Contents
ccoomm - coordinate matrix-matrix multiply
SUBROUTINE CCOOMM( TRANSA, M, N, K, ALPHA, DESCRA,
* VAL, INDX, JNDX, NNZ,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER TRANSA, M, N, K, DESCRA(5), NNZ
* LDB, LDC, LWORK
INTEGER INDX(NNZ), JNDX(NNZ)
COMPLEX ALPHA, BETA
COMPLEX VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
SUBROUTINE CCOOMM_64( TRANSA, M, N, K, ALPHA, DESCRA,
* VAL, INDX, JNDX, NNZ,
* B, LDB, BETA, C, LDC, WORK, LWORK )
INTEGER*8 TRANSA, M, N, K, DESCRA(5), NNZ
* LDB, LDC, LWORK
INTEGER*8 INDX(NNZ), JNDX(NNZ)
COMPLEX ALPHA, BETA
COMPLEX VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)
F95 INTERFACE
SUBROUTINE COOMM( TRANSA, M, [N], K, ALPHA, DESCRA,
* VAL, INDX, JNDX, NNZ, B, [LDB], BETA, C, [LDC],
* [WORK], [LWORK] )
INTEGER TRANSA, M, K, NNZ
INTEGER, DIMENSION(:) :: DESCRA, INDX, JNDX
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL
COMPLEX, DIMENSION(:, :) :: B, C
SUBROUTINE COOMM_64( TRANSA, M, [N], K, ALPHA, DESCRA,
* VAL, INDX, JNDX, NNZ, B, [LDB], BETA, C, [LDC],
* [WORK], [LWORK] )
INTEGER*8 TRANSA, M, K, NNZ
INTEGER*8, DIMENSION(:) :: DESCRA, INDX, JNDX
COMPLEX ALPHA, BETA
COMPLEX, DIMENSION(:) :: VAL
COMPLEX, DIMENSION(:, :) :: B, C
C INTERFACE
#include <sunperf.h>
void ccoomm (int transa, int m, int n, int k, complex
*alpha, int *descra, complex *val, int *indx, int *jndx, int
nnz, complex *b, int ldb, complex *beta, complex *c, int
ldc);
void ccoomm_64 (long transa, long m, long n, long k,
complex *alpha, long *descra, complex *val, long *indx,
long *jndx, long nnz, complex *b, long ldb,
complex *beta, complex *c, long ldc);
ccoomm performs one of the matrix-matrix operations
C <- alpha op(A) B + beta C
where op( A ) is one of
op( A ) = A or op( A ) = A' or op( A ) = conjg( A' )
( ' indicates matrix transpose),
A is an M-by-K sparse matrix represented in the coordinate format,
alpha and beta are scalars, C and B are dense matrices.
TRANSA(input) On entry, integer 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.
M(input) On entry, integer M specifies the number of 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.
K(input) On entry, integer K specifies the number of 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 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, VAL is a scalar array array of length
NNZ consisting of the non-zero entries of A,
in any order. Unchanged on exit.
INDX (input) On entry, INDX is an integer array of length NNZ
consisting of the corresponding row indices of
the entries of A. Unchanged on exit.
JNDX (input) On entry, JNDX is an integer array of length NNZ
consisting of the corresponding column indices of
the entries of A. Unchanged on exit.
NNZ (input) On entry, integer NNZ specifies the number of
non-zero elements in 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
NOTES/BUGS
The all complex sparse blas matrix-matrix multiply routines
except the skyline and jagged-diagonal format routines are
designed so that if DESCRA(1)> 0, the routines check the
validity of each sparse entry given in the sparse blas
representation. 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 just one
sparse matrix representation of a general matrix A for
computing matrix-matrix multiply for another sparse matrix
composed by triangles and/or the main diagonal of A .
Assume that there is the sparse matrix representation of a
general complex matrix A decomposed in the form
A = L + D + U
where L is the strictly lower triangle of A, U is the
strictly upper triangle of A, D is the 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
___________________________________________________________________
1 1 0 alpha*op(L+D+L')*B+beta*C
1 1 1 alpha*op(L+I+L')*B+beta*C
1 2 0 alpha*op(U'+D+U)*B+beta*C
1 2 1 alpha*op(U'+I+U)*B+beta*C
2 1 0 alpha*op(L+D+conjg(L'))*B+beta*C
2 1 1 alpha*op(L+I+conjg(L'))*B+beta*C
2 2 0 alpha*op(conjg(U')+D+U)*B+beta*C
2 2 1 alpha*op(conjg(U')+I+U)*B+beta*C
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
4 1 0 or 1 alpha*op(L-L')*B+beta*C
4 2 0 or 1 alpha*op(U-U')*B+beta*C
5 1 or 2 0 alpha*op(D)*B+beta*C
5 1 or 2 1 alpha*B+beta*C
6 1 0 or 1 alpha*op(L-conjg(L'))*B+beta*C
6 2 0 or 1 alpha*op(U-conjg(U'))*B+beta*C
___________________________________________________________________
Remarks to the table:
1. the value of DESCRA(3) is simply ignored and the
diagonal entries given in the sparse matrix representation
are not used by the routine, if DESCRA(1)= 4 or 6;
2. the diagonal entries are not used also, if DESCRA(3)=1
and DESCRA(1)is one of 1, 2, 3 or 5;
3. if DESCRA(3) is not 1 and DESCRA(1) is one of 1,2, 4 or
6, the type of D should correspond to the choosen value of
DESCRA(1) .