vbrsm, svbrsm, dvbrsm, cvbrsm, zvbrsm - variable block sparse row format triangular solve
SUBROUTINE SVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK INTEGER*4 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1), * BPNTRB(MB), BPNTRE(MB) REAL*4 ALPHA, BETA REAL*4 DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE DVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK INTEGER*4 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1), * BPNTRB(MB), BPNTRE(MB) REAL*8 ALPHA, BETA REAL*8 DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK ) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK INTEGER*4 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1), * BPNTRB(MB), BPNTRE(MB) COMPLEX*8 ALPHA, BETA COMPLEX*8 DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE ZVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE, * B, LDB, BETA, C, LDC, WORK, LWORK) INTEGER*4 TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK INTEGER*4 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1), * BPNTRB(MB), BPNTRE(MB) COMPLEX*16 ALPHA, BETA COMPLEX*16 DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
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 variable block sparse row 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 containing the block entries of the block diagonal matrix D. The size of the J-th block is RPNTR(J+1)-RPNTR(J) and each block contains matrix entries stored column-major. The total length of array DV is given by the formula:
sum over J from 1 to MB: ((RPNTR(J+1)-RPNTR(J))*(RPNTR(J+1)-RPNTR(J)))
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 NNZ consisting of the block entries of A where each block entry is a dense rectangular matrix stored column by column. NNZ is the total number of point entries in all nonzero block entries of a matrix A.
INDX() integer array of length BNNZ+1 where BNNZ is the number block entries of a matrix A such that the I-th element of INDX[] points to the location in VAL of the (1,1) element of the I-th block entry.
BINDX() integer array of length BNNZ consisting of the block column indices of the block entries of A where BNNZ is the number block entries of a matrix A. Block column indices MUST be sorted in increasing order for each block row.
RPNTR() integer array of length MB+1 such that RPNTR(I)-RPNTR(1)+1 is the row index of the first point row in the I-th block row. RPNTR(MB+1) is set to M+RPNTR(1) where M is the number of rows in square triangular matrix A. Thus, the number of point rows in the I-th block row is RPNTR(I+1)-RPNTR(I).
NOTE: For the current version CPNTR must equal RPNTR and a single array can be passed for both arguments
CPNTR() integer array of length MB+1 such that CPNTR(J)-CPNTR(1)+1 is the column index of the first point column in the J-th block column. CPNTR(MB+1) is set to M+CPNTR(1). Thus, the number of point columns in the J-th block column is CPNTR(J+1)-CPNTR(J).
NOTE: For the current version CPNTR must equal RPNTR and a single array can be passed for both arguments
BPNTRB() integer array of length MB such that BPNTRB(I)-BPNTRB(1)+1 points to location in BINDX of the first block entry of the I-th block row of A.
BPNTRE() integer array of length MB such that BPNTRE(I)-BPNTRB(1) points to location in BINDX of the last block entry of the I-th block row of 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 M = RPNTR(MB+1)-RPNTR(1).
For good performance, LWORK should generally be larger. For optimum performance on multiple processors, LWORK >=M*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 variable block sparse row format (see for example Y.Saad, ``Iterative Methods for Sparse Linear Systems'', WPS, 1996). Its data structure consists of six array instead of the seven used in the current implementation. The main difference is that only one array, IA, containing the pointers to the beginning of each block row in the array BINDX is used instead of two arrays BPNTRB and BPNTRE. To use the routine with this kind of variable block sparse row format the following calling sequence should be used SUBROUTINE SVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA, * VAL, INDX, BINDX, RPNTR, CPNTR, IA, IA(2), * B, LDB, BETA, C, LDC, WORK, LWORK )