bdism

NAME

bdism, sbdism, dbdism - block diagonal format triangular solve

SYNOPSIS 

  SUBROUTINE SBDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, BLDA, IBDIAG, NBDIAG, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB,
 *           LDB, LDC, LWORK
  INTEGER*4  IBDIAG(NBDIAG)
  REAL*4     ALPHA, BETA
  REAL*4     DV(NDV), VAL(LB*LB*BLDA*NBDIAG), B(LDB,*), C(LDC,*),
 *           WORK(LWORK)
  SUBROUTINE DBDISM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, BLDA, IBDIAG, NBDIAG, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, MB, N, UNITD, DESCRA(5), BLDA, NBDIAG, LB,
 *           LDB, LDC, LWORK
  INTEGER*4  IBDIAG(NBDIAG)
  REAL*8     ALPHA, BETA
  REAL*8     DV(NDV), VAL(LB*LB*BLDA*NBDIAG), B(LDB,*), C(LDC,*),
 *           WORK(LWORK)

DESCRIPTION 

 C <- ALPHA inv(A) B + BETA C      C <- ALPHA inv(A') B + BETA C
 C <- ALPHA D inv(A) B + BETA C    C <- ALPHA D inv(A') B + BETA C
 C <- ALPHA inv(A) D B + BETA C    C <- ALPHA inv(A') D B + BETA C
                                    ( ' indicates matrix transpose)
 where D is a scaling block diagonal matrix

ARGUMENTS 

 TRANSA        Indicates how to operate with the sparse matrix
                 0 : operate with matrix
                 1 : operate with transpose matrix
 MB            Number of block rows in matrix A
 N             Number of columns in matrix C
 UNITD         Type of scaling:
                 1 : Identity matrix (argument DV[] is ignored)
                 2 : Scale on left (row scaling)
                 3 : Scale on right (column scaling)
 DV()          Array of length MB*LB*LB containing the elements of
               the diagonal blocks of the matrix D.  The size of each
               square block is LB*LB and each block contains matrix
               entries stored column-major within each dense diagonal
               block 
 ALPHA         Scalar parameter
 DESCRA()      Descriptor argument.  Five element integer array
               DESCRA(1) matrix structure
                 0 : General (NOT IMPLEMENTED)
                 1 : Symmetric            (NOT IMPLEMENTED)
                 2 : Hermitian            (NOT IMPLEMENTED)
                 3 : Triangular
                 4 : Skew(Anti)-Symmetric (NOT IMPLEMENTED)
                 5 : Diagonal             (NOT IMPLEMENTED)
               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*BLDA*NBDIAG containing 
               matrix entries, stored column-major within each dense 
               block.
 BLDA          Leading block dimension of VAL().  Should be greater
               than or equal to MB.
 IBDIAG()      Integer array of length NBDIAG consisting of the
               corresponding indices of the non-zero block
               diagonals of A in VAL().
 NBDIAG        The number of non-zero block diagonals in 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.  LWORK should be at least
               MB*LB*MIN(LB,N).  For good performance, LWORK should
               generally be larger.
 LWORK         Length of WORK array.
               If LWORK = -1, then a workspace query is assumed; the routine
               only calculates the optimal 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

NIST FORTRAN Sparse Blas User's Guide available at:

http://math.nist.gov/mcsd/Staff/KRemington/fspblas/

NOTES/BUGS

The NIST FORTRAN Sparse BLAS are currently at version 0.5. Some features (including the ones so noted) may not yet be implemented.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.