splines

There are three functions in SMath for spline interpolation:

'''linterp'''('X-vector','Y-vector','x') - Returns a linearly interpolated value at x for data vectors X-vector and Y-vector of the same size.

'''cinterp'''('X-vector','Y-vector','x') - Returns a cubic spline interpolated value at x for data vectors X-vector and Y-vector of the same size.

'''ainterp'''('X-vector','Y-vector','x') - Returns Akima-spline interpolated value at x for data vectors X-vector and Y-vector of the same size.

Here is the example of presenting these functions:

[image|splines|{UP}splines/interp1.png|{UP}splines/interp1.png]

Notice how misleading all of these functions are outside the limits of the original datapoints, ie below x=1 and above x=5. Try and make sure that you only use these for interpolation, not extrapolation.

You can have the X-vector sorted in ascending order:

[image|X-vector ascending|{UP}splines/interp2.png|{UP}splines/interp2.png]

And also '''X-vector''' '''not sorted '''. As the main usage of the interpolation is to estimate y-value for the x-value not given in the table, this is '''not advisable''':

[image|X-vector not sorted|{UP}splines/interp3.png|{UP}splines/interp3.png]