◆ pchse()

function pchse	(	n::Integer	,
		x::Array{Float64}	,
		f::Array{Float64}	,
		d::Array{Float64}	,
		incfd::Integer	= `1`
	)

Piecewise cubic spline interpolation ("not a knot" condition)

Purpose: pchse computes the derivatives needed to determine the Hermite representation of the cubic spline interpolant to given data, with with the default boundary conditions ("not a knot" condition).

The resulting piecewise cubic spline function may be evaluated by pchfe or pchfd.

Returns: info (Int32)
= 0: Successful exit
= -1: The argument n had an illegal value (n < 2)
= -2: The argument x is invalid (e.g. not strictly increasing)
= -3: The argument f is invalid
= -4: The argument d is invalid
= -5: The argument incfd had an illegal value (incfd < 1)

Parameters

[in]	n	Number of data points. (n >= 2)
[in]	x	1-dimensional array (Float64, n) Independent variable values. The elements of x[] must be strictly increasing.
[in]	f	1-dimensional array (Float64, incfd(n - 1) + 1) Dependent variable values to be interpolated. f[iincfd] is the value corresponding to x[i] (i = 0 to n - 1).
[out]	d	1-dimensional array (Float64, incfd(n - 1) + 1) Derivative values at the data points. These values will determine the cubic spline interpolant with the requested boundary conditions. The value corresponding to x[i] is stored in d[iincfd] (i = 0 to n - 1). No other entries in d are changed.
[in]	incfd	(Optional) Increment between successive values in f and d. This argument is provided primarily for 2-D applications. (incfd >= 1) (default = 1)

Reference: SLATEC (PCHIP) (Driver for pchsp)

Example Program

Compute ln(0.115) and ln(0.125) by interpolating the following natural logarithm table with cubic spline.

  x       ln(x)
------ ---------
 0.10   -2.3026
 0.11   -2.2073
 0.12   -2.1203
 0.13   -2.0402
------ ---------

function TestPchse()
    n = 4
    x = [ 0.1, 0.11, 0.12, 0.13 ]
    y = [ -2.3026, -2.2073, -2.1203, -2.0402 ]
    d = Vector{Cdouble}(undef, n)
    info = pchse(n, x, y, d)
    println(info)
    if info == 0
        ne = 2
        xe = [ 0.115, 0.125 ]
        ye = Vector{Cdouble}(undef, ne)
        info = pchfe(n, x, y, d, ne, xe, ye)
        println(ye)
        println(info)
    end
end

Example Results: > TestPchse()

0

[-2.1628499999999997, -2.079475]

0