dchfcm Function

private function dchfcm(d1, d2, delta) result(ismon)

Check a single cubic for monotonicity

Called by dpchcm to determine the monotonicity properties of the cubic with boundary derivative values D1,D2 and chord slope DELTA.

Cautions

This is essentially the same as old DCHFMC, except that a new output value, -3, was added February 1989. (Formerly, -3 and +3 were lumped together in the single value 3.) Codes that flag nonmonotonicity by "IF (ISMON==2)" need not be changed. Codes that check via "IF (ISMON>=3)" should change the test to "IF (IABS(ISMON)>=3)". Codes that declare monotonicity via "IF (ISMON<=1)" should change to "IF (IABS(ISMON)<=1)".

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: d1

derivative value at the end of an interval.
real(kind=wp), intent(in) :: d2

derivative value at the end of an interval.
real(kind=wp), intent(in) :: delta

the data slope over that interval

Return Value integer

indicates the monotonicity of the cubic segment:

  • ISMON = -3 if function is probably decreasing
  • ISMON = -1 if function is strictly decreasing
  • ISMON = 0 if function is constant
  • ISMON = 1 if function is strictly increasing
  • ISMON = 2 if function is non-monotonic
  • ISMON = 3 if function is probably increasing

If ABS(ISMON)=3, the derivative values are too close to the boundary of the monotonicity region to declare monotonicity in the presence of roundoff error.


Called by

proc~~dchfcm~~CalledByGraph proc~dchfcm pchip_module::dchfcm proc~dpchcm pchip_module::dpchcm proc~dpchcm->proc~dchfcm

Source Code

    function dchfcm (d1, d2, delta) result(ismon)

    real(wp),intent(in) :: d1    !! derivative value at the end of an interval.
    real(wp),intent(in) :: d2    !! derivative value at the end of an interval.
    real(wp),intent(in) :: delta !! the data slope over that interval
    integer :: ismon        !! indicates the monotonicity of the cubic segment:
                            !!
                            !!  * ISMON = -3  if function is probably decreasing
                            !!  * ISMON = -1  if function is strictly decreasing
                            !!  * ISMON =  0  if function is constant
                            !!  * ISMON =  1  if function is strictly increasing
                            !!  * ISMON =  2  if function is non-monotonic
                            !!  * ISMON =  3  if function is probably increasing
                            !!
                            !! If ABS(ISMON)=3, the derivative values are too close to the
                            !! boundary of the monotonicity region to declare monotonicity
                            !! in the presence of roundoff error.

    integer :: itrue
    real(wp) :: a, b, phi

    real(wp),parameter :: eps = ten*d1mach4 !! machine-dependent parameter -- should be about 10*uround.
                                            !! TEN is actually a tuning parameter, which determines the
                                            !! width of the fuzz around the elliptical boundary.

    if (delta == zero) then
        ! case of constant data.
        if ((d1==zero) .and. (d2==zero)) then
            ismon = 0
        else
            ismon = 2
        endif
    else
        ! data is not constant -- pick up sign.
        itrue = int(sign (one, delta))
        a = d1/delta
        b = d2/delta
        if ((a<zero) .or. (b<zero)) then
            ismon = 2
        else if ((a<=three-eps) .and. (b<=three-eps)) then
            ! inside square (0,3)x(0,3) implies ok.
            ismon = itrue
        else if ((a>four+eps) .and. (b>four+eps)) then
            ! outside square (0,4)x(0,4) implies nonmonotonic.
            ismon = 2
        else
            ! must check against boundary of ellipse.
            a = a - two
            b = b - two
            phi = ((a*a + b*b) + a*b) - three
            if (phi < -eps) then
                ismon = itrue
            else if (phi > eps) then
                ismon = 2
            else
                ! to close to boundary to tell,
                ! in the presence of round-off errors.
                ismon = 3*itrue
            endif
        endif
    endif

    end function dchfcm