trmv(3F)

NAME
     STRMV, DTRMV, CTRMV, ZTRMV - Multiplies a real or complex vector by a
     real or complex triangular matrix

SYNOPSIS
     Real

        CALL STRMV (uplo, trans, diag, n, a, lda, x, incx)

     Double precision

        CALL DTRMV (uplo, trans, diag, n, a, lda, x, incx)

     Complex

        CALL CTRMV (uplo, trans, diag, n, a, lda, x, incx)

     Double complex

        CALL ZTRMV (uplo, trans, diag, n, a, lda, x, incx)

DESCRIPTION
     STRMV and DTRMV multiply a real vector by a real triangular matrix.

     CTRMV and ZTRMV multiply a complex vector by a complex triangular
     matrix.

     These routines perform one of the following matrix-vector operations:

          x <- Ax

          x <- ATx

          x <- AHx (CTRMV, ZTRMV only)

     where AT is the transpose of A, AH is the conjugate transpose of A, x
     is an n-element vector, and A may be either a unit or nonunit n-by-n
     upper or lower triangular matrix.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the matrix is upper or lower triangular,
               as follows:

               uplo = 'U' or 'u':  A is an upper triangular matrix.
               uplo = 'L' or 'l':  A is a lower triangular matrix.

     trans     Character *1.  (input)
               Specifies the operation to be performed, as follows:

               trans = 'N' or 'n':  x <- Ax


               trans = 'T' or 't':  x <- ATx


               trans = 'C' or 'c':  x <- ATx (STRMV, DTRMV), or x <- AHx
               (CTRMV, ZTRMV)

     diag      Character *1.  (input)
               Specifies whether 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.

     n         Integer.  (input)
               Specifies the order of matrix A.  n >= 0.

     a         Array of dimension (lda,n).  (input)
               STRMV: Real array.
               DTRMV: Double precision array.
               CTRMV: Complex array.
               ZTRMV: Double complex array.

               Before entry with uplo = 'U' or 'u', the leading n-by-n
               upper triangular part of array a must contain the upper
               triangular matrix.  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 array a must contain the lower
               triangular matrix.  The strictly upper triangular part of a
               is not referenced.

               When diag = 'U' or 'u', these routines assume that all
               elements of array a that represent diagonal elements of
               matrix A are 1.  In this case, neither of these routines
               will reference any of the diagonal elements.

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the
               calling program.  lda must be at least MAX(1,n).

     x         Array of dimension 1+(n-1) * |incx|.  (input and output)
               STRMV: Real array.
               DTRMV: Double precision array.
               CTRMV: Complex array.
               ZTRMV: Double complex array.
               Contains the vector x.  On exit, the transformed vector
               overwrites array x.

     incx      Integer.  (input)
               Specifies the increment for the elements of x.  incx must
               not be 0.

NOTES
     These routines are Level 2 Basic Linear Algebra Subprograms (Level 2
     BLAS).

     When working backward (incx < 0), each routine starts at the end of
     the vector and moves backward, as follows:

          x(1-incx * (n-1)), x(1-incx * (n-2)), ..., x(1)