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dbelsm(3P)		    Sun Performance Library		    dbelsm(3P)

NAME
       dbelsm - block Ellpack format triangular solve

SYNOPSIS
	SUBROUTINE DBELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
       *	   VAL, BINDX, BLDA, MAXBNZ, LB,
       *	   B, LDB, BETA, C, LDC, WORK, LWORK)
	INTEGER	   TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB,
       *	   LDB, LDC, LWORK
	INTEGER	   BINDX(BLDA,MAXBNZ)
	DOUBLE PRECISION ALPHA, BETA
	DOUBLE PRECISION DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*),
       *	   WORK(LWORK)

	SUBROUTINE DBELSM_64( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
       *	   VAL, BINDX, BLDA, MAXBNZ, LB,
       *	   B, LDB, BETA, C, LDC, WORK, LWORK)
	INTEGER*8  TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB,
       *	   LDB, LDC, LWORK
	INTEGER*8  BINDX(BLDA,MAXBNZ)
	DOUBLE PRECISION ALPHA, BETA
	DOUBLE PRECISION DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*),
       *	   WORK(LWORK)

   F95 INTERFACE
	SUBROUTINE BELSM( TRANSA, MB, [N], UNITD, DV, ALPHA, DESCRA, VAL, BINDX,
       *   BLDA, MAXBNZ, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
	INTEGER	   TRANSA, MB, UNITD,  BLDA, MAXBNZ, LB
	INTEGER, DIMENSION(:) ::    DESCRA,  BINDX
	DOUBLE PRECISION    ALPHA, BETA
	DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
	DOUBLE PRECISION, DIMENSION(:, :) ::   B, C

	SUBROUTINE BELSM_64( TRANSA, MB, [N], UNITD, DV, ALPHA, DESCRA, VAL, BINDX,
       *   BLDA, MAXBNZ, LB, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
	INTEGER*8  TRANSA, MB, UNITD,  BLDA, MAXBNZ, LB
	INTEGER*8, DIMENSION(:) ::    DESCRA,  BINDX
	DOUBLE PRECISION    ALPHA, BETA
	DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
	DOUBLE PRECISION, DIMENSION(:, :) ::   B, C

   C INTERFACE
       #include <sunperf.h>

       void dbelsm (const int transa, const int mb, const int n, const int
		 unitd, const double* dv, const double alpha, const int*
		 descra, const double* val, const int* bindx, const int blda,
		 const int maxbnz, const int lb, const double* b, const int
		 ldb, const double beta, double* c, const int ldc);

       void dbelsm_64 (const long transa, const long mb, const long n, const
		 long unitd, const double* dv, const double alpha, const long*
		 descra, const double* val, const long* bindx, const long
		 blda, const long maxbnz, const long lb, const double* b,
		 const long ldb, const double beta, double* c, const long
		 ldc);

DESCRIPTION
       dbelsm performs one of the matrix-matrix operations

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

       where alpha and beta are scalars, C and B are mb*lb by n dense matrices,
       D is a block  diagonal matrix,  A is a sparse mb*lb by mb*lb unit, or
       non-unit, upper or lower triangular matrix represented in the block ellpack
       format and  op( A )  is one  of

	op( A ) = inv(A) or  op( A ) = inv(A')	or  op( A ) =inv(conjg( A' ))
	(inv denotes matrix inverse,  ' indicates matrix transpose)

ARGUMENTS
       TRANSA(input)   Integer TRANSA specifies the form of op( A ) to be
		       used in the sparse matrix inverse 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,  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.

       UNITD(input)    On entry, integer  UNITD specifies the type of scaling:
			 1 : Identity matrix (argument DV[] is ignored)
			 2 : Scale on left (row scaling)
			 3 : Scale on right (column scaling)
		       Unchanged on exit.

       DV(input)       On entry, DV is an array of length MB*LB*LB consisting
		       of the elements of the diagonal blocks of the matrix D.
		       The size of each square block is LB-by-LB and each
		       block is stored in standard column-major form.
		       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'))
		       Note: For the routine, DESCRA(1)=3 is only supported.

		       DESCRA(2) upper/lower triangular indicator
			 1 : lower
			 2 : upper
		       DESCRA(3) main diagonal type
			  0 : non-identity blocks on the main diagonal
			  1 : identity diagonal blocks
			  2 : diagonal blocks are dense matrices
		       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 two-dimensional LB*LB*BLDA-by-MAXBNZ
		       array consisting of the non-zero blocks, stored
		       column-major within each dense block. Unchanged on exit.

       BINDX(input)    On entry, BINDX is an integer two-dimensional BLDA-MAXBNZ
		       array such BINDX(i,:) consists of the block column indices
		       of the nonzero blocks in block row i, padded by the integer
		       value i if the number of nonzero blocks is less than MAXBNZ.
		       The block column indices MUST be sorted in increasing order
		       for each block row. Unchanged on exit.

       BLDA(input)     On entry, BLDA specifies the leading dimension of BINDX(:,:).
		       Unchanged on exit.

       MAXBNZ (input)  On entry, MAXBNZ specifies the max number of nonzeros
		       blocks per row. Unchanged on exit.

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

       B (input)       Array of DIMENSION ( LDB, N ).
		       On entry, 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 ).
		       On entry, the leading mb*lb by n part of the array C
		       must contain the matrix C. On exit, the array C is
		       overwritten.

       LDC (input)     On entry, LDC specifies the first dimension of C as declared
		       in the calling (sub) program. Unchanged on exit.

       WORK(workspace)	 Scratch array of length LWORK.
		       On exit, if LWORK= -1, WORK(1) returns the optimum  size
		       of LWORK.

       LWORK (input)   On entry, LWORK specifies the length of WORK array. LWORK
		       should be at least MB*LB.

		       For good performance, LWORK should generally be larger.
		       For optimum performance on multiple processors, LWORK
		       >=MB*LB*N_CPUS where N_CPUS is the maximum number of
		       processors available to the program.

		       If LWORK=0, the routine is to allocate workspace needed.

		       If LWORK = -1, then a workspace query is assumed; the
		       routine only calculates the optimum size of the WORK array,
		       returns this value as the first entry of the WORK array,
		       and no error message related to LWORK is issued by XERBLA.

SEE ALSO
       Libsunperf SPARSE BLAS is parallelized with the help of OPENMP and it is
       fully  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
       1. No test for singularity or near-singularity is included in this rou‐
       tine. Such tests must be performed before calling this routine.

       2. If DESCRA(3)=0, the lower or upper triangular part of each diagonal
       block is used by the routine depending on DESCRA(2).

       3. If DESCRA(3)=1 , the diagonal blocks in the block ellpack represen‐
       tation of A  don't need to be the identity matrices because these block
       entries are not used by the routine in this case.

       4. If DESCRA(3)=2, diagonal blocks are considered as dense matrices and
       the LU factorization with partial pivoting is used by the routine.

       WORK(1)=0 on return if the factorization for all diagonal blocks has
       been completed successfully, otherwise WORK(1) = - i where i is the
       block number for which the LU factorization could not be computed.

       5. The routine is designed so that it checks 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 the sparse matrix repre‐
       sentation of a general matrix A for solving triangular systems with the
       upper or lower block triangle of A.  But DESCRA(1) MUST be equal to 3
       even in this case.

       Assume that there is the sparse matrix representation a general 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

	   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

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