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# pylint: disable=too-many-lines
"""The mathutils/function.py is a rocketpy module totally dedicated to function
operations, including interpolation, extrapolation, integration, differentiation
and more. This is a core class of our package, and should be maintained
carefully as it may impact all the rest of the project.
"""
import base64
import functools
import operator
import warnings
from bisect import bisect_left
from collections.abc import Iterable
from copy import deepcopy
from enum import Enum
from functools import cached_property
from inspect import signature
from pathlib import Path
import dill
import matplotlib.pyplot as plt
import numpy as np
from scipy import integrate, linalg, optimize
from scipy.interpolate import (
LinearNDInterpolator,
NearestNDInterpolator,
RBFInterpolator,
RegularGridInterpolator,
)
from rocketpy.plots.plot_helpers import show_or_save_plot
# Numpy 1.x compatibility,
# TODO: remove these lines when all dependencies support numpy>=2.0.0
if np.lib.NumpyVersion(np.__version__) >= "2.0.0b1":
# pylint: disable=no-name-in-module
from numpy import trapezoid # pragma: no cover
else:
from numpy import trapz as trapezoid # pragma: no cover
NUMERICAL_TYPES = (float, int, complex, np.integer, np.floating)
INTERPOLATION_TYPES = {
"linear": 0,
"polynomial": 1,
"akima": 2,
"spline": 3,
"shepard": 4,
"rbf": 5,
"regular_grid": 6,
}
EXTRAPOLATION_TYPES = {"zero": 0, "natural": 1, "constant": 2}
def deprecated(reason=None, version=None, alternative=None):
"""Decorator to mark functions or methods as deprecated.
This decorator issues a DeprecationWarning when the decorated function
is called, indicating that it will be removed in future versions.
"""
def decorator(func):
@functools.wraps(func)
def wrapper(*args, **kwargs):
if reason:
message = reason
else:
message = f"The function `{func.__name__}` is deprecated"
if version:
message += f" and will be removed in {version}"
if alternative:
message += f". Use `{alternative}` instead"
message += "."
warnings.warn(message, DeprecationWarning, stacklevel=2)
return func(*args, **kwargs)
return wrapper
return decorator
def to_hex_encode(obj, encoder=base64.b85encode):
"""Converts an object to hex representation using dill."""
return encoder(dill.dumps(obj)).hex()
def from_hex_decode(obj_bytes, decoder=base64.b85decode):
"""Converts an object from hex representation using dill."""
return dill.loads(decoder(bytes.fromhex(obj_bytes)))
class SourceType(Enum):
"""Enumeration of the source types for the Function class.
The source can be either a callable or an array.
"""
CALLABLE = 0
ARRAY = 1
class Function: # pylint: disable=too-many-public-methods
"""Class converts a python function or a data sequence into an object
which can be handled more naturally, enabling easy interpolation,
extrapolation, plotting and algebra.
"""
# Arithmetic priority
__array_ufunc__ = None
def __init__(
self,
source,
inputs=None,
outputs=None,
interpolation=None,
extrapolation=None,
title=None,
):
"""Convert source into a Function, to be used more naturally.
Set inputs, outputs, domain dimension, interpolation and extrapolation
method, and process the source.
Parameters
----------
source : callable, scalar, ndarray, string, or Function
The data source to be used for the function:
- ``Callable``: Called for evaluation with input values. Must have \
the desired inputs as arguments and return a single output \
value. Input order is important. Example: Python functions.
- ``int`` or ``float``: Treated as a constant value function.
- ``np.ndarray``: Used for interpolation. Format as [(x0, y0, z0), \
(x1, y1, z1), ..., (xn, yn, zn)], where 'x' and 'y' are inputs, \
and 'z' is the output.
- ``str``: Path to a CSV file. The file is read and converted into an \
ndarray. The file can optionally contain a single header line.
- ``Function``: Copies the source of the provided Function object, \
creating a new Function with adjusted inputs and outputs.
inputs : string, sequence of strings, optional
The name of the inputs of the function. Will be used for
representation and graphing (axis names). 'Scalar' is default.
If source is function, int or float and has multiple inputs,
this parameter must be given for correct operation.
outputs : string, sequence of strings, optional
The name of the outputs of the function. Will be used for
representation and graphing (axis names). Scalar is default.
interpolation : string, optional
Interpolation method to be used if source type is ndarray.
For 1-D functions, linear, polynomial, akima and spline are
supported. For N-D functions, linear, shepard, rbf and
regular_grid are supported.
Default for 1-D functions is spline and for N-D functions is
shepard.
extrapolation : string, optional
Extrapolation method to be used if source type is ndarray.
Options are 'natural', which keeps interpolation, 'constant',
which returns the value of the function at the nearest edge of
the domain, and 'zero', which returns zero for all points outside
of source range.
Multidimensional 'natural' extrapolation for 'linear' interpolation
use a 'rbf' algorithm for smoother results.
Default for 1-D functions is constant and for N-D functions
is natural.
title : string, optional
Title to be displayed in the plots' figures. If none, the title will
be constructed using the inputs and outputs arguments in the form
of "{inputs} x {outputs}".
Returns
-------
None
Notes
-----
(I) CSV files may include an optional single header line. If this
header line is present and contains names for each data column, those
names will be used to label the inputs and outputs unless specified
otherwise by the `inputs` and `outputs` arguments.
If the header is specified for only a few columns, it is ignored.
Commas in a header will be interpreted as a delimiter, which may cause
undesired input or output labeling. To avoid this, specify each input
and output name using the `inputs` and `outputs` arguments.
(II) Fields in CSV files may be enclosed in double quotes. If fields
are not quoted, double quotes should not appear inside them.
"""
# initialize parameters
self.source = source
self.__inputs__ = inputs
self.__outputs__ = outputs
self.__interpolation__ = interpolation
self.__extrapolation__ = extrapolation
self.title = title
self.__img_dim__ = 1 # always 1, here for backwards compatibility
self.__cropped_domain__ = (None, None) # the x interval if cropped
# args must be passed from self.
self.set_source(self.source)
self.set_inputs(self.__inputs__)
self.set_outputs(self.__outputs__)
self.set_title(self.title)
@classmethod
def from_regular_grid_csv(
cls, csv_source, variable_names, coeff_name, extrapolation
):
"""Create a regular-grid Function from CSV samples when possible.
Parameters
----------
csv_source : str
Path to the CSV file.
variable_names : list[str]
Ordered independent variable names present in the CSV.
coeff_name : str
Name of the output coefficient.
extrapolation : str
Extrapolation method passed to the Function constructor.
Returns
-------
Function or None
A ``Function`` configured with ``regular_grid`` interpolation when
the CSV forms a strict Cartesian grid, otherwise ``None``.
"""
try:
data = np.loadtxt(csv_source, delimiter=",", skiprows=1, dtype=np.float64)
except (OSError, ValueError):
return None
data = np.atleast_2d(data)
expected_columns = len(variable_names) + 1
if data.shape[1] != expected_columns:
return None
coordinates = data[:, :-1]
values = data[:, -1]
if np.unique(coordinates, axis=0).shape[0] != coordinates.shape[0]:
return None
axes = [np.unique(coordinates[:, i]) for i in range(len(variable_names))]
expected_size = int(np.prod([axis.size for axis in axes]))
if expected_size != coordinates.shape[0]:
return None
sorting_keys = [
coordinates[:, i] for i in range(len(variable_names) - 1, -1, -1)
]
sorted_indices = np.lexsort(tuple(sorting_keys))
sorted_coordinates = coordinates[sorted_indices]
sorted_values = values[sorted_indices]
expected_coordinates = np.column_stack(
[axis_values.ravel() for axis_values in np.meshgrid(*axes, indexing="ij")]
)
if not np.allclose(
sorted_coordinates, expected_coordinates, rtol=0, atol=1e-12
):
return None
grid_data = sorted_values.reshape(tuple(axis.size for axis in axes))
return cls(
(axes, grid_data),
inputs=variable_names,
outputs=[coeff_name],
interpolation="regular_grid",
extrapolation=extrapolation,
)
# Define all set methods
def set_inputs(self, inputs):
"""Set the name and number of the incoming arguments of the Function.
Parameters
----------
inputs : string, sequence of strings
The name of the parameters (inputs) of the Function.
Returns
-------
self : Function
"""
self.__inputs__ = self.__validate_inputs(inputs)
return self
def set_outputs(self, outputs):
"""Set the name and number of the output of the Function.
Parameters
----------
outputs : string, sequence of strings
The name of the output of the function. Example: Distance (m).
Returns
-------
self : Function
"""
self.__outputs__ = self.__validate_outputs(outputs)
return self
def set_source(self, source): # pylint: disable=too-many-statements
"""Sets the data source for the function, defining how the function
produces output from a given input.
Parameters
----------
source : callable, scalar, ndarray, string, or Function
The data source to be used for the function:
- ``Callable``: Called for evaluation with input values. Must have \
the desired inputs as arguments and return a single output \
value. Input order is important. Example: Python functions.
- ``int`` or ``float``: Treated as a constant value function.
- ``np.ndarray``: Used for interpolation. Format as [(x0, y0, z0), \
(x1, y1, z1), ..., (xn, yn, zn)], where 'x' and 'y' are inputs, \
and 'z' is the output.
- ``str``: Path to a CSV file. The file is read and converted into an \
ndarray. The file can optionally contain a single header line.
- ``Function``: Copies the source of the provided Function object, \
creating a new Function with adjusted inputs and outputs.
Notes
-----
(I) **CSV files may include an optional single header line**: \
If this header line is present and contains names for each data \
column, those names will be used to label the inputs and outputs \
unless specified otherwise. If the header is specified for only a \
few columns, it is ignored.
(II) **Commas in a header will be interpreted as a delimiter**: \
this may cause undesired input or output labeling. To avoid this, \
specify each input and output name using the `inputs` and `outputs` \
arguments.
(III) **Fields in CSV files may be enclosed in double quotes**: \
If fields are not quoted, double quotes should not appear inside them.
Returns
-------
self : Function
Returns the Function instance with the new source set.
"""
source = self.__validate_source(source)
# Handle callable source or number source
if callable(source):
self._source_type = SourceType.CALLABLE
self.get_value_opt = source
self.__interpolation__ = None
self.__extrapolation__ = None
# Set arguments name and domain dimensions
parameters = signature(source).parameters
self.__dom_dim__ = len(parameters)
if self.__inputs__ is None:
self.__inputs__ = list(parameters)
# Handle ndarray source
else:
self._source_type = SourceType.ARRAY
# Evaluate dimension
self.__dom_dim__ = source.shape[1] - 1
self._domain = source[:, :-1]
self._image = source[:, -1]
# set x and y. If Function is 2D, also set z
if self.__dom_dim__ == 1:
source = source[source[:, 0].argsort()]
self.x_array = source[:, 0]
self.x_initial, self.x_final = self.x_array[0], self.x_array[-1]
self.y_array = source[:, 1]
self.y_initial, self.y_final = self.y_array[0], self.y_array[-1]
self.get_value_opt = self.__get_value_opt_1d
elif self.__dom_dim__ > 1:
self.x_array = source[:, 0]
self.x_initial, self.x_final = self.x_array[0], self.x_array[-1]
self.y_array = source[:, 1]
self.y_initial, self.y_final = self.y_array[0], self.y_array[-1]
self.z_array = source[:, 2]
self.z_initial, self.z_final = self.z_array[0], self.z_array[-1]
self.get_value_opt = self.__get_value_opt_nd
self.source = source
self.set_interpolation(self.__interpolation__)
self.set_extrapolation(self.__extrapolation__)
return self
@cached_property
def min(self):
"""Get the minimum value of the Function y_array.
Raises an error if the Function is lambda based.
Returns
-------
minimum : float
"""
return self.y_array.min()
@cached_property
def max(self):
"""Get the maximum value of the Function y_array.
Raises an error if the Function is lambda based.
Returns
-------
maximum : float
"""
return self.y_array.max()
def set_interpolation(self, method="spline"):
"""Set interpolation method and process data is method requires.
Parameters
----------
method : string, optional
Interpolation method to be used if source type is ndarray.
For 1-D functions, linear, polynomial, akima and spline is
supported. For N-D functions, linear, shepard, rbf and
regular_grid are supported.
Default for 1-D functions is spline and for N-D functions is
shepard.
Returns
-------
self : Function
"""
if self._source_type is SourceType.ARRAY:
self.__interpolation__ = self.__validate_interpolation(method)
self.__update_interpolation_coefficients(self.__interpolation__)
self.__set_interpolation_func()
return self
def __update_interpolation_coefficients(self, method):
"""Update interpolation coefficients for the given method."""
# Spline, akima and polynomial need data processing
# Shepard, and linear do not
match method:
case "polynomial":
self.__interpolate_polynomial__()
self._coeffs = self.__polynomial_coefficients__
case "akima":
self.__interpolate_akima__()
self._coeffs = self.__akima_coefficients__
case "spline" | None:
self.__interpolate_spline__()
self._coeffs = self.__spline_coefficients__
case _:
self._coeffs = []
def set_extrapolation(self, method="constant"):
"""Set extrapolation behavior of data set.
Parameters
----------
extrapolation : string, optional
Extrapolation method to be used if source type is ndarray.
Options are 'natural', which keeps interpolation, 'constant',
which returns the value of the function at the nearest edge of
the domain, and 'zero', which returns zero for all points outside
of source range.
Multidimensional 'natural' extrapolation for 'linear' interpolation
use a 'rbf' algorithm for smoother results.
Default for 1-D functions is constant and for N-D functions
is natural.
Returns
-------
self : Function
The Function object.
"""
if self._source_type is SourceType.ARRAY:
self.__extrapolation__ = self.__validate_extrapolation(method)
self.__set_extrapolation_func()
return self
def __process_grid_source(self, source):
"""Validate and process a ``(axes, grid_data)`` tuple into a flat
scatter :class:`numpy.ndarray` ready for :meth:`set_source`.
As a side-effect, stores ``self._grid_axes`` and ``self._grid_data``
so that :meth:`__set_interpolation_func` (case 6) and
:meth:`__set_extrapolation_func` can build the
:class:`~scipy.interpolate.RegularGridInterpolator`.
Parameters
----------
source : tuple
A 2-element tuple ``(axes, grid_data)`` where *axes* is a list of
1-D arrays sorted in ascending order (one per input dimension) and
*grid_data* is a matching N-dimensional :class:`numpy.ndarray` of
values.
Returns
-------
flat_source : numpy.ndarray
Array of shape ``(n_points, n_dims + 1)`` with all grid points
unrolled in row-major (C) order.
Raises
------
ValueError
If *source* is not a 2-element tuple, if the number of axes
mismatches the grid dimensionality, or if an axis length mismatches
the corresponding grid dimension.
"""
if not (isinstance(source, Iterable) and len(source) == 2):
raise ValueError(
"For 'regular_grid' interpolation, source must be a "
"(axes, grid_data) tuple where axes is a list of 1-D arrays "
"and grid_data is a matching N-dimensional ndarray."
)
raw_axes, raw_data = source
if not isinstance(raw_axes, Iterable):
raise ValueError(
"The first element of the source tuple must be a list or tuple "
"of 1-D arrays representing the grid axes."
)
axes = [np.asarray(ax) for ax in raw_axes]
grid_data = np.asarray(raw_data, dtype=np.float64)
if len(axes) != grid_data.ndim:
raise ValueError(
f"Number of axes ({len(axes)}) must match grid_data dimensions "
f"({grid_data.ndim})."
)
for i, ax in enumerate(axes):
if len(ax) != grid_data.shape[i]:
raise ValueError(
f"Axis {i} has {len(ax)} points but grid dimension {i} has "
f"{grid_data.shape[i]} points."
)
if not np.all(np.diff(ax) > 0):
warnings.warn(
f"Axis {i} is not strictly sorted in ascending order. "
"RegularGridInterpolator requires sorted axes.",
UserWarning,
)
self._grid_axes = axes
self._grid_data = grid_data
mesh = np.meshgrid(*axes, indexing="ij")
domain_points = np.column_stack([m.ravel() for m in mesh])
return np.column_stack([domain_points, grid_data.ravel()])
def __set_interpolation_func(self): # pylint: disable=too-many-statements
"""Defines interpolation function used by the Function. Each
interpolation method has its own function`.
The function is stored in the attribute _interpolation_func."""
interpolation = INTERPOLATION_TYPES[self.__interpolation__]
match interpolation:
case 0: # linear
if self.__dom_dim__ == 1:
def linear_interpolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
x_interval = bisect_left(x_data, x)
x_left = x_data[x_interval - 1]
y_left = y_data[x_interval - 1]
dx = float(x_data[x_interval] - x_left)
dy = float(y_data[x_interval] - y_left)
return (x - x_left) * (dy / dx) + y_left
else:
interpolator = LinearNDInterpolator(self._domain, self._image)
def linear_interpolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
return interpolator(x)
self._interpolation_func = linear_interpolation
case 1: # polynomial
def polynomial_interpolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
return np.sum(coeffs * x ** np.arange(len(coeffs)))
self._interpolation_func = polynomial_interpolation
case 2: # akima
def akima_interpolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
x_interval = bisect_left(x_data, x)
x_interval = x_interval if x_interval != 0 else 1
a = coeffs[4 * x_interval - 4 : 4 * x_interval]
return a[3] * x**3 + a[2] * x**2 + a[1] * x + a[0]
self._interpolation_func = akima_interpolation
case 3: # spline
def spline_interpolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
x_interval = bisect_left(x_data, x)
x_interval = max(x_interval, 1)
a = coeffs[:, x_interval - 1]
x = x - x_data[x_interval - 1]
return a[3] * x**3 + a[2] * x**2 + a[1] * x + a[0]
self._interpolation_func = spline_interpolation
case 4: # shepard
# pylint: disable=unused-argument
def shepard_interpolation(x, x_min, x_max, x_data, y_data, _):
arg_qty, arg_dim = x.shape
result = np.empty(arg_qty)
x = x.reshape((arg_qty, 1, arg_dim))
sub_matrix = x_data - x
distances_squared = np.sum(sub_matrix**2, axis=2)
# Remove zero distances from further calculations
zero_distances = np.where(distances_squared == 0)
valid_indexes = np.ones(arg_qty, dtype=bool)
valid_indexes[zero_distances[0]] = False
weights = distances_squared[valid_indexes] ** (-1.5)
numerator_sum = np.sum(y_data * weights, axis=1)
denominator_sum = np.sum(weights, axis=1)
result[valid_indexes] = numerator_sum / denominator_sum
result[~valid_indexes] = y_data[zero_distances[1]]
return result
self._interpolation_func = shepard_interpolation
case 5: # RBF
interpolator = RBFInterpolator(self._domain, self._image, neighbors=100)
def rbf_interpolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
return interpolator(x)
self._interpolation_func = rbf_interpolation
case 6: # regular_grid (RegularGridInterpolator)
if not hasattr(self, "_grid_axes") or not hasattr(self, "_grid_data"):
raise AttributeError(
"The 'regular_grid' interpolation requires '_grid_axes' and "
"'_grid_data' to be set on the Function instance before calling "
"set_interpolation('regular_grid')."
)
grid_interpolator = RegularGridInterpolator(
self._grid_axes,
self._grid_data,
method="linear",
bounds_error=True,
)
# Store so extrapolation funcs can reuse it
self._grid_interpolator = grid_interpolator
def grid_interpolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
return grid_interpolator(x)
self._interpolation_func = grid_interpolation
case _:
raise ValueError(
f"Interpolation {interpolation} method not recognized."
)
def __set_extrapolation_func(self): # pylint: disable=too-many-statements
"""Defines extrapolation function used by the Function. Each
extrapolation method has its own function. The function is stored in
the attribute _extrapolation_func."""
interpolation = INTERPOLATION_TYPES[self.__interpolation__]
extrapolation = EXTRAPOLATION_TYPES[self.__extrapolation__]
match extrapolation:
case 0: # zero
def zero_extrapolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
return 0
self._extrapolation_func = zero_extrapolation
case 1: # natural
match interpolation:
case 0: # linear
if self.__dom_dim__ == 1:
def natural_extrapolation(
x, x_min, x_max, x_data, y_data, coeffs
): # pylint: disable=unused-argument
x_interval = 1 if x < x_min else -1
x_left = x_data[x_interval - 1]
y_left = y_data[x_interval - 1]
dx = float(x_data[x_interval] - x_left)
dy = float(y_data[x_interval] - y_left)
return (x - x_left) * (dy / dx) + y_left
else:
interpolator = RBFInterpolator(
self._domain, self._image, neighbors=100
)
def natural_extrapolation(
x, x_min, x_max, x_data, y_data, coeffs
): # pylint: disable=unused-argument
return interpolator(x)
case 1: # polynomial
def natural_extrapolation( # pylint: disable=function-redefined
x, x_min, x_max, x_data, y_data, coeffs
): # pylint: disable=unused-argument
return np.sum(coeffs * x ** np.arange(len(coeffs)))
case 2: # akima
def natural_extrapolation( # pylint: disable=function-redefined
x, x_min, x_max, x_data, y_data, coeffs
): # pylint: disable=unused-argument
a = coeffs[:4] if x < x_min else coeffs[-4:]
return a[3] * x**3 + a[2] * x**2 + a[1] * x + a[0]
case 3: # spline
def natural_extrapolation( # pylint: disable=function-redefined
x, x_min, x_max, x_data, y_data, coeffs
): # pylint: disable=unused-argument
if x < x_min:
a = coeffs[:, 0]
x_offset = x - x_data[0]
else:
a = coeffs[:, -1]
x_offset = x - x_data[-2]
return (
a[3] * x_offset**3
+ a[2] * x_offset**2
+ a[1] * x_offset
+ a[0]
)
case 4: # shepard
# pylint: disable=unused-argument,function-redefined
def natural_extrapolation(x, x_min, x_max, x_data, y_data, _):
arg_qty, arg_dim = x.shape
result = np.empty(arg_qty)
x = x.reshape((arg_qty, 1, arg_dim))
sub_matrix = x_data - x
distances_squared = np.sum(sub_matrix**2, axis=2)
# Remove zero distances from further calculations
zero_distances = np.where(distances_squared == 0)
valid_indexes = np.ones(arg_qty, dtype=bool)
valid_indexes[zero_distances[0]] = False
weights = distances_squared[valid_indexes] ** (-1.5)
numerator_sum = np.sum(y_data * weights, axis=1)
denominator_sum = np.sum(weights, axis=1)
result[valid_indexes] = numerator_sum / denominator_sum
result[~valid_indexes] = y_data[zero_distances[1]]
return result
case 5: # RBF
interpolator = RBFInterpolator(
self._domain, self._image, neighbors=100
)
def natural_extrapolation( # pylint: disable=function-redefined
x, x_min, x_max, x_data, y_data, coeffs
): # pylint: disable=unused-argument
return interpolator(x)
case 6: # regular_grid
grid_extrapolator = RegularGridInterpolator(
self._grid_axes,
self._grid_data,
method="linear",
bounds_error=False,
fill_value=None, # linear extrapolation beyond edges
)
def natural_extrapolation( # pylint: disable=function-redefined
x, x_min, x_max, x_data, y_data, coeffs
): # pylint: disable=unused-argument
return grid_extrapolator(x)
case _:
raise ValueError(
f"Natural extrapolation not defined for {interpolation}."
)
self._extrapolation_func = natural_extrapolation
case 2: # constant
if self.__dom_dim__ == 1:
def constant_extrapolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
return y_data[0] if x < x_min else y_data[-1]
elif self.__interpolation__ == "regular_grid":
grid_axes = self._grid_axes
grid_interpolator_const = self._grid_interpolator
def constant_extrapolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
# Clamp each coordinate to its axis bounds, then interpolate
x_clamped = np.copy(x)
for i, axis in enumerate(grid_axes):
x_clamped[:, i] = np.clip(
x_clamped[:, i], axis[0], axis[-1]
)
return grid_interpolator_const(x_clamped)
else:
extrapolator = NearestNDInterpolator(self._domain, self._image)
def constant_extrapolation(x, x_min, x_max, x_data, y_data, coeffs): # pylint: disable=unused-argument
return extrapolator(x)
self._extrapolation_func = constant_extrapolation
case _:
raise ValueError(
f"Extrapolation {extrapolation} method not recognized."
)
def set_get_value_opt(self):
"""Defines a method that evaluates interpolations.
Returns
-------
self : Function
"""
if self._source_type is SourceType.CALLABLE:
self.get_value_opt = self.source
elif self.__dom_dim__ == 1:
self.get_value_opt = self.__get_value_opt_1d
elif self.__dom_dim__ > 1:
self.get_value_opt = self.__get_value_opt_nd
return self
def __get_value_opt_1d(self, x):
"""Evaluate the Function at a single point x. This method is used
when the Function is 1-D.
Parameters
----------
x : scalar
Value where the Function is to be evaluated.
Returns
-------
y : scalar
Value of the Function at the specified point.
"""
# Retrieve general info
x_data = self.x_array
y_data = self.y_array
x_min, x_max = self.x_initial, self.x_final
coeffs = self._coeffs
if x_min <= x <= x_max:
y = self._interpolation_func(x, x_min, x_max, x_data, y_data, coeffs)
else:
y = self._extrapolation_func(x, x_min, x_max, x_data, y_data, coeffs)
return y
def __get_value_opt_nd(self, *args):
"""Evaluate the Function in a vectorized fashion for N-D domains.
Parameters
----------
args : tuple
Values where the Function is to be evaluated.
Returns
-------
result : scalar, ndarray
Value of the Function at the specified points.
"""
args = np.column_stack(args)
arg_qty = len(args)
result = np.empty(arg_qty)
min_domain = self._domain.T.min(axis=1)
max_domain = self._domain.T.max(axis=1)
lower, upper = args < min_domain, args > max_domain
extrap = np.logical_or(lower.any(axis=1), upper.any(axis=1))
if extrap.any():
result[extrap] = self._extrapolation_func(
args[extrap], min_domain, max_domain, self._domain, self._image, None
)
if (~extrap).any():
result[~extrap] = self._interpolation_func(
args[~extrap], min_domain, max_domain, self._domain, self._image, None
)
if arg_qty == 1:
return float(result[0])
return result
def __determine_1d_domain_bounds(self, lower, upper):
"""Determine domain bounds for 1-D function discretization.
Parameters
----------
lower : scalar, optional
Lower bound. If None, will use cropped domain or default.
upper : scalar, optional
Upper bound. If None, will use cropped domain or default.
Returns
-------
tuple
(lower_bound, upper_bound) for the domain.
"""
domain = [0, 10] # default boundaries
cropped = self.__cropped_domain__
if cropped[0] is not None and cropped[0] > domain[0]:
domain[0] = cropped[0]
if cropped[1] is not None and cropped[1] < domain[1]:
domain[1] = cropped[1]
# Input bounds have preference
domain[0] = lower if lower is not None else domain[0]
domain[1] = upper if upper is not None else domain[1]
return domain
def __determine_2d_domain_bounds(self, lower, upper, samples):
"""Determine domain bounds for 2-D function discretization.
Parameters
----------
lower : scalar or list, optional
Lower bounds. If None, will use cropped domain or default.
upper : scalar or list, optional
Upper bounds. If None, will use cropped domain or default.
samples : int or list
Number of samples for each dimension.
Returns
-------
tuple
(lower_bounds, upper_bounds, sample_counts) for the 2D domain.
"""
default_bounds = [[0, 10], [0, 10]]
# Apply cropped domain constraints if they exist
final_bounds = deepcopy(default_bounds)
if self.__cropped_domain__ is not None:
for dim in range(2):
cropped_limits = self.__cropped_domain__[dim]
if cropped_limits is not None:
# Use the more restrictive bounds (cropped domain takes precedence)
final_bounds[dim][0] = max(
default_bounds[dim][0], cropped_limits[0]
)
final_bounds[dim][1] = min(
default_bounds[dim][1], cropped_limits[1]
)
# Convert parameters to consistent list format
lower_bounds = self.__normalize_2d_parameter(
lower, [final_bounds[0][0], final_bounds[1][0]]
)
upper_bounds = self.__normalize_2d_parameter(
upper, [final_bounds[0][1], final_bounds[1][1]]
)
sample_counts = self.__normalize_2d_parameter(samples, samples)
return lower_bounds, upper_bounds, sample_counts
def __normalize_2d_parameter(self, param, default_values):
if param is None:
return (
default_values
if isinstance(default_values, list)
else [default_values, default_values]
)
if isinstance(param, NUMERICAL_TYPES):
return [param, param]
return param
def __discretize_1d_function(
self, func, lower, upper, samples, interpolation, extrapolation, one_by_one
):
lower, upper = self.__determine_1d_domain_bounds(lower, upper)
xs = np.linspace(lower, upper, samples)
ys = func.get_value(xs.tolist()) if one_by_one else func.get_value(xs)
func.__interpolation__ = interpolation
func.__extrapolation__ = extrapolation
func.set_source(np.column_stack((xs, ys)))
def __discretize_2d_function(self, func, lower, upper, samples):
lower, upper, sam = self.__determine_2d_domain_bounds(lower, upper, samples)
# Create nodes to evaluate function
xs = np.linspace(lower[0], upper[0], sam[0])
ys = np.linspace(lower[1], upper[1], sam[1])
xs, ys = np.array(np.meshgrid(xs, ys)).reshape(2, xs.size * ys.size)