! ! 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_d_nest_cg_test.F90 ! ! Program: psb_d_nest_cg_test ! Author: Simone Staccone (Stack-1) ! ! Solves a linear system with the nested operator using the standard PSBLAS CG ! (psb_krylov('CG', ...)) under every stock one-level preconditioner, to show ! that the nested operator plugs into the PSBLAS preconditioning infrastructure: ! NONE (operator only), ! DIAG (exercises the nested get_diag), ! BJAC (ILU(0), exercises the nested csgetrow through the ILU build). ! ! CG needs a SYMMETRIC POSITIVE DEFINITE operator and, to stress the test ! (hundreds of matvecs), an ILL-CONDITIONED one. We use a real case: the 1D ! Laplacian tridiag(-1, 2, -1) on m = 2*field_size nodes, REORDERED red-black ! (odd nodes -> field 1, even nodes -> field 2). Under this reordering the ! Laplacian becomes exactly ! ! M = [ 2I C ] C(r,r) = -1 , C(r,r-1) = -1 (the Laplacian edges) ! [ C^T 2I ] C^T = exact transpose ! ! (odd nodes are not adjacent to each other -> diagonal blocks = 2I; every -1 ! edge of the Laplacian becomes the coupling C). M is therefore the 1D ! Laplacian up to a permutation: SPD but with lambda_min ~ (pi/m)^2 => cond ~ ! N^2 => CG performs O(N) iterations that GROW with N. ! ! The operator is built with the psb_d_nest_matrix utility. The test passes if ! every solve converges to the exact solution and DIAG reproduces the NONE ! iteration count exactly (with the constant diagonal 2I, Jacobi is a pure ! rescaling, so any mismatch would expose a wrong nested get_diag). ! ! Run: ./psb_d_nest_cg_test ; mpirun -np 4 ./psb_d_nest_cg_test ! program psb_d_nest_cg_test use psb_base_mod use psb_util_mod use psb_prec_mod use psb_linsolve_mod use psb_d_nest_mod ! umbrella: includes psb_d_nest_matrix (builder) implicit none type(psb_ctxt_type) :: context integer(psb_ipk_) :: my_rank, num_procs, info, i_local_row, entry_idx integer(psb_ipk_) :: field1_local_rows, field2_local_rows integer(psb_lpk_) :: field1_global_row, field2_global_row, field_size type(psb_d_nest_matrix) :: nested_matrix type(psb_dprec_type) :: preconditioner type(psb_d_vect_type) :: x_solution, rhs, x_exact integer(psb_lpk_), allocatable :: entry_rows(:), entry_cols(:) integer(psb_lpk_), allocatable :: field1_rows(:), field2_rows(:) real(psb_dpk_), allocatable :: entry_vals(:) ! solver parameters real(psb_dpk_) :: diag_value, stop_tol, final_residual, norm_x_exact, solution_error integer(psb_ipk_) :: max_iter, trace_level, n_iter, stop_criterion real(psb_dpk_), parameter :: solution_tol = 1.0e-6_psb_dpk_ ! stock preconditioners to exercise on the nested operator integer(psb_ipk_), parameter :: n_precs = 3 character(len=6), parameter :: prec_names(n_precs) = ['NONE ', 'DIAG ', 'BJAC '] integer(psb_ipk_) :: i_prec, iter_none, iter_diag logical :: all_passed call psb_init(context) call psb_info(context, my_rank, num_procs) field_size = 512 ! global rows per field (global N = 2*field_size) diag_value = 2.0_psb_dpk_ ! Laplacian diagonal (diagonal blocks = diag*I) stop_tol = 1.0e-9_psb_dpk_ max_iter = 4000 trace_level = 0 stop_criterion = 2 ! stop on the relative residual !--------------------------------------------------------------- ! 1) create the nested operator: 2 fields of global size field_size !--------------------------------------------------------------- call nested_matrix%init(context, [field_size, field_size], info) if (info /= psb_success_) then if (my_rank==0) write(*,*) 'FAIL: nested_matrix%init info=', info; goto 9999 end if field1_rows = nested_matrix%get_owned_rows(1) field2_rows = nested_matrix%get_owned_rows(2) field1_local_rows = size(field1_rows) field2_local_rows = size(field2_rows) !--------------------------------------------------------------- ! 2) insert the blocks (owned rows only) !--------------------------------------------------------------- ! block (1,1) = diag*I allocate(entry_rows(field1_local_rows), entry_cols(field1_local_rows), entry_vals(field1_local_rows)) do i_local_row = 1, field1_local_rows field1_global_row = field1_rows(i_local_row) entry_rows(i_local_row) = field1_global_row entry_cols(i_local_row) = field1_global_row entry_vals(i_local_row) = diag_value end do call nested_matrix%ins(1, 1, field1_local_rows, entry_rows, entry_cols, entry_vals, info) deallocate(entry_rows, entry_cols, entry_vals) ! block (2,2) = diag*I allocate(entry_rows(field2_local_rows), entry_cols(field2_local_rows), entry_vals(field2_local_rows)) do i_local_row = 1, field2_local_rows field2_global_row = field2_rows(i_local_row) entry_rows(i_local_row) = field2_global_row entry_cols(i_local_row) = field2_global_row entry_vals(i_local_row) = diag_value end do call nested_matrix%ins(2, 2, field2_local_rows, entry_rows, entry_cols, entry_vals, info) deallocate(entry_rows, entry_cols, entry_vals) ! block (1,2) = C : rows field1, cols field2 ; C(r,r)=-1, C(r,r-1)=-1 allocate(entry_rows(2*field1_local_rows), entry_cols(2*field1_local_rows), entry_vals(2*field1_local_rows)) entry_idx = 0 do i_local_row = 1, field1_local_rows field1_global_row = field1_rows(i_local_row) entry_idx = entry_idx + 1 entry_rows(entry_idx) = field1_global_row entry_cols(entry_idx) = field1_global_row entry_vals(entry_idx) = -1.0_psb_dpk_ if (field1_global_row > 1) then entry_idx = entry_idx + 1 entry_rows(entry_idx) = field1_global_row entry_cols(entry_idx) = field1_global_row - 1_psb_lpk_ entry_vals(entry_idx) = -1.0_psb_dpk_ end if end do call nested_matrix%ins(1, 2, entry_idx, entry_rows, entry_cols, entry_vals, info) deallocate(entry_rows, entry_cols, entry_vals) ! block (2,1) = C^T : rows field2, cols field1 ; C^T(s,s)=-1, C^T(s,s+1)=-1 allocate(entry_rows(2*field2_local_rows), entry_cols(2*field2_local_rows), entry_vals(2*field2_local_rows)) entry_idx = 0 do i_local_row = 1, field2_local_rows field2_global_row = field2_rows(i_local_row) entry_idx = entry_idx + 1 entry_rows(entry_idx) = field2_global_row entry_cols(entry_idx) = field2_global_row entry_vals(entry_idx) = -1.0_psb_dpk_ if (field2_global_row < field_size) then entry_idx = entry_idx + 1 entry_rows(entry_idx) = field2_global_row entry_cols(entry_idx) = field2_global_row + 1_psb_lpk_ entry_vals(entry_idx) = -1.0_psb_dpk_ end if end do call nested_matrix%ins(2, 1, entry_idx, entry_rows, entry_cols, entry_vals, info) deallocate(entry_rows, entry_cols, entry_vals) !--------------------------------------------------------------- ! 3) assemble: nested_matrix%a_glob / nested_matrix%desc_glob are ready for Krylov !--------------------------------------------------------------- call nested_matrix%asb(info) if (info /= psb_success_) then if (my_rank==0) write(*,*) 'FAIL: nested_matrix%asb info=', info; goto 9999 end if !--------------------------------------------------------------- ! 4) consistent RHS: x_exact = 1, rhs = M * x_exact (via the nested operator) !--------------------------------------------------------------- call psb_geall(x_exact, nested_matrix%desc_glob, info) call psb_geasb(x_exact, nested_matrix%desc_glob, info) call x_exact%set(done) ! x_exact = 1 everywhere call psb_geall(rhs, nested_matrix%desc_glob, info); call psb_geasb(rhs, nested_matrix%desc_glob, info) call psb_spmm(done, nested_matrix%a_glob, x_exact, dzero, rhs, nested_matrix%desc_glob, info) if (info /= psb_success_) then if (my_rank == 0) write(*,*) 'FAIL: psb_spmm (RHS) info=', info goto 9999 end if norm_x_exact = psb_genrm2(x_exact, nested_matrix%desc_glob, info) !--------------------------------------------------------------- ! 5) solve with the standard PSBLAS CG under every stock preconditioner !--------------------------------------------------------------- if (my_rank == 0) write(*,'(a,i0,a,i0)') ' np=', num_procs, ' N(global)=', 2*field_size all_passed = .true. iter_none = 0 iter_diag = -1 do i_prec = 1, n_precs call preconditioner%init(context, trim(prec_names(i_prec)), info) call preconditioner%build(nested_matrix%a_glob, nested_matrix%desc_glob, info) if (info /= psb_success_) then if (my_rank == 0) write(*,*) 'FAIL: prec%build (', trim(prec_names(i_prec)), ') info=', info all_passed = .false.; exit end if call psb_geall(x_solution, nested_matrix%desc_glob, info) call psb_geasb(x_solution, nested_matrix%desc_glob, info) call psb_krylov('CG', nested_matrix%a_glob, preconditioner, rhs, x_solution, stop_tol, & & nested_matrix%desc_glob, info, & & itmax=max_iter, iter=n_iter, err=final_residual, itrace=trace_level, istop=stop_criterion) if (info /= psb_success_) then if (my_rank == 0) write(*,*) 'FAIL: psb_krylov(CG,', trim(prec_names(i_prec)), ') info=', info all_passed = .false.; exit end if ! solution error: || x_solution - x_exact || / || x_exact || call psb_geaxpby(-done, x_exact, done, x_solution, nested_matrix%desc_glob, info) solution_error = psb_genrm2(x_solution, nested_matrix%desc_glob, info) / norm_x_exact if (my_rank == 0) then write(*,'(a,a6,a,i6,a,es12.4,a,es12.4)') ' prec=', prec_names(i_prec), & & ' CG iterations=', n_iter, ' residual=', final_residual, & & ' ||x-x_ex||/||x_ex||=', solution_error end if if ((n_iter >= max_iter) .or. (solution_error > solution_tol)) all_passed = .false. if (trim(prec_names(i_prec)) == 'NONE') iter_none = n_iter if (trim(prec_names(i_prec)) == 'DIAG') iter_diag = n_iter call psb_gefree(x_solution, nested_matrix%desc_glob, info) call preconditioner%free(info) end do !--------------------------------------------------------------- ! 6) verdict: every preconditioner converges to the right solution, and DIAG ! reproduces the NONE iteration count exactly (Jacobi on the constant ! diagonal 2I is a pure rescaling -> exactness check of the nested get_diag) !--------------------------------------------------------------- if (my_rank == 0) then if (all_passed .and. (iter_diag == iter_none)) then write(*,*) '[PASS] CG converges on the nested operator with NONE/DIAG/BJAC' else write(*,*) '[FAIL] preconditioned CG on the nested operator (tol ', solution_tol, ')' end if end if call nested_matrix%free(info) 9999 continue call psb_exit(context) end program psb_d_nest_cg_test