Contents
cbscsm - block sparse column format triangular solve
SUBROUTINE CBSCSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BINDX, BPNTRB, BPNTRE, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, MB, N, UNITD, DESCRA(5), LB,
* LDB, LDC, LWORK
INTEGER BINDX(BNNZ), BPNTRB(MB), BPNTRE(MB)
COMPLEX ALPHA, BETA
COMPLEX DV(MB*LB*LB), VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CBSCSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BINDX, BPNTRB, BPNTRE, LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), LB,
* LDB, LDC, LWORK
INTEGER*8 BINDX(BNNZ), BPNTRB(MB), BPNTRE(MB)
COMPLEX ALPHA, BETA
COMPLEX DV(MB*LB*LB), VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where: BNNZ = BPNTRE(MB)- BPNTRB(1)
F95 INTERFACE
SUBROUTINE BSCSM(TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BINDX,
* BPNTRB, BPNTRE, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER TRANSA, MB, N, UNITD, LB
INTEGER, DIMENSION(:) :: DESCRA, BINDX, BPNTRB, BPNTRE
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL, DV
COMPLEX, DIMENSION(:, :) :: B, C
SUBROUTINE BSCSM_64(TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, VAL, BINDX,
* BPNTRB, BPNTRE, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, MB, N, UNITD, LB
INTEGER*8, DIMENSION(:) :: DESCRA, BINDX, BPNTRB, BPNTRE
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL, DV
COMPLEX, DIMENSION(:, :) :: B, C
C <- ALPHA op(A) B + BETA C C <- ALPHA D op(A) B + BETA C
C <- ALPHA op(A) D B + BETA C
where ALPHA and BETA are scalar, C and B are m by n dense matrices,
D is a block diagonal matrix, A is a unit, or non-unit, upper or
lower triangular matrix represented in block sparse column format
and op( A ) is one of
op( A ) = inv(A) or op( A ) = inv(A') or op( A ) =inv(conjg( A' ))
(inv denotes matrix inverse, ' indicates matrix transpose)
TRANSA Indicates how to operate with the sparse matrix
0 : operate with matrix
1 : operate with transpose matrix
2 : operate with the conjugate transpose of matrix.
2 is equivalent to 1 if matrix is real.
MB Number of block rows in matrix A
N Number of columns in matrix C
UNITD Type of scaling:
1 : Identity matrix (argument DV[] is ignored)
2 : Scale on left (row block scaling)
3 : Scale on right (column block scaling)
DV() Array of the length MB*LB*LB consisting of the block
entries of block diagonal matrix D where each
block is stored in standard column-major form.
ALPHA Scalar parameter
DESCRA() Descriptor argument. Five element integer array
DESCRA(1) matrix structure
0 : general
1 : symmetric (A=A')
2 : Hermitian (A= CONJG(A'))
3 : Triangular
4 : Skew(Anti)-Symmetric (A=-A')
5 : Diagonal
6 : Skew-Hermitian (A= -CONJG(A'))
Note: For the routine, DESCRA(1)=3 is only supported.
DESCRA(2) upper/lower triangular indicator
1 : lower
2 : upper
DESCRA(3) main diagonal type
0 : non-identity blocks on the main diagonal
1 : identity diagonal blocks
2 : diagonal blocks are dense matrices
DESCRA(4) Array base (NOT IMPLEMENTED)
0 : C/C++ compatible
1 : Fortran compatible
DESCRA(5) repeated indices? (NOT IMPLEMENTED)
0 : unknown
1 : no repeated indices
VAL() scalar array of length LB*LB*BNNZ consisting of the block
entries stored column-major within each dense block.
BINDX() integer array of length BNNZ consisting of the
block row indices of the block entries of A.
The block row indices MUST be sorted
in increasing order for each block column.
BPNTRB() integer array of length MB such that
BPNTRB(J)-BPNTRB(1)+1 points to location in BINDX
of the first block entry of the J-th block column of A.
BPNTRE() integer array of length MB such that
BPNTRE(J)-BPNTRB(1) points to location in BINDX
of the last block entry of the J-th block column of A.
LB dimension of dense blocks composing A.
B() rectangular array with first dimension LDB.
LDB leading dimension of B
BETA Scalar parameter
C() rectangular array with first dimension LDC.
LDC leading dimension of C
WORK() scratch array of length LWORK.
On exit, if LWORK= -1, WORK(1) returns the optimum
size of LWORK.
LWORK length of WORK array. LWORK should be at least
MB*LB.
For good performance, LWORK should generally be larger.
For optimum performance on multiple processors, LWORK
>=MB*LB*N_CPUS where N_CPUS is the maximum number of
processors available to the program.
If LWORK=0, the routine is to allocate workspace needed.
If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimum size of the WORK
array, returns this value as the first entry of the WORK
array, and no error message related to LWORK is issued
by XERBLA.
NIST FORTRAN Sparse Blas User's Guide available at:
http://math.nist.gov/mcsd/Staff/KRemington/fspblas/
"Document for the Basic Linear Algebra Subprograms (BLAS)
Standard", University of Tennessee, Knoxville, Tennessee,
1996:
http://www.netlib.org/utk/papers/sparse.ps
NOTES/BUGS
1. No test for singularity or near-singularity is included
in this routine. Such tests must be performed before calling
this routine.
2. If DESCRA(3)=0,the lower or upper triangular part of each
diagonal block is used by the routine depending on
DESCRA(2).
3. If DESCRA(3)=1, the unit diagonal blocks might or might
not be referenced in the BSC representation of a sparse
matrix. They are not used anyway.
4. If DESCRA(3)=2, diagonal blocks are considered as dense
matrices and the LU factorization with partial pivoting is
used by the routine. WORK(1)=0 on return if the
factorization for all diagonal blocks has been completed
successfully, otherwise WORK(1) = -i where i is the block
number for which the LU factorization could not be computed.
5. The routine can be applied for solving triangular systems
when the upper or lower triangle of the general sparse
matrix A is used. Howerver DESCRA(1) must be equal to 3 in
this case.
6. It is known that there exists another representation of
the block sparse column format (see for example Y.Saad,
"Iterative Methods for Sparse Linear Systems", WPS, 1996).
Its data structure consists of three array instead of the
four used in the current implementation. The main
difference is that only one array, IA, containing the
pointers to the beginning of each block column in the arrays
VAL and BINDX is used instead of two arrays BPNTRB and
BPNTRE. To use the routine with this kind of block sparse
column format the following calling sequence should be used
CALL SBSCSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, BINDX, IA, IA(2), LB,
* B, LDB, BETA, C, LDC, WORK, LWORK )