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dvbrmm(3P)		    Sun Performance Library		    dvbrmm(3P)

NAME
       dvbrmm - variable block sparse row format matrix-matrix multiply

SYNOPSIS
	SUBROUTINE DVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
       *	   VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
       *	   B, LDB, BETA, C, LDC, WORK, LWORK)
	INTEGER	   TRANSA, MB, N, KB, DESCRA(5), LDB, LDC, LWORK
	INTEGER	   INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(KB+1),
       *	   BPNTRB(MB), BPNTRE(MB)
	DOUBLE PRECISION ALPHA, BETA
	DOUBLE PRECISION VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)

	SUBROUTINE DVBRMM_64( TRANSA, MB, N, KB, ALPHA, DESCRA,
       *	   VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
       *	   B, LDB, BETA, C, LDC, WORK, LWORK)
	INTEGER*8  TRANSA, MB, N, KB, DESCRA(5), LDB, LDC, LWORK
	INTEGER*8  INDX(*), BINDX(*), RPNTR(MB+1), CPNTR(KB+1),
       *	   BPNTRB(MB), BPNTRE(MB)
	DOUBLE PRECISION ALPHA, BETA
	DOUBLE PRECISION VAL(*), B(LDB,*), C(LDC,*), WORK(LWORK)

   F95 INTERFACE
	SUBROUTINE VBRMM(TRANSA, MB, [N], KB, ALPHA, DESCRA,
       *	   VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
       *	   B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
	INTEGER	   TRANSA, MB, KB
	INTEGER, DIMENSION(:) ::  DESCRA, INDX, BINDX
	INTEGER, DIMENSION(:) ::  RPNTR, CPNTR, BPNTRB, BPNTRE
	REAL*8	  ALPHA, BETA
	REAL*8, DIMENSION(:) :: VAL
	REAL*8, DIMENSION(:, :) ::  B, C

	SUBROUTINE VBRMM_64(TRANSA, MB, [N], KB, ALPHA, DESCRA,
       *	   VAL, INDX, BINDX, RPNTR, CPNTR, BPNTRB, BPNTRE,
       *	   B, [LDB], BETA, C,[LDC], [WORK], [LWORK])
	INTEGER*8    TRANSA, MB, KB
	INTEGER*8, DIMENSION(:) ::  DESCRA, INDX, BINDX
	INTEGER*8, DIMENSION(:) ::  RPNTR, CPNTR, BPNTRB, BPNTRE
	REAL*8	  ALPHA, BETA
	REAL*8, DIMENSION(:) :: VAL
	REAL*8, DIMENSION(:, :) ::  B, C

   C INTERFACE
       #include <sunperf.h>

       void dvbrmm (const int transa, const int mb, const int n, const int kb,
		 const double alpha, const int* descra, const double* val,
		 const int* indx, const int* bindx, const int* rpntr, const
		 int* cpntr, const int* bpntrb, const int* bpntre, const dou‐
		 ble* b, const int ldb, const double beta, double* c, const
		 int ldc);

       void dvbrmm_64 (const long transa, const long mb, const long n, const
		 long kb, const double alpha, const long* descra, const dou‐
		 ble* val, const long* indx, const long* bindx, const long*
		 rpntr, const long* cpntr, const long* bpntrb, const long*
		 bpntre, const double* b, const long ldb, const double beta,
		 double* c, const long ldc);

DESCRIPTION
       dvbrmm performs one of the matrix-matrix operations

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

       where alpha and beta are scalars, C and B are dense matrices,
       A is a sparse M by K matrix represented in the variable block
       sparse row format and op( A )  is one  of

       op( A ) = A   or	  op( A ) = A'	 or   op( A ) = conjg( A' ).
					  ( ' indicates matrix transpose)
       The number of rows in A and  the number of columns in A are determined
       as follows

	      M=RPNTR(MB+1)-RPNTR(1),  K=CPNTR(KB+1)-CPNTR(1).

ARGUMENTS
       TRANSA(input)   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, integer 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,  scalar array VAL of length NNZ consists of the
		       block entries of A where each block entry is a dense
		       rectangular matrix stored column by column where NNZ
		       denotes the total number of point entries in all nonzero
		       block  entries of a matrix A. Unchanged on exit.

       INDX(input)     On entry, INDX is an integer array of length BNNZ+1 where BNNZ is
		       the number of block entries of the matrix A such that the
		       I-th element of INDX[] points to the location in VAL of
		       the (1,1) element of the I-th block entry. Unchanged on exit.

       BINDX(input)    On entry, BINDX is an  integer array of length BNNZ consisting
		       of the block column indices of the block entries of A where
		       BNNZ is the number block entries of the matrix A. Unchanged on
		       exit.

       RPNTR(input)    On entry, RPNTR is an integer array of length MB+1 such that
		       RPNTR(I)-RPNTR(1)+1 is the row index of the first point
		       row in the I-th block row. RPNTR(MB+1) is set to M+RPNTR(1)
		       where M is the number of rows in the matrix A.
		       Thus, the number of point rows in the I-th block row is
		       RPNTR(I+1)-RPNTR(I). Unchanged on exit.

       CPNTR(input)    On entry, CPNTR is an integer array of length KB+1 such that
		       CPNTR(J)-CPNTR(1)+1 is the column index of the first point
		       column in the J-th block column. CPNTR(KB+1) is set to
		       K+CPNTR(1) where K is the number of columns in the matrix A.
		       Thus, the number of point columns in the J-th block column
		       is CPNTR(J+1)-CPNTR(J). Unchanged on exit.

       BPNTRB(input)   On entry, BPNTRB is an integer array of length MB such that
		       BPNTRB(I)-BPNTRB(1)+1 points to location in BINDX of the
		       first block entry of the I-th block row of A.
		       Unchanged on exit.

       BPNTRE(input)   On entry, BPNTRE is an integer array of length MB such that
		       BPNTRE(I)-BPNTRB(1)points to location in BINDX of the
		       last block entry of the I-th block row of 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

       The routine is designed so that it provides a possibility to use just
       one sparse matrix representation of a general complex matrix A for com‐
       puting matrix-matrix multiply for another sparse matrix composed by
       block triangles and/or the main block diagonal of A. The full descrip‐
       tion of the feature for block entry formats is given in section
       NOTES/BUGS for the cbcomm manpage.

NOTES/BUGS
       1. For a general matrix (DESCRA(1)=0), array CPNTR can be different
       from RPNTR.  For all other matrix types,	 RPNTR must equal CPNTR and a
       single array can be passed for both arguments.

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

	SUBROUTINE SVBRMM( TRANSA, MB, N, KB, ALPHA, DESCRA,
       *	   VAL, INDX, BINDX, RPNTR, CPNTR, IA, IA(2),
       *	   B, LDB, BETA, C, LDC, WORK, LWORK )

3rd Berkeley Distribution	  6 Mar 2009			    dvbrmm(3P)
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