Interface for using the Interpolations object

We will again use the same data as the previous tutorial to demonstrate how to use the Interpolations object for computing interpolated values at any time point, its derivatives and integrals.

using DataInterpolations

# Dependent variable
u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]

# Independent variable
t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]

6-element Vector{Float64}:
   0.0
  62.25
 109.66
 162.66
 205.8
 252.3

Interpolated values

All Interpolation methods return an object from which we can compute the value of the dependent variable at any time point.

We will use CubicSpline method for demonstration but the API is same for all the methods.

A = CubicSpline(u, t)

# For interpolation do, A(t)
A(100.0)

10.101397401671347

Derivatives

Derivatives of the interpolated curves can also be computed at any point for all the methods.

We will continue with the above example, but the API is same for all the methods.

# derivative(A, t)
DataInterpolations.derivative(A, 1.0)

-0.051048168999699245

Integrals

Integrals of the interpolated curves can also be computed easily.

Currently, this is implemented only for a few methods - ConstantInterpolation, LinearInterpolation, QuadraticInterpolation, QuadraticSpline and CubicSpline.

To compute the integrals from the start of time points provided during interpolation to any point, we can do:

# integral(A, t)
DataInterpolations.integral(A, 5.0)

72.86338611822583

If we want to compute integrals between two points, we can do:

# integral(A, t1, t2)
DataInterpolations.integral(A, 1.0, 5.0)

114.9694509973317