ZTRMV(3)        BLAS routine of NEC Numeric Library Collection        ZTRMV(3)



NAME
       ZTRMV  -  perform  one  of the matrix-vector operations  x := A*x, x :=
       A'*x, x := conjg( A' )*x,

SYNOPSIS
       SUBROUTINE ZTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )

           INTEGER      INCX, LDA, N

           CHARACTER*1  DIAG, TRANS, UPLO

           COMPLEX*16   A( LDA, * ), X( * )

PURPOSE
       ZTRMV  performs one of the matrix-vector operations
          x := A*x
       or
          x := A'*x
       or
          x := conjg( A' )*x
       where x is an n element vector and  A is an n by n unit,  or  non-unit,
       upper or lower triangular matrix.


PARAMETERS
       UPLO   - CHARACTER*1.
              On entry, UPLO specifies whether the matrix is an upper or lower
              triangular matrix as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

              Unchanged on exit.

       TRANS  - CHARACTER*1.
              On entry, TRANS specifies the operation to be performed as  fol-
              lows:

              TRANS = 'N' or 'n'   x := A*x.

              TRANS = 'T' or 't'   x := A'*x.

              TRANS = 'C' or 'c'   x := conjg( A' )*x.

              Unchanged on exit.

       DIAG   - CHARACTER*1.
              On  entry, DIAG specifies whether or not A is unit triangular as
              follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit triangular.

              Unchanged on exit.

       N      - INTEGER.
              On entry, N specifies the order of the matrix A.  N must  be  at
              least zero.  Unchanged on exit.

       A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
              Before  entry  with  UPLO = 'U' or 'u', the leading n by n upper
              triangular part of the array A must contain the upper triangular
              matrix and the strictly lower triangular part of A is not refer-
              enced.  Before entry with UPLO = 'L' or 'l', the leading n by  n
              lower triangular part of the array A must contain the lower tri-
              angular matrix and the strictly upper triangular part  of  A  is
              not referenced.  Note that when  DIAG = 'U' or 'u', the diagonal
              elements of A are not referenced either, but are assumed  to  be
              unity.  Unchanged on exit.

       LDA    - INTEGER.
              On  entry, LDA specifies the first dimension of A as declared in
              the calling (sub) program. LDA must be at least  max(  1,  n  ).
              Unchanged on exit.

       X      - COMPLEX*16       array of dimension at least
              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
              array X must contain the n element vector x. On exit, X is over-
              written with the tranformed vector x.

       INCX   - INTEGER.
              On  entry,  INCX  specifies the increment for the elements of X.
              INCX must not be zero.  Unchanged on exit.

              Level 2 Blas routine.

              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
              Central Office.  Richard Hanson, Sandia National Labs.



BLAS routine                    16 October 1992                       ZTRMV(3)