Contents
cvbrsm - variable block sparse row format triangular solve
SUBROUTINE CVBRSM( 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)
COMPLEX ALPHA, BETA
COMPLEX DV(*), VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CVBRSM_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)
COMPLEX ALPHA, BETA
COMPLEX 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
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL, DV
COMPLEX, 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
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL, DV
COMPLEX, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void cvbrsm (int transa, int mb, int n, int unitd, complex
*dv, complex *alpha, int *descra, complex *val, int *indx,
int *bindx, int *rpntr, int *cpntr, int *bpntrb, int
*bpntre, complex *b, int ldb, complex *beta, complex *c, int
ldc);
void cvbrsm_64 (long transa, long mb, long n, long unitd,
complex *dv, complex *alpha, long *descra, complex *val,
long *indx, long *bindx, long *rpntr, long *cpntr, long
*bpntrb, long *bpntre, complex *b, long ldb, complex *beta,
complex *c, long ldc);
cvbrsm performs one of the matrix-matrix operations
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 scalars, C and B are m by n dense matrices,
D is a block diagonal matrix, A is a sparse m by m unit, or non-unit,
upper or lower triangular matrix represented in the 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).
The number of rows in A is determined as follows
m=RPNTR(MB+1)-RPNTR(1).
TRANSA(input) On entry, 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.
Unchanged on exit.
MB(input) On entry, integer MB specifies the number of block rows
in the matrix A. Unchanged on exit.
N(input) On entry, integer N specifies the number of columns
in the matrix C. Unchanged on exit.
DV(input) On entry, array DV contains 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)))
Unchanged on exit.
ALPHA(input) On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
DESCRA (input) 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(input) On entry, scalar array VAL of length NNZ consists of the
block entries of A where each block entry is a dense
rectangular matrix stored column by column where NNZ
denotes the total number of point entries in all nonzero
block entries of the matrix A. Unchanged on exit.
INDX(input) On entry, INDX is an integer array of length BNNZ+1 where BNNZ
is the number of block entries of the 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. Unchanged on exit.
BINDX(input) On entry, BINDX is an 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 the matrix A.
Block column indices MUST be sorted in increasing order
for each block row. Unchanged on exit.
RPNTR(input) On entry, RPNTR is an 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 the matrix A.
Thus, the number of point rows in the I-th block row is
RPNTR(I+1)-RPNTR(I). Unchanged on exit.
NOTE: For the current version CPNTR must equal RPNTR
and a single array can be passed for both arguments
CPNTR(input) On entry, CPNTR is integer array of length KB+1 such that
CPNTR(J)-CPNTR(1)+1 is the column index of the first point
column in the J-th block column. CPNTR(KB+1) is set to
K+CPNTR(1) where K is the number of columns in the matrix A.
Thus, the number of point columns in the J-th block column
is CPNTR(J+1)-CPNTR(J). Unchanged on exit.
NOTE: For the current version CPNTR must equal RPNTR
and a single array can be passed for both arguments
BPNTRB(input) On entry, BPNTRB is an 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.
Unchanged on exit.
BPNTRE(input) On entry, BPNTRE is an 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.
Unchanged on exit.
B (input) Array of DIMENSION ( LDB, N ).
Before entry with TRANSA = 0, the leading k by n
part of the array B must contain the matrix B, otherwise
the leading m by n part of the array B must contain the
matrix B. Unchanged on exit.
LDB (input) On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. Unchanged on exit.
BETA (input) On entry, BETA specifies the scalar beta. Unchanged on exit.
C(input/output) Array of DIMENSION ( LDC, N ).
Before entry with TRANSA = 0, the leading m by n
part of the array C must contain the matrix C, otherwise
the leading k by n part of the array C must contain the
matrix C. On exit, the array C is overwritten by the matrix
( alpha*op( A )* B + beta*C ).
LDC (input) On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. Unchanged on exit.
WORK(workspace) Scratch array of length LWORK.
On exit, if LWORK= -1, WORK(1) returns the optimum size
of LWORK.
LWORK (input) On entry, LWORK specifies the 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.
Libsunperf SPARSE BLAS is parallelized with the help of OPENMP and it is
fully compatible with NIST FORTRAN Sparse Blas but the sources are different.
Libsunperf SPARSE BLAS is free of bugs found in NIST FORTRAN Sparse Blas.
Besides several new features and routines are implemented.
NIST FORTRAN Sparse Blas User's Guide available at:
http://math.nist.gov/mcsd/Staff/KRemington/fspblas/
Based on the standard proposed in
"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 diagonal blocks in the variable
block row representationof A don't need to be the identity
matrices because these block entries are not used by the
routine in this case.
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 is designed so that it checks the validity of
each sparse block entry given in the sparse blas
representation. Block entries with incorrect indices are not
used and no error message related to the entries is issued.
The feature also provides a possibility to use the sparse
matrix representation of a general matrix A for solving
triangular systems with the upper or lower block triangle of
A. But DESCRA(1) MUST be equal to 3 even in this case.
Assume that there is the sparse matrix representation a
general matrix A decomposed in the form
A = L + D + U
where L is the strictly block lower triangle of A, U is the
strictly block upper triangle of A, D is the block diagonal
matrix. Let's I denotes the identity matrix.
Then the correspondence between the first three values of
DESCRA and the result matrix for the sparse representation
of A is
DESCRA(1) DESCRA(2) DESCRA(3) RESULT
3 1 1 alpha*op(L+I)*B+beta*C
3 1 0 alpha*op(L+D)*B+beta*C
3 2 1 alpha*op(U+I)*B+beta*C
3 2 0 alpha*op(U+D)*B+beta*C
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 CVBRSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, IA, IA(2),
* B, LDB, BETA, C, LDC, WORK, LWORK )