# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)


import numpy as np
import scipy as sp
import pylab as plt

class WarpingFunction(object):
    """
    abstract function for warping
    z = f(y)
    """

    def __init__(self):
        raise NotImplementedError

    def f(self,y,psi):
        """function transformation
        y is a list of values (GP training data) of shpape [N,1]
        """
        raise NotImplementedError

    def fgrad_y(self,y,psi):
        """gradient of f w.r.t to y"""
        raise NotImplementedError

    def fgrad_y_psi(self,y,psi):
        """gradient of f w.r.t to y"""
        raise NotImplementedError

    def f_inv(self,z,psi):
        """inverse function transformation"""
        raise NotImplementedError

    def _get_param_names(self):
        raise NotImplementedError

    def plot(self, psi, xmin, xmax):
        y = np.arange(xmin, xmax, 0.01)
        f_y = self.f(y, psi)
        plt.figure()
        plt.plot(y, f_y)
        plt.xlabel('y')
        plt.ylabel('f(y)')
        plt.title('warping function')

class TanhWarpingFunction(WarpingFunction):

    def __init__(self,n_terms=3):
        """n_terms specifies the number of tanh terms to be used"""
        self.n_terms = n_terms
        self.num_parameters = 3 * self.n_terms

    def f(self,y,psi):
        """
        transform y with f using parameter vector psi
        psi = [[a,b,c]]
        ::math::`f = \\sum_{terms} a * tanh(b*(y+c))`

        """

        #1. check that number of params is consistent
        assert psi.shape[0] == self.n_terms, 'inconsistent parameter dimensions'
        assert psi.shape[1] == 3, 'inconsistent parameter dimensions'

        #2. exponentiate the a and b (positive!)
        mpsi = psi.copy()

        #3. transform data
        z = y.copy()
        for i in range(len(mpsi)):
            a,b,c = mpsi[i]
            z += a*np.tanh(b*(y+c))
        return z


    def f_inv(self, y, psi, iterations = 10):
        """
        calculate the numerical inverse of f

        :param iterations: number of N.R. iterations

        """

        y = y.copy()
        z = np.ones_like(y)

        for i in range(iterations):
            z -= (self.f(z, psi) - y)/self.fgrad_y(z,psi)

        return z


    def fgrad_y(self, y, psi, return_precalc = False):
        """
        gradient of f w.r.t to y ([N x 1])
        returns: Nx1 vector of derivatives, unless return_precalc is true,
        then it also returns the precomputed stuff
        """

        mpsi = psi.copy()

        # vectorized version

        # S = (mpsi[:,1]*(y + mpsi[:,2])).T
        S = (mpsi[:,1]*(y[:,:,None] + mpsi[:,2])).T
        R = np.tanh(S)
        D = 1-R**2

        # GRAD = (1+(mpsi[:,0:1]*mpsi[:,1:2]*D).sum(axis=0))[:,np.newaxis]
        GRAD = (1+(mpsi[:,0:1][:,:,None]*mpsi[:,1:2][:,:,None]*D).sum(axis=0)).T

        if return_precalc:
            # return GRAD,S.sum(axis=1),R.sum(axis=1),D.sum(axis=1)
            return GRAD, S, R, D


        return GRAD


    def fgrad_y_psi(self, y, psi, return_covar_chain = False):
        """
        gradient of f w.r.t to y and psi

        returns: NxIx3 tensor of partial derivatives

        """

        # 1. exponentiate the a and b (positive!)
        mpsi = psi.copy()
        w, s, r, d = self.fgrad_y(y, psi, return_precalc = True)

        gradients = np.zeros((y.shape[0], y.shape[1], len(mpsi), 3))
        for i in range(len(mpsi)):
            a,b,c = mpsi[i]
            gradients[:,:,i,0] = (b*(1.0/np.cosh(s[i]))**2).T
            gradients[:,:,i,1] = a*(d[i] - 2.0*s[i]*r[i]*(1.0/np.cosh(s[i]))**2).T
            gradients[:,:,i,2] = (-2.0*a*(b**2)*r[i]*((1.0/np.cosh(s[i]))**2)).T


        if return_covar_chain:
            covar_grad_chain = np.zeros((y.shape[0], y.shape[1], len(mpsi), 3))

            for i in range(len(mpsi)):
                a,b,c = mpsi[i]
                covar_grad_chain[:, :, i, 0] = (r[i]).T
                covar_grad_chain[:, :, i, 1] = (a*(y + c) * ((1.0/np.cosh(s[i]))**2).T)
                covar_grad_chain[:, :, i, 2] = a*b*((1.0/np.cosh(s[i]))**2).T

            return gradients, covar_grad_chain

        return gradients

    def _get_param_names(self):
        variables = ['a', 'b', 'c']
        names = sum([['warp_tanh_%s_t%i' % (variables[n],q) for n in range(3)] for q in range(self.n_terms)],[])
        return names


class TanhWarpingFunction_d(WarpingFunction):

    def __init__(self,n_terms=3):
        """n_terms specifies the number of tanh terms to be used"""
        self.n_terms = n_terms
        self.num_parameters = 3 * self.n_terms + 1

    def f(self,y,psi):
        """
        Transform y with f using parameter vector psi
        psi = [[a,b,c]]

        :math:`f = \\sum_{terms} a * tanh(b*(y+c))`
        """

        #1. check that number of params is consistent
        # assert psi.shape[0] == self.n_terms, 'inconsistent parameter dimensions'
        # assert psi.shape[1] == 4, 'inconsistent parameter dimensions'
        mpsi = psi.copy()
        d = psi[-1]
        mpsi = mpsi[:self.num_parameters-1].reshape(self.n_terms, 3)

        #3. transform data
        z = d*y.copy()
        for i in range(len(mpsi)):
            a,b,c = mpsi[i]
            z += a*np.tanh(b*(y+c))
        return z


    def f_inv(self, z, psi, max_iterations=1000, y=None):
        """
        calculate the numerical inverse of f

        :param max_iterations: maximum number of N.R. iterations

        """

        z = z.copy()
        if y is None:
            y = np.ones_like(z)
            
        it = 0
        update = np.inf

        while it == 0 or (np.abs(update).sum() > 1e-10 and it < max_iterations):
            update = (self.f(y, psi) - z)/self.fgrad_y(y, psi)
            y -= update
            it += 1
        if it == max_iterations:
            print "WARNING!!! Maximum number of iterations reached in f_inv "

        return y


    def fgrad_y(self, y, psi, return_precalc = False):
        """
        gradient of f w.r.t to y ([N x 1])

        :returns: Nx1 vector of derivatives, unless return_precalc is true, then it also returns the precomputed stuff

        """


        mpsi = psi.copy()
        d = psi[-1]
        mpsi = mpsi[:self.num_parameters-1].reshape(self.n_terms, 3)

        # vectorized version

        S = (mpsi[:,1]*(y[:,:,None] + mpsi[:,2])).T
        R = np.tanh(S)
        D = 1-R**2

        GRAD = (d + (mpsi[:,0:1][:,:,None]*mpsi[:,1:2][:,:,None]*D).sum(axis=0)).T

        if return_precalc:
            return GRAD, S, R, D


        return GRAD


    def fgrad_y_psi(self, y, psi, return_covar_chain = False):
        """
        gradient of f w.r.t to y and psi

        :returns: NxIx4 tensor of partial derivatives

        """

        mpsi = psi.copy()
        mpsi = mpsi[:self.num_parameters-1].reshape(self.n_terms, 3)

        w, s, r, d = self.fgrad_y(y, psi, return_precalc = True)

        gradients = np.zeros((y.shape[0], y.shape[1], len(mpsi), 4))
        for i in range(len(mpsi)):
            a,b,c  = mpsi[i]
            gradients[:,:,i,0] = (b*(1.0/np.cosh(s[i]))**2).T
            gradients[:,:,i,1] = a*(d[i] - 2.0*s[i]*r[i]*(1.0/np.cosh(s[i]))**2).T
            gradients[:,:,i,2] = (-2.0*a*(b**2)*r[i]*((1.0/np.cosh(s[i]))**2)).T
        gradients[:,:,0,3] = 1.0

        if return_covar_chain:
            covar_grad_chain = np.zeros((y.shape[0], y.shape[1], len(mpsi), 4))

            for i in range(len(mpsi)):
                a,b,c = mpsi[i]
                covar_grad_chain[:, :, i, 0] = (r[i]).T
                covar_grad_chain[:, :, i, 1] = (a*(y + c) * ((1.0/np.cosh(s[i]))**2).T)
                covar_grad_chain[:, :, i, 2] = a*b*((1.0/np.cosh(s[i]))**2).T
            covar_grad_chain[:, :, 0, 3] = y

            return gradients, covar_grad_chain

        return gradients

    def _get_param_names(self):
        variables = ['a', 'b', 'c', 'd']
        names = sum([['warp_tanh_%s_t%i' % (variables[n],q) for n in range(3)] for q in range(self.n_terms)],[])
        names.append('warp_tanh_d')
        return names
