import numpy as np


def residual_map_from(*, data: np.ndarray, model_data: np.ndarray) -> np.ndarray:
    """
    Returns the residual-map of the fit of model-data to a masked dataset, where:

    Residuals = (Data - Model_Data).

    Parameters
    -----------
    data
        The data that is fitted.
    mask
        The mask applied to the dataset, where `False` entries are included in the calculation.
    model_data
        The model data used to fit the data.
    """
    return np.subtract(data, model_data, out=np.zeros_like(data))


def normalized_residual_map_from(
    *, residual_map: np.ndarray, noise_map: np.ndarray
) -> np.ndarray:
    """
    Returns the normalized residual-map of the fit of model-data to a masked dataset, where:

    Normalized_Residual = (Data - Model_Data) / Noise

    Parameters
    -----------
    residual_map
        The residual-map of the model-simulator fit to the dataset.
    noise_map
        The noise-map of the dataset.
    mask
        The mask applied to the residual-map, where `False` entries are included in the calculation.
    """
    return np.divide(residual_map, noise_map, out=np.zeros_like(residual_map))


def chi_squared_map_from(
    *, residual_map: np.ndarray, noise_map: np.ndarray
) -> np.ndarray:
    """
    Returns the chi-squared-map of the fit of model-data to a masked dataset, where:

    Chi_Squared = ((Residuals) / (Noise)) ** 2.0 = ((Data - Model)**2.0)/(Variances)

    Parameters
    -----------
    residual_map
        The residual-map of the model-simulator fit to the dataset.
    noise_map
        The noise-map of the dataset.
    """
    return np.square(
        np.divide(residual_map, noise_map, out=np.zeros_like(residual_map))
    )


def chi_squared_from(*, chi_squared_map: np.ndarray) -> float:
    """
    Returns the chi-squared terms of a model data's fit to an dataset, by summing the chi-squared-map.

    Parameters
    ----------
    chi_squared_map
        The chi-squared-map of values of the model-simulator fit to the dataset.
    """
    return float(np.sum(chi_squared_map))


def noise_normalization_from(*, noise_map: np.ndarray) -> float:
    """
    Returns the noise-map normalization term of the noise-map, summing the noise_map value in every pixel as:

    [Noise_Term] = sum(log(2*pi*[Noise]**2.0))

    Parameters
    ----------
    noise_map
        The masked noise-map of the dataset.
    """
    return float(np.sum(np.log(2 * np.pi * noise_map ** 2.0)))


def normalized_residual_map_complex_from(
    *, residual_map: np.ndarray, noise_map: np.ndarray
) -> np.ndarray:
    """
    Returns the normalized residual-map of the fit of complex model-data to a dataset, where:

    Normalized_Residual = (Data - Model_Data) / Noise

    Parameters
    -----------
    residual_map
        The residual-map of the model-simulator fit to the dataset.
    noise_map
        The noise-map of the dataset.
    """
    normalized_residual_map_real = np.divide(
        residual_map.real,
        noise_map.real,
        out=np.zeros_like(residual_map, dtype="complex128"),
    )

    normalized_residual_map_imag = np.divide(
        residual_map.imag,
        noise_map.imag,
        out=np.zeros_like(residual_map, dtype="complex128"),
    )

    return normalized_residual_map_real + 1j * normalized_residual_map_imag


def chi_squared_map_complex_from(
    *, residual_map: np.ndarray, noise_map: np.ndarray
) -> np.ndarray:
    """
    Returnss the chi-squared-map of the fit of complex model-data to a dataset, where:

    Chi_Squared = ((Residuals) / (Noise)) ** 2.0 = ((Data - Model)**2.0)/(Variances)

    Parameters
    -----------
    residual_map
        The residual-map of the model-simulator fit to the dataset.
    noise_map
        The noise-map of the dataset.
    """
    chi_squared_map_real = np.square(
        np.divide(residual_map.real, noise_map.real, out=np.zeros_like(residual_map))
    )
    chi_squared_map_imag = np.square(
        np.divide(residual_map.imag, noise_map.imag, out=np.zeros_like(residual_map))
    )
    return chi_squared_map_real + 1j * chi_squared_map_imag


def chi_squared_complex_from(*, chi_squared_map: np.ndarray) -> float:
    """
    Returns the chi-squared terms of each complex model data's fit to a masked dataset, by summing the masked
    chi-squared-map of the fit.

    The chi-squared values in masked pixels are omitted from the calculation.

    Parameters
    ----------
    chi_squared_map
        The chi-squared-map of values of the model-simulator fit to the dataset.
    """
    chi_squared_real = float(np.sum(chi_squared_map.real))
    chi_squared_imag = float(np.sum(chi_squared_map.imag))
    return chi_squared_real + chi_squared_imag


def noise_normalization_complex_from(*, noise_map: np.ndarray) -> float:
    """
    Returns the noise-map normalization terms of a complex noise-map, summing the noise_map value in every pixel as:

    [Noise_Term] = sum(log(2*pi*[Noise]**2.0))

    Parameters
    ----------
    noise_map
        The masked noise-map of the dataset.
    """
    noise_normalization_real = float(np.sum(np.log(2 * np.pi * noise_map.real ** 2.0)))
    noise_normalization_imag = float(np.sum(np.log(2 * np.pi * noise_map.imag ** 2.0)))
    return noise_normalization_real + noise_normalization_imag


def residual_map_with_mask_from(
    *, data: np.ndarray, mask: np.ndarray, model_data: np.ndarray
) -> np.ndarray:
    """
    Returns the residual-map of the fit of model-data to a masked dataset, where:

    Residuals = (Data - Model_Data).

    The residual-map values in masked pixels are returned as zero.

    Parameters
    -----------
    data
        The data that is fitted.
    mask
        The mask applied to the dataset, where `False` entries are included in the calculation.
    model_data
        The model data used to fit the data.
    """
    return np.subtract(
        data, model_data, out=np.zeros_like(data), where=np.asarray(mask) == 0
    )


def normalized_residual_map_with_mask_from(
    *, residual_map: np.ndarray, noise_map: np.ndarray, mask: np.ndarray
) -> np.ndarray:
    """
    Returns the normalized residual-map of the fit of model-data to a masked dataset, where:

    Normalized_Residual = (Data - Model_Data) / Noise

    The normalized residual-map values in masked pixels are returned as zero.

    Parameters
    -----------
    residual_map
        The residual-map of the model-simulator fit to the dataset.
    noise_map
        The noise-map of the dataset.
    mask
        The mask applied to the residual-map, where `False` entries are included in the calculation.
    """
    return np.divide(
        residual_map,
        noise_map,
        out=np.zeros_like(residual_map),
        where=np.asarray(mask) == 0,
    )


def chi_squared_map_with_mask_from(
    *, residual_map: np.ndarray, noise_map: np.ndarray, mask: np.ndarray
) -> np.ndarray:
    """
    Returnss the chi-squared-map of the fit of model-data to a masked dataset, where:

    Chi_Squared = ((Residuals) / (Noise)) ** 2.0 = ((Data - Model)**2.0)/(Variances)

    The chi-squared-map values in masked pixels are returned as zero.

    Parameters
    -----------
    residual_map
        The residual-map of the model-simulator fit to the dataset.
    noise_map
        The noise-map of the dataset.
    mask
        The mask applied to the residual-map, where `False` entries are included in the calculation.
    """
    return np.square(
        np.divide(
            residual_map,
            noise_map,
            out=np.zeros_like(residual_map),
            where=np.asarray(mask) == 0,
        )
    )


def chi_squared_with_mask_from(
    *, chi_squared_map: np.ndarray, mask: np.ndarray
) -> float:
    """
    Returns the chi-squared terms of each model data's fit to a masked dataset, by summing the masked
    chi-squared-map of the fit.

    The chi-squared values in masked pixels are omitted from the calculation.

    Parameters
    ----------
    chi_squared_map
        The chi-squared-map of values of the model-simulator fit to the dataset.
    mask
        The mask applied to the chi-squared-map, where `False` entries are included in the calculation.
    """
    return float(np.sum(chi_squared_map[np.asarray(mask) == 0]))


def noise_normalization_with_mask_from(
    *, noise_map: np.ndarray, mask: np.ndarray
) -> float:
    """
    Returns the noise-map normalization terms of masked noise-map, summing the noise_map value in every pixel as:

    [Noise_Term] = sum(log(2*pi*[Noise]**2.0))

    The noise-map values in masked pixels are omitted from the calculation.

    Parameters
    ----------
    noise_map
        The masked noise-map of the dataset.
    mask
        The mask applied to the noise-map, where `False` entries are included in the calculation.
    """
    return float(np.sum(np.log(2 * np.pi * noise_map[np.asarray(mask) == 0] ** 2.0)))


def normalized_residual_map_complex_with_mask_from(
    *, residual_map: np.ndarray, noise_map: np.ndarray, mask: np.ndarray
) -> np.ndarray:
    """
    Returns the normalized residual-map of the fit of complex model-data to a masked dataset, where:

    Normalized_Residual = (Data - Model_Data) / Noise

    The normalized residual-map values in masked pixels are returned as zero.

    Parameters
    -----------
    residual_map
        The residual-map of the model-simulator fit to the dataset.
    noise_map
        The noise-map of the dataset.
    mask
        The mask applied to the residual-map, where `False` entries are included in the calculation.
    """
    normalized_residual_map_real = np.divide(
        residual_map.real,
        noise_map.real,
        out=np.zeros_like(residual_map.real),
        where=np.asarray(mask) == 0,
    )

    normalized_residual_map_imag = np.divide(
        residual_map.imag,
        noise_map.imag,
        out=np.zeros_like(residual_map.imag),
        where=np.asarray(mask) == 0,
    )

    return normalized_residual_map_real + 1j * normalized_residual_map_imag


def chi_squared_map_complex_with_mask_from(
    *, residual_map: np.ndarray, noise_map: np.ndarray, mask: np.ndarray
) -> np.ndarray:
    """
    Returnss the chi-squared-map of the fit of complex model-data to a masked dataset, where:

    Chi_Squared = ((Residuals) / (Noise)) ** 2.0 = ((Data - Model)**2.0)/(Variances)

    The chi-squared-map values in masked pixels are returned as zero.

    Parameters
    -----------
    residual_map
        The residual-map of the model-simulator fit to the dataset.
    noise_map
        The noise-map of the dataset.
    mask
        The mask applied to the residual-map, where `False` entries are included in the calculation.
    """

    chi_squared_map_real = np.square(
        np.divide(
            residual_map.real,
            noise_map.real,
            out=np.zeros_like(residual_map.real),
            where=np.asarray(mask) == 0,
        )
    )
    chi_squared_map_imag = np.square(
        np.divide(
            residual_map.imag,
            noise_map.imag,
            out=np.zeros_like(residual_map.imag),
            where=np.asarray(mask) == 0,
        )
    )
    return chi_squared_map_real + 1j * chi_squared_map_imag


def chi_squared_complex_with_mask_from(
    *, chi_squared_map: np.ndarray, mask: np.ndarray
) -> float:
    """
    Returns the chi-squared terms of each complex model data's fit to a masked dataset, by summing the masked
    chi-squared-map of the fit.

    The chi-squared values in masked pixels are omitted from the calculation.

    Parameters
    ----------
    chi_squared_map
        The chi-squared-map of values of the model-simulator fit to the dataset.
    mask
        The mask applied to the chi-squared-map, where `False` entries are included in the calculation.
    """
    chi_squared_real = float(np.sum(chi_squared_map[np.asarray(mask) == 0].real))
    chi_squared_imag = float(np.sum(chi_squared_map[np.asarray(mask) == 0].imag))
    return chi_squared_real + chi_squared_imag


def noise_normalization_complex_with_mask_from(
    *, noise_map: np.ndarray, mask: np.ndarray
) -> float:
    """
    Returns the noise-map normalization terms of a complex masked noise-map, summing the noise_map value in every pixel as:

    [Noise_Term] = sum(log(2*pi*[Noise]**2.0))

    The noise-map values in masked pixels are omitted from the calculation.

    Parameters
    ----------
    noise_map
        The masked noise-map of the dataset.
    mask
        The mask applied to the noise-map, where `False` entries are included in the calculation.
    """
    noise_normalization_real = float(
        np.sum(np.log(2 * np.pi * noise_map[np.asarray(mask) == 0].real ** 2.0))
    )
    noise_normalization_imag = float(
        np.sum(np.log(2 * np.pi * noise_map[np.asarray(mask) == 0].imag ** 2.0))
    )
    return noise_normalization_real + noise_normalization_imag


def log_likelihood_from(*, chi_squared: float, noise_normalization: float) -> float:
    """
    Returns the log likelihood of each model data point's fit to the dataset, where:

    Log Likelihood = -0.5*[Chi_Squared_Term + Noise_Term] (see functions above for these definitions)

    Parameters
    ----------
    chi_squared
        The chi-squared term for the model-simulator fit to the dataset.
    noise_normalization
        The normalization noise_map-term for the dataset's noise-map.
    """
    return float(-0.5 * (chi_squared + noise_normalization))


def log_likelihood_with_regularization_from(
    *, chi_squared: float, regularization_term: float, noise_normalization: float
) -> float:
    """
    Returns the log likelihood of an inversion's fit to the dataset, including a regularization term which comes from
    an inversion:

    Log Likelihood = -0.5*[Chi_Squared_Term + Regularization_Term + Noise_Term]

    Parameters
    ----------
    chi_squared
        The chi-squared term of the inversion's fit to the dataset.
    regularization_term
        The regularization term of the inversion, which is the sum of the difference between reconstructed
        flux of every pixel multiplied by the regularization coefficient.
    noise_normalization
        The normalization noise_map-term for the dataset's noise-map.
    """
    return float(-0.5 * (chi_squared + regularization_term + noise_normalization))


def log_evidence_from(
    *,
    chi_squared: float,
    regularization_term: float,
    log_curvature_regularization_term: float,
    log_regularization_term: float,
    noise_normalization: float,
) -> float:
    """
    Returns the log evidence of an inversion's fit to a dataset, where the log evidence includes a number of terms which
    quantify the complexity of an inversion's reconstruction (see the `LEq` module):

    Log Evidence = -0.5*[Chi_Squared_Term + Regularization_Term + Log(Covariance_Regularization_Term) -
                           Log(Regularization_Matrix_Term) + Noise_Term]

    Parameters
    ----------
    chi_squared
        The chi-squared term of the inversion's fit to the dataset.
    regularization_term
        The regularization term of the inversion, which is the sum of the difference between reconstructed
        flux of every pixel multiplied by the regularization coefficient.
    log_curvature_regularization_term
        The log of the determinant of the sum of the curvature and regularization matrices.
    log_regularization_term
        The log of the determinant o the regularization matrix.
    noise_normalization
        The normalization noise_map-term for the dataset's noise-map.
    """
    return float(
        -0.5
        * (
            chi_squared
            + regularization_term
            + log_curvature_regularization_term
            - log_regularization_term
            + noise_normalization
        )
    )
