Dear PETSc Users/Developers,
I have the following sequential Fortran PETSc code that I have been
developing (on and off) based on the kind advice given by members of
this list, with respect to solving an inverse sparse matrix problem.
Essentially, the code reads in a square double complex matrix from
external file of size (order x order) and then proceeds to do a
MatMatSolve(), where A is the sparse matrix to invert, B is a dense
identity matrix and X is the resultant dense matrix....hope that makes
sense.
My main problem is that the code stalls on the MatSetValues() for the
sparse matrix A. With a trivial test matrix of (224 x 224) the program
terminates successfully (by successfully I mean all instructions
execute...I am not interested in the validity of X right now).
Unfortunately, when I move up to a (2352 x 2352) matrix the
MatSetValues() routine for matrix A is still in progress after 15
minutes on one processor of our AMD Opteron IBM Cluster. I know that
people will be screaming "preallocation"...but I have tried to take this
into account by running a loop over the rows in A and counting the
non-zero values explicitly prior to creation. I then pass this vector
into the creation routine for the nnz argument. For the large (2352 x
2352) problem that seems to be taking forever to set...at most there are
only 200 elements per row that are non-zero according to the counts.
Can anyone explain why the MatSetValues() routine is taking such a long
time. Maybe this expected for this specific task...although it seems
very long?
I did notice that on the trivial (224 x 224) run that I was still
getting mallocs (approx 2000) for the A assembly when I used the -info
command line parameter. I thought that it should be 0 if my
preallocation counts were exact? Does this hint that I am doing
something wrong. I have checked the code but don't see any obvious
problems in the logic...not that means anything.
I would be grateful if someone could advise on this matter. Also, if you
have a few seconds to spare I would be grateful if some experts could
scan the remaining logic of the code (not in fine detail) to make sure
that I am doing all that I need to do to get this calculation
working...assuming I can resolve the MatSetValues() problem.
Once again many thanks in advance,
Tim.
! Initialise the PETSc MPI Harness
call PetscInitialize(PETSC_NULL_CHARACTER,error);CHKERRQ(error)
call MPI_COMM_SIZE(PETSC_COMM_SELF,processes,error);CHKERRQ(error)
call MPI_COMM_RANK(PETSC_COMM_SELF,ID,error);CHKERRQ(error)
! Read in Matrix
open(321,file='Hamiltonian.bin',form='unformatted')
read(321) order
if (ID==0) then
print *
print *,processes," Processing Elements being used"
print *
print *,"Matrix has order ",order," rows by ",order," columns"
print *
end if
allocate(matrix(order,order))
read(321) matrix
close(321)
! Allocate array for nnz
allocate(numberZero(order))
! Count number of non-zero elements in each matrix row
do row=1,order
count=0
do column=1,order
if (matrix(row,column).ne.(0,0)) count=count+1
end do
numberZero(row)=count
end do
! Declare a PETSc Matrices
call
MatCreateSeqAIJ(PETSC_COMM_SELF,order,order,PETSC_NULL_INTEGER,numberZero,A,error);CHKERRQ(error)
call
MatCreateSeqAIJ(PETSC_COMM_SELF,order,order,0,PETSC_NULL_INTEGER,factorMat,error);CHKERRQ(error)
call
MatCreateSeqDense(PETSC_COMM_SELF,order,order,PETSC_NULL_SCALAR,X,error);CHKERRQ(error)
call
MatCreateSeqDense(PETSC_COMM_SELF,order,order,PETSC_NULL_SCALAR,B,error);CHKERRQ(error)
! Set up zero-based array indexing for use in MatSetValues
allocate(columnIndices(order))
do column=1,order
columnIndices(column)=column-1
end do
! Need to transpose values array as row-major arrays are used.
call
MatSetValues(A,order,columnIndices,order,columnIndices,transpose(matrix),INSERT_VALUES,error);CHKERRQ(error)
! Assemble Matrix A
call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,error);CHKERRQ(error)
call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,error);CHKERRQ(error)
deallocate(matrix)
! Create Index Sets for Factorisation
call
ISCreateGeneral(PETSC_COMM_SELF,order,columnIndices,indexSet,error);CHKERRQ(error)
call MatFactorInfoInitialize(info,error);CHKERRQ(error)
call ISSetPermutation(indexSet,error);CHKERRQ(error)
call
MatLUFactorSymbolic(A,indexSet,indexSet,info,factorMat,error);CHKERRQ(error)
call MatLUFactorNumeric(A,info,factorMat,error);CHKERRQ(error)
! A no-longer needed
call MatDestroy(A,error);CHKERRQ(error)
one=(1,0)
! Set Diagonal elements in Identity Matrix B
do row=0,order-1
call MatSetValue(B,row,row,one,INSERT_VALUES,error);CHKERRQ(error)
end do
! Assemble B
call MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY,error);CHKERRQ(error)
call MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY,error);CHKERRQ(error)
! Assemble X
call MatAssemblyBegin(X,MAT_FINAL_ASSEMBLY,error);CHKERRQ(error)
call MatAssemblyEnd(X,MAT_FINAL_ASSEMBLY,error);CHKERRQ(error)
! Solve AX=B
call MatMatSolve(factorMat,B,X,error);CHKERRQ(error)
! Deallocate Storage
deallocate(columnIndices)
call MatDestroy(factorMat,error);CHKERRQ(error)
call MatDestroy(B,error);CHKERRQ(error)
call MatDestroy(X,error);CHKERRQ(error)
call PetscFinalize(error)
--
Dr. Timothy Stitt <timothy_dot_stitt_at_ichec.ie>
HPC Application Consultant - ICHEC (www.ichec.ie)
Dublin Institute for Advanced Studies
5 Merrion Square - Dublin 2 - Ireland
+353-1-6621333 (tel) / +353-1-6621477 (fax)