integration.py

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r"""
Contains functionality for integrating discretized funtions.
\author Bertram Richter
\date 2023
"""
 
import numpy as np
import scipy.integrate
 
from . import base
 
class Integrator(base.Task):
    r"""
    Object to integrate a function \f$y = f(x)\f$ given by discrete argument data \f$x\f$ and associated values \f$y\f$.
    """
    def __init__(self,
                interpolation: str = "trapezoidal",
            *args, **kwargs):
        r"""
        Constructs an Integrator object.
        \param interpolation \copybrief interpolation For more, see \ref interpolation.
        \param *args Additional positional arguments, will be passed to the superconstructor.
        \param **kwargs Additional keyword arguments, will be passed to the superconstructor.
        """
        super().__init__(*args, **kwargs)
        
        self.interpolation = interpolation
    def antiderivative(self,
            x_values: np.array,
            y_values: np.array,
            initial: float = 0.0,
            interpolation: str = None,
            *args, **kwargs) -> np.array:
        r"""
        Calculates the antiderivative \f$F(x) = \int f(x) dx + C\f$ to the given function over the given segment (indicated by `start_index` and `end_index`).
        The given values are assumed to be preprocessed (`NaN`s are stripped already).
        \param x_values List of x-positions \f$x\f$.
        \param y_values List of y-values \f$y\f$ matching \f$x\f$.
        \param initial The interpolation constant \f$C\f$.
        \param interpolation \copybrief interpolation Defaults to \ref interpolation. For more, see \ref interpolation.
        \param *args Additional positional arguments, will be passed to the called integration function.
        \param **kwargs Additional keyword arguments, will be passed to the called integration function.
        """
        interpolation = interpolation if interpolation is not None else self.interpolation
        # Prepare the segments
        if interpolation == "trapezoidal":
            return scipy.integrate.cumulative_trapezoid(y=y_values, x=x_values, initial=initial, *args, **kwargs)
        else:
            raise RuntimeError("No such option '{}' known for `interpolation`.".format(interpolation))
    def integrate_segment(self,
            x_values: np.array,
            y_values: np.array,
            start_index: int = None,
            end_index: int = None,
            initial: float = 0.0,
            interpolation: str = None,
            *args, **kwargs) -> float:
        r"""
        Calculates integral over the given segment (indicated by `start_index` and `end_index`) \f$F(x)|_{a}^{b} = \int_{a}^{b} f(x) dx + C\f$.
        The given values are assumed to be preprocessed (`NaN`s are stripped already).
        \param x_values List of x-positions \f$x\f$.
        \param y_values List of y-values \f$y\f$ matching \f$x\f$.
        \param start_index Index, where the integration should start (index of \f$a\f$). Defaults to the first item of `x_values` (`0`).
        \param end_index Index, where the integration should stop (index of \f$b\f$). This index is included. Defaults to the first item of `x_values` (`len(x_values) -1`).
        \param initial The interpolation constant \f$C\f$.
        \param interpolation \copybrief interpolation For more, see \ref interpolation.
        \param *args Additional positional arguments, will be passed to the called integration function.
        \param **kwargs Additional keyword arguments, will be passed to the called integration function.
        """
        interpolation = interpolation if interpolation is not None else self.interpolation
        start_index = start_index if start_index is not None else 0
        end_index = end_index if end_index is not None else len(x_values) - 1
        x_segment = x_values[start_index:end_index+1]
        y_segment = y_values[start_index:end_index+1]
        # Prepare the segments
        if interpolation == "trapezoidal":
            return scipy.integrate.trapezoid(y=y_segment, x=x_segment, *args, **kwargs) + initial
        else:
            raise RuntimeError("No such option '{}' known for `interpolation`.".format(interpolation))