NAME

belsm, sbelsm, dbelsm, cbelsm, zbelsm - block Ellpack format triangular solve

SYNOPSIS

  SUBROUTINE SBELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, BINDX, BLDA, MAXBNZ, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB,
 *           LDB, LDC, LWORK
  INTEGER*4  BINDX(BLDA,MAXBNZ)
  REAL*4     ALPHA, BETA
  REAL*4     DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*),
 *           WORK(LWORK)

  SUBROUTINE DBELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, BINDX, BLDA, MAXBNZ, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB,
 *           LDB, LDC, LWORK
  INTEGER*4  BINDX(BLDA,MAXBNZ)
  REAL*8     ALPHA, BETA
  REAL*8     DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*),
 *           WORK(LWORK)

  SUBROUTINE CBELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, BINDX, BLDA, MAXBNZ, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK )
  INTEGER*4  TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB,
 *           LDB, LDC, LWORK
  INTEGER*4  BINDX(BLDA,MAXBNZ)
  COMPLEX*8  ALPHA, BETA
  COMPLEX*8  DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), B(LDB,*), C(LDC,*),
 *           WORK(LWORK)

  SUBROUTINE ZBELSM( TRANSA, MB, N, UNITD, DV, ALPHA, DESCRA,
 *           VAL, BINDX, BLDA, MAXBNZ, LB,
 *           B, LDB, BETA, C, LDC, WORK, LWORK)
  INTEGER*4  TRANSA, MB, N, UNITD, DESCRA(5), BLDA, MAXBNZ, LB,
 *           LDB, LDC, LWORK
  INTEGER*4  BINDX(BLDA,MAXBNZ)
  COMPLEX*16 ALPHA, BETA
  COMPLEX*16 DV(MB*LB*LB), VAL(LB*LB*BLDA*MAXBNZ), 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 block  diagonal matrix,  A is a unit, or non-unit, upper or 
 lower triangular matrix represented in block Ellpack 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)

 All blocks of A on the main diagonal MUST be triangular matrices.

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.

 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 the length MB*LB*LB consisting of the block 
               entries of block diagonal matrix D where each 
               block is stored in standard column-major form.

 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-identity blocks on the main diagonal
                 1 : identity diagonal block
               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*MAXBNZ containing 
               matrix entries, stored column-major within each dense 
               block.

 BINDX()       two-dimensional integer BLDA-by-MAXBNZ array such 
               BINDX(i,:) consists of the block column indices of the 
               nonzero blocks in block row i, padded by the integer 
               value i if the number of nonzero blocks is less than 
               MAXBNZ.  The block column indices MUST be sorted                 
               in increasing order for each block row.

 BLDA          leading dimension of BINDX(:,:).

 MAXBNZ        max number of nonzeros blocks per row.

 LB            row and column dimension of the 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.  
               On exit, if LWORK= -1, WORK(1) returns the minimum
               size of LWORK.


 LWORK         length of WORK array. LWORK should be at least
               MB*LB.


               For good performance, LWORK should generally be larger. 
               For optimum performance on multiple processors, LWORK 
               >=MB*LB*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