ccoomm(3P) Sun Performance Library ccoomm(3P)NAMEccoomm - coordinate matrix-matrix multiply
SYNOPSIS
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 (const int transa, const int m, const int n, const int k,
const floatcomplex* alpha, const int* descra, const floatcom‐
plex* val, const int* indx, const int* jndx, const int nnz,
const floatcomplex* b, const int ldb, const floatcomplex*
beta, floatcomplex* c, const int ldc);
void ccoomm_64 (const long transa, const long m, const long n, const
long k, const floatcomplex* alpha, const long* descra, const
floatcomplex* val, const long* indx, const long* jndx, const
long nnz, const floatcomplex* b, const long ldb, const float‐
complex* beta, floatcomplex* c, const long ldc);
DESCRIPTIONccoomm 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.
ARGUMENTSTRANSA(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)
SEE ALSO
Libsunperf SPARSE BLAS is fully parallel and compatible with NIST FOR‐
TRAN 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 mul‐
tiply 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 com‐
plex 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) .
3rd Berkeley Distribution 6 Mar 2009 ccoomm(3P)
