Interpolation functions

interpolation.py

def create_interpolation_function(x_ref: list[float], y_ref: list[float]):
    """
    Create an interpolation function with the given points.

    Parameters
    ----------
    x_ref : list[float]
        X values.
    y_ref : list[float]
        Y values.

    Returns
    -------
    Callable
        Interpolation function.
    """

    def interpolation_func(x: float):
        if x < x_ref[0]:
            return single_linear_interpolate(x_ref, y_ref, 0, 1, x)

        for i in range(len(x_ref) - 1):
            if x < x_ref[i + 1]:
                return single_linear_interpolate(x_ref, y_ref, i, i + 1, x)

        return single_linear_interpolate(x_ref, y_ref, len(x_ref) - 2, len(x_ref) - 1, x)

    return interpolation_func


def get_slope(x_array: list[float], y_array: list[float], i: int, j: int):
    """
    Get the slope of the curve between the two specified points.

    Parameters
    ----------
    x_array : list[float]
        X values.
    y_array : list[float]
        Y values.
    i : int
        First point index.
    j : int
        Second point index.

    Returns
    -------
    float
        Slope of the curve.
    """

    slope = (y_array[j] - y_array[i]) / (x_array[j] - x_array[i])

    return slope


def single_linear_interpolate(x_array: list[float], y_array: list[float], i: int, j: int, x: float):
    """
    Interpolate a single value on an affine curve.

    Parameters
    ----------
    x_array : list[float]
        X values.
    y_array : list[float]
        Y values.
    i : int
        First point index.
    j : int
        Second point index.
    x : float
        Interpolation position.

    Returns
    -------
    float
        Interpolation value.
    """

    slope = get_slope(x_array, y_array, i, j)
    value = slope * (x - x_array[i]) + y_array[i]

    return value


def interpolate(x_ref: list[float], y_ref: list[float], x_exp: list[float]):
    """
    Interpolate the values defined on the ref points on the exp points.

    Parameters
    ----------
    x_ref : list[float]
    y_ref : list[float]
    x_exp : list[float]

    Returns
    -------

    """

    interpolation_func = create_interpolation_function(x_ref, y_ref)

    y_exp = []

    for x in x_exp:
        y_exp.append(interpolation_func(x))

    return y_exp