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335 lines
16 KiB
Fortran
335 lines
16 KiB
Fortran
!
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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:
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! 1. Redistributions of source code must retain the above copyright
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! notice, this list of conditions and the following disclaimer.
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! 2. Redistributions in binary form must reproduce the above copyright
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! notice, this list of conditions, and the following disclaimer in the
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! documentation and/or other materials provided with the distribution.
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! 3. The name of the PSBLAS group or the names of its contributors may
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! not be used to endorse or promote products derived from this
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! software without specific prior written permission.
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!
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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
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! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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! 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
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! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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! POSSIBILITY OF SUCH DAMAGE.
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!
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!
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! File: psb_d_nest_cg_test.F90
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!
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! Program: psb_d_nest_cg_test
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! Author: Simone Staccone (Stack-1)
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!
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! Solves a linear system with the GLOBAL nested operator using the standard
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! PSBLAS CG (psb_krylov('CG', ...)). This test builds the operator on the
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! LOW-LEVEL path (per-field descriptors, blocks, compose, setup, wrap) to
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! directly validate the machinery the psb_d_nest_matrix utility relies on; the
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! same solve through the utility is in psb_d_nest_builder_test.
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!
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! CG needs a SYMMETRIC POSITIVE DEFINITE operator and, to stress the test
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! (hundreds of matvecs), an ILL-CONDITIONED one. We use a real case: the 1D
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! Laplacian tridiag(-1, 2, -1) on m = 2*field_size nodes, REORDERED red-black
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! (odd nodes -> field 1, even nodes -> field 2). Under this reordering the
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! Laplacian becomes exactly
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!
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! M = [ 2I C ] C(r,r) = -1 , C(r,r-1) = -1 (the Laplacian edges)
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! [ C^T 2I ] C^T = exact transpose
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!
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! (odd nodes are not adjacent to each other -> diagonal blocks = 2I; every -1
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! edge of the Laplacian becomes the coupling C). M is therefore the 1D
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! Laplacian up to a permutation: SPD but with lambda_min ~ (pi/m)^2 => cond ~
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! N^2 => CG performs O(N) iterations that GROW with N.
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!
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! The system is solved under every stock PSBLAS preconditioner: NONE (operator
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! only), DIAG (exercises the nested get_diag) and BJAC/ILU(0) (exercises the
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! nested csgetrow through the ILU factorization). The test passes if every
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! solve converges to the exact solution and DIAG reproduces the NONE iteration
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! count exactly (with the constant diagonal 2I, Jacobi is a pure rescaling, so
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! any mismatch would expose a wrong nested get_diag).
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!
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! Run: ./psb_d_nest_cg_test ; mpirun -np 4 ./psb_d_nest_cg_test
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!
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program psb_d_nest_cg_test
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use psb_base_mod
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use psb_util_mod
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use psb_prec_mod
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use psb_linsolve_mod
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use psb_d_nest_mod
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implicit none
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type(psb_ctxt_type) :: context
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integer(psb_ipk_) :: my_rank, num_procs, info, i_local_row, entry_idx, field_local_rows
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integer(psb_lpk_) :: field1_global_row, field2_global_row, field_size
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! per-field descriptors + blocks
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type(psb_desc_type) :: field1_desc, field2_desc
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type(psb_dspmat_type) :: diag_block1, coupling_12, coupling_21, diag_block2
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! nested storage + grid descriptor + composed global path
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type(psb_d_nest_sparse_mat) :: block_storage
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type(psb_desc_nest_type) :: grid_desc
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type(psb_desc_type) :: desc_global
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type(psb_d_nest_base_mat) :: nest_operator
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type(psb_dspmat_type) :: global_operator
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! preconditioner + vectors
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type(psb_dprec_type) :: preconditioner
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type(psb_d_vect_type) :: x_solution, rhs, x_exact
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real(psb_dpk_) :: insert_value(1)
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! global triplets for the coupling blocks
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integer(psb_lpk_), allocatable :: entry_rows(:), entry_cols(:)
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real(psb_dpk_), allocatable :: entry_vals(:)
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! solver parameters
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real(psb_dpk_) :: diag_value, stop_tol, final_residual, norm_x_exact, solution_error
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integer(psb_ipk_) :: max_iter, trace_level, n_iter, stop_criterion
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real(psb_dpk_), parameter :: solution_tol = 1.0e-6_psb_dpk_
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! stock preconditioners to exercise on the nested operator
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integer(psb_ipk_), parameter :: n_precs = 3
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character(len=6), parameter :: prec_names(n_precs) = ['NONE ', 'DIAG ', 'BJAC ']
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integer(psb_ipk_) :: i_prec, iter_none, iter_diag
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logical :: all_passed
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call psb_init(context)
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call psb_info(context, my_rank, num_procs)
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field_size = 512 ! global rows per field (global N = 2*field_size)
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diag_value = 2.0_psb_dpk_ ! Laplacian diagonal (diagonal blocks = diag*I)
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stop_tol = 1.0e-9_psb_dpk_
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max_iter = 4000
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trace_level = 0
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stop_criterion = 2 ! stop on the relative residual
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!---------------------------------------------------------------
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! 1) per-field descriptors: block distribution of field_size global rows
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! over num_procs processes (total size independent of num_procs)
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!---------------------------------------------------------------
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field_local_rows = int(field_size / int(num_procs, psb_lpk_), psb_ipk_)
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if (int(my_rank, psb_lpk_) < mod(field_size, int(num_procs, psb_lpk_))) &
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& field_local_rows = field_local_rows + 1
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call psb_cdall(context, field1_desc, info, nl=field_local_rows)
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call psb_cdall(context, field2_desc, info, nl=field_local_rows)
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!---------------------------------------------------------------
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! 2) diagonal blocks A = B = diag*I (odd/even nodes of the red-black
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! reordered Laplacian are not adjacent to each other)
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!---------------------------------------------------------------
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call psb_spall(diag_block1, field1_desc, info, nnz=field1_desc%get_local_rows())
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call psb_spall(diag_block2, field2_desc, info, nnz=field2_desc%get_local_rows())
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do i_local_row = 1, field1_desc%get_local_rows()
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call field1_desc%l2g(i_local_row, field1_global_row, info)
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insert_value(1) = diag_value
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call psb_spins(1,[field1_global_row],[field1_global_row],insert_value,diag_block1,field1_desc,info)
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end do
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do i_local_row = 1, field2_desc%get_local_rows()
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call field2_desc%l2g(i_local_row, field2_global_row, info)
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insert_value(1) = diag_value
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call psb_spins(1,[field2_global_row],[field2_global_row],insert_value,diag_block2,field2_desc,info)
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end do
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!---------------------------------------------------------------
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! 3) register, in the union halo, the cross-field columns of the coupling blocks
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! C (row field1, col field2): columns {r, r-1} in field2 -> into field2_desc
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! C^T (row field2, col field1): columns {s, s+1} in field1 -> into field1_desc
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!---------------------------------------------------------------
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do i_local_row = 1, field1_desc%get_local_rows()
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call field1_desc%l2g(i_local_row, field1_global_row, info)
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call psb_cdins(1, [field1_global_row], field2_desc, info)
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if (field1_global_row > 1) call psb_cdins(1, [field1_global_row-1_psb_lpk_], field2_desc, info)
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end do
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do i_local_row = 1, field2_desc%get_local_rows()
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call field2_desc%l2g(i_local_row, field2_global_row, info)
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call psb_cdins(1, [field2_global_row], field1_desc, info)
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if (field2_global_row < field_size) call psb_cdins(1, [field2_global_row+1_psb_lpk_], field1_desc, info)
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end do
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call psb_cdasb(field1_desc, info)
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call psb_cdasb(field2_desc, info)
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call psb_spasb(diag_block1, field1_desc, info, dupl=psb_dupl_add_)
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call psb_spasb(diag_block2, field2_desc, info, dupl=psb_dupl_add_)
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!---------------------------------------------------------------
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! 4) coupling C (1,2): rows field1 (field1_desc), columns field2 (field2_desc)
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! C(r,r) = -1 , C(r,r-1) = -1 (odd node 2r-1 -> even nodes 2r and 2r-2)
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!---------------------------------------------------------------
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allocate(entry_rows(2*field1_desc%get_local_rows()), entry_cols(2*field1_desc%get_local_rows()), &
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& entry_vals(2*field1_desc%get_local_rows()))
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entry_idx = 0
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do i_local_row = 1, field1_desc%get_local_rows()
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call field1_desc%l2g(i_local_row, field1_global_row, info)
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entry_idx = entry_idx + 1
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entry_rows(entry_idx) = field1_global_row
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entry_cols(entry_idx) = field1_global_row
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entry_vals(entry_idx) = -1.0_psb_dpk_
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if (field1_global_row > 1) then
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entry_idx = entry_idx + 1
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entry_rows(entry_idx) = field1_global_row
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entry_cols(entry_idx) = field1_global_row - 1_psb_lpk_
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entry_vals(entry_idx) = -1.0_psb_dpk_
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end if
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end do
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call psb_d_nest_rect_block(coupling_12, entry_idx, entry_rows, entry_cols, entry_vals, field1_desc, field2_desc, info)
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deallocate(entry_rows, entry_cols, entry_vals)
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!---------------------------------------------------------------
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! 5) coupling C^T (2,1) = exact transpose of C:
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! rows field2 (field2_desc), columns field1 (field1_desc)
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! C^T(s,s) = -1 , C^T(s,s+1) = -1 (even node 2s -> odd nodes 2s-1 and 2s+1)
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!---------------------------------------------------------------
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allocate(entry_rows(2*field2_desc%get_local_rows()), entry_cols(2*field2_desc%get_local_rows()), &
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& entry_vals(2*field2_desc%get_local_rows()))
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entry_idx = 0
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do i_local_row = 1, field2_desc%get_local_rows()
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call field2_desc%l2g(i_local_row, field2_global_row, info)
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entry_idx = entry_idx + 1
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entry_rows(entry_idx) = field2_global_row
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entry_cols(entry_idx) = field2_global_row
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entry_vals(entry_idx) = -1.0_psb_dpk_
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if (field2_global_row < field_size) then
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entry_idx = entry_idx + 1
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entry_rows(entry_idx) = field2_global_row
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entry_cols(entry_idx) = field2_global_row + 1_psb_lpk_
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entry_vals(entry_idx) = -1.0_psb_dpk_
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end if
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end do
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call psb_d_nest_rect_block(coupling_21, entry_idx, entry_rows, entry_cols, entry_vals, field2_desc, field1_desc, info)
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deallocate(entry_rows, entry_cols, entry_vals)
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!---------------------------------------------------------------
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! 6) nested grid (all four blocks present)
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!---------------------------------------------------------------
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block_storage%nrblocks = 2
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block_storage%ncblocks = 2
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allocate(block_storage%mats(2,2))
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call psb_move_alloc(diag_block1, block_storage%mats(1,1), info)
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call psb_move_alloc(coupling_12, block_storage%mats(1,2), info)
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call psb_move_alloc(coupling_21, block_storage%mats(2,1), info)
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call psb_move_alloc(diag_block2, block_storage%mats(2,2), info)
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grid_desc%nrblocks = 2
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grid_desc%ncblocks = 2
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allocate(grid_desc%descs(2,2))
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call field1_desc%clone(grid_desc%descs(1,1), info)
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call field2_desc%clone(grid_desc%descs(1,2), info)
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call field1_desc%clone(grid_desc%descs(2,1), info)
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call field2_desc%clone(grid_desc%descs(2,2), info)
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!---------------------------------------------------------------
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! 7) composed global operator (what CG will use as its matrix)
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!---------------------------------------------------------------
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call psb_cd_nest_compose(grid_desc, desc_global, info)
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if (info /= psb_success_) then
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if (my_rank == 0) write(*,*) 'FAIL: psb_cd_nest_compose info=', info
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goto 9999
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end if
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call psb_d_nest_base_setup(nest_operator, block_storage, grid_desc, desc_global, info)
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if (info /= psb_success_) then
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if (my_rank == 0) write(*,*) 'FAIL: psb_d_nest_base_setup info=', info
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goto 9999
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end if
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allocate(global_operator%a, source=nest_operator)
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call global_operator%set_nrows(desc_global%get_local_rows())
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call global_operator%set_ncols(desc_global%get_local_cols())
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call global_operator%set_asb()
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!---------------------------------------------------------------
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! 8) consistent RHS: x_exact = 1, rhs = M * x_exact (via the nested operator)
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!---------------------------------------------------------------
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call psb_geall(x_exact, desc_global, info)
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do i_local_row = 1, desc_global%get_local_rows()
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call desc_global%l2g(i_local_row, field1_global_row, info)
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insert_value(1) = 1.0_psb_dpk_
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call psb_geins(1, [field1_global_row], insert_value, x_exact, desc_global, info)
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end do
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call psb_geasb(x_exact, desc_global, info)
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call psb_geall(rhs, desc_global, info); call psb_geasb(rhs, desc_global, info)
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call psb_spmm(done, global_operator, x_exact, dzero, rhs, desc_global, info)
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if (info /= psb_success_) then
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if (my_rank == 0) write(*,*) 'FAIL: psb_spmm (RHS) info=', info
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goto 9999
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end if
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norm_x_exact = psb_genrm2(x_exact, desc_global, info)
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!---------------------------------------------------------------
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! 9) solve with the standard PSBLAS CG under every stock preconditioner:
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! NONE (operator only), DIAG (exercises the nested get_diag),
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! BJAC/ILU(0) (exercises the nested csgetrow through the ILU build)
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!---------------------------------------------------------------
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if (my_rank == 0) write(*,'(a,i0,a,i0)') ' np=', num_procs, ' N(global)=', 2*field_size
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all_passed = .true.
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iter_none = 0
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iter_diag = -1
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do i_prec = 1, n_precs
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call preconditioner%init(context, trim(prec_names(i_prec)), info)
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call preconditioner%build(global_operator, desc_global, info)
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if (info /= psb_success_) then
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if (my_rank == 0) write(*,*) 'FAIL: prec%build (', trim(prec_names(i_prec)), ') info=', info
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all_passed = .false.; exit
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end if
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call psb_geall(x_solution, desc_global, info); call psb_geasb(x_solution, desc_global, info)
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call psb_krylov('CG', global_operator, preconditioner, rhs, x_solution, stop_tol, desc_global, info, &
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& itmax=max_iter, iter=n_iter, err=final_residual, itrace=trace_level, istop=stop_criterion)
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if (info /= psb_success_) then
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if (my_rank == 0) write(*,*) 'FAIL: psb_krylov(CG,', trim(prec_names(i_prec)), ') info=', info
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all_passed = .false.; exit
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end if
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! solution error: || x_solution - x_exact || / || x_exact ||
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call psb_geaxpby(-done, x_exact, done, x_solution, desc_global, info)
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solution_error = psb_genrm2(x_solution, desc_global, info) / norm_x_exact
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if (my_rank == 0) then
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write(*,'(a,a6,a,i6,a,es12.4,a,es12.4)') ' prec=', prec_names(i_prec), &
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& ' CG iterations=', n_iter, ' residual=', final_residual, &
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& ' ||x-x_ex||/||x_ex||=', solution_error
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end if
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if ((n_iter >= max_iter) .or. (solution_error > solution_tol)) all_passed = .false.
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if (trim(prec_names(i_prec)) == 'NONE') iter_none = n_iter
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if (trim(prec_names(i_prec)) == 'DIAG') iter_diag = n_iter
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call psb_gefree(x_solution, desc_global, info)
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call preconditioner%free(info)
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end do
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!---------------------------------------------------------------
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! 10) verdict: every preconditioner converges to the right solution.
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! With the constant diagonal 2I, Jacobi is a pure rescaling, so DIAG
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! must reproduce the unpreconditioned iteration count EXACTLY: this is
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! a bit-precise check that the nested get_diag returns exact values.
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! (BJAC/ILU(0) on a red-black ordering drops all fill, so it cannot
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! reduce the iteration count of this exact-convergence regime; its
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! much smaller final residual shows the ILU factors are consistent.)
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!---------------------------------------------------------------
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if (my_rank == 0) then
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if (all_passed .and. (iter_diag == iter_none)) then
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write(*,*) '[PASS] CG converges on the global nested operator with NONE/DIAG/BJAC'
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else
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write(*,*) '[FAIL] preconditioned CG on the nested operator (tol ', solution_tol, ')'
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end if
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end if
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9999 continue
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call psb_exit(context)
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end program psb_d_nest_cg_test
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