Function Repository Resource:

CubicSplineInterpolation

Source Notebook

Interpolate data with a cubic spline

Contributed by: Jan Mangaldan

ResourceFunction["CubicSplineInterpolation"][{f₁,f₂,…}]

constructs a cubic spline interpolation of the function values f_i, assumed to correspond to x values 1, 2, ….

ResourceFunction["CubicSplineInterpolation"][{{x₁,f₁},{x₂,f₂},…}]

constructs a cubic spline interpolation of the function values f_i corresponding to x values x_i.

ResourceFunction["CubicSplineInterpolation"][data,cond]

uses conditions for the left and right endpoints specified by cond.

Details

ResourceFunction["CubicSplineInterpolation"] returns an InterpolatingFunction object, which can be used like any other pure function.

The interpolation function returned by ResourceFunction["CubicSplineInterpolation"][data] is set up so as to agree with data at every point explicitly specified in data.

ResourceFunction["CubicSplineInterpolation"] yields an interpolant with continuous first and second derivatives.

The function values f_i are expected to be real or complex numbers.

The function arguments x_i must be real numbers.

ResourceFunction["CubicSplineInterpolation"][data] generates an InterpolatingFunction object that returns values with the same precision as those in data.

The following endpoint conditions can be specified for cond:

"NotAKnot"

not-a-knot end condition

"Natural"

natural end condition (zero second derivative)

"Clamped"

set derivative at endpoint equal to the derivative of the polynomial passing through first (or last) four points

{"Clamped",d}

set derivative at endpoint equal to d

{"Clamped",InterpolationOrder→m}

set derivative at endpoint equal to the derivative of the polynomial passing through first (or last) m+1 points

"Second"

set second derivative at endpoint equal to 0

{"Second",d}

set second derivative at endpoint equal to d

{"Second",InterpolationOrder→m}

set second derivative at endpoint equal to the second derivative of the polynomial passing through first (or last) m+1 points

"Periodic"

periodic

ResourceFunction["CubicSplineInterpolation"][data] is equivalent to ResourceFunction["CubicSplineInterpolation"][data,"Periodic"] if the left and right endpoints of data have the same ordinate, and ResourceFunction["CubicSplineInterpolation"][data,"NotAKnot"] otherwise.

ResourceFunction["CubicSplineInterpolation"][data,{cond₁,cond₂}] uses cond₁ for the left endpoint condition and cond₂ for the right endpoint condition.