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dellsm(3P)		    Sun Performance Library		    dellsm(3P)

NAME
       dellsm - Ellpack format triangular solve

SYNOPSIS
	SUBROUTINE DELLSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
       *	   VAL, INDX, LDA, MAXNZ,
       *	   B, LDB, BETA, C, LDC, WORK, LWORK)
	INTEGER	   TRANSA, M, N, UNITD, DESCRA(5), LDA, MAXNZ,
       *	   LDB, LDC, LWORK
	INTEGER	   INDX(LDA,MAXNZ)
	DOUBLE PRECISION ALPHA, BETA
	DOUBLE PRECISION DV(M), VAL(LDA,MAXNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

	SUBROUTINE DELLSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
       *	   VAL, INDX, LDA, MAXNZ,
       *	   B, LDB, BETA, C, LDC, WORK, LWORK)
	INTEGER*8  TRANSA, M, N, UNITD, DESCRA(5), LDA, MAXNZ,
       *	   LDB, LDC, LWORK
	INTEGER*8  INDX(LDA,MAXNZ)
	DOUBLE PRECISION ALPHA, BETA
	DOUBLE PRECISION DV(M), VAL(LDA,MAXNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

   F95 INTERFACE
	SUBROUTINE ELLSM( TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
       *    INDX, [LDA], MAXNZ, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
	INTEGER	   TRANSA, M,  MAXNZ
	INTEGER, DIMENSION(:) ::  DESCRA
	INTEGER, DIMENSION(:, :) ::    INDX
	DOUBLE PRECISION    ALPHA, BETA
	DOUBLE PRECISION, DIMENSION(:) ::  DV
	DOUBLE PRECISION, DIMENSION(:, :) ::  VAL, B, C

	SUBROUTINE ELLSM_64( TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL,
       *    INDX, [LDA], MAXNZ, B, [LDB], BETA, C, [LDC], [WORK], [LWORK])
	INTEGER*8    TRANSA, M,	 MAXNZ
	INTEGER*8, DIMENSION(:) ::  DESCRA
	INTEGER*8, DIMENSION(:, :) ::	 INDX
	DOUBLE PRECISION    ALPHA, BETA
	DOUBLE PRECISION, DIMENSION(:) ::  DV
	DOUBLE PRECISION, DIMENSION(:, :) ::  VAL, B, C

   C INTERFACE
       #include <sunperf.h>

       void dellsm (const int transa, const int m, const int n, const int
		 unitd, const double* dv, const double alpha, const int*
		 descra, const double* val, const int* indx, const int lda,
		 const int maxnz, const double* b, const int ldb, const double
		 beta, double* c, const int ldc);

       void dellsm_64 (const long transa, const long m, const long n, const
		 long unitd, const double* dv, const double alpha, const long*
		 descra, const double* val, const long* indx, const long lda,
		 const long maxnz, const double* b, const long ldb, const dou‐
		 ble beta, double* c, const long ldc);

DESCRIPTION
       dellsm 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 m by n dense matrices,
       D is a diagonal scaling matrix,	A is a sparse m by m unit, or non-unit,
       upper or lower triangular matrix represented in the ellpack/itpack 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)   On entry, 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.
		       Unchanged on exit.

       M(input)	       On entry,  M  specifies the number of 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,  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)
			 4 : Automatic row scaling (see section NOTES for
			      further details)
		       Unchanged on exit.

       DV(input)       On entry, DV is an array of length M consisting of the
		       diagonal entries of the diagonal scaling matrix D.
		       If UNITD is 4, DV contains diagonal matrix by which
		       the rows have been scaled (see section NOTES for further
		       details). Otherwise, 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-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 two-dimensional LDA-by-MAXNZ array
		       such that VAL(I,:) consists of non-zero elements
		       in row I of A, padded by zero values if the row
		       contains less than MAXNZ. If UNITD is 4, VAL contains
		       the scaled matrix  D*A  (see section NOTES for further
		       details). Otherwise, unchanged on exit.

       INDX(input)     On entry, INDX  is an integer two-dimensional
		       LDA-by-MAXNZ array such that INDX(I,:) consists
		       of the column indices of the nonzero elements
		       in row I, padded by the integer value I if the
		       number of nonzeros is less than MAXNZ.
		       The column indices MUST be sorted in increasing order
		       for each row. Unchanged on exit.

       LDA(input)      On entry,  LDA specifies the leading dimension of VAL
		       and INDX.  Unchanged on exit.

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

       B (input)       Array of DIMENSION ( LDB, N ).
		       On entry, 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 ).
		       On entry, the leading m 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 M.

		       For good performance, LWORK should generally be larger.
		       For optimum performance on multiple processors, LWORK
		       >=M*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 UNITD =4, the routine scales the rows of A such that their
       2-norms are one. The scaling may improve the accuracy of the computed
       solution. Corresponding entries of VAL are changed only in the particu‐
       lar case. On return DV matrix stored as a vector contains the diagonal
       matrix by which the rows have been scaled. UNITD=2 should be used for
       the next calls to the routine with overwritten VAL and DV.

       WORK(1)=0 on return if the scaling has been completed successfully,
       otherwise WORK(1) = - i where i is the row number which 2-norm is
       exactly zero.

       3. If DESCRA(3)=1 and  UNITD < 4, the diagonal entries are each used
       with the mathematical value 1. The entries of the main diagonal in the
       ELL representation of a sparse matrix do not need to be 1.0 in this
       usage. They are not used by the routine in these cases. But if UNITD=4,
       the unit diagonal elements MUST be referenced in the ELL representa‐
       tion.

       4. The routine is designed so that it checks 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 the sparse matrix repre‐
       sentation of a general matrix A for solving triangular systems with the
       upper or lower 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 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

	   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			    dellsm(3P)
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