Contents
svbrsm - 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 TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK
INTEGER INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1),
* BPNTRB(MB), BPNTRE(MB)
REAL ALPHA, BETA
REAL DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE SVBRSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, MB, N, UNITD, DESCRA(5), LDB, LDC, LWORK
INTEGER*8 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(MB+1),
* BPNTRB(MB), BPNTRE(MB)
REAL ALPHA, BETA
REAL DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
F95 INTERFACE
SUBROUTINE VBRSM(TRANSA, MB, [N], UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
* B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
INTEGER TRANSA, MB, UNITD
INTEGER, DIMENSION(:) :: DESCRA, INDX, BINDX
INTEGER, DIMENSION(:) :: RPNTR, CPNTR, BPNTRB, BPNTRE
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL, DV
REAL, DIMENSION(:, :) :: B, C
SUBROUTINE VBRSM_64(TRANSA, MB, [N], UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
* B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, MB, UNITD
INTEGER*8, DIMENSION(:) :: DESCRA, INDX, BINDX
INTEGER*8, DIMENSION(:) :: RPNTR, CPNTR, BPNTRB, BPNTRE
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL, DV
REAL, 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 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)
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
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 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/
"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 VBR 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.
6. It is known that there exists 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 SVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, IA, IA(2),
* B, LDB, BETA, C, LDC, WORK, LWORK )