Contents
svbrmm - variable block sparse row format matrix-matrix
multiply
SUBROUTINE SVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, MB, N, KB, DESCRA(5), LDB, LDC, LWORK
INTEGER INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(KB+1),
* BPNTRB(MB), BPNTRE(MB)
REAL ALPHA, BETA
REAL VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE SVBRMM_64( TRANSA, MB, N, KB, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, MB, N, KB, DESCRA(5), LDB, LDC, LWORK
INTEGER*8 INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(KB+1),
* BPNTRB(MB), BPNTRE(MB)
REAL ALPHA, BETA
REAL VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)
F95 INTERFACE
SUBROUTINE VBRMM(TRANSA, MB, [N], KB, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
* B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
INTEGER TRANSA, MB, KB
INTEGER, DIMENSION(:) :: DESCRA, INDX, BINDX
INTEGER, DIMENSION(:) :: RPNTR, CPNTR, BPNTRB, BPNTRE
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL
REAL, DIMENSION(:, :) :: B, C
SUBROUTINE VBRMM_64(TRANSA, MB, [N], KB, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
* B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
INTEGER*8 TRANSA, MB, KB
INTEGER*8, DIMENSION(:) :: DESCRA, INDX, BINDX
INTEGER*8, DIMENSION(:) :: RPNTR, CPNTR, BPNTRB, BPNTRE
REAL ALPHA, BETA
REAL, DIMENSION(:) :: VAL
REAL, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void svbrmm (int transa, int mb, int n, int kb, float alpha,
int *descra, float *val, int *indx, int *bindx, int *rpntr,
int *cpntr, int *bpntrb, int *bpntre, float *b, int ldb,
float beta, float *c, int ldc);
void svbrmm_64 (long transa, long mb, long n, long kb,
float alpha, long *descra, float *val, long *indx,
long *bindx, long *rpntr, long *cpntr, long *bpntrb,
long *bpntre, float *b, long ldb, float beta, float *c,
long ldc);
svbrmm performs one of the matrix-matrix operations
C <- alpha op(A) B + beta C
where alpha and beta are scalars, C and B are dense matrices,
A is a sparse M by K matrix represented in the variable block
sparse row format and op( A ) is one of
op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).
( ' indicates matrix transpose)
The number of rows in A and the number of columns in A are determined
as follows
M=RPNTR(MB+1)-RPNTR(1), K=CPNTR(KB+1)-CPNTR(1).
TRANSA(input) TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
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.
KB(input) On entry, integer KB specifies the number of block columns in
the matrix A. 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'))
DESCRA(2) upper/lower triangular indicator
1 : lower
2 : upper
DESCRA(3) main block diagonal type
0 : non-unit
1 : unit
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 a 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. 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.
CPNTR(input) On entry, CPNTR is an 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.
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 (is not referenced in the current version)
LWORK (is not referenced in the current version)
Libsunperf SPARSE BLAS is fully parallel and 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
The routine is designed so that it provides a possibility to
use just one sparse matrix representation of a general
matrix A for computing matrix-matrix multiply for another
sparse matrix composed by block triangles and/or the main
block diagonal of A. The full description of the feature for
block entry formats is given in section NOTES/BUGS for the
sbcomm manpage.
NOTES/BUGS
1. For a general matrix (DESCRA(1)=0), array CPNTR can be
different from RPNTR. For all other matrix types, RPNTR
must equal CPNTR and a single array can be passed for both
arguments.
2. 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 SVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
* VAL, INDX, BINDX, RPNTR, CPNTR, IA, IA(2),
* B, LDB, BETA, C, LDC, WORK, LWORK )