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docs: update interface tutorial #211

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Dec 6, 2023
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docs: update interface tutorial #211

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33 changes: 25 additions & 8 deletions docs/src/interface.md
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Expand Up @@ -16,13 +16,18 @@ t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]

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.
We will use `CubicSpline` method for demonstration but the API is same for all the methods. We can also pass `extrapolate=true` keyword if we want to allow the interpolation to go beyond the range of the timepoints. The default value is `extrapolate=false`.

```@example interface
A = CubicSpline(u, t)
A1 = CubicSpline(u, t)

# For interpolation do, A(t)
A(100.0)
A1(100.0)

A2 = CubicSpline(u, t; extrapolate = true)

# Extrapolation
A2(300.0)
```

!!! note
Expand All @@ -33,31 +38,43 @@ A(100.0)

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.
We will continue with the above example, but the API is same for all the methods. If the interpolation is defined with `extrapolate=true`, derivatives can also be extrapolated.

```@example interface
# derivative(A, t)
DataInterpolations.derivative(A, 1.0)
DataInterpolations.derivative(A1, 1.0)

# Extrapolation
DataInterpolations.derivative(A2, 300.0)
```

## 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`.
!!! note

Integrals for `LagrangeInterpolation`, `BSplineInterpolation`, `BSplineApprox`, `Curvefit` will error as there are no simple analytical solutions available. Please use numerical methods for the same such as [Integrals.jl](https://docs.sciml.ai/Integrals/stable/).

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

```@example interface
# integral(A, t)
DataInterpolations.integral(A, 5.0)
DataInterpolations.integral(A1, 5.0)
```

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

```@example interface
# integral(A, t1, t2)
DataInterpolations.integral(A, 1.0, 5.0)
DataInterpolations.integral(A1, 1.0, 5.0)
```

Again, if the interpolation is defined with `extrapolate=true`, the integral can be computed beyond the range of the timepoints.

```@example interface
# integral(A, t1, t2)
DataInterpolations.integral(A2, 200.0, 300.0)
```

!!! note
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