Contents


NAME

     ccoomm - 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 (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);

DESCRIPTION

      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.

ARGUMENTS

      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)

SEE ALSO

     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) .