import numpy as np

def _make_index(prob,size):
    """
    Returns a boolean index for given probabilities.

    Notes
    ---------
    prob = [.75,.25] means that there is a 75% chance of the first column
    being True and a 25% chance of the second column being True. The
    columns are mutually exclusive.
    """
    rv = np.random.uniform(size=(size,1))
    cumprob = np.cumsum(prob)
    return np.logical_and(np.r_[0,cumprob[:-1]] <= rv, rv < cumprob)

def mixture_rvs(prob, size, dist, kwargs=None):
    """
    Sample from a mixture of distributions.

    Parameters
    ----------
    prob : array-like
        Probability of sampling from each distribution in dist
    size : int
        The length of the returned sample.
    dist : array-like
        An iterable of distributions objects from scipy.stats.
    kwargs : tuple of dicts, optional
        A tuple of dicts.  Each dict in kwargs can have keys loc, scale, and
        args to be passed to the respective distribution in dist.  If not
        provided, the distribution defaults are used.

    Examples
    --------
    Say we want 5000 random variables from mixture of normals with two
    distributions norm(-1,.5) and norm(1,.5) and we want to sample from the
    first with probability .75 and the second with probability .25.

    >>> from scipy import stats
    >>> prob = [.75,.25]
    >>> Y = mixture_rvs(prob, 5000, dist=[stats.norm, stats.norm], kwargs =
                (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))
    """
    if len(prob) != len(dist):
        raise ValueError("You must provide as many probabilities as distributions")
    if not np.allclose(np.sum(prob), 1):
        raise ValueError("prob does not sum to 1")

    if kwargs is None:
        kwargs = ({},)*len(prob)

    idx = _make_index(prob,size)
    sample = np.empty(size)
    for i in range(len(prob)):
        sample_idx = idx[...,i]
        sample_size = sample_idx.sum()
        loc = kwargs[i].get('loc',0)
        scale = kwargs[i].get('scale',1)
        args = kwargs[i].get('args',())
        sample[sample_idx] = dist[i].rvs(*args, **dict(loc=loc,scale=scale,
            size=sample_size))
    return sample


class MixtureDistribution(object):
    '''univariate mixture distribution

    for simple case for now (unbound support)
    does not yet inherit from scipy.stats.distributions

    adding pdf to mixture_rvs, some restrictions on broadcasting
    Currently it does not hold any state, all arguments included in each method.
    '''

    #def __init__(self, prob, size, dist, kwargs=None):

    def rvs(self, prob, size, dist, kwargs=None):
        return mixture_rvs(prob, size, dist, kwargs=kwargs)


    def pdf(self, x, prob, dist, kwargs=None):
        """
        pdf a mixture of distributions.

        Parameters
        ----------
        prob : array-like
            Probability of sampling from each distribution in dist
        dist : array-like
            An iterable of distributions objects from scipy.stats.
        kwargs : tuple of dicts, optional
            A tuple of dicts.  Each dict in kwargs can have keys loc, scale, and
            args to be passed to the respective distribution in dist.  If not
            provided, the distribution defaults are used.

        Examples
        --------
        Say we want 5000 random variables from mixture of normals with two
        distributions norm(-1,.5) and norm(1,.5) and we want to sample from the
        first with probability .75 and the second with probability .25.

        >>> from scipy import stats
        >>> prob = [.75,.25]
        >>> Y = mixture.pdf(x, prob, dist=[stats.norm, stats.norm], kwargs =
                    (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))
        """
        if len(prob) != len(dist):
            raise ValueError("You must provide as many probabilities as distributions")
        if not np.allclose(np.sum(prob), 1):
            raise ValueError("prob does not sum to 1")

        if kwargs is None:
            kwargs = ({},)*len(prob)

        for i in range(len(prob)):
            loc = kwargs[i].get('loc',0)
            scale = kwargs[i].get('scale',1)
            args = kwargs[i].get('args',())
            if i == 0:  #assume all broadcast the same as the first dist
                pdf_ = prob[i] * dist[i].pdf(x, *args, loc=loc, scale=scale)
            else:
                pdf_ += prob[i] * dist[i].pdf(x, *args, loc=loc, scale=scale)
        return pdf_

    def cdf(self, x, prob, dist, kwargs=None):
        """
        cdf of a mixture of distributions.

        Parameters
        ----------
        prob : array-like
            Probability of sampling from each distribution in dist
        size : int
            The length of the returned sample.
        dist : array-like
            An iterable of distributions objects from scipy.stats.
        kwargs : tuple of dicts, optional
            A tuple of dicts.  Each dict in kwargs can have keys loc, scale, and
            args to be passed to the respective distribution in dist.  If not
            provided, the distribution defaults are used.

        Examples
        --------
        Say we want 5000 random variables from mixture of normals with two
        distributions norm(-1,.5) and norm(1,.5) and we want to sample from the
        first with probability .75 and the second with probability .25.

        >>> from scipy import stats
        >>> prob = [.75,.25]
        >>> Y = mixture.pdf(x, prob, dist=[stats.norm, stats.norm], kwargs =
                    (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))
        """
        if len(prob) != len(dist):
            raise ValueError("You must provide as many probabilities as distributions")
        if not np.allclose(np.sum(prob), 1):
            raise ValueError("prob does not sum to 1")

        if kwargs is None:
            kwargs = ({},)*len(prob)

        for i in range(len(prob)):
            loc = kwargs[i].get('loc',0)
            scale = kwargs[i].get('scale',1)
            args = kwargs[i].get('args',())
            if i == 0:  #assume all broadcast the same as the first dist
                cdf_ = prob[i] * dist[i].cdf(x, *args, loc=loc, scale=scale)
            else:
                cdf_ += prob[i] * dist[i].cdf(x, *args, loc=loc, scale=scale)
        return cdf_


def mv_mixture_rvs(prob, size, dist, nvars, **kwargs):
    """
    Sample from a mixture of multivariate distributions.

    Parameters
    ----------
    prob : array-like
        Probability of sampling from each distribution in dist
    size : int
        The length of the returned sample.
    dist : array-like
        An iterable of distributions instances with callable method rvs.
    nvargs : int
        dimension of the multivariate distribution, could be inferred instead
    kwargs : tuple of dicts, optional
        ignored

    Examples
    --------
    Say we want 2000 random variables from mixture of normals with two
    multivariate normal distributions, and we want to sample from the
    first with probability .4 and the second with probability .6.

    import statsmodels.sandbox.distributions.mv_normal as mvd

    cov3 = np.array([[ 1.  ,  0.5 ,  0.75],
                       [ 0.5 ,  1.5 ,  0.6 ],
                       [ 0.75,  0.6 ,  2.  ]])

    mu = np.array([-1, 0.0, 2.0])
    mu2 = np.array([4, 2.0, 2.0])
    mvn3 = mvd.MVNormal(mu, cov3)
    mvn32 = mvd.MVNormal(mu2, cov3/2., 4)
    rvs = mix.mv_mixture_rvs([0.4, 0.6], 2000, [mvn3, mvn32], 3)

    """
    if len(prob) != len(dist):
        raise ValueError("You must provide as many probabilities as distributions")
    if not np.allclose(np.sum(prob), 1):
        raise ValueError("prob does not sum to 1")

    if kwargs is None:
        kwargs = ({},)*len(prob)

    idx = _make_index(prob,size)
    sample = np.empty((size, nvars))
    for i in range(len(prob)):
        sample_idx = idx[...,i]
        sample_size = sample_idx.sum()
        #loc = kwargs[i].get('loc',0)
        #scale = kwargs[i].get('scale',1)
        #args = kwargs[i].get('args',())
        # use int to avoid numpy bug with np.random.multivariate_normal
        sample[sample_idx] = dist[i].rvs(size=int(sample_size))
    return sample



if __name__ == '__main__':

    from scipy import stats

    obs_dist = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.beta],
                kwargs=(dict(loc=-1,scale=.5),dict(loc=1,scale=1,args=(1,.5))))



    nobs = 10000
    mix = MixtureDistribution()
##    mrvs = mixture_rvs([1/3.,2/3.], size=nobs, dist=[stats.norm, stats.norm],
##                   kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.75)))

    mix_kwds = (dict(loc=-1,scale=.25),dict(loc=1,scale=.75))
    mrvs = mix.rvs([1/3.,2/3.], size=nobs, dist=[stats.norm, stats.norm],
                   kwargs=mix_kwds)

    grid = np.linspace(-4,4, 100)
    mpdf = mix.pdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm],
                   kwargs=mix_kwds)
    mcdf = mix.cdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm],
                   kwargs=mix_kwds)

    doplot = 1
    if doplot:
        import matplotlib.pyplot as plt
        plt.figure()
        plt.hist(mrvs, bins=50, normed=True, color='red')
        plt.title('histogram of sample and pdf')
        plt.plot(grid, mpdf, lw=2, color='black')

        plt.figure()
        plt.hist(mrvs, bins=50, normed=True, cumulative=True, color='red')
        plt.title('histogram of sample and pdf')
        plt.plot(grid, mcdf, lw=2, color='black')

        plt.show()

