aerosandbox.modeling
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Subpackages#
Submodules#
Package Contents#
Classes#
A model that is fitted to data. Maps from R^N -> R^1. |
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A model that is interpolated to structured (i.e., gridded) N-dimensional data. Maps from R^N -> R^1. |
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A model that is interpolated to unstructured (i.e., point cloud) N-dimensional data. Maps from R^N -> R^1. |
Functions#
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Wraps a function as a black box, allowing it to be used in AeroSandbox / CasADi optimization problems. |
- class aerosandbox.modeling.FittedModel(model, x_data, y_data, parameter_guesses, parameter_bounds=None, residual_norm_type='L2', fit_type='best', weights=None, put_residuals_in_logspace=False, verbose=True)[source]#
Bases:
aerosandbox.modeling.surrogate_model.SurrogateModel
A model that is fitted to data. Maps from R^N -> R^1.
You can evaluate this model at a given point by calling it just like a function, e.g.:
>>> my_fitted_model = FittedModel(...) # See FittedModel.__init__ docstring for syntax >>> y = my_fitted_model(x)
- The input to the model (x in the example above) is of the type:
in the general N-dimensional case, a dictionary where: keys are variable names and values are float/array
in the case of a 1-dimensional input (R^1 -> R^1), a float/array.
If you’re not sure what the input type of my_fitted_model should be, just do:
>>> print(my_fitted_model) # Displays the valid input type to the model
The output of the model (y in the example above) is always a float or array.
See the docstring __init__ method of FittedModel for more details of how to instantiate and use FittedModel.
One might have expected a fitted model to be a literal Python function rather than a Python class - the benefit of having FittedModel as a class rather than a function is that you can easily save (pickle) classes including data (e.g. parameters, x_data, y_data), but you can’t do that with functions. And, because the FittedModel class has a __call__ method, you can basically still just think of it like a function.
- Parameters:
model (Callable[[Union[aerosandbox.numpy.ndarray, Dict[str, aerosandbox.numpy.ndarray]], Dict[str, float]], aerosandbox.numpy.ndarray]) –
x_data (Union[aerosandbox.numpy.ndarray, Dict[str, aerosandbox.numpy.ndarray]]) –
y_data (aerosandbox.numpy.ndarray) –
parameter_guesses (Dict[str, float]) –
parameter_bounds (Dict[str, tuple]) –
residual_norm_type (str) –
fit_type (str) –
weights (aerosandbox.numpy.ndarray) –
put_residuals_in_logspace (bool) –
- __call__(x)[source]#
Evaluates the surrogate model at some given input x.
- The input x is of the type:
in the general N-dimensional case, a dictionary where keys are variable names and values are float/array.
in the case of a 1-dimensional input (R^1 -> R^2), a float/array.
- goodness_of_fit(type='R^2')[source]#
Returns a metric of the goodness of the fit.
- Parameters:
type –
Type of metric to use for goodness of fit. One of:
”R^2”: The coefficient of determination. Strictly speaking only mathematically rigorous to use this
for linear fits.
”mean_absolute_error” or “mae” or “L1”: The mean absolute error of the fit.
”root_mean_squared_error” or “rms” or “L2”: The root mean squared error of the fit.
”max_absolute_error” or “Linf”: The maximum deviation of the fit from any of the data points.
Returns: The metric of the goodness of the fit.
- class aerosandbox.modeling.InterpolatedModel(x_data_coordinates, y_data_structured, method='bspline', fill_value=np.nan)[source]#
Bases:
aerosandbox.modeling.surrogate_model.SurrogateModel
A model that is interpolated to structured (i.e., gridded) N-dimensional data. Maps from R^N -> R^1.
You can evaluate this model at a given point by calling it just like a function, e.g.:
>>> y = my_interpolated_model(x)
- The input to the model (x in the example above) is of the type:
in the general N-dimensional case, a dictionary where: keys are variable names and values are float/array
in the case of a 1-dimensional input (R^1 -> R^1), it can optionally just be a float/array.
If you’re not sure what the input type of my_interpolated_model should be, just do:
>>> print(my_interpolated_model) # Displays the valid input type to the model
The output of the model (y in the example above) is always a float or array.
See the docstring __init__ method of InterpolatedModel for more details of how to instantiate and use InterpolatedModel.
One might have expected a interpolated model to be a literal Python function rather than a Python class - the benefit of having InterpolatedModel as a class rather than a function is that you can easily save (pickle) classes including data (e.g. parameters, x_data, y_data), but you can’t do that with functions. And, because the InterpolatedModel class has a __call__ method, you can basically still just think of it like a function.
- Parameters:
x_data_coordinates (Union[aerosandbox.numpy.ndarray, Dict[str, aerosandbox.numpy.ndarray]]) –
y_data_structured (aerosandbox.numpy.ndarray) –
method (str) –
- class aerosandbox.modeling.UnstructuredInterpolatedModel(x_data, y_data, x_data_resample=10, resampling_interpolator=interpolate.RBFInterpolator, resampling_interpolator_kwargs=None, fill_value=np.nan, interpolated_model_kwargs=None)[source]#
Bases:
aerosandbox.modeling.interpolation.InterpolatedModel
A model that is interpolated to unstructured (i.e., point cloud) N-dimensional data. Maps from R^N -> R^1.
You can evaluate this model at a given point by calling it just like a function, e.g.:
>>> y = my_interpolated_model(x)
- The input to the model (x in the example above) is of the type:
in the general N-dimensional case, a dictionary where: keys are variable names and values are float/array
in the case of a 1-dimensional input (R^1 -> R^1), it can optionally just be a float/array.
If you’re not sure what the input type of my_interpolated_model should be, just do:
>>> print(my_interpolated_model) # Displays the valid input type to the model
The output of the model (y in the example above) is always a float or array.
See the docstring __init__ method of InterpolatedModel for more details of how to instantiate and use UnstructuredInterpolatedModel.
- Parameters:
x_data (Union[aerosandbox.numpy.ndarray, Dict[str, aerosandbox.numpy.ndarray]]) –
y_data (aerosandbox.numpy.ndarray) –
x_data_resample (Union[int, Dict[str, Union[int, aerosandbox.numpy.ndarray]]]) –
resampling_interpolator (object) –
resampling_interpolator_kwargs (Dict[str, Any]) –
interpolated_model_kwargs (Dict[str, Any]) –
- aerosandbox.modeling.black_box(function, n_in=None, n_out=1, fd_method='central', fd_step=None, fd_step_iter=None)[source]#
Wraps a function as a black box, allowing it to be used in AeroSandbox / CasADi optimization problems.
Obtains gradients via finite differences. Assumes that the function’s Jacobian is fully dense, always.
- Parameters:
function (Callable[[Any], float]) –
n_in (int) –
n_out (int) –
fd_method (str) – One of: - ‘forward’ - ‘backward’ - ‘central’ - ‘smoothed’
fd_step (Optional[float]) –
fd_step_iter (Optional[bool]) –
- Return type:
Callable[[Any], float]
Returns: