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 here.
General procedure
The manner in which to use the tudat interpolators is similar to that of the various models for numerical propagation:
create settings for the interpolation (see Available types of interpolators);
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:
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from tudatpy.kernel.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 above examplee, 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 variablevalue: 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:
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 \(t_{i}\):
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from tudatpy.kernel.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 thelagrange_interpolation()only).