Interpolators

Tudat contains a number of interpolators for discrete data sets. The input to an interpolator is a set of combinations of independent variables \(t_{i}\), and state variables \(\mathbf{x}_{i}\), where \(\mathbf{x}\) may be a scalar, vector or matrix. A data sets that is often interpolated using tudat is the the state history, as generated from the propagation of dynamics (see Single-arc Variational Equations Propagation). The general operation of an interpolator is to take a set of combinations \([t_{i},\mathbf{x}_{i}]\) and turn this into a continuous function \(\mathbf{x}(t)\).

See also

The full API documentation for interpolators can be found here.

General procedure

The manner in which to use the tudat interpolators is similar to that of the various models for numerical propagation:

1. create settings for the interpolation (see Available types of interpolators);

2. create interpolator based on the settings and the data that is to be interpolated.

An example, for the case of a linear interpolator, is shown below:

Python

Required

from tudatpy.math import interpolators

# Generate data to interpolate
data_to_interpolate = dict( )
data_to_interpolate = ...

# Create settings for interpolation
linear_interpolation_settings = interpolators.linear_interpolation( )

# Create interpolator
interpolator = interpolators.create_one_dimensional_scalar_interpolator( data_to_interpolate, linear_interpolation_settings )

# Interpolate data set in data_to_interpolate at t=100
independent_variable = 100
interpolated_value = interpolator.interpolate( independent_variable )

In the example above, the linear scheme is used to interpolate the data_to_interpolate data set at \(t=100\) (where typically, but not necessarily, the independent variable in interpolation will represent time, in the context of Tudat).

The data that is to be interpolated must be provided as a dict (in Python) or a std::map (in C++):

• key: independent variable

• value: dependent variable to be interpolated

Based on the type of independent variable, different functions to create the interpolator are available:

• scalar interpolator (see the create_one_dimensional_scalar_interpolator() function, as in the example above)

• vector interpolator (see the create_one_dimensional_vector_interpolator() function)

• matrix interpolator (see the create_one_dimensional_matrix_interpolator() function)

Available types of interpolators

Tudat includes the following interpolators for a data set with a single independent variable:

• piecewise_constant_interpolation()

• linear_interpolation()

• cubic_spline_interpolation()

• hermite_spline_interpolation()

• lagrange_interpolation()

To use the Hermite spline interpolator, the user must provide not only the states \(\mathbf{x}_{i}\) and the state derivatives \(d\mathbf{x}_{i}/dt\) at the independent variable values \(t_{i}\):

Python

Required

from tudatpy.math import interpolators

# Generate data to interpolate
data_to_interpolate = dict( )
data_derivatives = dict( )
data_to_interpolate = ...
data_derivatives = ...

# Create settings for Hermite spline interpolation
linear_interpolation_settings = interpolators.hermite_interpolation( )

# Create interpolator
interpolator = interpolators.create_one_dimensional_scalar_interpolator( data_to_interpolate, linear_interpolation_settings, data_derivatives )

# Interpolate data set in data_to_interpolate at t=100
independent_variable = 100
interpolated_value = interpolator.interpolate( independent_variable )

Additional settings

To create interpolator settings, there are a number of additional settings that a user may want to modify (these have default values in the factory functions for the interpolator settings), related to:

• the look-up scheme, through the enum AvailableLookupScheme;

• the behaviour beyond the boundaries of the domain, through the enum BoundaryInterpolationType;

• the behaviour close to the boundaries of the domain, through the enum LagrangeInterpolatorBoundaryHandling (for the lagrange_interpolation() only).