Contents


NAME

     sbcomm - block coordinate matrix-matrix multiply

SYNOPSIS

       SUBROUTINE SBCOMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
      *           VAL, BINDX, BJNDX, BNNZ, LB,
      *           B, LDB, BETA, C, LDC, WORK, LWORK )
       INTEGER    TRANSA, MB, N, KB, DESCRA(5), BNNZ, LB,
      *           LDB, LDC, LWORK
       INTEGER    BINDX(BNNZ), BJNDX(BNNZ)
       REAL       ALPHA, BETA
       REAL       VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

       SUBROUTINE SBCOMM_64( TRANSA, MB, N, KB, ALPHA, DESCRA,
      *           VAL, BINDX, BJNDX, BNNZ, LB,
      *           B, LDB, BETA, C, LDC, WORK, LWORK )
       INTEGER*8  TRANSA, MB, N, KB, DESCRA(5), BNNZ, LB,
      *           LDB, LDC, LWORK
       INTEGER*8  BINDX(BNNZ), BJNDX(BNNZ)
       REAL       ALPHA, BETA
       REAL       VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

     F95 INTERFACE

        SUBROUTINE BCOMM(TRANSA,MB,[N],KB,ALPHA,DESCRA,VAL,BINDX, BJNDX,
      *   BNNZ, LB, B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
       INTEGER    TRANSA, MB, N, KB, BNNZ, LB
       INTEGER, DIMENSION(:) ::   DESCRA, BINDX, BJNDX
       REAL    ALPHA, BETA
       REAL, DIMENSION(:) :: VAL
       REAL, DIMENSION(:, :) ::  B, C

        SUBROUTINE BCOMM_64(TRANSA,MB,[N],KB,ALPHA,DESCRA,VAL,BINDX, BJNDX,
      *   BNNZ, LB, B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
       INTEGER*8    TRANSA, MB, N, KB, BNNZ, LB
       INTEGER*8, DIMENSION(:) ::  DESCRA,  BINDX, BJNDX
       REAL    ALPHA, BETA
       REAL, DIMENSION(:) :: VAL
       REAL, DIMENSION(:, :) ::  B, C

     C INTERFACE

     #include <sunperf.h>

     void sbcomm (int transa, int mb, int n, int kb, float alpha,
     int* descra, float *val, int *bindx, int *bjndx, int bnnz,
     int lb, float *b, int ldb, float beta, float *c, int ldc);

     void sbcomm_64(long transa, long mb, long n, long kb, float
     alpha, long *descra, float *val, long *bindx, long *bjndx,
     long bnnz, long lb, float *b, long ldb,
      float beta, float *c, long ldc);

DESCRIPTION

      cbcomm 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 (mb*lb) by (kb*lb) sparse matrix represented in the block
      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.

      MB(input)       On entry, integer MB specifies the number of block rows
                      in the matrix A. Unchanged on exit.

      N(input)        On entry,  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,  VAL is a scalar array of length
                      LB*LB*BNNZ consisting of the non-zero block
                      entries of A, in any order. Each block
                      is stored in standard column-major form.
                      Unchanged on exit.

      BINDX(input)    On entry, BINDX is an integer array of length BNNZ
                      consisting of the block row indices of the non-zero
                      block entries of A. Unchanged on exit.

      BJNDX(input)    On entry, BJNDX is an integer array of length BNNZ
                      consisting of the block column indices of the non-zero
                      block entries of A. Unchanged on exit.

      BNNZ (input)    On entry, integer BNNZ specifies the number of nonzero
                      block entries in A. Unchanged on exit.

      LB (input)      On entry, integer LB specifies the  dimension of dense
                      blocks composing A.  Unchanged on exit.

      B (input)       Array of DIMENSION ( LDB, N ).
                      Before entry with  TRANSA = 0,  the leading  kb*lb by n
                      part of the array  B  must contain the matrix  B,  otherwise
                      the leading  mb*lb 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  mb*lb by n
                      part of the array  C  must contain the matrix C,  otherwise
                      the leading  kb*lb 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 sparse blas matrix-matrix multiply routines for
     block entry formats  are designed so that if DESCRA(1)> 0,
     the routines check 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 just one
     sparse matrix representation of a general block matrix A for
     computing  matrix-matrix multiply for another sparse matrix
     composed  by block triangles and/or the main block diagonal
     of A .

     Assume that there is the sparse matrix representation of a
     general real 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

     ___________________________________________________________________

        1 or 2       1           0      alpha*op(L+D+L')*B+beta*C

        1 or 2       1           1      alpha*op(L+I+L')*B+beta*C

        1 or 2       2           0      alpha*op(U'+D+U)*B+beta*C

        1 or 2       2           1      alpha*op(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 or 6       1         0 or 1   alpha*op(L+D-L')*B+beta*C

        4 or 6       2         0 or 1   alpha*op(U+D-U')*B+beta*C

          5       1 or 2         0      alpha*op(D)*B+beta*C

          5       1 or 2         1      alpha*B+beta*C
     ___________________________________________________________________

     Remarks to the table:

     1. the value of  DESCRA(3) is simply ignored , if DESCRA(1)=
     4 or 6 but  the diagonal blocks which are referenced in the
     sparse matrix representation are used;

     2.  the diagonal blocks which are referenced in the sparse
     matrix representation are not used, 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) .