# -*- coding: utf-8 -*-
"""some measures for evaluation of prediction, tests and model selection

Created on Tue Nov 08 15:23:20 2011

Author: Josef Perktold
License: BSD-3

"""
import numpy as np

from statsmodels.tools.validation import array_like


def mse(x1, x2, axis=0):
    """mean squared error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    mse : ndarray or float
       mean squared error along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass, for example
    numpy matrices will silently produce an incorrect result.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.mean((x1-x2)**2, axis=axis)


def rmse(x1, x2, axis=0):
    """root mean squared error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    rmse : ndarray or float
       root mean squared error along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass, for example
    numpy matrices will silently produce an incorrect result.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.sqrt(mse(x1, x2, axis=axis))


def maxabs(x1, x2, axis=0):
    """maximum absolute error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    maxabs : ndarray or float
       maximum absolute difference along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.max(np.abs(x1-x2), axis=axis)


def meanabs(x1, x2, axis=0):
    """mean absolute error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    meanabs : ndarray or float
       mean absolute difference along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.mean(np.abs(x1-x2), axis=axis)


def medianabs(x1, x2, axis=0):
    """median absolute error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    medianabs : ndarray or float
       median absolute difference along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.median(np.abs(x1-x2), axis=axis)


def bias(x1, x2, axis=0):
    """bias, mean error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    bias : ndarray or float
       bias, or mean difference along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.mean(x1-x2, axis=axis)


def medianbias(x1, x2, axis=0):
    """median bias, median error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    medianbias : ndarray or float
       median bias, or median difference along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.median(x1-x2, axis=axis)


def vare(x1, x2, ddof=0, axis=0):
    """variance of error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    vare : ndarray or float
       variance of difference along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.var(x1-x2, ddof=ddof, axis=axis)


def stde(x1, x2, ddof=0, axis=0):
    """standard deviation of error

    Parameters
    ----------
    x1, x2 : array_like
       The performance measure depends on the difference between these two
       arrays.
    axis : int
       axis along which the summary statistic is calculated

    Returns
    -------
    stde : ndarray or float
       standard deviation of difference along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they need to broadcast.
    This uses ``numpy.asanyarray`` to convert the input. Whether this is the
    desired result or not depends on the array subclass.
    """
    x1 = np.asanyarray(x1)
    x2 = np.asanyarray(x2)
    return np.std(x1-x2, ddof=ddof, axis=axis)


def iqr(x1, x2, axis=0):
    """
    Interquartile range of error

    Parameters
    ----------
    x1 : array_like
       One of the inputs into the IQR calculation.
    x2 : array_like
       The other input into the IQR calculation.
    axis : {None, int}
       axis along which the summary statistic is calculated

    Returns
    -------
    irq : {float, ndarray}
       Interquartile range along given axis.

    Notes
    -----
    If ``x1`` and ``x2`` have different shapes, then they must broadcast.
    """
    x1 = array_like(x1, 'x1', dtype=None, ndim=None)
    x2 = array_like(x2, 'x1', dtype=None, ndim=None)
    if axis is None:
        x1 = x1.ravel()
        x2 = x2.ravel()
        axis = 0
    xdiff = np.sort(x1 - x2, axis=axis)
    nobs = x1.shape[axis]
    idx = np.round((nobs-1) * np.array([0.25, 0.75])).astype(int)
    sl = [slice(None)] * xdiff.ndim
    sl[axis] = idx
    iqr = np.diff(xdiff[tuple(sl)], axis=axis)
    iqr = np.squeeze(iqr)  # drop reduced dimension
    return iqr


# Information Criteria
# ---------------------

def aic(llf, nobs, df_modelwc):
    """Akaike information criterion

    Parameters
    ----------
    llf : float
        value of the loglikelihood
    nobs : int
        number of observations
    df_modelwc : int
        number of parameters including constant

    Returns
    -------
    aic : float
        information criterion

    References
    ----------
    https://en.wikipedia.org/wiki/Akaike_information_criterion
    """
    return -2. * llf + 2. * df_modelwc


def aicc(llf, nobs, df_modelwc):
    """Akaike information criterion (AIC) with small sample correction

    Parameters
    ----------
    llf : float
        value of the loglikelihood
    nobs : int
        number of observations
    df_modelwc : int
        number of parameters including constant

    Returns
    -------
    aicc : float
        information criterion

    References
    ----------
    https://en.wikipedia.org/wiki/Akaike_information_criterion#AICc
    """