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@ -34,9 +34,10 @@
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module psb_d_pde3d_mod
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use psb_base_mod, only : psb_dpk_, psb_ipk_, psb_desc_type,&
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use psb_base_mod, only : psb_dpk_, psb_ipk_, psb_lpk_, psb_desc_type,&
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& psb_dspmat_type, psb_d_vect_type, dzero,&
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& psb_d_base_sparse_mat, psb_d_base_vect_type, psb_i_base_vect_type
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& psb_d_base_sparse_mat, psb_d_base_vect_type, &
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& psb_i_base_vect_type, psb_l_base_vect_type
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interface
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function d_func_3d(x,y,z) result(val)
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@ -50,7 +51,6 @@ module psb_d_pde3d_mod
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module procedure psb_d_gen_pde3d
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end interface psb_gen_pde3d
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contains
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function d_null_func_3d(x,y,z) result(val)
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@ -61,14 +61,90 @@ contains
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val = dzero
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end function d_null_func_3d
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!
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! functions parametrizing the differential equation
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!
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!
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! Note: b1, b2 and b3 are the coefficients of the first
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! derivative of the unknown function. The default
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! we apply here is to have them zero, so that the resulting
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! matrix is symmetric/hermitian and suitable for
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! testing with CG and FCG.
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! When testing methods for non-hermitian matrices you can
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! change the B1/B2/B3 functions to e.g. done/sqrt((3*done))
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!
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function b1(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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implicit none
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real(psb_dpk_) :: b1
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real(psb_dpk_), intent(in) :: x,y,z
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b1=dzero
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end function b1
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function b2(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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implicit none
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real(psb_dpk_) :: b2
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real(psb_dpk_), intent(in) :: x,y,z
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b2=dzero
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end function b2
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function b3(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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implicit none
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real(psb_dpk_) :: b3
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real(psb_dpk_), intent(in) :: x,y,z
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b3=dzero
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end function b3
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function c(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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implicit none
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real(psb_dpk_) :: c
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real(psb_dpk_), intent(in) :: x,y,z
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c=dzero
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end function c
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function a1(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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implicit none
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real(psb_dpk_) :: a1
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real(psb_dpk_), intent(in) :: x,y,z
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a1=done/80
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end function a1
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function a2(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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implicit none
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real(psb_dpk_) :: a2
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real(psb_dpk_), intent(in) :: x,y,z
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a2=done/80
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end function a2
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function a3(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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implicit none
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real(psb_dpk_) :: a3
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real(psb_dpk_), intent(in) :: x,y,z
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a3=done/80
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end function a3
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function g(x,y,z)
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use psb_base_mod, only : psb_dpk_, done, dzero
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implicit none
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real(psb_dpk_) :: g
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real(psb_dpk_), intent(in) :: x,y,z
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g = dzero
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if (x == done) then
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g = done
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else if (x == dzero) then
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g = exp(y**2-z**2)
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end if
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end function g
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!
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! subroutine to allocate and fill in the coefficient matrix and
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! the rhs.
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!
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subroutine psb_d_gen_pde3d(ictxt,idim,a,bv,xv,desc_a,afmt,&
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& a1,a2,a3,b1,b2,b3,c,g,info,f,amold,vmold,imold,nrl,iv)
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subroutine psb_d_gen_pde3d(ictxt,idim,a,bv,xv,desc_a,afmt,info,&
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& f,amold,vmold,imold,partition,nrl,iv)
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use psb_base_mod
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use psb_util_mod
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!
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! Discretizes the partial differential equation
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!
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@ -85,7 +161,6 @@ contains
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! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation.
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!
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implicit none
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procedure(d_func_3d) :: b1,b2,b3,c,a1,a2,a3,g
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integer(psb_ipk_) :: idim
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type(psb_dspmat_type) :: a
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type(psb_d_vect_type) :: xv,bv
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@ -96,7 +171,7 @@ contains
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class(psb_d_base_sparse_mat), optional :: amold
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class(psb_d_base_vect_type), optional :: vmold
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class(psb_i_base_vect_type), optional :: imold
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integer(psb_ipk_), optional :: nrl,iv(:)
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integer(psb_ipk_), optional :: partition, nrl,iv(:)
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! Local variables.
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@ -105,16 +180,24 @@ contains
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type(psb_d_coo_sparse_mat) :: acoo
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type(psb_d_csr_sparse_mat) :: acsr
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real(psb_dpk_) :: zt(nb),x,y,z
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integer(psb_ipk_) :: m,n,nnz,glob_row,nlr,i,ii,ib,k
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integer(psb_ipk_) :: nnz,nr,nlr,i,j,ii,ib,k, partition_
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integer(psb_lpk_) :: m,n,glob_row,nt
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integer(psb_ipk_) :: ix,iy,iz,ia,indx_owner
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integer(psb_ipk_) :: np, iam, nr, nt
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! For 3D partition
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! Note: integer control variables going directly into an MPI call
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! must be 4 bytes, i.e. psb_mpk_
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integer(psb_mpk_) :: npdims(3), npp, minfo
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integer(psb_ipk_) :: npx,npy,npz, iamx,iamy,iamz,mynx,myny,mynz
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integer(psb_ipk_), allocatable :: bndx(:),bndy(:),bndz(:)
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! Process grid
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integer(psb_ipk_) :: np, iam
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integer(psb_ipk_) :: icoeff
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integer(psb_ipk_), allocatable :: irow(:),icol(:),myidx(:)
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integer(psb_lpk_), allocatable :: irow(:),icol(:),myidx(:)
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real(psb_dpk_), allocatable :: val(:)
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! deltah dimension of each grid cell
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! deltat discretization time
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real(psb_dpk_) :: deltah, sqdeltah, deltah2
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real(psb_dpk_), parameter :: rhs=0.d0,one=1.d0,zero=0.d0
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real(psb_dpk_), parameter :: rhs=dzero,one=done,zero=dzero
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real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen, tcdasb
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integer(psb_ipk_) :: err_act
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procedure(d_func_3d), pointer :: f_
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@ -133,19 +216,32 @@ contains
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f_ => d_null_func_3d
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end if
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deltah = 1.d0/(idim+2)
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deltah = done/(idim+1)
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sqdeltah = deltah*deltah
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deltah2 = 2.d0* deltah
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deltah2 = (2*done)* deltah
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if (present(partition)) then
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if ((1<= partition).and.(partition <= 3)) then
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partition_ = partition
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else
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write(*,*) 'Invalid partition choice ',partition,' defaulting to 3'
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partition_ = 3
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end if
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else
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partition_ = 3
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end if
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! initialize array descriptor and sparse matrix storage. provide an
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! estimate of the number of non zeroes
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m = idim*idim*idim
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m = (1_psb_lpk_*idim)*idim*idim
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n = m
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nnz = ((n*9)/(np))
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nnz = ((n*7)/(np))
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if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
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if (.not.present(iv)) then
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t0 = psb_wtime()
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select case(partition_)
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case(1)
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! A BLOCK partition
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if (present(nrl)) then
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nr = nrl
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else
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@ -165,23 +261,98 @@ contains
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call psb_abort(ictxt)
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return
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end if
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else
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if (size(iv) /= m) then
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write(psb_err_unit,*) iam, 'Initialization error IV',size(iv),m
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!
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! First example of use of CDALL: specify for each process a number of
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! contiguous rows
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!
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call psb_cdall(ictxt,desc_a,info,nl=nr)
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myidx = desc_a%get_global_indices()
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nlr = size(myidx)
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case(2)
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! A partition defined by the user through IV
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if (present(iv)) then
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if (size(iv) /= m) then
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write(psb_err_unit,*) iam, 'Initialization error: wrong IV size',size(iv),m
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info = -1
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call psb_barrier(ictxt)
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call psb_abort(ictxt)
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return
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end if
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else
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write(psb_err_unit,*) iam, 'Initialization error: IV not present'
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info = -1
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call psb_barrier(ictxt)
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call psb_abort(ictxt)
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return
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end if
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end if
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call psb_barrier(ictxt)
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t0 = psb_wtime()
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if (present(iv)) then
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!
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! Second example of use of CDALL: specify for each row the
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! process that owns it
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!
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call psb_cdall(ictxt,desc_a,info,vg=iv)
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else
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call psb_cdall(ictxt,desc_a,info,nl=nr)
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end if
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myidx = desc_a%get_global_indices()
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nlr = size(myidx)
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case(3)
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! A 3-dimensional partition
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! A nifty MPI function will split the process list
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npdims = 0
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call mpi_dims_create(np,3,npdims,info)
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npx = npdims(1)
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npy = npdims(2)
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npz = npdims(3)
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allocate(bndx(0:npx),bndy(0:npy),bndz(0:npz))
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! We can reuse idx2ijk for process indices as well.
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call idx2ijk(iamx,iamy,iamz,iam,npx,npy,npz,base=0)
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! Now let's split the 3D cube in hexahedra
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call dist1Didx(bndx,idim,npx)
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mynx = bndx(iamx+1)-bndx(iamx)
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call dist1Didx(bndy,idim,npy)
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myny = bndy(iamy+1)-bndy(iamy)
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call dist1Didx(bndz,idim,npz)
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mynz = bndz(iamz+1)-bndz(iamz)
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! How many indices do I own?
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nlr = mynx*myny*mynz
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allocate(myidx(nlr))
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! Now, let's generate the list of indices I own
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nr = 0
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do i=bndx(iamx),bndx(iamx+1)-1
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do j=bndy(iamy),bndy(iamy+1)-1
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do k=bndz(iamz),bndz(iamz+1)-1
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nr = nr + 1
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call ijk2idx(myidx(nr),i,j,k,idim,idim,idim)
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end do
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end do
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end do
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if (nr /= nlr) then
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write(psb_err_unit,*) iam,iamx,iamy,iamz, 'Initialization error: NR vs NLR ',&
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& nr,nlr,mynx,myny,mynz
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info = -1
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call psb_barrier(ictxt)
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call psb_abort(ictxt)
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end if
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!
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! Third example of use of CDALL: specify for each process
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! the set of global indices it owns.
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!
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call psb_cdall(ictxt,desc_a,info,vl=myidx)
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case default
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write(psb_err_unit,*) iam, 'Initialization error: should not get here'
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info = -1
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|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
call psb_abort(ictxt)
|
|
|
|
|
return
|
|
|
|
|
end select
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz)
|
|
|
|
|
! define rhs from boundary conditions; also build initial guess
|
|
|
|
@ -210,8 +381,6 @@ contains
|
|
|
|
|
goto 9999
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
myidx = desc_a%get_global_indices()
|
|
|
|
|
nlr = size(myidx)
|
|
|
|
|
|
|
|
|
|
! loop over rows belonging to current process in a block
|
|
|
|
|
! distribution.
|
|
|
|
@ -226,18 +395,8 @@ contains
|
|
|
|
|
! local matrix pointer
|
|
|
|
|
glob_row=myidx(i)
|
|
|
|
|
! compute gridpoint coordinates
|
|
|
|
|
if (mod(glob_row,(idim*idim)) == 0) then
|
|
|
|
|
ix = glob_row/(idim*idim)
|
|
|
|
|
else
|
|
|
|
|
ix = glob_row/(idim*idim)+1
|
|
|
|
|
endif
|
|
|
|
|
if (mod((glob_row-(ix-1)*idim*idim),idim) == 0) then
|
|
|
|
|
iy = (glob_row-(ix-1)*idim*idim)/idim
|
|
|
|
|
else
|
|
|
|
|
iy = (glob_row-(ix-1)*idim*idim)/idim+1
|
|
|
|
|
endif
|
|
|
|
|
iz = glob_row-(ix-1)*idim*idim-(iy-1)*idim
|
|
|
|
|
! x, y, x coordinates
|
|
|
|
|
call idx2ijk(ix,iy,iz,glob_row,idim,idim,idim)
|
|
|
|
|
! x, y, z coordinates
|
|
|
|
|
x = (ix-1)*deltah
|
|
|
|
|
y = (iy-1)*deltah
|
|
|
|
|
z = (iz-1)*deltah
|
|
|
|
@ -250,7 +409,7 @@ contains
|
|
|
|
|
if (ix == 1) then
|
|
|
|
|
zt(k) = g(dzero,y,z)*(-val(icoeff)) + zt(k)
|
|
|
|
|
else
|
|
|
|
|
icol(icoeff) = (ix-2)*idim*idim+(iy-1)*idim+(iz)
|
|
|
|
|
call ijk2idx(icol(icoeff),ix-1,iy,iz,idim,idim,idim)
|
|
|
|
|
irow(icoeff) = glob_row
|
|
|
|
|
icoeff = icoeff+1
|
|
|
|
|
endif
|
|
|
|
@ -259,7 +418,7 @@ contains
|
|
|
|
|
if (iy == 1) then
|
|
|
|
|
zt(k) = g(x,dzero,z)*(-val(icoeff)) + zt(k)
|
|
|
|
|
else
|
|
|
|
|
icol(icoeff) = (ix-1)*idim*idim+(iy-2)*idim+(iz)
|
|
|
|
|
call ijk2idx(icol(icoeff),ix,iy-1,iz,idim,idim,idim)
|
|
|
|
|
irow(icoeff) = glob_row
|
|
|
|
|
icoeff = icoeff+1
|
|
|
|
|
endif
|
|
|
|
@ -268,15 +427,15 @@ contains
|
|
|
|
|
if (iz == 1) then
|
|
|
|
|
zt(k) = g(x,y,dzero)*(-val(icoeff)) + zt(k)
|
|
|
|
|
else
|
|
|
|
|
icol(icoeff) = (ix-1)*idim*idim+(iy-1)*idim+(iz-1)
|
|
|
|
|
call ijk2idx(icol(icoeff),ix,iy,iz-1,idim,idim,idim)
|
|
|
|
|
irow(icoeff) = glob_row
|
|
|
|
|
icoeff = icoeff+1
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
! term depending on (x,y,z)
|
|
|
|
|
val(icoeff)=2.d0*(a1(x,y,z)+a2(x,y,z)+a3(x,y,z))/sqdeltah &
|
|
|
|
|
val(icoeff)=(2*done)*(a1(x,y,z)+a2(x,y,z)+a3(x,y,z))/sqdeltah &
|
|
|
|
|
& + c(x,y,z)
|
|
|
|
|
icol(icoeff) = (ix-1)*idim*idim+(iy-1)*idim+(iz)
|
|
|
|
|
call ijk2idx(icol(icoeff),ix,iy,iz,idim,idim,idim)
|
|
|
|
|
irow(icoeff) = glob_row
|
|
|
|
|
icoeff = icoeff+1
|
|
|
|
|
! term depending on (x,y,z+1)
|
|
|
|
@ -284,7 +443,7 @@ contains
|
|
|
|
|
if (iz == idim) then
|
|
|
|
|
zt(k) = g(x,y,done)*(-val(icoeff)) + zt(k)
|
|
|
|
|
else
|
|
|
|
|
icol(icoeff) = (ix-1)*idim*idim+(iy-1)*idim+(iz+1)
|
|
|
|
|
call ijk2idx(icol(icoeff),ix,iy,iz+1,idim,idim,idim)
|
|
|
|
|
irow(icoeff) = glob_row
|
|
|
|
|
icoeff = icoeff+1
|
|
|
|
|
endif
|
|
|
|
@ -293,7 +452,7 @@ contains
|
|
|
|
|
if (iy == idim) then
|
|
|
|
|
zt(k) = g(x,done,z)*(-val(icoeff)) + zt(k)
|
|
|
|
|
else
|
|
|
|
|
icol(icoeff) = (ix-1)*idim*idim+(iy)*idim+(iz)
|
|
|
|
|
call ijk2idx(icol(icoeff),ix,iy+1,iz,idim,idim,idim)
|
|
|
|
|
irow(icoeff) = glob_row
|
|
|
|
|
icoeff = icoeff+1
|
|
|
|
|
endif
|
|
|
|
@ -302,7 +461,7 @@ contains
|
|
|
|
|
if (ix==idim) then
|
|
|
|
|
zt(k) = g(done,y,z)*(-val(icoeff)) + zt(k)
|
|
|
|
|
else
|
|
|
|
|
icol(icoeff) = (ix)*idim*idim+(iy-1)*idim+(iz)
|
|
|
|
|
call ijk2idx(icol(icoeff),ix+1,iy,iz,idim,idim,idim)
|
|
|
|
|
irow(icoeff) = glob_row
|
|
|
|
|
icoeff = icoeff+1
|
|
|
|
|
endif
|
|
|
|
@ -312,7 +471,7 @@ contains
|
|
|
|
|
if(info /= psb_success_) exit
|
|
|
|
|
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),bv,desc_a,info)
|
|
|
|
|
if(info /= psb_success_) exit
|
|
|
|
|
zt(:)=0.d0
|
|
|
|
|
zt(:)=dzero
|
|
|
|
|
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,desc_a,info)
|
|
|
|
|
if(info /= psb_success_) exit
|
|
|
|
|
end do
|
|
|
|
@ -397,7 +556,7 @@ program pdgenspmv
|
|
|
|
|
integer(psb_ipk_) :: idim
|
|
|
|
|
|
|
|
|
|
! miscellaneous
|
|
|
|
|
real(psb_dpk_), parameter :: one = 1.d0
|
|
|
|
|
real(psb_dpk_), parameter :: one = done
|
|
|
|
|
real(psb_dpk_) :: t1, t2, tprec, flops, tflops, tt1, tt2, bdwdth
|
|
|
|
|
|
|
|
|
|
! sparse matrix and preconditioner
|
|
|
|
@ -411,7 +570,7 @@ program pdgenspmv
|
|
|
|
|
integer(psb_ipk_) :: ictxt, iam, np
|
|
|
|
|
|
|
|
|
|
! solver parameters
|
|
|
|
|
integer(psb_ipk_) :: iter, itmax,itrace, istopc, irst, nr
|
|
|
|
|
integer(psb_ipk_) :: iter, itmax,itrace, istopc, irst, nr, ipart
|
|
|
|
|
integer(psb_epk_) :: amatsize, precsize, descsize, d2size, annz, nbytes
|
|
|
|
|
real(psb_dpk_) :: err, eps
|
|
|
|
|
integer(psb_ipk_), parameter :: times=10
|
|
|
|
@ -452,8 +611,7 @@ program pdgenspmv
|
|
|
|
|
!
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
t1 = psb_wtime()
|
|
|
|
|
call psb_gen_pde3d(ictxt,idim,a,bv,xv,desc_a,afmt,&
|
|
|
|
|
& a1,a2,a3,b1,b2,b3,c,g,info)
|
|
|
|
|
call psb_gen_pde3d(ictxt,idim,a,bv,xv,desc_a,afmt,info)
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
t2 = psb_wtime() - t1
|
|
|
|
|
if(info /= psb_success_) then
|
|
|
|
@ -607,61 +765,4 @@ contains
|
|
|
|
|
write(iout,*)' >= 1 do tracing every itrace'
|
|
|
|
|
write(iout,*)' iterations '
|
|
|
|
|
end subroutine pr_usage
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! functions parametrizing the differential equation
|
|
|
|
|
!
|
|
|
|
|
function b1(x,y,z)
|
|
|
|
|
use psb_base_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: b1
|
|
|
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
|
|
|
b1=1.d0/sqrt(3.d0)
|
|
|
|
|
end function b1
|
|
|
|
|
function b2(x,y,z)
|
|
|
|
|
use psb_base_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: b2
|
|
|
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
|
|
|
b2=1.d0/sqrt(3.d0)
|
|
|
|
|
end function b2
|
|
|
|
|
function b3(x,y,z)
|
|
|
|
|
use psb_base_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: b3
|
|
|
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
|
|
|
b3=1.d0/sqrt(3.d0)
|
|
|
|
|
end function b3
|
|
|
|
|
function c(x,y,z)
|
|
|
|
|
use psb_base_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: c
|
|
|
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
|
|
|
c=0.d0
|
|
|
|
|
end function c
|
|
|
|
|
function a1(x,y,z)
|
|
|
|
|
use psb_base_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: a1
|
|
|
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
|
|
|
a1=1.d0/80
|
|
|
|
|
end function a1
|
|
|
|
|
function a2(x,y,z)
|
|
|
|
|
use psb_base_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: a2
|
|
|
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
|
|
|
a2=1.d0/80
|
|
|
|
|
end function a2
|
|
|
|
|
function a3(x,y,z)
|
|
|
|
|
use psb_base_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: a3
|
|
|
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
|
|
|
a3=1.d0/80
|
|
|
|
|
end function a3
|
|
|
|
|
function g(x,y,z)
|
|
|
|
|
use psb_base_mod, only : psb_dpk_, done
|
|
|
|
|
real(psb_dpk_) :: g
|
|
|
|
|
real(psb_dpk_), intent(in) :: x,y,z
|
|
|
|
|
g = dzero
|
|
|
|
|
if (x == done) then
|
|
|
|
|
g = done
|
|
|
|
|
else if (x == dzero) then
|
|
|
|
|
g = exp(y**2-z**2)
|
|
|
|
|
end if
|
|
|
|
|
end function g
|
|
|
|
|
end program pdgenspmv
|
|
|
|
|