|
|
|
|
!
|
|
|
|
|
program d_coo_matgen
|
|
|
|
|
use psb_sparse_mod
|
|
|
|
|
!!$ use psb_prec_mod
|
|
|
|
|
!!$ use psb_krylov_mod
|
|
|
|
|
use psb_d_base_mat_mod
|
|
|
|
|
use psb_d_csr_mat_mod
|
|
|
|
|
implicit none
|
|
|
|
|
|
|
|
|
|
! input parameters
|
|
|
|
|
character(len=20) :: kmethd, ptype
|
|
|
|
|
character(len=5) :: afmt
|
|
|
|
|
integer :: idim
|
|
|
|
|
|
|
|
|
|
! miscellaneous
|
|
|
|
|
real(psb_dpk_), parameter :: one = 1.d0
|
|
|
|
|
real(psb_dpk_) :: t1, t2, tprec
|
|
|
|
|
|
|
|
|
|
! sparse matrix and preconditioner
|
|
|
|
|
type(psb_d_sparse_mat) :: a
|
|
|
|
|
!!$ type(psb_dprec_type) :: prec
|
|
|
|
|
! descriptor
|
|
|
|
|
type(psb_desc_type) :: desc_a
|
|
|
|
|
! dense matrices
|
|
|
|
|
real(psb_dpk_), allocatable :: b(:), x(:)
|
|
|
|
|
! blacs parameters
|
|
|
|
|
integer :: ictxt, iam, np
|
|
|
|
|
|
|
|
|
|
! solver parameters
|
|
|
|
|
integer :: iter, itmax,itrace, istopc, irst
|
|
|
|
|
integer(psb_long_int_k_) :: amatsize, precsize, descsize
|
|
|
|
|
real(psb_dpk_) :: err, eps
|
|
|
|
|
|
|
|
|
|
! other variables
|
|
|
|
|
integer :: info, err_act
|
|
|
|
|
character(len=20) :: name,ch_err
|
|
|
|
|
|
|
|
|
|
info=psb_success_
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
call psb_init(ictxt)
|
|
|
|
|
call psb_info(ictxt,iam,np)
|
|
|
|
|
|
|
|
|
|
if (iam < 0) then
|
|
|
|
|
! This should not happen, but just in case
|
|
|
|
|
call psb_exit(ictxt)
|
|
|
|
|
stop
|
|
|
|
|
endif
|
|
|
|
|
if(psb_get_errstatus() /= 0) goto 9999
|
|
|
|
|
|
|
|
|
|
call psb_set_errverbosity(2)
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! get parameters
|
|
|
|
|
!
|
|
|
|
|
call get_parms(ictxt,idim)
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! allocate and fill in the coefficient matrix, rhs and initial guess
|
|
|
|
|
!
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
t1 = psb_wtime()
|
|
|
|
|
call create_matrix(idim,a,b,x,desc_a,ictxt,afmt,info)
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
t2 = psb_wtime() - t1
|
|
|
|
|
if(info /= psb_success_) then
|
|
|
|
|
call psb_error(ictxt)
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
call psb_exit(ictxt)
|
|
|
|
|
stop
|
|
|
|
|
|
|
|
|
|
9999 continue
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
if (err_act == psb_act_abort_) then
|
|
|
|
|
call psb_error(ictxt)
|
|
|
|
|
end if
|
|
|
|
|
stop
|
|
|
|
|
|
|
|
|
|
contains
|
|
|
|
|
!
|
|
|
|
|
! get iteration parameters from standard input
|
|
|
|
|
!
|
|
|
|
|
subroutine get_parms(ictxt,idim)
|
|
|
|
|
integer :: ictxt
|
|
|
|
|
integer :: idim
|
|
|
|
|
integer :: np, iam
|
|
|
|
|
integer :: intbuf(10), ip
|
|
|
|
|
|
|
|
|
|
call psb_info(ictxt, iam, np)
|
|
|
|
|
|
|
|
|
|
read(psb_inp_unit,*) idim
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
end subroutine get_parms
|
|
|
|
|
!
|
|
|
|
|
! print an error message
|
|
|
|
|
!
|
|
|
|
|
subroutine pr_usage(iout)
|
|
|
|
|
integer :: iout
|
|
|
|
|
write(iout,*)'incorrect parameter(s) found'
|
|
|
|
|
write(iout,*)' usage: pde90 methd prec dim &
|
|
|
|
|
&[istop itmax itrace]'
|
|
|
|
|
write(iout,*)' where:'
|
|
|
|
|
write(iout,*)' methd: cgstab cgs rgmres bicgstabl'
|
|
|
|
|
write(iout,*)' prec : bjac diag none'
|
|
|
|
|
write(iout,*)' dim number of points along each axis'
|
|
|
|
|
write(iout,*)' the size of the resulting linear '
|
|
|
|
|
write(iout,*)' system is dim**3'
|
|
|
|
|
write(iout,*)' istop stopping criterion 1, 2 '
|
|
|
|
|
write(iout,*)' itmax maximum number of iterations [500] '
|
|
|
|
|
write(iout,*)' itrace <=0 (no tracing, default) or '
|
|
|
|
|
write(iout,*)' >= 1 do tracing every itrace'
|
|
|
|
|
write(iout,*)' iterations '
|
|
|
|
|
end subroutine pr_usage
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! subroutine to allocate and fill in the coefficient matrix and
|
|
|
|
|
! the rhs.
|
|
|
|
|
!
|
|
|
|
|
subroutine create_matrix(idim,a,b,xv,desc_a,ictxt,afmt,info)
|
|
|
|
|
!
|
|
|
|
|
! discretize the partial diferential equation
|
|
|
|
|
!
|
|
|
|
|
! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
|
|
|
|
|
! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u
|
|
|
|
|
! dxdx dydy dzdz dx dy dz
|
|
|
|
|
!
|
|
|
|
|
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
|
|
|
|
|
!
|
|
|
|
|
! Boundary conditions are set in a very simple way, by adding
|
|
|
|
|
! equations of the form
|
|
|
|
|
!
|
|
|
|
|
! u(x,y) = exp(-x^2-y^2-z^2)
|
|
|
|
|
!
|
|
|
|
|
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
|
|
|
|
|
!
|
|
|
|
|
use psb_sparse_mod
|
|
|
|
|
!!$ use psb_d_base_mat_mod
|
|
|
|
|
use psb_d_csr_mat_mod
|
|
|
|
|
implicit none
|
|
|
|
|
integer :: idim
|
|
|
|
|
integer, parameter :: nb=20
|
|
|
|
|
real(psb_dpk_), allocatable :: b(:),xv(:)
|
|
|
|
|
type(psb_desc_type) :: desc_a
|
|
|
|
|
integer :: ictxt, info
|
|
|
|
|
character :: afmt*5
|
|
|
|
|
type(psb_d_sparse_mat) :: a
|
|
|
|
|
real(psb_dpk_) :: zt(nb),glob_x,glob_y,glob_z
|
|
|
|
|
integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k
|
|
|
|
|
integer :: x,y,z,ia,indx_owner
|
|
|
|
|
integer :: np, iam, nr, nt,nz,isz
|
|
|
|
|
integer :: element
|
|
|
|
|
integer, allocatable :: irow(:),icol(:),myidx(:)
|
|
|
|
|
real(psb_dpk_), allocatable :: val(:)
|
|
|
|
|
type(psb_d_coo_sparse_mat) :: acoo
|
|
|
|
|
type(psb_d_csr_sparse_mat) :: acsr
|
|
|
|
|
! deltah dimension of each grid cell
|
|
|
|
|
! deltat discretization time
|
|
|
|
|
real(psb_dpk_) :: deltah
|
|
|
|
|
real(psb_dpk_),parameter :: rhs=0.d0,one=1.d0,zero=0.d0
|
|
|
|
|
real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen, tcpy, tmov
|
|
|
|
|
real(psb_dpk_) :: a1, a2, a3, a4, b1, b2, b3
|
|
|
|
|
external :: a1, a2, a3, a4, b1, b2, b3
|
|
|
|
|
integer :: err_act
|
|
|
|
|
|
|
|
|
|
character(len=20) :: name, ch_err, asbfmt
|
|
|
|
|
|
|
|
|
|
info = psb_success_
|
|
|
|
|
name = 'creatae_matrix'
|
|
|
|
|
call psb_erractionsave(err_act)
|
|
|
|
|
|
|
|
|
|
call psb_info(ictxt, iam, np)
|
|
|
|
|
|
|
|
|
|
deltah = 1.d0/(idim-1)
|
|
|
|
|
|
|
|
|
|
! initialize array descriptor and sparse matrix storage. provide an
|
|
|
|
|
! estimate of the number of non zeroes
|
|
|
|
|
|
|
|
|
|
m = idim*idim*idim
|
|
|
|
|
n = m
|
|
|
|
|
nnz = ((n*9)/(np))
|
|
|
|
|
if(iam == psb_root_) write(psb_err_unit,'("Generating Matrix (size=",i0,")...")')n
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! Using a simple BLOCK distribution.
|
|
|
|
|
!
|
|
|
|
|
nt = (m+np-1)/np
|
|
|
|
|
nr = max(0,min(nt,m-(iam*nt)))
|
|
|
|
|
|
|
|
|
|
nt = nr
|
|
|
|
|
call psb_sum(ictxt,nt)
|
|
|
|
|
if (nt /= m) write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m
|
|
|
|
|
write(psb_err_unit,*) iam, 'Initialization ',nr,nt,m
|
|
|
|
|
nlr = nt
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
|
|
|
|
|
call acoo%set_null()
|
|
|
|
|
t0 = psb_wtime()
|
|
|
|
|
|
|
|
|
|
call acoo%allocate(nr,nr)
|
|
|
|
|
|
|
|
|
|
talc = psb_wtime()-t0
|
|
|
|
|
|
|
|
|
|
!!$ write(psb_out_unit,*) 'Test get size:',d_coo_get_size(acoo)
|
|
|
|
|
!!$ write(psb_out_unit,*) 'Test 2 get size:',acoo%get_size(),acoo%get_nzeros()
|
|
|
|
|
|
|
|
|
|
if (info /= psb_success_) then
|
|
|
|
|
info=psb_err_from_subroutine_
|
|
|
|
|
ch_err='allocation rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
! we build an auxiliary matrix consisting of one row at a
|
|
|
|
|
! time; just a small matrix. might be extended to generate
|
|
|
|
|
! a bunch of rows per call.
|
|
|
|
|
!
|
|
|
|
|
allocate(val(20*nb),irow(20*nb),&
|
|
|
|
|
&icol(20*nb),myidx(nlr),stat=info)
|
|
|
|
|
if (info /= psb_success_ ) then
|
|
|
|
|
info=psb_err_alloc_dealloc_
|
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
! loop over rows belonging to current process in a block
|
|
|
|
|
! distribution.
|
|
|
|
|
|
|
|
|
|
call psb_barrier(ictxt)
|
|
|
|
|
t1 = psb_wtime()
|
|
|
|
|
do ii=1, nlr,nb
|
|
|
|
|
ib = min(nb,nlr-ii+1)
|
|
|
|
|
!!$ write(psb_err_unit,*) 'Row ',ii,ib
|
|
|
|
|
element = 1
|
|
|
|
|
do k=1,ib
|
|
|
|
|
i=ii+k-1
|
|
|
|
|
! local matrix pointer
|
|
|
|
|
glob_row=i
|
|
|
|
|
! compute gridpoint coordinates
|
|
|
|
|
if (mod(glob_row,(idim*idim)) == 0) then
|
|
|
|
|
x = glob_row/(idim*idim)
|
|
|
|
|
else
|
|
|
|
|
x = glob_row/(idim*idim)+1
|
|
|
|
|
endif
|
|
|
|
|
if (mod((glob_row-(x-1)*idim*idim),idim) == 0) then
|
|
|
|
|
y = (glob_row-(x-1)*idim*idim)/idim
|
|
|
|
|
else
|
|
|
|
|
y = (glob_row-(x-1)*idim*idim)/idim+1
|
|
|
|
|
endif
|
|
|
|
|
z = glob_row-(x-1)*idim*idim-(y-1)*idim
|
|
|
|
|
! glob_x, glob_y, glob_x coordinates
|
|
|
|
|
glob_x=x*deltah
|
|
|
|
|
glob_y=y*deltah
|
|
|
|
|
glob_z=z*deltah
|
|
|
|
|
|
|
|
|
|
! check on boundary points
|
|
|
|
|
zt(k) = 0.d0
|
|
|
|
|
! internal point: build discretization
|
|
|
|
|
!
|
|
|
|
|
! term depending on (x-1,y,z)
|
|
|
|
|
!
|
|
|
|
|
if (x == 1) then
|
|
|
|
|
val(element)=-b1(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a1(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
zt(k) = exp(-glob_y**2-glob_z**2)*(-val(element))
|
|
|
|
|
else
|
|
|
|
|
val(element)=-b1(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a1(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
icol(element) = (x-2)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
irow(element) = glob_row
|
|
|
|
|
element = element+1
|
|
|
|
|
endif
|
|
|
|
|
! term depending on (x,y-1,z)
|
|
|
|
|
if (y == 1) then
|
|
|
|
|
val(element)=-b2(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a2(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
zt(k) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
|
|
|
|
|
else
|
|
|
|
|
val(element)=-b2(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a2(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
icol(element) = (x-1)*idim*idim+(y-2)*idim+(z)
|
|
|
|
|
irow(element) = glob_row
|
|
|
|
|
element = element+1
|
|
|
|
|
endif
|
|
|
|
|
! term depending on (x,y,z-1)
|
|
|
|
|
if (z == 1) then
|
|
|
|
|
val(element)=-b3(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a3(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
zt(k) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
|
|
|
|
|
else
|
|
|
|
|
val(element)=-b3(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a3(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
icol(element) = (x-1)*idim*idim+(y-1)*idim+(z-1)
|
|
|
|
|
irow(element) = glob_row
|
|
|
|
|
element = element+1
|
|
|
|
|
endif
|
|
|
|
|
! term depending on (x,y,z)
|
|
|
|
|
val(element)=2*b1(glob_x,glob_y,glob_z)&
|
|
|
|
|
& +2*b2(glob_x,glob_y,glob_z)&
|
|
|
|
|
& +2*b3(glob_x,glob_y,glob_z)&
|
|
|
|
|
& +a1(glob_x,glob_y,glob_z)&
|
|
|
|
|
& +a2(glob_x,glob_y,glob_z)&
|
|
|
|
|
& +a3(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
icol(element) = (x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
irow(element) = glob_row
|
|
|
|
|
element = element+1
|
|
|
|
|
! term depending on (x,y,z+1)
|
|
|
|
|
if (z == idim) then
|
|
|
|
|
val(element)=-b1(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
zt(k) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
|
|
|
|
|
else
|
|
|
|
|
val(element)=-b1(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
icol(element) = (x-1)*idim*idim+(y-1)*idim+(z+1)
|
|
|
|
|
irow(element) = glob_row
|
|
|
|
|
element = element+1
|
|
|
|
|
endif
|
|
|
|
|
! term depending on (x,y+1,z)
|
|
|
|
|
if (y == idim) then
|
|
|
|
|
val(element)=-b2(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
zt(k) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
|
|
|
|
|
else
|
|
|
|
|
val(element)=-b2(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
icol(element) = (x-1)*idim*idim+(y)*idim+(z)
|
|
|
|
|
irow(element) = glob_row
|
|
|
|
|
element = element+1
|
|
|
|
|
endif
|
|
|
|
|
! term depending on (x+1,y,z)
|
|
|
|
|
if (x<idim) then
|
|
|
|
|
val(element)=-b3(glob_x,glob_y,glob_z)
|
|
|
|
|
val(element) = val(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
icol(element) = (x)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
irow(element) = glob_row
|
|
|
|
|
element = element+1
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
end do
|
|
|
|
|
call acoo%csput(element-1,irow,icol,val,1,nr,1,nr,info)
|
|
|
|
|
|
|
|
|
|
end do
|
|
|
|
|
|
|
|
|
|
tgen = psb_wtime()-t1
|
|
|
|
|
if(info /= psb_success_) then
|
|
|
|
|
info=psb_err_from_subroutine_
|
|
|
|
|
ch_err='insert rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
!!$ call acoo%print(19)
|
|
|
|
|
t1 = psb_wtime()
|
|
|
|
|
!!$ write(psb_err_unit,*) 'out of loop ',acoo%get_nzeros()
|
|
|
|
|
call acoo%fix(info)
|
|
|
|
|
!!$ write(psb_err_unit,*) '2 out of loop ',acoo%get_nzeros()
|
|
|
|
|
|
|
|
|
|
if(info /= psb_success_) then
|
|
|
|
|
info=psb_err_from_subroutine_
|
|
|
|
|
ch_err='asb rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
tasb = psb_wtime()-t1
|
|
|
|
|
!!$ call acoo%print(20)
|
|
|
|
|
t1 = psb_wtime()
|
|
|
|
|
call acsr%cp_from_coo(acoo,info)
|
|
|
|
|
if(info /= psb_success_) then
|
|
|
|
|
info=psb_err_from_subroutine_
|
|
|
|
|
ch_err='cp rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
tcpy = psb_wtime()-t1
|
|
|
|
|
!!$ call acsr%print(21)
|
|
|
|
|
t1 = psb_wtime()
|
|
|
|
|
call acsr%mv_from_coo(acoo,info)
|
|
|
|
|
if(info /= psb_success_) then
|
|
|
|
|
info=psb_err_from_subroutine_
|
|
|
|
|
ch_err='mv rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
tmov = psb_wtime()-t1
|
|
|
|
|
!!$ call acsr%print(22)
|
|
|
|
|
if(iam == psb_root_) then
|
|
|
|
|
asbfmt = acsr%get_fmt()
|
|
|
|
|
write(psb_out_unit,'("The matrix has been generated and assembled in ",a3," format.")')&
|
|
|
|
|
& asbfmt
|
|
|
|
|
write(psb_out_unit,'("-allocation time : ",es12.5)') talc
|
|
|
|
|
write(psb_out_unit,'("-coeff. gen. time : ",es12.5)') tgen
|
|
|
|
|
write(psb_out_unit,'("-assembly time : ",es12.5)') tasb
|
|
|
|
|
write(psb_out_unit,'("-copy time : ",es12.5)') tcpy
|
|
|
|
|
write(psb_out_unit,'("-move time : ",es12.5)') tmov
|
|
|
|
|
!!$ write(psb_out_unit,'("-total time : ",es12.5)') ttot
|
|
|
|
|
|
|
|
|
|
end if
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
9999 continue
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
if (err_act == psb_act_abort_) then
|
|
|
|
|
call psb_error(ictxt)
|
|
|
|
|
return
|
|
|
|
|
end if
|
|
|
|
|
return
|
|
|
|
|
end subroutine create_matrix
|
|
|
|
|
end program d_coo_matgen
|
|
|
|
|
!
|
|
|
|
|
! functions parametrizing the differential equation
|
|
|
|
|
!
|
|
|
|
|
function a1(x,y,z)
|
|
|
|
|
use psb_sparse_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: a1
|
|
|
|
|
real(psb_dpk_) :: x,y,z
|
|
|
|
|
a1=1.d0
|
|
|
|
|
end function a1
|
|
|
|
|
function a2(x,y,z)
|
|
|
|
|
use psb_sparse_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: a2
|
|
|
|
|
real(psb_dpk_) :: x,y,z
|
|
|
|
|
a2=2.d1*y
|
|
|
|
|
end function a2
|
|
|
|
|
function a3(x,y,z)
|
|
|
|
|
use psb_sparse_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: a3
|
|
|
|
|
real(psb_dpk_) :: x,y,z
|
|
|
|
|
a3=1.d0
|
|
|
|
|
end function a3
|
|
|
|
|
function a4(x,y,z)
|
|
|
|
|
use psb_sparse_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: a4
|
|
|
|
|
real(psb_dpk_) :: x,y,z
|
|
|
|
|
a4=1.d0
|
|
|
|
|
end function a4
|
|
|
|
|
function b1(x,y,z)
|
|
|
|
|
use psb_sparse_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: b1
|
|
|
|
|
real(psb_dpk_) :: x,y,z
|
|
|
|
|
b1=1.d0
|
|
|
|
|
end function b1
|
|
|
|
|
function b2(x,y,z)
|
|
|
|
|
use psb_sparse_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: b2
|
|
|
|
|
real(psb_dpk_) :: x,y,z
|
|
|
|
|
b2=1.d0
|
|
|
|
|
end function b2
|
|
|
|
|
function b3(x,y,z)
|
|
|
|
|
use psb_sparse_mod, only : psb_dpk_
|
|
|
|
|
real(psb_dpk_) :: b3
|
|
|
|
|
real(psb_dpk_) :: x,y,z
|
|
|
|
|
b3=1.d0
|
|
|
|
|
end function b3
|
|
|
|
|
|
|
|
|
|
|
