! ! Parallel Sparse BLAS version 3.5.1 ! (C) Copyright 2015 ! 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 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: ppde.f90 ! module psb_d_pde3d_mod use psb_base_mod, only : psb_dpk_, psb_ipk_, psb_lpk_, psb_desc_type,& & psb_dspmat_type, psb_d_vect_type, dzero,& & psb_d_base_sparse_mat, psb_d_base_vect_type, & & psb_i_base_vect_type, psb_l_base_vect_type interface function d_func_3d(x,y,z) result(val) import :: psb_dpk_ real(psb_dpk_), intent(in) :: x,y,z real(psb_dpk_) :: val end function d_func_3d end interface interface psb_gen_pde3d module procedure psb_d_gen_pde3d end interface psb_gen_pde3d contains function d_null_func_3d(x,y,z) result(val) real(psb_dpk_), intent(in) :: x,y,z real(psb_dpk_) :: val val = dzero end function d_null_func_3d ! ! functions parametrizing the differential equation ! ! ! Note: b1, b2 and b3 are the coefficients of the first ! derivative of the unknown function. The default ! we apply here is to have them zero, so that the resulting ! matrix is symmetric/hermitian and suitable for ! testing with CG and FCG. ! When testing methods for non-hermitian matrices you can ! change the B1/B2/B3 functions to e.g. done/sqrt((3*done)) ! function b1(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: b1 real(psb_dpk_), intent(in) :: x,y,z b1=dzero end function b1 function b2(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: b2 real(psb_dpk_), intent(in) :: x,y,z b2=dzero end function b2 function b3(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: b3 real(psb_dpk_), intent(in) :: x,y,z b3=dzero end function b3 function c(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: c real(psb_dpk_), intent(in) :: x,y,z c=dzero end function c function a1(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: a1 real(psb_dpk_), intent(in) :: x,y,z a1=done/80 end function a1 function a2(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: a2 real(psb_dpk_), intent(in) :: x,y,z a2=done/80 end function a2 function a3(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: a3 real(psb_dpk_), intent(in) :: x,y,z a3=done/80 end function a3 function g(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none 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 ! ! subroutine to allocate and fill in the coefficient matrix and ! the rhs. ! subroutine psb_d_gen_pde3d(ictxt,idim,a,bv,xv,desc_a,afmt,info,& & f,amold,vmold,imold,partition,nrl,iv) use psb_base_mod use psb_util_mod ! ! Discretizes the partial differential equation ! ! a1 dd(u) a2 dd(u) a3 dd(u) b1 d(u) b2 d(u) b3 d(u) ! - ------ - ------ - ------ + ----- + ------ + ------ + c u = f ! dxdx dydy dzdz dx dy dz ! ! with Dirichlet boundary conditions ! u = g ! ! on the unit cube 0<=x,y,z<=1. ! ! ! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation. ! implicit none integer(psb_ipk_) :: idim type(psb_dspmat_type) :: a type(psb_d_vect_type) :: xv,bv type(psb_desc_type) :: desc_a type(psb_ctxt_type) :: ictxt integer(psb_ipk_) :: info character(len=*) :: afmt procedure(d_func_3d), optional :: f class(psb_d_base_sparse_mat), optional :: amold class(psb_d_base_vect_type), optional :: vmold class(psb_i_base_vect_type), optional :: imold integer(psb_ipk_), optional :: partition, nrl,iv(:) ! Local variables. integer(psb_ipk_), parameter :: nb=20 type(psb_d_csc_sparse_mat) :: acsc type(psb_d_coo_sparse_mat) :: acoo type(psb_d_csr_sparse_mat) :: acsr real(psb_dpk_) :: zt(nb),x,y,z integer(psb_ipk_) :: nnz,nr,nlr,i,j,ii,ib,k, partition_ integer(psb_lpk_) :: m,n,glob_row,nt integer(psb_ipk_) :: ix,iy,iz,ia,indx_owner ! For 3D partition ! Note: integer control variables going directly into an MPI call ! must be 4 bytes, i.e. psb_mpk_ integer(psb_mpk_) :: npdims(3), npp, minfo integer(psb_ipk_) :: npx,npy,npz, iamx,iamy,iamz,mynx,myny,mynz integer(psb_ipk_), allocatable :: bndx(:),bndy(:),bndz(:) ! Process grid integer(psb_ipk_) :: np, iam integer(psb_ipk_) :: icoeff integer(psb_lpk_), allocatable :: irow(:),icol(:),myidx(:) real(psb_dpk_), allocatable :: val(:) ! deltah dimension of each grid cell ! deltat discretization time real(psb_dpk_) :: deltah, sqdeltah, deltah2 real(psb_dpk_), parameter :: rhs=dzero,one=done,zero=dzero real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen, tcdasb integer(psb_ipk_) :: err_act procedure(d_func_3d), pointer :: f_ character(len=20) :: name, ch_err,tmpfmt info = psb_success_ name = 'create_matrix' call psb_erractionsave(err_act) call psb_info(ictxt, iam, np) if (present(f)) then f_ => f else f_ => d_null_func_3d end if deltah = done/(idim+1) sqdeltah = deltah*deltah deltah2 = (2*done)* deltah if (present(partition)) then if ((1<= partition).and.(partition <= 3)) then partition_ = partition else write(*,*) 'Invalid partition choice ',partition,' defaulting to 3' partition_ = 3 end if else partition_ = 3 end if ! initialize array descriptor and sparse matrix storage. provide an ! estimate of the number of non zeroes m = (1_psb_lpk_*idim)*idim*idim n = m nnz = ((n*7)/(np)) if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n t0 = psb_wtime() select case(partition_) case(1) ! A BLOCK partition if (present(nrl)) then nr = nrl else ! ! Using a simple BLOCK distribution. ! nt = (m+np-1)/np nr = max(0,min(nt,m-(iam*nt))) end if nt = nr call psb_sum(ictxt,nt) if (nt /= m) then write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m info = -1 call psb_barrier(ictxt) call psb_abort(ictxt) return end if ! ! First example of use of CDALL: specify for each process a number of ! contiguous rows ! call psb_cdall(ictxt,desc_a,info,nl=nr) myidx = desc_a%get_global_indices() nlr = size(myidx) case(2) ! A partition defined by the user through IV if (present(iv)) then if (size(iv) /= m) then write(psb_err_unit,*) iam, 'Initialization error: wrong IV size',size(iv),m info = -1 call psb_barrier(ictxt) call psb_abort(ictxt) return end if else write(psb_err_unit,*) iam, 'Initialization error: IV not present' info = -1 call psb_barrier(ictxt) call psb_abort(ictxt) return end if ! ! Second example of use of CDALL: specify for each row the ! process that owns it ! call psb_cdall(ictxt,desc_a,info,vg=iv) myidx = desc_a%get_global_indices() nlr = size(myidx) case(3) ! A 3-dimensional partition ! A nifty MPI function will split the process list npdims = 0 call mpi_dims_create(np,3,npdims,info) npx = npdims(1) npy = npdims(2) npz = npdims(3) allocate(bndx(0:npx),bndy(0:npy),bndz(0:npz)) ! We can reuse idx2ijk for process indices as well. call idx2ijk(iamx,iamy,iamz,iam,npx,npy,npz,base=0) ! Now let's split the 3D cube in hexahedra call dist1Didx(bndx,idim,npx) mynx = bndx(iamx+1)-bndx(iamx) call dist1Didx(bndy,idim,npy) myny = bndy(iamy+1)-bndy(iamy) call dist1Didx(bndz,idim,npz) mynz = bndz(iamz+1)-bndz(iamz) ! How many indices do I own? nlr = mynx*myny*mynz allocate(myidx(nlr)) ! Now, let's generate the list of indices I own nr = 0 do i=bndx(iamx),bndx(iamx+1)-1 do j=bndy(iamy),bndy(iamy+1)-1 do k=bndz(iamz),bndz(iamz+1)-1 nr = nr + 1 call ijk2idx(myidx(nr),i,j,k,idim,idim,idim) end do end do end do if (nr /= nlr) then write(psb_err_unit,*) iam,iamx,iamy,iamz, 'Initialization error: NR vs NLR ',& & nr,nlr,mynx,myny,mynz info = -1 call psb_barrier(ictxt) call psb_abort(ictxt) end if ! ! Third example of use of CDALL: specify for each process ! the set of global indices it owns. ! call psb_cdall(ictxt,desc_a,info,vl=myidx) case default write(psb_err_unit,*) iam, 'Initialization error: should not get here' info = -1 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 if (info == psb_success_) call psb_geall(xv,desc_a,info) if (info == psb_success_) call psb_geall(bv,desc_a,info) call psb_barrier(ictxt) talc = psb_wtime()-t0 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),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) icoeff = 1 do k=1,ib i=ii+k-1 ! local matrix pointer glob_row=myidx(i) ! compute gridpoint 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 zt(k) = f_(x,y,z) ! internal point: build discretization ! ! term depending on (x-1,y,z) ! val(icoeff) = -a1(x,y,z)/sqdeltah-b1(x,y,z)/deltah2 if (ix == 1) then zt(k) = g(dzero,y,z)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix-1,iy,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x,y-1,z) val(icoeff) = -a2(x,y,z)/sqdeltah-b2(x,y,z)/deltah2 if (iy == 1) then zt(k) = g(x,dzero,z)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix,iy-1,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x,y,z-1) val(icoeff)=-a3(x,y,z)/sqdeltah-b3(x,y,z)/deltah2 if (iz == 1) then zt(k) = g(x,y,dzero)*(-val(icoeff)) + zt(k) else 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*done)*(a1(x,y,z)+a2(x,y,z)+a3(x,y,z))/sqdeltah & & + c(x,y,z) call ijk2idx(icol(icoeff),ix,iy,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 ! term depending on (x,y,z+1) val(icoeff)=-a3(x,y,z)/sqdeltah+b3(x,y,z)/deltah2 if (iz == idim) then zt(k) = g(x,y,done)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix,iy,iz+1,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x,y+1,z) val(icoeff)=-a2(x,y,z)/sqdeltah+b2(x,y,z)/deltah2 if (iy == idim) then zt(k) = g(x,done,z)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix,iy+1,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x+1,y,z) val(icoeff)=-a1(x,y,z)/sqdeltah+b1(x,y,z)/deltah2 if (ix==idim) then zt(k) = g(done,y,z)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix+1,iy,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif end do call psb_spins(icoeff-1,irow,icol,val,a,desc_a,info) 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(:)=dzero call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,desc_a,info) if(info /= psb_success_) exit 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 deallocate(val,irow,icol) call psb_barrier(ictxt) t1 = psb_wtime() call psb_cdasb(desc_a,info,mold=imold) tcdasb = psb_wtime()-t1 call psb_barrier(ictxt) t1 = psb_wtime() if (info == psb_success_) then if (present(amold)) then call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_,mold=amold) else call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_,afmt=afmt) end if end if call psb_barrier(ictxt) 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 if (info == psb_success_) call psb_geasb(xv,desc_a,info,mold=vmold) if (info == psb_success_) call psb_geasb(bv,desc_a,info,mold=vmold) 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 psb_barrier(ictxt) ttot = psb_wtime() - t0 call psb_amx(ictxt,talc) call psb_amx(ictxt,tgen) call psb_amx(ictxt,tasb) call psb_amx(ictxt,ttot) if(iam == psb_root_) then tmpfmt = a%get_fmt() write(psb_out_unit,'("The matrix has been generated and assembled in ",a3," format.")')& & tmpfmt write(psb_out_unit,'("-allocation time : ",es12.5)') talc write(psb_out_unit,'("-coeff. gen. time : ",es12.5)') tgen write(psb_out_unit,'("-desc asbly time : ",es12.5)') tcdasb write(psb_out_unit,'("- mat asbly time : ",es12.5)') tasb write(psb_out_unit,'("-total time : ",es12.5)') ttot end if call psb_erractionrestore(err_act) return 9999 call psb_error_handler(ictxt,err_act) return end subroutine psb_d_gen_pde3d end module psb_d_pde3d_mod program pdgenspmv use psb_base_mod use psb_util_mod use psb_d_pde3d_mod implicit none ! input parameters character(len=20) :: kmethd, ptype character(len=5) :: afmt integer(psb_ipk_) :: idim ! miscellaneous real(psb_dpk_), parameter :: one = done real(psb_dpk_) :: t1, t2, tprec, flops, tflops, tt1, tt2, bdwdth ! sparse matrix and preconditioner type(psb_dspmat_type) :: a ! descriptor type(psb_desc_type) :: desc_a ! dense matrices type(psb_d_vect_type) :: xv,bv, vtst real(psb_dpk_), allocatable :: tst(:) ! blacs parameters type(psb_ctxt_type) :: ictxt integer(psb_ipk_) :: iam, np ! solver parameters 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 ! other variables integer(psb_ipk_) :: info, i character(len=20) :: name,ch_err character(len=40) :: fname 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 name='pde90' call psb_set_errverbosity(itwo) ! ! Hello world ! if (iam == psb_root_) then write(*,*) 'Welcome to PSBLAS version: ',psb_version_string_ write(*,*) 'This is the ',trim(name),' sample program' end if ! ! get parameters ! call get_parms(ictxt,afmt,idim) ! ! allocate and fill in the coefficient matrix, rhs and initial guess ! call psb_barrier(ictxt) t1 = psb_wtime() 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 info=psb_err_from_subroutine_ ch_err='psb_gen_pde3d' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if if (iam == psb_root_) write(psb_out_unit,'("Overall matrix creation time : ",es12.5)')t2 if (iam == psb_root_) write(psb_out_unit,'(" ")') call xv%set(done) call psb_barrier(ictxt) t1 = psb_wtime() ! ! Perform Ax multiple times to compute average performance ! do i=1,times call psb_spmm(done,a,xv,dzero,bv,desc_a,info,'n') end do call psb_barrier(ictxt) t2 = psb_wtime() - t1 call psb_amx(ictxt,t2) ! FIXME: cache flush needed here call psb_barrier(ictxt) tt1 = psb_wtime() ! ! Perform A^Tx multiple times to compute average performance ! do i=1,times call psb_spmm(done,a,xv,dzero,bv,desc_a,info,'t') end do call psb_barrier(ictxt) tt2 = psb_wtime() - tt1 call psb_amx(ictxt,tt2) call psb_amx(ictxt,t2) nr = desc_a%get_global_rows() annz = a%get_nzeros() amatsize = a%sizeof() descsize = psb_sizeof(desc_a) call psb_sum(ictxt,annz) call psb_sum(ictxt,amatsize) call psb_sum(ictxt,descsize) if (iam == psb_root_) then flops = 2.d0*times*annz tflops=flops write(psb_out_unit,'("Matrix: ell1 ",i0)') idim write(psb_out_unit,'("Test on : ",i20," processors")') np write(psb_out_unit,'("Size of matrix : ",i20," ")') nr write(psb_out_unit,'("Number of nonzeros : ",i20," ")') annz write(psb_out_unit,'("Memory occupation : ",i20," ")') amatsize write(psb_out_unit,'("Number of flops (",i0," prod) : ",F20.0," ")') times,flops flops = flops / (t2) tflops = tflops / (tt2) write(psb_out_unit,'("Time for ",i0," products (s) : ",F20.3)')times, t2 write(psb_out_unit,'("Time per product (ms) : ",F20.3)') t2*1.d3/(1.d0*times) write(psb_out_unit,'("MFLOPS : ",F20.3)') flops/1.d6 write(psb_out_unit,'("Time for ",i0," products (s) (trans.): ",F20.3)') times,tt2 write(psb_out_unit,'("Time per product (ms) (trans.): ",F20.3)') tt2*1.d3/(1.d0*times) write(psb_out_unit,'("MFLOPS (trans.): ",F20.3)') tflops/1.d6 ! ! This computation is valid for CSR ! nbytes = nr*(2*psb_sizeof_dp + psb_sizeof_ip)+& & annz*(psb_sizeof_dp + psb_sizeof_ip) bdwdth = times*nbytes/(t2*1.d6) write(psb_out_unit,*) write(psb_out_unit,'("MBYTES/S : ",F20.3)') bdwdth bdwdth = times*nbytes/(tt2*1.d6) write(psb_out_unit,'("MBYTES/S (trans): ",F20.3)') bdwdth write(psb_out_unit,'("Storage type for DESC_A: ",a)') desc_a%get_fmt() write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)')descsize end if ! ! cleanup storage and exit ! call psb_gefree(bv,desc_a,info) call psb_gefree(xv,desc_a,info) call psb_spfree(a,desc_a,info) call psb_cdfree(desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='free routine' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if call psb_exit(ictxt) stop 9999 call psb_error(ictxt) stop contains ! ! get iteration parameters from standard input ! subroutine get_parms(ictxt,afmt,idim) type(psb_ctxt_type) :: ictxt character(len=*) :: afmt integer(psb_ipk_) :: idim integer(psb_ipk_) :: np, iam integer(psb_ipk_) :: intbuf(10), ip call psb_info(ictxt, iam, np) if (iam == 0) then read(psb_inp_unit,*) afmt read(psb_inp_unit,*) idim endif call psb_bcast(ictxt,afmt) call psb_bcast(ictxt,idim) if (iam == 0) then write(psb_out_unit,'("Testing matrix : ell1")') write(psb_out_unit,'("Grid dimensions : ",i4,"x",i4,"x",i4)')idim,idim,idim write(psb_out_unit,'("Number of processors : ",i0)')np write(psb_out_unit,'("Data distribution : BLOCK")') write(psb_out_unit,'(" ")') end if return end subroutine get_parms ! ! print an error message ! subroutine pr_usage(iout) integer(psb_ipk_) :: 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 end program pdgenspmv