dtrmv

DTRMV(l)                         BLAS routine                         DTRMV(l)



NAME
       DTRMV - perform one of the matrix-vector operations   x := A*x, or x :=
       A'*x,

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

           INTEGER      INCX, LDA, N

           CHARACTER*1  DIAG, TRANS, UPLO

           DOUBLE       PRECISION A( LDA, * ), X( * )

PURPOSE
       DTRMV  performs one of the matrix-vector operations

       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
              follows:

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

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

              TRANS = 'C' or 'c'   x := 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      - DOUBLE PRECISION 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
              referenced.  Before entry with UPLO = 'L' or 'l', the leading n
              by n lower triangular part of the array A must contain the lower
              triangular 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      - DOUBLE PRECISION 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
              overwritten 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                       DTRMV(l)