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! info - integer. Output: Return code
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!
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! itmax - integer(optional) Input: maximum number of iterations to be
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! performed.
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! iter - integer(optional) Output: how many iterations have been
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! performed.
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! performed.
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! err - real (optional) Output: error estimate on exit. If the
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! denominator of the estimate is exactly
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! 0, it is changed into 1.
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! itrace - integer(optional) Input: print an informational message
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! with the error estimate every itrace
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! iterations
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! istop - integer(optional) Input: stopping criterion, or how
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! to estimate the error.
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! 1: err = |r|/(|a||x|+|b|); here the iteration is
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! stopped when |r| <= eps * (|a||x|+|b|)
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! 2: err = |r|/|b|; here the iteration is
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! stopped when |r| <= eps * |b|
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! where r is the (preconditioned, recursive
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! estimate of) residual.
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!
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!
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subroutine psb_cminres_vect(a,prec,b,x,eps,desc_a,info,&
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& itmax,iter,err,itrace,istop,cond)
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use psb_base_mod
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use psb_prec_mod
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use psb_c_linsolve_conv_mod
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use psb_linsolve_mod
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implicit none
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type(psb_cspmat_type), intent(in) :: a
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Type(psb_desc_type), Intent(in) :: desc_a
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class(psb_cprec_type), intent(inout) :: prec
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type(psb_c_vect_type), Intent(inout) :: b
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type(psb_c_vect_type), Intent(inout) :: x
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Real(psb_spk_), Intent(in) :: eps
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integer(psb_ipk_), intent(out) :: info
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integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, istop
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integer(psb_ipk_), Optional, Intent(out) :: iter
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Real(psb_spk_), Optional, Intent(out) :: err, cond
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! = Local data
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complex(psb_spk_), allocatable, target :: aux(:)
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type(psb_c_vect_type), allocatable, target :: wwrk(:)
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type(psb_c_vect_type), pointer :: y, r1, r2, v, w, w1, w2, wtmp, res
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complex(psb_spk_) :: alfa, beta, beta1, dbar, delta, denom
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complex(psb_spk_) :: epsln, gamma, gbar, oldb, oldeps, phi, phibar
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complex(psb_spk_) :: rhs1, rhs2, s, zeta, betatmp
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complex(psb_spk_) :: rotx(1), roty(1)
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real(psb_spk_) :: cs
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complex(psb_spk_) :: sn
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integer(psb_ipk_) :: itmax_, istop_, naux, itx, itrace_, n_col, n_row, err_act
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integer(psb_lpk_) :: mglob
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integer(psb_ipk_) :: debug_level, debug_unit
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type(psb_ctxt_type) :: ctxt
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integer(psb_ipk_) :: np, me
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real(psb_dpk_) :: derr, errnum, errden, deps
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logical :: do_cond
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logical :: converged
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real(psb_spk_) :: epsmach
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real(psb_spk_) :: gmax, gmin, tnorm2, ynorm2
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real(psb_spk_) :: rni, xni, bni, ani, bn2, r0n2
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character(len=20) :: name
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character(len=*), parameter :: methdname='MINRES'
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info = psb_success_
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name = 'psb_cminres'
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call psb_erractionsave(err_act)
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debug_unit = psb_get_debug_unit()
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debug_level = psb_get_debug_level()
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ctxt = desc_a%get_context()
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call psb_info(ctxt, me, np)
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if (.not.allocated(b%v)) then
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info = psb_err_invalid_vect_state_
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call psb_errpush(info,name)
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goto 9999
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endif
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if (.not.allocated(x%v)) then
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info = psb_err_invalid_vect_state_
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call psb_errpush(info,name)
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goto 9999
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endif
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mglob = desc_a%get_global_rows()
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n_row = desc_a%get_local_rows()
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n_col = desc_a%get_local_cols()
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if (present(istop)) then
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istop_ = istop
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else
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istop_ = psb_get_istop_default()
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endif
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if (.not.psb_is_valid_istop(istop_)) then
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info=psb_err_invalid_istop_
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err=info
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call psb_errpush(info,name,i_err=(/istop_/))
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goto 9999
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end if
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!
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! istop_ = 1: normwise backward error, infinity norm
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! istop_ = 2: ||r||/||b|| norm 2
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!
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select case(istop_)
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case(psb_istop_ani_,psb_istop_bn2_,&
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& psb_istop_rn2_abs_, psb_istop_rrn2_)
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! nothing needed
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case default
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! should never get here
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info=psb_err_internal_error_
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err=info
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call psb_errpush(info,name,a_err="invalid istop_")
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goto 9999
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end select
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call psb_chkvect(mglob,lone,x%get_nrows(),lone,lone,desc_a,info)
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if (info == psb_success_)&
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& call psb_chkvect(mglob,lone,b%get_nrows(),lone,lone,desc_a,info)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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call psb_errpush(info,name,a_err='psb_chkvect on X/B')
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goto 9999
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end if
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naux=4*n_col
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allocate(aux(naux), stat=info)
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if (info == psb_success_) call psb_geall(wwrk,desc_a,info,n=9_psb_ipk_)
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if (info == psb_success_) call psb_geasb(wwrk,desc_a,info,mold=x%v,scratch=.true.)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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if (present(itmax)) then
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itmax_ = itmax
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else
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itmax_ = 1000
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endif
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if (present(itrace)) then
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itrace_ = itrace
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else
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itrace_ = 0
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end if
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y => wwrk(1)
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r1 => wwrk(2)
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r2 => wwrk(3)
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v => wwrk(4)
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w => wwrk(5)
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w1 => wwrk(6)
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w2 => wwrk(7)
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wtmp => wwrk(8)
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res => wwrk(9)
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do_cond = present(cond)
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epsmach = epsilon(sone)
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! res = b - A*x
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call psb_geaxpby(cone,b,czero,res,desc_a,info)
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if (info == psb_success_) call psb_spmm(-cone,a,x,cone,res,desc_a,info,work=aux)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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select case(istop_)
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case(psb_istop_ani_)
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ani = psb_spnrmi(a,desc_a,info)
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bni = psb_geamax(b,desc_a,info)
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case(psb_istop_bn2_)
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bn2 = psb_genrm2(b,desc_a,info)
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case(psb_istop_rn2_abs_)
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! nothing needed
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case(psb_istop_rrn2_)
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r0n2 = psb_genrm2(res,desc_a,info)
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end select
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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errnum = czero
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errden = cone
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deps = eps
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converged = .false.
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if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
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! y = beta1 * P' * v1, with v1 the first Lanczos vector.
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call psb_geaxpby(cone,res,czero,y,desc_a,info)
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if (info == psb_success_) call psb_geaxpby(cone,res,czero,r1,desc_a,info)
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if (info == psb_success_) call prec%apply(res,y,desc_a,info,work=aux)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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beta1 = sqrt(psb_gedot(res,y,desc_a,info))
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! If beta1 is numerically zero, x is already acceptable.
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if (abs(beta1) <= epsmach) then
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itx = 0
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converged = .true.
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if (do_cond) cond = szero
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select case(istop_)
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case(psb_istop_ani_)
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rni = psb_geamax(res,desc_a,info)
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xni = psb_geamax(x,desc_a,info)
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errnum = rni
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errden = ani*xni + bni
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case(psb_istop_bn2_)
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errnum = abs(beta1)
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errden = bn2
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case(psb_istop_rn2_abs_)
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errnum = abs(beta1)
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errden = sone
|
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case(psb_istop_rrn2_)
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errnum = abs(beta1)
|
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errden = r0n2
|
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end select
|
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if (errden == szero) errden = sone
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
|
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goto 9999
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||||
end if
|
||||
end if
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|
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beta = beta1
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||||
oldb = czero
|
||||
dbar = czero
|
||||
epsln = czero
|
||||
phibar = beta1
|
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rhs1 = beta1
|
||||
rhs2 = czero
|
||||
cs = -sone
|
||||
sn = czero
|
||||
itx = 0
|
||||
|
||||
if (do_cond) then
|
||||
tnorm2 = 0.0_psb_spk_
|
||||
ynorm2 = 0.0_psb_spk_
|
||||
gmax = 0.0_psb_spk_
|
||||
gmin = huge(sone)
|
||||
end if
|
||||
|
||||
call psb_geaxpby(cone,r1,czero,r2,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(czero,x,czero,w,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(czero,x,czero,w1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(czero,x,czero,w2,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (.not.converged) then
|
||||
do while (itx < itmax_)
|
||||
if (abs(beta) <= epsmach) exit
|
||||
itx = itx + 1
|
||||
|
||||
s = cone/beta
|
||||
call psb_geaxpby(s,y,czero,v,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(cone,a,v,czero,y,desc_a,info,work=aux)
|
||||
if (itx >= 2 .and. info == psb_success_) then
|
||||
call psb_geaxpby((-beta/oldb),r1,cone,y,desc_a,info)
|
||||
end if
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
alfa = psb_gedot(v,y,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
call psb_geaxpby((-alfa/beta),r2,cone,y,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(cone,r2,czero,r1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(cone,y,czero,r2,desc_a,info)
|
||||
if (info == psb_success_) call prec%apply(r2,y,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
|
||||
|
||||
oldb = beta
|
||||
beta = sqrt(psb_gedot(r2,y,desc_a,info))
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
tnorm2 = tnorm2 + abs(alfa)**2 + abs(oldb)**2 + abs(beta)**2
|
||||
if (itx == 1) then
|
||||
gmax = abs(alfa)
|
||||
gmin = gmax
|
||||
end if
|
||||
end if
|
||||
|
||||
oldeps = epsln
|
||||
delta = dbar
|
||||
gbar = alfa
|
||||
rotx(1) = delta
|
||||
roty(1) = gbar
|
||||
call crot(1,rotx,1,roty,1,cs,sn)
|
||||
delta = rotx(1)
|
||||
gbar = -roty(1)
|
||||
|
||||
epsln = czero
|
||||
dbar = beta
|
||||
rotx(1) = epsln
|
||||
roty(1) = dbar
|
||||
call crot(1,rotx,1,roty,1,cs,sn)
|
||||
epsln = rotx(1)
|
||||
dbar = -roty(1)
|
||||
|
||||
gamma = gbar
|
||||
betatmp = beta
|
||||
call crotg(gamma,betatmp,cs,sn)
|
||||
if (abs(gamma) <= epsmach) exit
|
||||
|
||||
phi = phibar
|
||||
phibar = czero
|
||||
rotx(1) = phi
|
||||
roty(1) = phibar
|
||||
call crot(1,rotx,1,roty,1,cs,-sn)
|
||||
phi = rotx(1)
|
||||
phibar = roty(1)
|
||||
|
||||
denom = cone/gamma
|
||||
call psb_geaxpby(cone,w2,czero,w1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(cone,w,czero,w2,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(cone,v,czero,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(-oldeps,w1,cone,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(-delta,w2,cone,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(denom,wtmp,czero,w,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(phi,w,cone,x,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
gmax = max(gmax,abs(gamma))
|
||||
gmin = min(gmin,abs(gamma))
|
||||
zeta = rhs1/gamma
|
||||
ynorm2 = ynorm2 + abs(zeta)**2
|
||||
rhs1 = rhs2 - delta*zeta
|
||||
rhs2 = -epsln*zeta
|
||||
end if
|
||||
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
! Compute true residual only for the ANI stopping criterion.
|
||||
call psb_geaxpby(cone,b,czero,res,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(-cone,a,x,cone,res,desc_a,info,work=aux)
|
||||
if (info == psb_success_) rni = psb_geamax(res,desc_a,info)
|
||||
if (info == psb_success_) xni = psb_geamax(x,desc_a,info)
|
||||
errnum = rni
|
||||
errden = ani*xni + bni
|
||||
case(psb_istop_bn2_)
|
||||
errnum = abs(phibar)
|
||||
errden = bn2
|
||||
case(psb_istop_rn2_abs_)
|
||||
errnum = abs(phibar)
|
||||
errden = sone
|
||||
case(psb_istop_rrn2_)
|
||||
errnum = abs(phibar)
|
||||
errden = r0n2
|
||||
end select
|
||||
if (errden == szero) errden = sone
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (itrace_ > 0) &
|
||||
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
||||
|
||||
if (errnum <= eps*errden) then
|
||||
converged = .true.
|
||||
exit
|
||||
end if
|
||||
end do
|
||||
end if
|
||||
|
||||
if ((.not.converged) .and. (itx >= itmax_)) then
|
||||
if (debug_level >= psb_debug_ext_)&
|
||||
& write(debug_unit,*) me,' ',trim(name),': MINRES reached iteration limit'
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
if (gmin > 0.0_psb_spk_) then
|
||||
cond = gmax/gmin
|
||||
else
|
||||
cond = huge(sone)
|
||||
end if
|
||||
end if
|
||||
|
||||
call log_end(methdname,me,itx,itrace_,errnum,errden,deps,err=derr,iter=iter)
|
||||
if (present(err)) err = derr
|
||||
|
||||
if (info == psb_success_) call psb_gefree(wwrk,desc_a,info)
|
||||
if (info == psb_success_) deallocate(aux,stat=info)
|
||||
if (info /= psb_success_) then
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
|
||||
call psb_erractionrestore(err_act)
|
||||
return
|
||||
|
||||
9999 call psb_error_handler(err_act)
|
||||
return
|
||||
|
||||
end subroutine psb_cminres_vect
|
||||
@ -0,0 +1,526 @@
|
||||
!
|
||||
! Parallel Sparse BLAS version 3.5
|
||||
! (C) Copyright 2006-2018
|
||||
! Salvatore Filippone
|
||||
! Alfredo Buttari
|
||||
!
|
||||
! 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 prior 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_dminres.f90
|
||||
! 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 C
|
||||
! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
|
||||
! File: psb_dminres.f90
|
||||
!
|
||||
! Subroutine: psb_dminres
|
||||
! This subroutine implements the MINRES method.
|
||||
!
|
||||
!
|
||||
! Arguments:
|
||||
!
|
||||
! a - type(psb_dspmat_type) Input: sparse matrix containing A.
|
||||
! prec - class(psb_dprec_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.
|
||||
!
|
||||
!
|
||||
subroutine psb_dminres_vect(a,prec,b,x,eps,desc_a,info,&
|
||||
& itmax,iter,err,itrace,istop,cond)
|
||||
use psb_base_mod
|
||||
use psb_prec_mod
|
||||
use psb_d_linsolve_conv_mod
|
||||
use psb_linsolve_mod
|
||||
implicit none
|
||||
type(psb_dspmat_type), intent(in) :: a
|
||||
Type(psb_desc_type), Intent(in) :: desc_a
|
||||
class(psb_dprec_type), intent(inout) :: prec
|
||||
type(psb_d_vect_type), Intent(inout) :: b
|
||||
type(psb_d_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, istop
|
||||
integer(psb_ipk_), Optional, Intent(out) :: iter
|
||||
Real(psb_dpk_), Optional, Intent(out) :: err, cond
|
||||
! = Local data
|
||||
real(psb_dpk_), allocatable, target :: aux(:)
|
||||
type(psb_d_vect_type), allocatable, target :: wwrk(:)
|
||||
type(psb_d_vect_type), pointer :: y, r1, r2, v, w, w1, w2, wtmp, res
|
||||
real(psb_dpk_) :: alfa, beta, beta1, dbar, delta, denom
|
||||
real(psb_dpk_) :: epsln, gamma, gbar, oldb, oldeps, phi, phibar
|
||||
real(psb_dpk_) :: rhs1, rhs2, s, zeta, betatmp
|
||||
real(psb_dpk_) :: rotx(1), roty(1)
|
||||
real(psb_dpk_) :: cs
|
||||
real(psb_dpk_) :: sn
|
||||
integer(psb_ipk_) :: itmax_, istop_, naux, itx, itrace_, n_col, n_row, err_act
|
||||
integer(psb_lpk_) :: mglob
|
||||
integer(psb_ipk_) :: debug_level, debug_unit
|
||||
type(psb_ctxt_type) :: ctxt
|
||||
integer(psb_ipk_) :: np, me
|
||||
real(psb_dpk_) :: derr, errnum, errden, deps
|
||||
logical :: do_cond
|
||||
logical :: converged
|
||||
real(psb_dpk_) :: epsmach
|
||||
real(psb_dpk_) :: gmax, gmin, tnorm2, ynorm2
|
||||
real(psb_dpk_) :: rni, xni, bni, ani, bn2, r0n2
|
||||
real(psb_dpk_) :: dotv
|
||||
character(len=20) :: name
|
||||
character(len=*), parameter :: methdname='MINRES'
|
||||
|
||||
info = psb_success_
|
||||
name = 'psb_dminres'
|
||||
call psb_erractionsave(err_act)
|
||||
debug_unit = psb_get_debug_unit()
|
||||
debug_level = psb_get_debug_level()
|
||||
|
||||
ctxt = desc_a%get_context()
|
||||
|
||||
call psb_info(ctxt, 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_row = desc_a%get_local_rows()
|
||||
n_col = desc_a%get_local_cols()
|
||||
|
||||
|
||||
if (present(istop)) then
|
||||
istop_ = istop
|
||||
else
|
||||
istop_ = psb_get_istop_default()
|
||||
endif
|
||||
if (.not.psb_is_valid_istop(istop_)) then
|
||||
info=psb_err_invalid_istop_
|
||||
err=info
|
||||
call psb_errpush(info,name,i_err=(/istop_/))
|
||||
goto 9999
|
||||
end if
|
||||
!
|
||||
! istop_ = 1: normwise backward error, infinity norm
|
||||
! istop_ = 2: ||r||/||b|| norm 2
|
||||
!
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_,psb_istop_bn2_,&
|
||||
& psb_istop_rn2_abs_, psb_istop_rrn2_)
|
||||
! nothing needed
|
||||
case default
|
||||
! should never get here
|
||||
info=psb_err_internal_error_
|
||||
err=info
|
||||
call psb_errpush(info,name,a_err="invalid istop_")
|
||||
goto 9999
|
||||
end select
|
||||
|
||||
call psb_chkvect(mglob,lone,x%get_nrows(),lone,lone,desc_a,info)
|
||||
if (info == psb_success_)&
|
||||
& call psb_chkvect(mglob,lone,b%get_nrows(),lone,lone,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
|
||||
|
||||
naux=4*n_col
|
||||
allocate(aux(naux), stat=info)
|
||||
if (info == psb_success_) call psb_geall(wwrk,desc_a,info,n=9_psb_ipk_)
|
||||
if (info == psb_success_) call psb_geasb(wwrk,desc_a,info,mold=x%v,scratch=.true.)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
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
|
||||
|
||||
y => wwrk(1)
|
||||
r1 => wwrk(2)
|
||||
r2 => wwrk(3)
|
||||
v => wwrk(4)
|
||||
w => wwrk(5)
|
||||
w1 => wwrk(6)
|
||||
w2 => wwrk(7)
|
||||
wtmp => wwrk(8)
|
||||
res => wwrk(9)
|
||||
|
||||
do_cond = present(cond)
|
||||
epsmach = epsilon(done)
|
||||
|
||||
! res = b - A*x
|
||||
call psb_geaxpby(done,b,dzero,res,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(-done,a,x,done,res,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
|
||||
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
ani = psb_spnrmi(a,desc_a,info)
|
||||
bni = psb_geamax(b,desc_a,info)
|
||||
case(psb_istop_bn2_)
|
||||
bn2 = psb_genrm2(b,desc_a,info)
|
||||
case(psb_istop_rn2_abs_)
|
||||
! nothing needed
|
||||
case(psb_istop_rrn2_)
|
||||
r0n2 = psb_genrm2(res,desc_a,info)
|
||||
end select
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
errnum = dzero
|
||||
errden = done
|
||||
deps = eps
|
||||
converged = .false.
|
||||
if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
|
||||
|
||||
! y = beta1 * P' * v1, with v1 the first Lanczos vector.
|
||||
call psb_geaxpby(done,res,dzero,y,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(done,res,dzero,r1,desc_a,info)
|
||||
if (info == psb_success_) call prec%apply(res,y,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
|
||||
|
||||
dotv = psb_gedot(res,y,desc_a,info)
|
||||
if (dotv < -epsmach*max(done,abs(dotv))) then
|
||||
info=psb_err_pivot_too_small_
|
||||
call psb_errpush(info,name,a_err='MINRES breakdown: negative (r,z)')
|
||||
goto 9999
|
||||
end if
|
||||
if (dotv < dzero) dotv = dzero
|
||||
beta1 = sqrt(dotv)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
! If beta1 is numerically zero, x is already acceptable.
|
||||
if (abs(beta1) <= epsmach) then
|
||||
itx = 0
|
||||
converged = .true.
|
||||
if (do_cond) cond = dzero
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
rni = psb_geamax(res,desc_a,info)
|
||||
xni = psb_geamax(x,desc_a,info)
|
||||
errnum = rni
|
||||
errden = ani*xni + bni
|
||||
case(psb_istop_bn2_)
|
||||
errnum = abs(beta1)
|
||||
errden = bn2
|
||||
case(psb_istop_rn2_abs_)
|
||||
errnum = abs(beta1)
|
||||
errden = done
|
||||
case(psb_istop_rrn2_)
|
||||
errnum = abs(beta1)
|
||||
errden = r0n2
|
||||
end select
|
||||
if (errden == dzero) errden = done
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
end if
|
||||
|
||||
beta = beta1
|
||||
oldb = dzero
|
||||
dbar = dzero
|
||||
epsln = dzero
|
||||
phibar = beta1
|
||||
rhs1 = beta1
|
||||
rhs2 = dzero
|
||||
cs = -done
|
||||
sn = dzero
|
||||
itx = 0
|
||||
|
||||
if (do_cond) then
|
||||
tnorm2 = 0.0_psb_dpk_
|
||||
ynorm2 = 0.0_psb_dpk_
|
||||
gmax = 0.0_psb_dpk_
|
||||
gmin = huge(done)
|
||||
end if
|
||||
|
||||
call psb_geaxpby(done,r1,dzero,r2,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(dzero,x,dzero,w,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(dzero,x,dzero,w1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(dzero,x,dzero,w2,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (.not.converged) then
|
||||
do while (itx < itmax_)
|
||||
if (abs(beta) <= epsmach) exit
|
||||
itx = itx + 1
|
||||
|
||||
s = done/beta
|
||||
call psb_geaxpby(s,y,dzero,v,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(done,a,v,dzero,y,desc_a,info,work=aux)
|
||||
if (itx >= 2 .and. info == psb_success_) then
|
||||
call psb_geaxpby((-beta/oldb),r1,done,y,desc_a,info)
|
||||
end if
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
alfa = psb_gedot(v,y,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
call psb_geaxpby((-alfa/beta),r2,done,y,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(done,r2,dzero,r1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(done,y,dzero,r2,desc_a,info)
|
||||
if (info == psb_success_) call prec%apply(r2,y,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
|
||||
|
||||
oldb = beta
|
||||
dotv = psb_gedot(r2,y,desc_a,info)
|
||||
if (dotv < -epsmach*max(done,abs(dotv))) then
|
||||
info=psb_err_pivot_too_small_
|
||||
call psb_errpush(info,name,a_err='MINRES breakdown: negative (r2,z2)')
|
||||
goto 9999
|
||||
end if
|
||||
if (dotv < dzero) dotv = dzero
|
||||
beta = sqrt(dotv)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
tnorm2 = tnorm2 + abs(alfa)**2 + abs(oldb)**2 + abs(beta)**2
|
||||
if (itx == 1) then
|
||||
gmax = abs(alfa)
|
||||
gmin = gmax
|
||||
end if
|
||||
end if
|
||||
|
||||
oldeps = epsln
|
||||
delta = dbar
|
||||
gbar = alfa
|
||||
rotx(1) = delta
|
||||
roty(1) = gbar
|
||||
call drot(1,rotx,1,roty,1,cs,sn)
|
||||
delta = rotx(1)
|
||||
gbar = -roty(1)
|
||||
|
||||
epsln = dzero
|
||||
dbar = beta
|
||||
rotx(1) = epsln
|
||||
roty(1) = dbar
|
||||
call drot(1,rotx,1,roty,1,cs,sn)
|
||||
epsln = rotx(1)
|
||||
dbar = -roty(1)
|
||||
|
||||
gamma = gbar
|
||||
betatmp = beta
|
||||
call drotg(gamma,betatmp,cs,sn)
|
||||
if (abs(gamma) <= epsmach) exit
|
||||
|
||||
phi = phibar
|
||||
phibar = dzero
|
||||
rotx(1) = phi
|
||||
roty(1) = phibar
|
||||
call drot(1,rotx,1,roty,1,cs,-sn)
|
||||
phi = rotx(1)
|
||||
phibar = roty(1)
|
||||
|
||||
denom = done/gamma
|
||||
call psb_geaxpby(done,w2,dzero,w1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(done,w,dzero,w2,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(done,v,dzero,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(-oldeps,w1,done,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(-delta,w2,done,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(denom,wtmp,dzero,w,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(phi,w,done,x,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
gmax = max(gmax,abs(gamma))
|
||||
gmin = min(gmin,abs(gamma))
|
||||
zeta = rhs1/gamma
|
||||
ynorm2 = ynorm2 + abs(zeta)**2
|
||||
rhs1 = rhs2 - delta*zeta
|
||||
rhs2 = -epsln*zeta
|
||||
end if
|
||||
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
! Compute true residual only for the ANI stopping criterion.
|
||||
call psb_geaxpby(done,b,dzero,res,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(-done,a,x,done,res,desc_a,info,work=aux)
|
||||
if (info == psb_success_) rni = psb_geamax(res,desc_a,info)
|
||||
if (info == psb_success_) xni = psb_geamax(x,desc_a,info)
|
||||
errnum = rni
|
||||
errden = ani*xni + bni
|
||||
case(psb_istop_bn2_)
|
||||
errnum = abs(phibar)
|
||||
errden = bn2
|
||||
case(psb_istop_rn2_abs_)
|
||||
errnum = abs(phibar)
|
||||
errden = done
|
||||
case(psb_istop_rrn2_)
|
||||
errnum = abs(phibar)
|
||||
errden = r0n2
|
||||
end select
|
||||
if (errden == dzero) errden = done
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (itrace_ > 0) &
|
||||
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
||||
|
||||
if (errnum <= eps*errden) then
|
||||
converged = .true.
|
||||
exit
|
||||
end if
|
||||
end do
|
||||
end if
|
||||
|
||||
if ((.not.converged) .and. (itx >= itmax_)) then
|
||||
if (debug_level >= psb_debug_ext_)&
|
||||
& write(debug_unit,*) me,' ',trim(name),': MINRES reached iteration limit'
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
if (gmin > 0.0_psb_dpk_) then
|
||||
cond = gmax/gmin
|
||||
else
|
||||
cond = huge(done)
|
||||
end if
|
||||
end if
|
||||
|
||||
call log_end(methdname,me,itx,itrace_,errnum,errden,deps,err=derr,iter=iter)
|
||||
if (present(err)) err = derr
|
||||
|
||||
if (info == psb_success_) call psb_gefree(wwrk,desc_a,info)
|
||||
if (info == psb_success_) deallocate(aux,stat=info)
|
||||
if (info /= psb_success_) then
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
|
||||
call psb_erractionrestore(err_act)
|
||||
return
|
||||
|
||||
9999 call psb_error_handler(err_act)
|
||||
return
|
||||
|
||||
end subroutine psb_dminres_vect
|
||||
@ -0,0 +1,526 @@
|
||||
!
|
||||
! Parallel Sparse BLAS version 3.5
|
||||
! (C) Copyright 2006-2018
|
||||
! Salvatore Filippone
|
||||
! Alfredo Buttari
|
||||
!
|
||||
! 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 prior 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_sminres.f90
|
||||
! 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 C
|
||||
! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
|
||||
! File: psb_sminres.f90
|
||||
!
|
||||
! Subroutine: psb_sminres
|
||||
! This subroutine implements the MINRES method.
|
||||
!
|
||||
!
|
||||
! Arguments:
|
||||
!
|
||||
! a - type(psb_sspmat_type) Input: sparse matrix containing A.
|
||||
! prec - class(psb_sprec_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.
|
||||
!
|
||||
!
|
||||
subroutine psb_sminres_vect(a,prec,b,x,eps,desc_a,info,&
|
||||
& itmax,iter,err,itrace,istop,cond)
|
||||
use psb_base_mod
|
||||
use psb_prec_mod
|
||||
use psb_s_linsolve_conv_mod
|
||||
use psb_linsolve_mod
|
||||
implicit none
|
||||
type(psb_sspmat_type), intent(in) :: a
|
||||
Type(psb_desc_type), Intent(in) :: desc_a
|
||||
class(psb_sprec_type), intent(inout) :: prec
|
||||
type(psb_s_vect_type), Intent(inout) :: b
|
||||
type(psb_s_vect_type), Intent(inout) :: x
|
||||
Real(psb_spk_), Intent(in) :: eps
|
||||
integer(psb_ipk_), intent(out) :: info
|
||||
integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, istop
|
||||
integer(psb_ipk_), Optional, Intent(out) :: iter
|
||||
Real(psb_spk_), Optional, Intent(out) :: err, cond
|
||||
! = Local data
|
||||
real(psb_spk_), allocatable, target :: aux(:)
|
||||
type(psb_s_vect_type), allocatable, target :: wwrk(:)
|
||||
type(psb_s_vect_type), pointer :: y, r1, r2, v, w, w1, w2, wtmp, res
|
||||
real(psb_spk_) :: alfa, beta, beta1, dbar, delta, denom
|
||||
real(psb_spk_) :: epsln, gamma, gbar, oldb, oldeps, phi, phibar
|
||||
real(psb_spk_) :: rhs1, rhs2, s, zeta, betatmp
|
||||
real(psb_spk_) :: rotx(1), roty(1)
|
||||
real(psb_spk_) :: cs
|
||||
real(psb_spk_) :: sn
|
||||
integer(psb_ipk_) :: itmax_, istop_, naux, itx, itrace_, n_col, n_row, err_act
|
||||
integer(psb_lpk_) :: mglob
|
||||
integer(psb_ipk_) :: debug_level, debug_unit
|
||||
type(psb_ctxt_type) :: ctxt
|
||||
integer(psb_ipk_) :: np, me
|
||||
real(psb_dpk_) :: derr, errnum, errden, deps
|
||||
logical :: do_cond
|
||||
logical :: converged
|
||||
real(psb_spk_) :: epsmach
|
||||
real(psb_spk_) :: gmax, gmin, tnorm2, ynorm2
|
||||
real(psb_spk_) :: rni, xni, bni, ani, bn2, r0n2
|
||||
real(psb_spk_) :: dotv
|
||||
character(len=20) :: name
|
||||
character(len=*), parameter :: methdname='MINRES'
|
||||
|
||||
info = psb_success_
|
||||
name = 'psb_sminres'
|
||||
call psb_erractionsave(err_act)
|
||||
debug_unit = psb_get_debug_unit()
|
||||
debug_level = psb_get_debug_level()
|
||||
|
||||
ctxt = desc_a%get_context()
|
||||
|
||||
call psb_info(ctxt, 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_row = desc_a%get_local_rows()
|
||||
n_col = desc_a%get_local_cols()
|
||||
|
||||
|
||||
if (present(istop)) then
|
||||
istop_ = istop
|
||||
else
|
||||
istop_ = psb_get_istop_default()
|
||||
endif
|
||||
if (.not.psb_is_valid_istop(istop_)) then
|
||||
info=psb_err_invalid_istop_
|
||||
err=info
|
||||
call psb_errpush(info,name,i_err=(/istop_/))
|
||||
goto 9999
|
||||
end if
|
||||
!
|
||||
! istop_ = 1: normwise backward error, infinity norm
|
||||
! istop_ = 2: ||r||/||b|| norm 2
|
||||
!
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_,psb_istop_bn2_,&
|
||||
& psb_istop_rn2_abs_, psb_istop_rrn2_)
|
||||
! nothing needed
|
||||
case default
|
||||
! should never get here
|
||||
info=psb_err_internal_error_
|
||||
err=info
|
||||
call psb_errpush(info,name,a_err="invalid istop_")
|
||||
goto 9999
|
||||
end select
|
||||
|
||||
call psb_chkvect(mglob,lone,x%get_nrows(),lone,lone,desc_a,info)
|
||||
if (info == psb_success_)&
|
||||
& call psb_chkvect(mglob,lone,b%get_nrows(),lone,lone,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
|
||||
|
||||
naux=4*n_col
|
||||
allocate(aux(naux), stat=info)
|
||||
if (info == psb_success_) call psb_geall(wwrk,desc_a,info,n=9_psb_ipk_)
|
||||
if (info == psb_success_) call psb_geasb(wwrk,desc_a,info,mold=x%v,scratch=.true.)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
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
|
||||
|
||||
y => wwrk(1)
|
||||
r1 => wwrk(2)
|
||||
r2 => wwrk(3)
|
||||
v => wwrk(4)
|
||||
w => wwrk(5)
|
||||
w1 => wwrk(6)
|
||||
w2 => wwrk(7)
|
||||
wtmp => wwrk(8)
|
||||
res => wwrk(9)
|
||||
|
||||
do_cond = present(cond)
|
||||
epsmach = epsilon(sone)
|
||||
|
||||
! res = b - A*x
|
||||
call psb_geaxpby(sone,b,szero,res,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(-sone,a,x,sone,res,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
|
||||
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
ani = psb_spnrmi(a,desc_a,info)
|
||||
bni = psb_geamax(b,desc_a,info)
|
||||
case(psb_istop_bn2_)
|
||||
bn2 = psb_genrm2(b,desc_a,info)
|
||||
case(psb_istop_rn2_abs_)
|
||||
! nothing needed
|
||||
case(psb_istop_rrn2_)
|
||||
r0n2 = psb_genrm2(res,desc_a,info)
|
||||
end select
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
errnum = szero
|
||||
errden = sone
|
||||
deps = eps
|
||||
converged = .false.
|
||||
if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
|
||||
|
||||
! y = beta1 * P' * v1, with v1 the first Lanczos vector.
|
||||
call psb_geaxpby(sone,res,szero,y,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(sone,res,szero,r1,desc_a,info)
|
||||
if (info == psb_success_) call prec%apply(res,y,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
|
||||
|
||||
dotv = psb_gedot(res,y,desc_a,info)
|
||||
if (dotv < -epsmach*max(sone,abs(dotv))) then
|
||||
info=psb_err_pivot_too_small_
|
||||
call psb_errpush(info,name,a_err='MINRES breakdown: negative (r,z)')
|
||||
goto 9999
|
||||
end if
|
||||
if (dotv < szero) dotv = szero
|
||||
beta1 = sqrt(dotv)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
! If beta1 is numerically zero, x is already acceptable.
|
||||
if (abs(beta1) <= epsmach) then
|
||||
itx = 0
|
||||
converged = .true.
|
||||
if (do_cond) cond = szero
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
rni = psb_geamax(res,desc_a,info)
|
||||
xni = psb_geamax(x,desc_a,info)
|
||||
errnum = rni
|
||||
errden = ani*xni + bni
|
||||
case(psb_istop_bn2_)
|
||||
errnum = abs(beta1)
|
||||
errden = bn2
|
||||
case(psb_istop_rn2_abs_)
|
||||
errnum = abs(beta1)
|
||||
errden = sone
|
||||
case(psb_istop_rrn2_)
|
||||
errnum = abs(beta1)
|
||||
errden = r0n2
|
||||
end select
|
||||
if (errden == szero) errden = sone
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
end if
|
||||
|
||||
beta = beta1
|
||||
oldb = szero
|
||||
dbar = szero
|
||||
epsln = szero
|
||||
phibar = beta1
|
||||
rhs1 = beta1
|
||||
rhs2 = szero
|
||||
cs = -sone
|
||||
sn = szero
|
||||
itx = 0
|
||||
|
||||
if (do_cond) then
|
||||
tnorm2 = 0.0_psb_spk_
|
||||
ynorm2 = 0.0_psb_spk_
|
||||
gmax = 0.0_psb_spk_
|
||||
gmin = huge(sone)
|
||||
end if
|
||||
|
||||
call psb_geaxpby(sone,r1,szero,r2,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(szero,x,szero,w,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(szero,x,szero,w1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(szero,x,szero,w2,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (.not.converged) then
|
||||
do while (itx < itmax_)
|
||||
if (abs(beta) <= epsmach) exit
|
||||
itx = itx + 1
|
||||
|
||||
s = sone/beta
|
||||
call psb_geaxpby(s,y,szero,v,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(sone,a,v,szero,y,desc_a,info,work=aux)
|
||||
if (itx >= 2 .and. info == psb_success_) then
|
||||
call psb_geaxpby((-beta/oldb),r1,sone,y,desc_a,info)
|
||||
end if
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
alfa = psb_gedot(v,y,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
call psb_geaxpby((-alfa/beta),r2,sone,y,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(sone,r2,szero,r1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(sone,y,szero,r2,desc_a,info)
|
||||
if (info == psb_success_) call prec%apply(r2,y,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
|
||||
|
||||
oldb = beta
|
||||
dotv = psb_gedot(r2,y,desc_a,info)
|
||||
if (dotv < -epsmach*max(sone,abs(dotv))) then
|
||||
info=psb_err_pivot_too_small_
|
||||
call psb_errpush(info,name,a_err='MINRES breakdown: negative (r2,z2)')
|
||||
goto 9999
|
||||
end if
|
||||
if (dotv < szero) dotv = szero
|
||||
beta = sqrt(dotv)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
tnorm2 = tnorm2 + abs(alfa)**2 + abs(oldb)**2 + abs(beta)**2
|
||||
if (itx == 1) then
|
||||
gmax = abs(alfa)
|
||||
gmin = gmax
|
||||
end if
|
||||
end if
|
||||
|
||||
oldeps = epsln
|
||||
delta = dbar
|
||||
gbar = alfa
|
||||
rotx(1) = delta
|
||||
roty(1) = gbar
|
||||
call srot(1,rotx,1,roty,1,cs,sn)
|
||||
delta = rotx(1)
|
||||
gbar = -roty(1)
|
||||
|
||||
epsln = szero
|
||||
dbar = beta
|
||||
rotx(1) = epsln
|
||||
roty(1) = dbar
|
||||
call srot(1,rotx,1,roty,1,cs,sn)
|
||||
epsln = rotx(1)
|
||||
dbar = -roty(1)
|
||||
|
||||
gamma = gbar
|
||||
betatmp = beta
|
||||
call srotg(gamma,betatmp,cs,sn)
|
||||
if (abs(gamma) <= epsmach) exit
|
||||
|
||||
phi = phibar
|
||||
phibar = szero
|
||||
rotx(1) = phi
|
||||
roty(1) = phibar
|
||||
call srot(1,rotx,1,roty,1,cs,-sn)
|
||||
phi = rotx(1)
|
||||
phibar = roty(1)
|
||||
|
||||
denom = sone/gamma
|
||||
call psb_geaxpby(sone,w2,szero,w1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(sone,w,szero,w2,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(sone,v,szero,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(-oldeps,w1,sone,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(-delta,w2,sone,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(denom,wtmp,szero,w,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(phi,w,sone,x,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
gmax = max(gmax,abs(gamma))
|
||||
gmin = min(gmin,abs(gamma))
|
||||
zeta = rhs1/gamma
|
||||
ynorm2 = ynorm2 + abs(zeta)**2
|
||||
rhs1 = rhs2 - delta*zeta
|
||||
rhs2 = -epsln*zeta
|
||||
end if
|
||||
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
! Compute true residual only for the ANI stopping criterion.
|
||||
call psb_geaxpby(sone,b,szero,res,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(-sone,a,x,sone,res,desc_a,info,work=aux)
|
||||
if (info == psb_success_) rni = psb_geamax(res,desc_a,info)
|
||||
if (info == psb_success_) xni = psb_geamax(x,desc_a,info)
|
||||
errnum = rni
|
||||
errden = ani*xni + bni
|
||||
case(psb_istop_bn2_)
|
||||
errnum = abs(phibar)
|
||||
errden = bn2
|
||||
case(psb_istop_rn2_abs_)
|
||||
errnum = abs(phibar)
|
||||
errden = sone
|
||||
case(psb_istop_rrn2_)
|
||||
errnum = abs(phibar)
|
||||
errden = r0n2
|
||||
end select
|
||||
if (errden == szero) errden = sone
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (itrace_ > 0) &
|
||||
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
||||
|
||||
if (errnum <= eps*errden) then
|
||||
converged = .true.
|
||||
exit
|
||||
end if
|
||||
end do
|
||||
end if
|
||||
|
||||
if ((.not.converged) .and. (itx >= itmax_)) then
|
||||
if (debug_level >= psb_debug_ext_)&
|
||||
& write(debug_unit,*) me,' ',trim(name),': MINRES reached iteration limit'
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
if (gmin > 0.0_psb_spk_) then
|
||||
cond = gmax/gmin
|
||||
else
|
||||
cond = huge(sone)
|
||||
end if
|
||||
end if
|
||||
|
||||
call log_end(methdname,me,itx,itrace_,errnum,errden,deps,err=derr,iter=iter)
|
||||
if (present(err)) err = derr
|
||||
|
||||
if (info == psb_success_) call psb_gefree(wwrk,desc_a,info)
|
||||
if (info == psb_success_) deallocate(aux,stat=info)
|
||||
if (info /= psb_success_) then
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
|
||||
call psb_erractionrestore(err_act)
|
||||
return
|
||||
|
||||
9999 call psb_error_handler(err_act)
|
||||
return
|
||||
|
||||
end subroutine psb_sminres_vect
|
||||
@ -0,0 +1,511 @@
|
||||
!
|
||||
! Parallel Sparse BLAS version 3.5
|
||||
! (C) Copyright 2006-2018
|
||||
! Salvatore Filippone
|
||||
! Alfredo Buttari
|
||||
!
|
||||
! 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 prior 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_zminres.f90
|
||||
! 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 C
|
||||
! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
|
||||
! File: psb_zminres.f90
|
||||
!
|
||||
! Subroutine: psb_zminres
|
||||
! This subroutine implements the MINRES method.
|
||||
!
|
||||
!
|
||||
! Arguments:
|
||||
!
|
||||
! a - type(psb_zspmat_type) Input: sparse matrix containing A.
|
||||
! prec - class(psb_zprec_type) Input: preconditioner
|
||||
! b(:) - complex Input: vector containing the
|
||||
! right hand side B
|
||||
! x(:) - complex 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.
|
||||
!
|
||||
!
|
||||
subroutine psb_zminres_vect(a,prec,b,x,eps,desc_a,info,&
|
||||
& itmax,iter,err,itrace,istop,cond)
|
||||
use psb_base_mod
|
||||
use psb_prec_mod
|
||||
use psb_z_linsolve_conv_mod
|
||||
use psb_linsolve_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, istop
|
||||
integer(psb_ipk_), Optional, Intent(out) :: iter
|
||||
Real(psb_dpk_), Optional, Intent(out) :: err, cond
|
||||
! = Local data
|
||||
complex(psb_dpk_), allocatable, target :: aux(:)
|
||||
type(psb_z_vect_type), allocatable, target :: wwrk(:)
|
||||
type(psb_z_vect_type), pointer :: y, r1, r2, v, w, w1, w2, wtmp, res
|
||||
complex(psb_dpk_) :: alfa, beta, beta1, dbar, delta, denom
|
||||
complex(psb_dpk_) :: epsln, gamma, gbar, oldb, oldeps, phi, phibar
|
||||
complex(psb_dpk_) :: rhs1, rhs2, s, zeta, betatmp
|
||||
complex(psb_dpk_) :: rotx(1), roty(1)
|
||||
real(psb_dpk_) :: cs
|
||||
complex(psb_dpk_) :: sn
|
||||
integer(psb_ipk_) :: itmax_, istop_, naux, itx, itrace_, n_col, n_row, err_act
|
||||
integer(psb_lpk_) :: mglob
|
||||
integer(psb_ipk_) :: debug_level, debug_unit
|
||||
type(psb_ctxt_type) :: ctxt
|
||||
integer(psb_ipk_) :: np, me
|
||||
real(psb_dpk_) :: derr, errnum, errden, deps
|
||||
logical :: do_cond
|
||||
logical :: converged
|
||||
real(psb_dpk_) :: epsmach
|
||||
real(psb_dpk_) :: gmax, gmin, tnorm2, ynorm2
|
||||
real(psb_dpk_) :: rni, xni, bni, ani, bn2, r0n2
|
||||
character(len=20) :: name
|
||||
character(len=*), parameter :: methdname='MINRES'
|
||||
|
||||
info = psb_success_
|
||||
name = 'psb_zminres'
|
||||
call psb_erractionsave(err_act)
|
||||
debug_unit = psb_get_debug_unit()
|
||||
debug_level = psb_get_debug_level()
|
||||
|
||||
ctxt = desc_a%get_context()
|
||||
|
||||
call psb_info(ctxt, 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_row = desc_a%get_local_rows()
|
||||
n_col = desc_a%get_local_cols()
|
||||
|
||||
|
||||
if (present(istop)) then
|
||||
istop_ = istop
|
||||
else
|
||||
istop_ = psb_get_istop_default()
|
||||
endif
|
||||
if (.not.psb_is_valid_istop(istop_)) then
|
||||
info=psb_err_invalid_istop_
|
||||
err=info
|
||||
call psb_errpush(info,name,i_err=(/istop_/))
|
||||
goto 9999
|
||||
end if
|
||||
!
|
||||
! istop_ = 1: normwise backward error, infinity norm
|
||||
! istop_ = 2: ||r||/||b|| norm 2
|
||||
!
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_,psb_istop_bn2_,&
|
||||
& psb_istop_rn2_abs_, psb_istop_rrn2_)
|
||||
! nothing needed
|
||||
case default
|
||||
! should never get here
|
||||
info=psb_err_internal_error_
|
||||
err=info
|
||||
call psb_errpush(info,name,a_err="invalid istop_")
|
||||
goto 9999
|
||||
end select
|
||||
|
||||
call psb_chkvect(mglob,lone,x%get_nrows(),lone,lone,desc_a,info)
|
||||
if (info == psb_success_)&
|
||||
& call psb_chkvect(mglob,lone,b%get_nrows(),lone,lone,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
|
||||
|
||||
naux=4*n_col
|
||||
allocate(aux(naux), stat=info)
|
||||
if (info == psb_success_) call psb_geall(wwrk,desc_a,info,n=9_psb_ipk_)
|
||||
if (info == psb_success_) call psb_geasb(wwrk,desc_a,info,mold=x%v,scratch=.true.)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
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
|
||||
|
||||
y => wwrk(1)
|
||||
r1 => wwrk(2)
|
||||
r2 => wwrk(3)
|
||||
v => wwrk(4)
|
||||
w => wwrk(5)
|
||||
w1 => wwrk(6)
|
||||
w2 => wwrk(7)
|
||||
wtmp => wwrk(8)
|
||||
res => wwrk(9)
|
||||
|
||||
do_cond = present(cond)
|
||||
epsmach = epsilon(done)
|
||||
|
||||
! res = b - A*x
|
||||
call psb_geaxpby(zone,b,zzero,res,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(-zone,a,x,zone,res,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
|
||||
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
ani = psb_spnrmi(a,desc_a,info)
|
||||
bni = psb_geamax(b,desc_a,info)
|
||||
case(psb_istop_bn2_)
|
||||
bn2 = psb_genrm2(b,desc_a,info)
|
||||
case(psb_istop_rn2_abs_)
|
||||
! nothing needed
|
||||
case(psb_istop_rrn2_)
|
||||
r0n2 = psb_genrm2(res,desc_a,info)
|
||||
end select
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
errnum = zzero
|
||||
errden = zone
|
||||
deps = eps
|
||||
converged = .false.
|
||||
if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
|
||||
|
||||
! y = beta1 * P' * v1, with v1 the first Lanczos vector.
|
||||
call psb_geaxpby(zone,res,zzero,y,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(zone,res,zzero,r1,desc_a,info)
|
||||
if (info == psb_success_) call prec%apply(res,y,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
|
||||
|
||||
beta1 = sqrt(psb_gedot(res,y,desc_a,info))
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
! If beta1 is numerically zero, x is already acceptable.
|
||||
if (abs(beta1) <= epsmach) then
|
||||
itx = 0
|
||||
converged = .true.
|
||||
if (do_cond) cond = dzero
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
rni = psb_geamax(res,desc_a,info)
|
||||
xni = psb_geamax(x,desc_a,info)
|
||||
errnum = rni
|
||||
errden = ani*xni + bni
|
||||
case(psb_istop_bn2_)
|
||||
errnum = abs(beta1)
|
||||
errden = bn2
|
||||
case(psb_istop_rn2_abs_)
|
||||
errnum = abs(beta1)
|
||||
errden = done
|
||||
case(psb_istop_rrn2_)
|
||||
errnum = abs(beta1)
|
||||
errden = r0n2
|
||||
end select
|
||||
if (errden == dzero) errden = done
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
end if
|
||||
|
||||
beta = beta1
|
||||
oldb = zzero
|
||||
dbar = zzero
|
||||
epsln = zzero
|
||||
phibar = beta1
|
||||
rhs1 = beta1
|
||||
rhs2 = zzero
|
||||
cs = -done
|
||||
sn = zzero
|
||||
itx = 0
|
||||
|
||||
if (do_cond) then
|
||||
tnorm2 = 0.0_psb_dpk_
|
||||
ynorm2 = 0.0_psb_dpk_
|
||||
gmax = 0.0_psb_dpk_
|
||||
gmin = huge(done)
|
||||
end if
|
||||
|
||||
call psb_geaxpby(zone,r1,zzero,r2,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(zzero,x,zzero,w,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(zzero,x,zzero,w1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(zzero,x,zzero,w2,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (.not.converged) then
|
||||
do while (itx < itmax_)
|
||||
if (abs(beta) <= epsmach) exit
|
||||
itx = itx + 1
|
||||
|
||||
s = zone/beta
|
||||
call psb_geaxpby(s,y,zzero,v,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(zone,a,v,zzero,y,desc_a,info,work=aux)
|
||||
if (itx >= 2 .and. info == psb_success_) then
|
||||
call psb_geaxpby((-beta/oldb),r1,zone,y,desc_a,info)
|
||||
end if
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
alfa = psb_gedot(v,y,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
call psb_geaxpby((-alfa/beta),r2,zone,y,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(zone,r2,zzero,r1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(zone,y,zzero,r2,desc_a,info)
|
||||
if (info == psb_success_) call prec%apply(r2,y,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
|
||||
|
||||
oldb = beta
|
||||
beta = sqrt(psb_gedot(r2,y,desc_a,info))
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
tnorm2 = tnorm2 + abs(alfa)**2 + abs(oldb)**2 + abs(beta)**2
|
||||
if (itx == 1) then
|
||||
gmax = abs(alfa)
|
||||
gmin = gmax
|
||||
end if
|
||||
end if
|
||||
|
||||
oldeps = epsln
|
||||
delta = dbar
|
||||
gbar = alfa
|
||||
rotx(1) = delta
|
||||
roty(1) = gbar
|
||||
call zrot(1,rotx,1,roty,1,cs,sn)
|
||||
delta = rotx(1)
|
||||
gbar = -roty(1)
|
||||
|
||||
epsln = zzero
|
||||
dbar = beta
|
||||
rotx(1) = epsln
|
||||
roty(1) = dbar
|
||||
call zrot(1,rotx,1,roty,1,cs,sn)
|
||||
epsln = rotx(1)
|
||||
dbar = -roty(1)
|
||||
|
||||
gamma = gbar
|
||||
betatmp = beta
|
||||
call zrotg(gamma,betatmp,cs,sn)
|
||||
if (abs(gamma) <= epsmach) exit
|
||||
|
||||
phi = phibar
|
||||
phibar = zzero
|
||||
rotx(1) = phi
|
||||
roty(1) = phibar
|
||||
call zrot(1,rotx,1,roty,1,cs,-sn)
|
||||
phi = rotx(1)
|
||||
phibar = roty(1)
|
||||
|
||||
denom = zone/gamma
|
||||
call psb_geaxpby(zone,w2,zzero,w1,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(zone,w,zzero,w2,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(zone,v,zzero,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(-oldeps,w1,zone,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(-delta,w2,zone,wtmp,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(denom,wtmp,zzero,w,desc_a,info)
|
||||
if (info == psb_success_) call psb_geaxpby(phi,w,zone,x,desc_a,info)
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
gmax = max(gmax,abs(gamma))
|
||||
gmin = min(gmin,abs(gamma))
|
||||
zeta = rhs1/gamma
|
||||
ynorm2 = ynorm2 + abs(zeta)**2
|
||||
rhs1 = rhs2 - delta*zeta
|
||||
rhs2 = -epsln*zeta
|
||||
end if
|
||||
|
||||
select case(istop_)
|
||||
case(psb_istop_ani_)
|
||||
! Compute true residual only for the ANI stopping criterion.
|
||||
call psb_geaxpby(zone,b,zzero,res,desc_a,info)
|
||||
if (info == psb_success_) call psb_spmm(-zone,a,x,zone,res,desc_a,info,work=aux)
|
||||
if (info == psb_success_) rni = psb_geamax(res,desc_a,info)
|
||||
if (info == psb_success_) xni = psb_geamax(x,desc_a,info)
|
||||
errnum = rni
|
||||
errden = ani*xni + bni
|
||||
case(psb_istop_bn2_)
|
||||
errnum = abs(phibar)
|
||||
errden = bn2
|
||||
case(psb_istop_rn2_abs_)
|
||||
errnum = abs(phibar)
|
||||
errden = done
|
||||
case(psb_istop_rrn2_)
|
||||
errnum = abs(phibar)
|
||||
errden = r0n2
|
||||
end select
|
||||
if (errden == dzero) errden = done
|
||||
if (info /= psb_success_) then
|
||||
info=psb_err_from_subroutine_non_
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
if (itrace_ > 0) &
|
||||
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
||||
|
||||
if (errnum <= eps*errden) then
|
||||
converged = .true.
|
||||
exit
|
||||
end if
|
||||
end do
|
||||
end if
|
||||
|
||||
if ((.not.converged) .and. (itx >= itmax_)) then
|
||||
if (debug_level >= psb_debug_ext_)&
|
||||
& write(debug_unit,*) me,' ',trim(name),': MINRES reached iteration limit'
|
||||
end if
|
||||
|
||||
if (do_cond) then
|
||||
if (gmin > 0.0_psb_dpk_) then
|
||||
cond = gmax/gmin
|
||||
else
|
||||
cond = huge(done)
|
||||
end if
|
||||
end if
|
||||
|
||||
call log_end(methdname,me,itx,itrace_,errnum,errden,deps,err=derr,iter=iter)
|
||||
if (present(err)) err = derr
|
||||
|
||||
if (info == psb_success_) call psb_gefree(wwrk,desc_a,info)
|
||||
if (info == psb_success_) deallocate(aux,stat=info)
|
||||
if (info /= psb_success_) then
|
||||
call psb_errpush(info,name)
|
||||
goto 9999
|
||||
end if
|
||||
|
||||
|
||||
call psb_erractionrestore(err_act)
|
||||
return
|
||||
|
||||
9999 call psb_error_handler(err_act)
|
||||
return
|
||||
|
||||
end subroutine psb_zminres_vect
|
||||
Some files were not shown because too many files have changed in this diff Show More
Loading…
Reference in New Issue