import numpy as np

__all__ = ["Kernel", "Uncorrelated", "ExpSquared", "Matern"]


class Kernel(object):

    def __init__(self, parnames=[], name=''):
        """
        :param parnames:
            A list of names of the kernel params, used to alias the intrinsic
            parameter names.  This way different instances of the same kernel
            can have different parameter names.
        """
        if len(parnames) == 0:
            parnames = self.kernel_params
        assert len(parnames) == len(self.kernel_params)
        self.param_alias = dict(zip(self.kernel_params, parnames))
        self.params = {}
        self.name = name

    def __repr__(self):
        return '{}({})'.format(self.__class__, self.param_alias.items())

    def update(self, **kwargs):
        """Take a dictionary of parameters, pick out the properly named
        parameters according to the alias, and put them in the param state
        dictionary.
        """
        for k in self.kernel_params:
            self.params[k] = kwargs[self.param_alias[k]]

    def __call__(self, metric, weights=None, ndim=2, **extras):
        """Return a covariance matrix, given a metric.  Optionally, multiply
        the output kernel by a weight function to induce non-stationarity.
        """
        k = self.construct_kernel(metric)
        if ndim != k.ndim:
            # Either promote to 2 dimensions or demote to 1.
            # The latter should never happen...
            k = np.diag(k)
        if weights is None:
            return k
        elif ndim == 2:
            Sigma = weights[None, :] * k * weights[:, None]
        else:
            Sigma = k * weights**2
        return Sigma


class Uncorrelated(Kernel):

    # Simple uncorrelated noise model
    ndim = 1
    kernel_params = ['amplitude']

    def construct_kernel(self, metric):
        s = metric.shape[0]
        jitter = self.params['amplitude']**2 * np.ones(s)
        if metric.ndim == 2:
            return np.diag(jitter)
        elif metric.ndim == 1:
            return jitter
        else:
            raise(NotImplementedError)


class ExpSquared(Kernel):

    ndim = 2
    npars = 2
    kernel_params = ['amplitude', 'length']

    def construct_kernel(self, metric):
        """Construct an exponential squared covariance matrix.
        """
        a, l = self.params['amplitude'], self.params['length']
        Sigma = a**2 * np.exp(-(metric[:, None] - metric[None, :])**2 / (2 * l**2))
        return Sigma


class Matern(Kernel):

    ndim = 2
    npars = 2
    kernel_params = ['amplitude', 'length']

    def construct_kernel(self, metric):
        """Construct a Matern kernel covariance matrix, for \nu=3/2.
        """
        a, l = self.params['amplitude'], self.params['length']
        Sigma = np.sqrt(3) * np.abs(metric[:, None] - metric[None, :]) / l
        Sigma = a**2 * (1 + Sigma) * np.exp(-Sigma)
        return Sigma


class Outliers(Kernel):
    kernel_params = ['amplitude', 'location']

    def construct_kernel(self, metric):
        raise(NotImplementedError)

numpy.ones numpy.exp numpy.abs numpy.sqrt numpy.diag