tpmv(3F)

NAME
     STPMV, DTPMV, CTPMV, ZTPMV - Multiplies a real or complex vector by a
     real or complex triangular packed matrix

SYNOPSIS
     Real

        CALL STPMV (uplo, trans, diag, n, ap, x, incx)

     Double precision

        CALL DTPMV (uplo, trans, diag, n, ap, x, incx)

     Complex

        CALL CTPMV (uplo, trans, diag, n, ap, x, incx)

     Double complex

        CALL ZTPMV (uplo, trans, diag, n, ap, x, incx)

IMPLEMENTATION
     IRIX systems

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

          x <- Ax
                T
          x <- A x
                H
          x <- A x (CTPMV, ZTPMV only)
            T                         H
     where A  is the transpose of A, A  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 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.

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

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

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

                                          T                            H
               trans = 'C' or 'c':  x <- A x  (STPMV, DTPMV), or x <- A x
               (CTPMV, ZTPMV)

     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.

     ap        Array of dimension (n(n+1))/2.  (input)
               STPMV: Real array.
               DTPMV: Double precision array.
               CTPMV: Complex array.
               ZTPMV: Double complex array.

               Before entry with uplo = 'U' or 'u', array ap must contain
               the upper triangular matrix packed sequentially,
               column-by-column, so that ap(1) contains A(1,1), ap(2)
               contains A(1,2), ap(3) contains A(2,2), and so on.

               Before entry with uplo = 'L' or 'l', array ap must contain
               the lower triangular matrix packed sequentially,
               column-by-column, so that ap(1) contains A(1,1), ap(2)
               contains A(2,1), ap(3) contains A(3,1), and so on.

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

     x         Array of dimension 1+(n-1) * |incx|.  (input and output)
               STPMV: Real array.
               DTPMV: Double precision array.
               CTPMV: Complex array.
               ZTPMV: 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)

SEE ALSO
     This man page is available only online.