##############################################################################
#
# Copyright (c) 2003-2020 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
# Development from 2019 by School of Earth and Environmental Sciences
#
##############################################################################

from __future__ import print_function, division

__copyright__="""Copyright (c) 2003-2020 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"

__all__ = ['Regularization']


import logging
import numpy as np
from esys.escript import Function, outer, Data, Scalar, grad, inner, integrate, interpolate, kronecker, boundingBoxEdgeLengths, vol, sqrt, length,Lsup, transpose
from esys.escript.linearPDEs import LinearPDE, IllegalCoefficientValue,SolverOptions
from esys.escript.pdetools import ArithmeticTuple
from .coordinates import makeTransformation
from .costfunctions import CostFunction

class Regularization(CostFunction):
    """
    The regularization term for the level set function ``m`` within the cost
    function J for an inversion:

    *J(m)=1/2 * sum_k integrate( mu[k] * ( w0[k] * m_k**2 * w1[k,i] * m_{k,i}**2) + sum_l<k mu_c[l,k] wc[l,k] * | curl(m_k) x curl(m_l) |^2*

    where w0[k], w1[k,i] and  wc[k,l] are non-negative weighting factors and
    mu[k] and mu_c[l,k] are trade-off factors which may be altered
    during the inversion. The weighting factors are normalized such that their
    integrals over the domain are constant:

    *integrate(w0[k] + inner(w1[k,:],1/L[:]**2))=scale[k]* volume(domain)*
    *integrate(wc[l,k]*1/L**4)=scale_c[k]* volume(domain) *

    """
    def __init__(self, domain, numLevelSets=1,
                       w0=None, w1=None, wc=None,
                       location_of_set_m=Data(),
                       useDiagonalHessianApproximation=False, tol=1e-8,
                       coordinates=None,
                       scale=None, scale_c=None):
        """
        initialization.

        :param domain: domain
        :type domain: `Domain`
        :param numLevelSets: number of level sets
        :type numLevelSets: ``int``
        :param w0: weighting factor for the m**2 term. If not set zero is assumed.
        :type w0: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of shape
                  (``numLevelSets`` ,) if ``numLevelSets`` > 1
        :param w1: weighting factor for the grad(m_i) terms. If not set zero is assumed
        :type w1: ``Vector`` if ``numLevelSets`` == 1 or `Data` object of shape
                  (``numLevelSets`` , DIM) if ``numLevelSets`` > 1
        :param wc: weighting factor for the cross gradient terms. If not set
                   zero is assumed. Used for the case if ``numLevelSets`` > 1
                   only. Only values ``wc[l,k]`` in the lower triangle (l<k)
                   are used.
        :type wc: `Data` object of shape (``numLevelSets`` , ``numLevelSets``)
        :param location_of_set_m: marks location of zero values of the level
                                  set function ``m`` by a positive entry.
        :type location_of_set_m: ``Scalar`` if ``numLevelSets`` == 1 or `Data`
                object of shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
        :param useDiagonalHessianApproximation: if True cross gradient terms
                    between level set components are ignored when calculating
                    approximations of the inverse of the Hessian Operator.
                    This can speed-up the calculation of the inverse but may
                    lead to an increase of the number of iteration steps in the
                    inversion.
        :type useDiagonalHessianApproximation: ``bool``
        :param tol: tolerance when solving the PDE for the inverse of the
                    Hessian Operator
        :type tol: positive ``float``

        :param coordinates: defines coordinate system to be used
        :type coordinates: ReferenceSystem` or `SpatialCoordinateTransformation`
        :param scale: weighting factor for level set function variation terms.
                      If not set one is used.
        :type scale: ``Scalar`` if ``numLevelSets`` == 1 or `Data` object of
                     shape (``numLevelSets`` ,) if ``numLevelSets`` > 1
        :param scale_c: scale for the cross gradient terms. If not set
                   one is assumed. Used for the case if ``numLevelSets`` > 1
                   only. Only values ``scale_c[l,k]`` in the lower triangle
                   (l<k) are used.
        :type scale_c: `Data` object of shape (``numLevelSets``,``numLevelSets``)

        """
        if w0 is None and w1 is None:
            raise ValueError("Values for w0 or for w1 must be given.")
        if wc is None and numLevelSets>1:
            raise ValueError("Values for wc must be given.")

        self.logger = logging.getLogger('inv.%s'%self.__class__.__name__)
        self.__domain=domain
        DIM=self.__domain.getDim()
        self.__numLevelSets=numLevelSets
        self.__trafo=makeTransformation(domain, coordinates)
        self.__pde=LinearPDE(self.__domain, numEquations=self.__numLevelSets, numSolutions=self.__numLevelSets)
        self.__pde.getSolverOptions().setTolerance(tol)
        self.__pde.setSymmetryOn()
        self.__pde.setValue(A=self.__pde.createCoefficient('A'), D=self.__pde.createCoefficient('D'), )
        try:
            self.__pde.setValue(q=location_of_set_m)
        except IllegalCoefficientValue:
            raise ValueError("Unable to set location of fixed level set function.")

        # =========== check the shape of the scales: ========================
        if scale is None:
            if numLevelSets == 1 :
                scale = 1.
            else:
                scale = np.ones((numLevelSets,))
        else:
            scale=np.asarray(scale)
            if numLevelSets == 1:
                if scale.shape == ():
                    if not scale > 0 :
                        raise ValueError("Value for scale must be positive.")
                else:
                    raise ValueError("Unexpected shape %s for scale."%scale.shape)
            else:
                if scale.shape is (numLevelSets,):
                    if not min(scale) > 0:
                        raise ValueError("All values for scale must be positive.")
                else:
                    raise ValueError("Unexpected shape %s for scale."%scale.shape)

        if scale_c is None or numLevelSets < 2:
            scale_c = np.ones((numLevelSets,numLevelSets))
        else:
            scale_c=np.asarray(scale_c)
            if scale_c.shape == (numLevelSets,numLevelSets):
                if not all( [ [ scale_c[l,k] > 0. for l in range(k) ] for k in range(1,numLevelSets) ]):
                    raise ValueError("All values in the lower triangle of scale_c must be positive.")
            else:
                raise ValueError("Unexpected shape %s for scale."%scale_c.shape)
        # ===== check the shape of the weights: =============================
        if w0 is not None:
            w0 = interpolate(w0,self.__pde.getFunctionSpaceForCoefficient('D'))
            s0=w0.getShape()
            if numLevelSets == 1:
                if not s0 == () :
                    raise ValueError("Unexpected shape %s for weight w0."%(s0,))
            else:
                if not s0 == (numLevelSets,):
                    raise ValueError("Unexpected shape %s for weight w0."%(s0,))
            if not self.__trafo.isCartesian():
                w0*=self.__trafo.getVolumeFactor()
        if not w1 is None:
            w1 = interpolate(w1,self.__pde.getFunctionSpaceForCoefficient('A'))
            s1=w1.getShape()
            if numLevelSets == 1 :
                if not s1 == (DIM,) :
                    raise ValueError("Unexpected shape %s for weight w1."%(s1,))
            else:
                if not s1 == (numLevelSets,DIM):
                    raise ValueError("Unexpected shape %s for weight w1."%(s1,))
            if not self.__trafo.isCartesian():
                f=self.__trafo.getScalingFactors()**2*self.__trafo.getVolumeFactor()
                if numLevelSets == 1:
                    w1*=f
                else:
                    for i in range(numLevelSets): w1[i,:]*=f

        if numLevelSets == 1:
            wc=None
        else:
            wc = interpolate(wc,self.__pde.getFunctionSpaceForCoefficient('A'))
            sc=wc.getShape()
            if not sc == (numLevelSets, numLevelSets):
                raise ValueError("Unexpected shape %s for weight wc."%(sc,))
            if not self.__trafo.isCartesian():
                raise ValueError("Non-cartesian coordinates for cross-gradient term is not supported yet.")
        # ============= now we rescale weights: =============================
        L2s=np.asarray(boundingBoxEdgeLengths(domain))**2
        L4=1/np.sum(1/L2s)**2
        if numLevelSets == 1:
            A=0
            if w0 is not None:
                A = integrate(w0)
            if w1 is not None:
                A += integrate(inner(w1, 1/L2s))
            if A > 0:
                f = scale/A
                if w0 is not None:
                    w0*=f
                if w1 is not None:
                    w1*=f
            else:
                raise ValueError("Non-positive weighting factor detected.")
        else: # numLevelSets > 1
            for k in range(numLevelSets):
                A=0
                if w0 is not None:
                    A = integrate(w0[k])
                if w1 is not None:
                    A += integrate(inner(w1[k,:], 1/L2s))
                if A > 0:
                    f = scale[k]/A
                    if w0 is not None:
                        w0[k]*=f
                    if w1 is not None:
                        w1[k,:]*=f
                else:
                    raise ValueError("Non-positive weighting factor for level set component %d detected."%k)

                # and now the cross-gradient:
                if wc is not None:
                    for l in range(k):
                        A = integrate(wc[l,k])/L4
                        if A > 0:
                            f = scale_c[l,k]/A
                            wc[l,k]*=f
#                       else:
#                           raise ValueError("Non-positive weighting factor for cross-gradient level set components %d and %d detected."%(l,k))

        self.__w0=w0
        self.__w1=w1
        self.__wc=wc

        self.__pde_is_set=False
        if self.__numLevelSets > 1:
            self.__useDiagonalHessianApproximation=useDiagonalHessianApproximation
        else:
            self.__useDiagonalHessianApproximation=True
        self._update_Hessian=True

        self.__num_tradeoff_factors=numLevelSets+((numLevelSets-1)*numLevelSets)//2
        self.setTradeOffFactors()
        self.__vol_d=vol(self.__domain)

    def getDomain(self):
        """
        returns the domain of the regularization term

        :rtype: ``Domain``
        """
        return self.__domain

    def getCoordinateTransformation(self):
        """
        returns the coordinate transformation being used

        :rtype: `CoordinateTransformation`
        """
        return self.__trafo

    def getNumLevelSets(self):
        """
        returns the number of level set functions

        :rtype: ``int``
        """
        return self.__numLevelSets

    def getPDE(self):
        """
        returns the linear PDE to be solved for the Hessian Operator inverse

        :rtype: `LinearPDE`
        """
        return self.__pde

    def getDualProduct(self, m, r):
        """
        returns the dual product of a gradient represented by X=r[1] and Y=r[0]
        with a level set function m:

             *Y_i*m_i + X_ij*m_{i,j}*

        :type m: `Data`
        :type r: `ArithmeticTuple`
        :rtype: ``float``
        """
        A=0
        if not r[0].isEmpty(): A+=integrate(inner(r[0], m))
        if not r[1].isEmpty(): A+=integrate(inner(r[1], grad(m)))
        return A

    def getNumTradeOffFactors(self):
        """
        returns the number of trade-off factors being used.

        :rtype: ``int``
        """
        return self.__num_tradeoff_factors

    def setTradeOffFactors(self, mu=None):
        """
        sets the trade-off factors for the level-set variation and the
        cross-gradient.

        :param mu: new values for the trade-off factors where values
                   mu[:numLevelSets] are the trade-off factors for the
                   level-set variation and the remaining values for
                   the cross-gradient part with
                   mu_c[l,k]=mu[numLevelSets+l+((k-1)*k)/2] (l<k).
                   If no values for mu are given ones are used.
                   Values must be positive.
        :type mu: ``list`` of ``float`` or ```numpy.array```
        """
        numLS=self.getNumLevelSets()
        numTF=self.getNumTradeOffFactors()
        if mu is None:
            mu = np.ones((numTF,))
        else:
            mu = np.asarray(mu)

        if mu.shape == (numTF,):
            self.setTradeOffFactorsForVariation(mu[:numLS])
            mu_c2=np.zeros((numLS,numLS))
            for k in range(numLS):
                for l in range(k):
                    mu_c2[l,k] = mu[numLS+l+((k-1)*k)//2]
            self.setTradeOffFactorsForCrossGradient(mu_c2)
        elif mu.shape == () and numLS ==1:
            self.setTradeOffFactorsForVariation(mu)
        else:
            raise ValueError("Unexpected shape %s for mu."%(mu.shape,))

    def setTradeOffFactorsForVariation(self, mu=None):
        """
        sets the trade-off factors for the level-set variation part.

        :param mu: new values for the trade-off factors. Values must be positive.
        :type mu: ``float``, ``list`` of ``float`` or ```numpy.array```
        """
        numLS=self.getNumLevelSets()
        if mu is None:
            if numLS == 1:
                mu = 1.
            else:
                mu = np.ones((numLS,))
        if type(mu) == list:
            #this is a fix for older versions of numpy where passing in an a list of ints causes
            #this code to break.
            mu=np.asarray([float(i) for i in mu])
        else:
            mu=np.asarray(mu)
        if numLS == 1:
            if mu.shape == (1,): mu=mu[0]
            if mu.shape == ():
                if mu > 0:
                    self.__mu= mu
                    self._new_mu=True
                else:
                    raise ValueError("Value for trade-off factor must be positive.")
            else:
                raise ValueError("Unexpected shape %s for mu."%str(mu.shape))
        else:
            if mu.shape == (numLS,):
                if min(mu) > 0:
                    self.__mu= mu
                    self._new_mu=True
                else:
                    raise ValueError("All values for mu must be positive.")
            else:
                raise ValueError("Unexpected shape %s for trade-off factor."%str(mu.shape))

    def setTradeOffFactorsForCrossGradient(self, mu_c=None):
        """
        sets the trade-off factors for the cross-gradient terms.

        :param mu_c: new values for the trade-off factors for the cross-gradient
                     terms. Values must be positive. If no value is given ones
                     are used. Only value mu_c[l,k] for l<k are used.
        :type mu_c: ``float``, ``list`` of ``float`` or ``numpy.array``
        """
        numLS=self.getNumLevelSets()
        if mu_c is None or numLS < 2:
            self.__mu_c = np.ones((numLS,numLS))
        elif isinstance(mu_c, float) or isinstance(mu_c, int):
            self.__mu_c = np.zeros((numLS,numLS))
            self.__mu_c[:,:]=mu_c
        else:
            mu_c=np.asarray(mu_c)
            if mu_c.shape == (numLS,numLS):
                if not all( [ [ mu_c[l,k] > 0. for l in range(k) ] for k in range(1,numLS) ]):
                    raise ValueError("All trade-off factors in the lower triangle of mu_c must be positive.")
                else:
                    self.__mu_c =  mu_c
                    self._new_mu=True
            else:
                raise ValueError("Unexpected shape %s for mu."%(mu_c.shape,))

    def getArguments(self, m):
        """
        """
        return grad(m),

    def getValue(self, m, grad_m):
        """
        returns the value of the cost function J with respect to m.
        This equation is specified in the inversion cookbook.

        :rtype: ``float``
        """
        mu=self.__mu
        mu_c=self.__mu_c
        DIM=self.getDomain().getDim()
        numLS=self.getNumLevelSets()

        A=0
        if self.__w0 is not None:
            r = inner(integrate(m**2 * self.__w0), mu)
            self.logger.debug("J_R[m^2] = %e"%r)
            A += r

        if self.__w1 is not None:
            if numLS == 1:
                r = integrate(inner(grad_m**2, self.__w1))*mu
                self.logger.debug("J_R[grad(m)] = %e"%r)
                A += r
            else:
                for k in range(numLS):
                    r = mu[k]*integrate(inner(grad_m[k,:]**2,self.__w1[k,:]))
                    self.logger.debug("J_R[grad(m)][%d] = %e"%(k,r))
                    A += r

        if numLS > 1:
            for k in range(numLS):
                gk=grad_m[k,:]
                len_gk=length(gk)
                for l in range(k):
                    gl=grad_m[l,:]
                    r = mu_c[l,k] * integrate( self.__wc[l,k] * ( ( len_gk * length(gl) )**2 - inner(gk, gl)**2 ) )
                    self.logger.debug("J_R[cross][%d,%d] = %e"%(l,k,r))
                    A += r
        return A/2

    def getGradient(self, m,  grad_m):
        """
        returns the gradient of the cost function J with respect to m.

        :note: This implementation returns Y_k=dPsi/dm_k and X_kj=dPsi/dm_kj
        """

        mu=self.__mu
        mu_c=self.__mu_c
        DIM=self.getDomain().getDim()
        numLS=self.getNumLevelSets()

        grad_m=grad(m, Function(m.getDomain()))
        if self.__w0 is not None:
            Y = m * self.__w0 * mu
        else:
            if numLS == 1:
                Y = Scalar(0,  grad_m.getFunctionSpace())
            else:
                Y = Data(0, (numLS,) , grad_m.getFunctionSpace())

        if self.__w1 is not None:

            if numLS == 1:
                X=grad_m* self.__w1*mu
            else:
                X=grad_m*self.__w1
                for k in range(numLS):
                    X[k,:]*=mu[k]
        else:
            X = Data(0, grad_m.getShape(), grad_m.getFunctionSpace())

        # cross gradient terms:
        if numLS > 1:
            for k in range(numLS):
                grad_m_k=grad_m[k,:]
                l2_grad_m_k = length(grad_m_k)**2
                for l in range(k):
                    grad_m_l=grad_m[l,:]
                    l2_grad_m_l = length(grad_m_l)**2
                    grad_m_lk = inner(grad_m_l, grad_m_k)
                    f = mu_c[l,k]* self.__wc[l,k]
                    X[l,:] += f * (l2_grad_m_k*grad_m_l - grad_m_lk*grad_m_k)
                    X[k,:] += f * (l2_grad_m_l*grad_m_k - grad_m_lk*grad_m_l)

        return ArithmeticTuple(Y, X)

    def getInverseHessianApproximation(self, m, r, grad_m, solve=True):
        """
        """
        if self._new_mu or self._update_Hessian:
            self._new_mu=False
            self._update_Hessian=False
            mu=self.__mu
            mu_c=self.__mu_c

            DIM=self.getDomain().getDim()
            numLS=self.getNumLevelSets()
            if self.__w0 is not None:
                if numLS == 1:
                    D=self.__w0 * mu
                else:
                    D=self.getPDE().getCoefficient("D")
                    D.setToZero()
                    for k in range(numLS): D[k,k]=self.__w0[k] * mu[k]
                self.getPDE().setValue(D=D)

            A=self.getPDE().getCoefficient("A")
            A.setToZero()
            if self.__w1 is not None:
                if numLS == 1:
                    for i in range(DIM): A[i,i]=self.__w1[i] * mu
                else:
                    for k in range(numLS):
                        for i in range(DIM): A[k,i,k,i]=self.__w1[k,i] * mu[k]

            if numLS > 1:
                # this could be make faster by creating caches for grad_m_k, l2_grad_m_k  and o_kk
                for k in range(numLS):
                    grad_m_k=grad_m[k,:]
                    l2_grad_m_k = length(grad_m_k)**2
                    o_kk=outer(grad_m_k, grad_m_k)
                    for l in range(k):
                        grad_m_l=grad_m[l,:]
                        l2_grad_m_l = length(grad_m_l)**2
                        i_lk = inner(grad_m_l, grad_m_k)
                        o_lk = outer(grad_m_l, grad_m_k)
                        o_kl = outer(grad_m_k, grad_m_l)
                        o_ll=outer(grad_m_l, grad_m_l)
                        f=  mu_c[l,k]* self.__wc[l,k]
                        Z=f * (2*o_lk - o_kl - i_lk*kronecker(DIM))
                        A[l,:,l,:] += f * (l2_grad_m_k*kronecker(DIM) - o_kk)
                        A[l,:,k,:] += Z
                        A[k,:,l,:] += transpose(Z)
                        A[k,:,k,:] += f * (l2_grad_m_l*kronecker(DIM) - o_ll)
            self.getPDE().setValue(A=A)
        #self.getPDE().resetRightHandSideCoefficients()
        #self.getPDE().setValue(X=r[1])
        #print "X only: ",self.getPDE().getSolution()
        #self.getPDE().resetRightHandSideCoefficients()
        #self.getPDE().setValue(Y=r[0])
        #print "Y only: ",self.getPDE().getSolution()

        self.getPDE().resetRightHandSideCoefficients()
        self.getPDE().setValue(X=r[1], Y=r[0])
        if not solve:
            return self.getPDE()
        oldsettings = self.getPDE().getSolverOptions().getSolverMethod()
        self.getPDE().getSolverOptions().setSolverMethod(SolverOptions.GMRES)
        solution = self.getPDE().getSolution()
        self.getPDE().getSolverOptions().setSolverMethod(oldsettings)
        return solution

    def updateHessian(self):
        """
        notifies the class to recalculate the Hessian operator.
        """
        if not self.__useDiagonalHessianApproximation:
            self._update_Hessian=True

    def getNorm(self, m):
        """
        returns the norm of ``m``.

        :param m: level set function
        :type m: `Data`
        :rtype: ``float``
        """
        return sqrt(integrate(length(m)**2)/self.__vol_d)