!>
!> @file test_transf2d.f90
!>
!> @brief
!>
!> @copyright
!> Copyright (©) 2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
!> SPC (Swiss Plasma Center)
!>
!> SPClibs is free software: you can redistribute it and/or modify it under
!> the terms of the GNU Lesser General Public License as published by the Free
!> Software Foundation, either version 3 of the License, or (at your option)
!> any later version.
!>
!> SPClibs is distributed in the hope that it will be useful, but WITHOUT ANY
!> WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
!> FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
!>
!> You should have received a copy of the GNU Lesser General Public License
!> along with this program. If not, see <https://www.gnu.org/licenses/>.
!>
!> @author
!> (in alphabetical order)
!> @author Trach-Minh Tran <trach-minh.tran@epfl.ch>
!>
PROGRAM main
!
!   Test 2d multigrid 
!
  USE multigrid
  USE csr
  IMPLICIT NONE
  INCLUDE 'mpif.h'
!
  DOUBLE PRECISION, PARAMETER :: PI=4.0d0*ATAN(1.0d0)
  INTEGER, DIMENSION(2) :: n, nidbas, ngauss, alpha
  DOUBLE PRECISION :: kx=4.d0, ky=3.d0, sigma=10.0d0
  INTEGER :: levels=1
  DOUBLE PRECISION :: omega=2.0d0/3.0d0
!
  DOUBLE PRECISION, ALLOCATABLE :: x(:), y(:)
  DOUBLE PRECISION :: dx, dy
  INTEGER :: ix, iy
!
  DOUBLE PRECISION, ALLOCATABLE :: sol_direct_grid(:,:)
  DOUBLE PRECISION, ALLOCATABLE :: sol_anal_grid(:,:)
  DOUBLE PRECISION, ALLOCATABLE :: errdisc(:), resid(:)
!
  DOUBLE PRECISION, ALLOCATABLE, TARGET :: fcoarse(:,:)
  DOUBLE PRECISION, POINTER :: fcoarse_1d(:)
  DOUBLE PRECISION, ALLOCATABLE, TARGET :: vfine(:,:)
  DOUBLE PRECISION, POINTER :: vfine_1d(:)
  DOUBLE PRECISION, ALLOCATABLE :: vfine_grid(:,:)
  DOUBLE PRECISION, ALLOCATABLE :: err_restrict(:), err_prolong(:), &
       &                           disc_err_prolong(:)
!
  INTEGER :: ierr, me
  INTEGER :: l, nterms
  INTEGER :: its
!
  TYPE(grid2d), ALLOCATABLE :: grids(:)
!
  NAMELIST /newrun/ n, nidbas, ngauss, kx, ky, sigma, alpha, levels
!--------------------------------------------------------------------------------
!                    1.   Prologue
!
  CALL mpi_init(ierr)
  CALL mpi_comm_rank(MPI_COMM_WORLD, me, ierr)
!
!   Inputs
!
  n = (/8, 8/)
  nidbas=(/3,3/)
  ngauss=(/2,2/)
  alpha = (/0,0/)
  kx=4
  ky=3
  sigma=10.0d0
  levels=2
!
  IF(me.EQ.0) THEN
     READ(*,newrun)
     WRITE(*,newrun)
  END IF
     CALL mpi_bcast(n, 2, MPI_INTEGER, 0, MPI_COMM_WORLD, ierr)
     CALL mpi_bcast(nidbas, 2, MPI_INTEGER, 0, MPI_COMM_WORLD, ierr)
     CALL mpi_bcast(ngauss, 2, MPI_INTEGER, 0, MPI_COMM_WORLD, ierr)
     CALL mpi_bcast(alpha, 2, MPI_DOUBLE_PRECISION, 0, MPI_COMM_WORLD, ierr)
     CALL mpi_bcast(kx, 1, MPI_DOUBLE_PRECISION, 0, MPI_COMM_WORLD, ierr)
     CALL mpi_bcast(ky, 1, MPI_DOUBLE_PRECISION, 0, MPI_COMM_WORLD, ierr)
     CALL mpi_bcast(sigma, 1, MPI_DOUBLE_PRECISION, 0, MPI_COMM_WORLD, ierr)
     CALL mpi_bcast(levels, 1, MPI_INTEGER, 0, MPI_COMM_WORLD, ierr)
!
!   Adjust number of levels
!
  levels = MIN(levels, get_lmax(n(1)), get_lmax(n(2)))
!
!   Create grids
!
  dx = 1.0d0/REAL(n(1),8)
  dy = 1.0d0/REAL(n(2),8)
  ALLOCATE(x(0:n(1)), y(0:n(2)))
  DO ix=0,n(1)
     x(ix) = ix*dx
  END DO
  DO iy=0,n(2)
     y(iy) = iy*dy
  END DO
!
  ALLOCATE(grids(levels))
  CALL create_grid(x, y, nidbas, ngauss, alpha, grids)
  WRITE(*,'(5a6)') 'l', 'nx', 'ny', 'rx', 'ry'
  WRITE(*,'(5i6)') (l, grids(l)%n, grids(l)%rank, l=1,levels)
!
!   Build FE matrices and set BC
!
  nterms = 3
  DO l=1,levels
     CALL femat(grids(l)%spl, grids(l)%mata, coefeq, nterms)
     CALL ibcmat(grids(l), grids(l)%mata)
     CALL to_mat(grids(l)%mata)
  END DO
!
!   Set BC on grid transfer matrices
!
  CALL ibc_transf(grids,1,3)
  CALL ibc_transf(grids,2,3)
!--------------------------------------------------------------------------------
!                   1.  Direct solutions
!
  WRITE(*,'(/a)') 'Direct solutions for all levels ...'
  ALLOCATE(errdisc(levels))
  ALLOCATE(resid(levels))
  WRITE(*,'(3a5,2a12)') 'l', 'nx', 'ny', 'err', 'resid'
  DO l=1,levels
     CALL disrhs(grids(l)%spl, grids(l)%f, rhs)
     CALL ibcrhs(grids(l), grids(l)%f)
     grids(l)%v = grids(l)%f
     CALL direct_solve(grids(l), grids(l)%v1d, debug=.FALSE.)
     errdisc(l) = disc_err(grids(l)%spl, grids(l)%v, sol)
     resid(l) = residue(grids(l)%mata, grids(l)%f1d, grids(l)%v1d)
     WRITE(*,'(3i5,2(1pe12.3))') l, grids(l)%n, Errdisc(l), resid(l)
  END DO
!
!  Grid values of direct solutions at the finest levels
  ALLOCATE(sol_direct_grid(0:n(1),0:n(2)))
  ALLOCATE(sol_anal_grid(0:n(1),0:n(2)))
  CALL gridval(grids(1)%spl, grids(1)%x, grids(1)%y, sol_direct_grid, &
       &       [0,0], grids(1)%v)
  sol_anal_grid = sol(grids(1)%x, grids(1)%y)
!--------------------------------------------------------------------------------
!                   2.  Test restrict and prolong
!
  WRITE(*,'(/a)') 'Testing restrict and prolong...'
  WRITE(*,'(3a5,3a12)') 'l', 'nx', 'ny', 'rhs', 'sol', 'disc_err'
  ALLOCATE(err_restrict(2:levels))
  ALLOCATE(err_prolong(2:levels))
  ALLOCATE(disc_err_prolong(2:levels))
  ALLOCATE(vfine_grid(0:n(1),0:n(2)))
  DO l=2,levels
     ALLOCATE(fcoarse(SIZE(grids(l)%f,1),SIZE(grids(l)%f,2)))
     fcoarse_1d(1:SIZE(grids(l)%f1d)) => fcoarse
     ALLOCATE(vfine(SIZE(grids(l-1)%v,1),SIZE(grids(l-1)%v,2)))
     vfine_1d(1:SIZE(grids(l-1)%v1d)) => vfine
!
     fcoarse = restrict(grids(l)%matp,  grids(l-1)%f)
     err_restrict(l) =  MAXVAL(ABS(fcoarse_1d-grids(l)%f1d))
!
     CALL direct_solve(grids(l), fcoarse_1d)
     vfine = prolong(grids(l)%matp, fcoarse)
     disc_err_prolong(l) = disc_err(grids(l-1)%spl, vfine, sol)
     err_prolong(l) = MAXVAL(ABS(vfine_1d-grids(l-1)%v1d))
!
     IF(l.EQ.2) THEN   ! Grid val on finest grid
        CALL gridval(grids(1)%spl, grids(1)%x, grids(1)%y, vfine_grid, &
             &       [0,0], vfine)
     END IF
!
     WRITE(*,'(3i5,3(1pe12.3))') l, grids(l)%n, err_restrict(l), err_prolong(l), &
          &                      disc_err_prolong(l)
     DEALLOCATE(fcoarse)
     DEALLOCATE(vfine)
  END DO
!--------------------------------------------------------------------------------
!                   9.  Epilogue
!
!   Creata HDF5 file
!
  IF(me.EQ.0) CALL h5file
!
  CALL mpi_finalize(ierr)
!--------------------------------------------------------------------------------
CONTAINS
!+++
  FUNCTION rhs(x, y)
!
! Return problem RHS
!
    DOUBLE PRECISION, INTENT(in) :: x, y
    DOUBLE PRECISION :: rhs
    rhs = SIN(PI*kx*x)*SIN(PI*ky*y)
  END FUNCTION rhs
!+++
  FUNCTION sol(x, y)
!
! Return exact problem solution
!
    DOUBLE PRECISION, INTENT(in) :: x(:), y(:)
    DOUBLE PRECISION :: sol(SIZE(x),SIZE(y))
    DOUBLE PRECISION :: c
    INTEGER :: j
    DO j=1,SIZE(y)
       c = SIN(PI*ky*y(j)) / (PI**2*(kx**2+ky**2) + sigma**2)
       sol(:,j) = c * SIN(PI*kx*x(:))
    END DO
  END FUNCTION sol
!+++
  SUBROUTINE coefeq(x, y, idt, idw, c)
!
! Weak form = Int( \nabla(w).\nabla(t) + \sigma.t.w) dV)
!
    DOUBLE PRECISION, INTENT(in)  :: x, y
    INTEGER, INTENT(out)           :: idt(:,:), idw(:,:)
    DOUBLE PRECISION, INTENT(out) :: c(:)
!
    c(1) = 1.0d0
    idt(1,1) = 1
    idt(1,2) = 0
    idw(1,1) = 1
    idw(1,2) = 0
!
    c(2) = 1.0d0
    idt(2,1) = 0
    idt(2,2) = 1
    idw(2,1) = 0
    idw(2,2) = 1
!
    c(3) = sigma
    idt(3,1) = 0
    idt(3,2) = 0
    idw(3,1) = 0
    idw(3,2) = 0

  END SUBROUTINE coefeq
!+++
  SUBROUTINE h5file
    USE futils
    CHARACTER(len=128) :: file='test_transf2d.h5'
    INTEGER :: fid
    INTEGER :: l
    CHARACTER(len=64) :: dsname
    CALL creatf(file, fid, real_prec='d')
    CALL attach(fid, '/', 'NX', n(1))
    CALL attach(fid, '/', 'NY', n(2))
    CALL attach(fid, '/', 'NIDBAS1', nidbas(1))
    CALL attach(fid, '/', 'NIDBAS2', nidbas(2))
    CALL attach(fid, '/', 'KX', kx)
    CALL attach(fid, '/', 'KY', ky)
    CALL attach(fid, '/', 'SIGMA', sigma)
    CALL attach(fid, '/', 'ALPHA1', alpha(1))
    CALL attach(fid, '/', 'ALPHA2', alpha(2))
    CALL attach(fid, '/', 'LEVELS', levels)
    CALL creatg(fid, '/mglevels')
    DO l=1,levels
       WRITE(dsname,'("/mglevels/level.",i2.2)') l
       CALL creatg(fid, TRIM(dsname))
       CALL putmat(fid, TRIM(dsname)//'/mata', grids(l)%mata)
       IF(l.GT.1) THEN
          CALL putmat(fid, TRIM(dsname)//'/matpx', grids(l)%matp(1))
          CALL putmat(fid, TRIM(dsname)//'/matpy', grids(l)%matp(2))
       END IF
       CALL putarr(fid, TRIM(dsname)//'/x', grids(l)%x)
       CALL putarr(fid, TRIM(dsname)//'/y', grids(l)%y)
       CALL putarr(fid, TRIM(dsname)//'/f', grids(l)%f)
       CALL putarr(fid, TRIM(dsname)//'/v', grids(l)%v)
       CALL putarr(fid, TRIM(dsname)//'/f1d', grids(l)%f1d)
       CALL putarr(fid, TRIM(dsname)//'/v1d', grids(l)%v1d)
    END DO
!
!  Solutions at finest grid
!
    CALL creatg(fid, '/solutions')
    CALL putarr(fid, '/solutions/xg', grids(1)%x)
    CALL putarr(fid, '/solutions/yg', grids(1)%y)
    CALL putarr(fid, '/solutions/direct', sol_direct_grid)
    CALL putarr(fid, '/solutions/anal', sol_anal_grid)
    CALL putarr(fid, '/solutions/vfine', vfine_grid)
!
!   Some errors
!
    CALL creatg(fid, '/errors')
    CALL putarr(fid, '/errors/errdisc', errdisc)
    CALL putarr(fid, '/errors/resid', resid)
    CALL putarr(fid, '/errors/restrict', err_restrict)
    CALL putarr(fid, '/errors/prolong', err_prolong)
    CALL putarr(fid, '/errors/disc_err_prolong', disc_err_prolong)
!
    CALL closef(fid)
  END SUBROUTINE h5file
!+++
END PROGRAM