bscsm, sbscsm, dbscsm, cbscsm, zbscsm - block sparse column format triangular solve
SUBROUTINE SBSCSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BINDX, BPNTRB, BPNTRE, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), LB, * LDB, LDC, LWORK INTEGER*4 BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB) REAL*4 ALPHA, BETA REAL*4 DV(MB*LB*LB), VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DBSCSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BINDX, BPNTRB, BPNTRE, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), LB, * LDB, LDC, LWORK INTEGER*4 BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB) REAL*8 ALPHA, BETA REAL*8 DV(MB*LB*LB), VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CBSCSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BINDX, BPNTRB, BPNTRE, LB, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), LB, * LDB, LDC, LWORK INTEGER*4 BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB) COMPLEX*8 ALPHA, BETA COMPLEX*8 DV(MB*LB*LB), VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZBSCSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, BINDX, BPNTRB, BPNTRE, LB, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), LB, * LDB, LDC, LWORK INTEGER*4 BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB) COMPLEX*16 ALPHA, BETA COMPLEX*16 DV(MB*LB*LB), VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
where: BNNZ = BPNTRE(KB)- BPNTRB(1)
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)
All blocks of A on the main diagonal MUST be triangular matrices.
=head1 ARGUMENTS
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 block
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 KB 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 KB 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/
1. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.
2. It is known that there exits 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 )