stpmv, dtpmv, ctpmv, ztpmv 

Matrix-vector product for a triangular matrix in packed form

FORMAT

  {S,D,C,Z}TPMV (uplo, trans, diag, n, ap, x, incx)

Arguments

  uplo                character*1
                      On entry, specifies whether the matrix A is an upper-
                      or lower-triangular matrix:

                      If uplo = 'U' or 'u', A is an upper-triangular matrix.

                      If uplo = 'L' or 'l', A is a lower-triangular matrix.
                      On exit, uplo is unchanged.

  trans               character*1
                      On entry, specifies the operation to be performed:

                      If trans = 'N' or 'n', the operation is x  =  Ax.

                      If trans = 'T' or 't', the operation is x  =
                      transp(A)*x.

                      If trans = 'C' or 'c', the operation is x  =
                      conjug_transp(A)*x.
                      On exit, trans is unchanged.

  diag                character*1
                      On entry, specifies whether the matrix A is unit-
                      triangular:

                      If diag = 'U' or 'u', A is a unit-triangular matrix.

                      If diag = 'N' or 'n', A is not a unit-triangular
                      matrix.
                      On exit, diag is unchanged.

  n                   integer*4
                      On entry, the order of the matrix A; n >= 0.
                      On exit, n is unchanged.

  ap                  real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array AP of length at least
                      n(n + 1)/2.

  If uplo specifies the upper triangular part of the matrix A, the array
  contains those elements of the matrix, packed sequentially, column by
  column, so that AP(1) contains a(11), AP(2) and AP(3) contain a(12) and
  a(22) respectively, and so on.

  If uplo specifies the lower triangular part to the matrix A, so that AP(1)
  contains a(11), AP(2) and AP(3) contain a(21) and a(31) respectively, and
  so on.

  If diag is equal to the diagonal elements of A are not referenced, but are
  assumed to be unity.

  On exit, ap is unchanged.

  x                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array X of length at least
                      (1+(n-1)*|incx|).  Array X contains the vector x.
                      On exit, x is overwritten with the transformed vector
                      x.

  incx                integer*4
                      On entry, the increment for the elements of X; incx
                      must not equal zero.
                      On exit, incx is unchanged.

Description

  The _TPMV subprograms compute a matrix-vector product for a triangular
  matrix stored in packed form or its transpose:
   x  =  Ax or x  =  transp(A)*x.  In addition to these operations, the CTPMV
  and ZTPMV subprograms compute a matrix-vector product for the conjugate
  transpose: x  =  conjug_transp(A)*x .

  x is a vector with n elements and A is an n by n, unit or non-unit, upper-
  or lower-triangular matrix, supplied in packed form.

Example

  REAL*4 AP(250), X(20)
  INCX = 1
  N = 20
  CALL STPMV('U','N','N',N,AP,X,INCX)

  This FORTRAN code computes the product x  =  Ax where A is an upper-
  triangular matrix of order 20, with non-unit diagonal, stored in packed
  form.