This is part of the HicEst documentation

INTPOL: Linear, Cubic, Inverse, Derivatives, Integral


HicEst numerical linear or cubic Akima interpolation of xy data. Roots, Find, 1st and 2nd derivative, integration.

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  ⇒cubic_akima_interpolation   ⇒extrapolation   ⇒first_derivative   ⇒interpolated_roots   ⇒linear_interpolation   ⇒numeric_integration   ⇒second_derivative   ⇒y_interpolated

Optional keywords:


(Syntax of optional keywords)
D2ydx DYdx ERror Find Init X2 XVector Xi YVector
keyword type mini sample keyword sequence is insignificant
XVector vec XV=year (

required

) a vector with N nodes of the independent variable in rising order
  • nodes may be unequally spaced
YVector arr YV=linear (

required

)
  • linear interpolation (XV and YV have same length):
    • REAL :: x_linear(N), y_linear(N)
  • cubic interpolation (YV has 4 times the elements of XV):
    • REAL x_cubic(N), y_cubic(4,N)
    • For x < node(2) or x > node(N-1): Interpolation is always linear. This means that is also linear.
    • the outermost 2 nodes determine the

      slope at boundaries

      (force boundary slopes by inserting extra nodes close to the first/last node)
    • the Akima polynomial coefficients are in y(N+1, ..., 4*N) after the 1st call with Init
Init --- Init (

required on 1st call to cubic interpolation

) to initialize the Akima coefficients
Xi num X=3.1 interpolate at Xi,

default is Xi=0

X2 num x2=3.9 integrate the interpolated data from Xi to X2
Find num find=y find x closest to Xi with interpolated value equal to y
DYdx --- dy 1st derivative of interpolated data at Xi
DYdx num dy=yprime find x closest to Xi with 1st derivative equal to yprime
D2ydx --- d2y 2nd derivative of interpolated data at Xi
D2ydy num d2y=y2prime find x closest to Xi with 2nd derivative equal to y2prime
ERror LBL ER=99 on error jump to ⇒ label 99



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