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dcscsm(3P)		    Sun Performance Library		    dcscsm(3P)

NAME
       dcscsm - compressed sparse column format triangular solve

SYNOPSIS
	SUBROUTINE DCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
       *	   VAL, INDX, PNTRB, PNTRE,
       *	   B, LDB, BETA, C, LDC, WORK, LWORK)
	INTEGER	   TRANSA, M, N, UNITD, DESCRA(5),
       *	   LDB, LDC, LWORK
	INTEGER	   INDX(NNZ), PNTRB(M), PNTRE(M)
	DOUBLE PRECISION ALPHA, BETA
	DOUBLE PRECISION DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

	SUBROUTINE DCSCSM_64( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
       *	   VAL, INDX, PNTRB, PNTRE,
       *	   B, LDB, BETA, C, LDC, WORK, LWORK)
	INTEGER*8  TRANSA, M, N, UNITD, DESCRA(5),
       *	   LDB, LDC, LWORK
	INTEGER*8  INDX(NNZ), PNTRB(M), PNTRE(M)
	DOUBLE PRECISION ALPHA, BETA
	DOUBLE PRECISION DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

	where NNZ = PNTRE(M)-PNTRB(1)

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

	SUBROUTINE CSCSM_64(TRANSA, M, [N], UNITD, DV, ALPHA, DESCRA, VAL, INDX,
       *   PNTRB, PNTRE, B, [LDB], BETA, C, [LDC], [WORK], [LWORK] )
	INTEGER*8 TRANSA, M, UNITD
	INTEGER*8, DIMENSION(:) ::   DESCRA, INDX, PNTRB, PNTRE
	DOUBLE PRECISION    ALPHA, BETA
	DOUBLE PRECISION, DIMENSION(:) :: VAL, DV
	DOUBLE PRECISION, DIMENSION(:, :) ::  B, C

   C INTERFACE
       #include <sunperf.h>

       void dcscsm (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* pntrb,
		 const int* pntre, const double* b, const int ldb, const dou‐
		 ble beta, double* c, const int ldc);

       void dcscsm_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*
		 pntrb, const long* pntre, const double* b, const long ldb,
		 const double beta, double* c, const long ldc);

DESCRIPTION
       dcscsm 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 compressed sparse
       column 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, integer 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 column 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 columns of A 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 scalar array of length
		       NNZ = PNTRE(M)-PNTRB(1) consisting of nonzero
		       entries of A. If UNITD is 4, VAL contains
		       the scaled matrix  A*D  (see section NOTES for
		       further details). Otherwise, unchanged on exit.

       INDX(input)     On entry, INDX is an integer array of length
		       NNZ = PNTRE(M)-PNTRB(1) consisting of the row
		       indices of nonzero entries of A.
		       Row indices MUST be sorted in increasing order
		       for each column. Unchanged on exit.

       PNTRB(input)    On entry, PNTRB is an integer array of length M
		       such that PNTRB(J)-PNTRB(1)+1 points to location
		       in VAL of the first nonzero element in column J.
		       Unchanged on exit.

       PNTRE(input)    On entry, PNTRE is an integer array of length M
		       such that PNTRE(J)-PNTRB(1) points to location
		       in VAL of the last nonzero element in column J.
		       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 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

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 columns 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 columns have been scaled. UNITD=3 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)= - k where k is the column 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
       CSC 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 CSC 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

       5. It is known that there exists another representation of the com‐
       pressed sparse column format (see for example Y.Saad, "Iterative Meth‐
       ods 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 column	in the arrays VAL and INDX is used
       instead of two arrays PNTRB and PNTRE. To use the routine with this
       kind of sparse column format the following calling sequence should be
       used

	SUBROUTINE DCSCSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
       *	   VAL, INDX, IA, IA(2), B, LDB, BETA,
       *	   C, LDC, WORK, LWORK )

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