module PCHFE_95_m

  implicit none

contains

    ! PURPOSE  Evaluate a piecewise cubic Hermite function at an array of

    !            points.  May be used by itself for Hermite interpolation,

    !            or as an evaluator for PCHIM or PCHIC.

    ! CATEGORY  E3

    ! KEYWORDS  CUBIC HERMITE EVALUATION, HERMITE INTERPOLATION, PCHIP,

    !             PIECEWISE CUBIC EVALUATION

    !          PCHFE:  Piecewise Cubic Hermite Function Evaluator

    ! Evaluates the cubic Hermite function defined by  X, F, D  at

    ! the points  XE.

    use assert_eq_m, only: assert_eq

    REAL, intent(in):: X(:) ! real array of independent variable values

    ! The elements of X must be strictly increasing.

    REAL, intent(in):: F(:) ! real array of function values

    ! F(I) is the value corresponding to X(I).

    REAL, intent(in):: D(:) ! real array of derivative values

    ! D(I) is the value corresponding to X(I).

    LOGICAL, intent(inout):: SKIP

    ! request to skip checks for validity of "x"

    ! If "skip" is false then "pchfe" will check that size(x) >= 2 and

    ! "x" is in strictly ascending order.

    ! Setting "skip" to true will save time in case these checks have

    ! already been performed (say, in "PCHIM" or "PCHIC").

    ! "SKIP" will be set to TRUE on normal return.

    real, intent(in):: XE(:) ! points at which the function is to be evaluated

    ! NOTES:

    ! 1. The evaluation will be most efficient if the elements of XE

    ! are increasing relative to X.

    ! That is,   XE(J) .GE. X(I)

    ! implies    XE(K) .GE. X(I),  all K.GE.J

    ! 2. If any of the XE are outside the interval [X(1),X(N)], values

    ! are extrapolated from the nearest extreme cubic, and a warning

    ! error is returned.

    real, intent(out):: FE(:) ! values of the cubic Hermite function

    ! defined by X, F, D at the points XE

    integer, intent(out):: IERR ! error flag

    ! Normal return:

    ! IERR = 0  no error

    ! Warning error:

    ! IERR > 0  means that extrapolation was performed at IERR points

    ! "Recoverable" errors:

    !              IERR = -1  if N < 2

    !              IERR = -3  if the X-array is not strictly increasing

    !              IERR = -4  if NE < 1

    ! NOTE: The above errors are checked in the order listed, and

    ! following arguments have **NOT** been validated.

    ! Variables local to the procedure:

    INTEGER  N, NE

    !---------------------------------------

end module PCHFE_95_m