NAME

diasm, sdiasm, ddiasm, cdiasm, zdiasm - diagonal format triangular solve

SYNOPSIS

  SUBROUTINE SDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, LDA, IDIAG, NDIAG,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG,
 *           LDB, LDC, LWORK
  INTEGER*4  IDIAG(NDIAG)
  REAL*4     ALPHA, BETA
  REAL*4     DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)

  SUBROUTINE DDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, LDA, IDIAG, NDIAG,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG,
 *           LDB, LDC, LWORK
  INTEGER*4  IDIAG(NDIAG)
  REAL*8     ALPHA, BETA
  REAL*8     DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)

  SUBROUTINE CDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, LDA, IDIAG, NDIAG,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG,
 *           LDB, LDC, LWORK
  INTEGER*4  IDIAG(NDIAG)
  COMPLEX*8  ALPHA, BETA
  COMPLEX*8  DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)

  SUBROUTINE ZDIASM( TRANSA, M, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, LDA, IDIAG, NDIAG,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, M, N, UNITD, DESCRA(5), LDA, NDIAG,
 *           LDB, LDC, LWORK
  INTEGER*4  IDIAG(NDIAG)
  COMPLEX*16 ALPHA, BETA
  COMPLEX*16 DV(M), VAL(LDA,NDIAG), B(LDB,*), C(LDC,*), WORK(LWORK)

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 diagonal 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, only DESCRA(1)=3 is 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()         two-dimensional LDA-by-NDIAG array such that VAL(:,I)
               consists of non-zero elements on diagonal IDIAG(I)
               of A.  Diagonals in the lower triangular part of A
               are padded from the top, and those in the upper
               triangular part are padded from the bottom.

 LDA           leading dimension of VAL, must be .GE. MIN(M,K)

 IDIAG()       integer array of length NDIAG consisting of the
               corresponding diagonal offsets of the non-zero 
               diagonals of A in VAL.  Lower triangular diagonals 
               have negative offsets, the main diagonal has offset
               0, and upper triangular diagonals have positive offset. 
               Elements of IDIAG of MUST be sorted in  increasing order.

 NDIAG         number of non-zero diagonals in 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.
               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