NAME

bscmm, sbscmm, dbscmm, cbscmm, zbscmm - block sparse column matrix-matrix multiply

SYNOPSIS

  SUBROUTINE SBSCMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
 *           VAL, BINDX, BPNTRB, BPNTRE, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, MB, N, KB, DESCRA(5), LB,
 *           LDB, LDC, LWORK
  INTEGER*4  BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB)
  REAL*4     ALPHA, BETA
  REAL*4     VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

  SUBROUTINE DBSCMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
 *           VAL, BINDX, BPNTRB, BPNTRE, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, MB, N, KB, DESCRA(5), LB,
 *           LDB, LDC, LWORK
  INTEGER*4  BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB)
  REAL*8     ALPHA, BETA
  REAL*8     VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)


  SUBROUTINE CBSCMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
 *           VAL, BINDX, BPNTRB, BPNTRE, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, MB, N, KB, DESCRA(5), LB,
 *           LDB, LDC, LWORK
  INTEGER*4  BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB)
  COMPLEX*8  ALPHA, BETA
  COMPLEX*8  VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

  SUBROUTINE ZBSCMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
 *           VAL, BINDX, BPNTRB, BPNTRE, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, MB, N, KB, DESCRA(5), LB,
 *           LDB, LDC, LWORK
  INTEGER*4  BINDX(BNNZ), BPNTRB(KB), BPNTRE(KB)
  COMPLEX*16 ALPHA, BETA
  COMPLEX*16 VAL(LB*LB*BNNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

  where: BNNZ = BPNTRE(KB)-BPNTRB(1)

DESCRIPTION

          C <- alpha op(A) B + beta C


 where ALPHA and BETA are scalar, C and B are dense matrices,
 A is a matrix represented in block sparse column format and    
 op( A )  is one  of

 op( A ) = A   or   op( A ) = A'   or   op( A ) = conjg( A' ).
                                    ( ' indicates matrix transpose)

ARGUMENTS

 TRANSA        Indicates how to operate with the sparse matrix
                 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.

 MB            Number of block rows in matrix A

 N             Number of columns in matrix C

 KB            Number of block columns in matrix A

 ALPHA         Scalar parameter

 DESCRA()      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()         scalar array of length LB*LB*BNNZ consisting of
               the block entries stored column-major within each
               dense block.

 BINDX()       integer array of length BNNZ consisting of the
               block row indices of the block entries of A.

 BPNTRB()      integer array of length KB such that 
               BPNTRB(J)-BPNTRB(1)+1 points to location in BINDX
               of the first block entry of the J-th block column
               of A.

 BPNTRE()      integer array of length KB such that 
               BPNTRE(J)-BPNTRB(1) points to location in BINDX
               of the last block entry of the J-th block column
               of A.

 LB            dimension of dense blocks composing A.

 B()           rectangular array with first dimension LDB.

 LDB           leading dimension of B

 BETA          Scalar parameter

 C()           rectangular array with first dimension LDC.

 LDC           leading dimension of C

 WORK()        scratch array of length LWORK. WORK is not
               referenced in the current version.

 LWORK         length of WORK array. LWORK is not referenced
               in the current version.

NOTES/BUGS

It is known that there exits another representation of the block sparse column format (see for example Y.Saad, ``Iterative Methods for Sparse Linear Systems'', WPS, 1996). Its data structure consists of three array instead of the four used in the current implementation. The main difference is that only one array, IA, containing the pointers to the beginning of each block column in the arrays VAL and BINDX is used instead of two arrays BPNTRB and BPNTRE. To use the routine with this kind of block sparse column format the following calling sequence should be used

  CALL SBSCMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
 *           VAL, BINDX, IA, IA(2), LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )


=cut

NAME

SYNOPSIS

DESCRIPTION

ARGUMENTS

SEE ALSO

NOTES/BUGS