NAME

skysm, sskysm, dskysm, cskysm, zskysm - Skyline format triangular solve

SYNOPSIS

  SUBROUTINE SSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, PNTR,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, M, N, UNITD, DESCRA(5),
 *           LDB, LDC, LWORK
  INTEGER*4  PNTR(*),
  REAL*4     ALPHA, BETA
  REAL*4     DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

  SUBROUTINE DSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, PNTR,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, M, N, UNITD, DESCRA(5),
 *           LDB, LDC, LWORK
  INTEGER*4  PNTR(*),
  REAL*8     ALPHA, BETA
  REAL*8     DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

  SUBROUTINE CSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, PNTR,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, M, N, UNITD, DESCRA(5),
 *           LDB, LDC, LWORK
  INTEGER*4  PNTR(*),
  COMPLEX*8  ALPHA, BETA
  COMPLEX*8  DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)

  SUBROUTINE ZSKYSM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, PNTR,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, M, N, UNITD, DESCRA(5),
 *           LDB, LDC, LWORK
  INTEGER*4  PNTR(*),
  COMPLEX*16 ALPHA, BETA
  COMPLEX*16 DV(M), VAL(NNZ), B(LDB,*), C(LDC,*), WORK(LWORK)


  where NNZ = PNTR(M+1)-PNTR(1) (upper triangular)
        NNZ = PNTR(K+1)-PNTR(1) (lower triangular)
        PNTR() size = (M+1) (upper triangular)
        PNTR() size = (K+1) (lower triangular)

DESCRIPTION

   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 scalar, C and B are m by n dense matrices,
 D is a diagonal scaling matrix,  A is a unit, or non-unit, upper or 
 lower triangular matrix represented in skyline 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        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.

 M             Number of 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 M containing the diagonal entries of the
               scaling diagonal matrix D.

 ALPHA         Scalar parameter

 DESCRA()      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()         array contain the nonzeros of A in skyline profile form.
               Row-oriented if DESCRA(2) = 1 (lower triangular), 
               column oriented if DESCRA(2) = 2 (upper triangular).

 PNTR()        integer array of length M+1 (lower triangular) or
               K+1 (upper triangular) such that PNTR(I)-PNTR(1)+1
               points to the location in VAL of the first element of
               the skyline profile in row (column) I.

 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.
               On exit,  if LWORK = -1, WORK(1) returns the optimum LWORK.

 LWORK         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.

NOTES/BUGS

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

NAME

SYNOPSIS

DESCRIPTION

ARGUMENTS

SEE ALSO

NOTES/BUGS