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 )