from __future__ import division
from __future__ import unicode_literals
from __future__ import print_function
from __future__ import absolute_import
from future import standard_library
standard_library.install_aliases()
from SimPEG import Survey, Utils, Problem, np, sp, mkvc
from scipy.constants import mu_0
import sys
from numpy.lib import recfunctions as recFunc
from SimPEG.EM.Utils import omega

##############
### Fields ###
##############
class BaseMTFields(Problem.Fields):
    """Field Storage for a MT survey."""
    knownFields = {}
    dtype = complex


class Fields1D_e(BaseMTFields):
    """
    Fields storage for the 1D MT solution.
    """
    knownFields = {'e_1dSolution':'F'}
    aliasFields = {
                    'e_1d' : ['e_1dSolution','F','_e'],
                    'e_1dPrimary' : ['e_1dSolution','F','_ePrimary'],
                    'e_1dSecondary' : ['e_1dSolution','F','_eSecondary'],
                    'b_1d' : ['e_1dSolution','E','_b'],
                    'b_1dPrimary' : ['e_1dSolution','E','_bPrimary'],
                    'b_1dSecondary' : ['e_1dSolution','E','_bSecondary']
                  }

    def __init__(self,mesh,survey,**kwargs):
        BaseMTFields.__init__(self,mesh,survey,**kwargs)

    def _ePrimary(self, eSolution, srcList):
        ePrimary = np.zeros_like(eSolution)
        for i, src in enumerate(srcList):
            ep = src.ePrimary(self.survey.prob)
            if ep is not None:
                ePrimary[:,i] = ep[:,-1]
        return ePrimary

    def _eSecondary(self, eSolution, srcList):
        return eSolution

    def _e(self, eSolution, srcList):
        return self._ePrimary(eSolution,srcList) + self._eSecondary(eSolution,srcList)

    def _eDeriv_u(self, src, v, adjoint = False):
        return v

    def _eDeriv_m(self, src, v, adjoint = False):
        # assuming primary does not depend on the model
        return None

    def _bPrimary(self, eSolution, srcList):
        bPrimary = np.zeros([self.survey.mesh.nE,eSolution.shape[1]], dtype = complex)
        for i, src in enumerate(srcList):
            bp = src.bPrimary(self.survey.prob)
            if bp is not None:
                bPrimary[:,i] += bp[:,-1]
        return bPrimary

    def _bSecondary(self, eSolution, srcList):
        C = self.mesh.nodalGrad
        b = (C * eSolution)
        for i, src in enumerate(srcList):
            b[:,i] *= -1./(1j*omega(src.freq))
            # There is no magnetic source in the MT problem
            # S_m, _ = src.eval(self.survey.prob)
            # if S_m is not None:
            #     b[:,i] += 1./(1j*omega(src.freq)) * S_m
        return b

    def _b(self, eSolution, srcList):
        return self._bPrimary(eSolution, srcList) + self._bSecondary(eSolution, srcList)

    def _bSecondaryDeriv_u(self, src, v, adjoint = False):
        C = self.mesh.nodalGrad
        if adjoint:
            return - 1./(1j*omega(src.freq)) * (C.T * v)
        return - 1./(1j*omega(src.freq)) * (C * v)

    def _bSecondaryDeriv_m(self, src, v, adjoint = False):
        # Doesn't depend on m
        # _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
        # S_eDeriv = S_eDeriv(v)
        # if S_eDeriv is not None:
        #     return 1./(1j * omega(src.freq)) * S_eDeriv
        return None

    def _bDeriv_u(self, src, v, adjoint=False):
        # Primary does not depend on u
        return self._bSecondaryDeriv_u(src, v, adjoint)

    def _bDeriv_m(self, src, v, adjoint=False):
        # Assuming the primary does not depend on the model
        return self._bSecondaryDeriv_m(src, v, adjoint)

    def _fDeriv_u(self, src, v, adjoint=False):
        """
        Derivative of the fields object wrt u.

        :param MTsrc src: MT source
        :param numpy.ndarray v: random vector of f_sol.size
        This function stacks the fields derivatives appropriately

        return a vector of size (nreEle+nrbEle)
        """

        de_du = v #Utils.spdiag(np.ones((self.nF,)))
        db_du = self._bDeriv_u(src, v, adjoint)
        # Return the stack
        # This doesn't work...
        return np.vstack((de_du,db_du))

    def _fDeriv_m(self, src, v, adjoint=False):
        """
        Derivative of the fields object wrt m.

        This function stacks the fields derivatives appropriately
        """
        return None

class Fields3D_e(BaseMTFields):
    """
    Fields storage for the 3D MT solution. Labels polarizations by px and py.

        :param SimPEG object mesh: The solution mesh
        :param SimPEG object survey: A survey object
    """
    # Define the known the alias fields
    # Assume that the solution of e on the E.
    ## NOTE: Need to make this more general, to allow for other solutions formats.
    knownFields = {'e_pxSolution':'E','e_pySolution':'E'}
    aliasFields = {
                    'e_px' : ['e_pxSolution','E','_e_px'],
                    'e_pxPrimary' : ['e_pxSolution','E','_e_pxPrimary'],
                    'e_pxSecondary' : ['e_pxSolution','E','_e_pxSecondary'],
                    'e_py' : ['e_pySolution','E','_e_py'],
                    'e_pyPrimary' : ['e_pySolution','E','_e_pyPrimary'],
                    'e_pySecondary' : ['e_pySolution','E','_e_pySecondary'],
                    'b_px' : ['e_pxSolution','F','_b_px'],
                    'b_pxPrimary' : ['e_pxSolution','F','_b_pxPrimary'],
                    'b_pxSecondary' : ['e_pxSolution','F','_b_pxSecondary'],
                    'b_py' : ['e_pySolution','F','_b_py'],
                    'b_pyPrimary' : ['e_pySolution','F','_b_pyPrimary'],
                    'b_pySecondary' : ['e_pySolution','F','_b_pySecondary']
                  }

    def __init__(self,mesh,survey,**kwargs):
        BaseMTFields.__init__(self,mesh,survey,**kwargs)

    def _e_pxPrimary(self, e_pxSolution, srcList):
        e_pxPrimary = np.zeros_like(e_pxSolution)
        for i, src in enumerate(srcList):
            ep = src.ePrimary(self.survey.prob)
            if ep is not None:
                e_pxPrimary[:,i] = ep[:,0]
        return e_pxPrimary

    def _e_pyPrimary(self, e_pySolution, srcList):
        e_pyPrimary = np.zeros_like(e_pySolution)
        for i, src in enumerate(srcList):
            ep = src.ePrimary(self.survey.prob)
            if ep is not None:
                e_pyPrimary[:,i] = ep[:,1]
        return e_pyPrimary

    def _e_pxSecondary(self, e_pxSolution, srcList):
        return e_pxSolution

    def _e_pySecondary(self, e_pySolution, srcList):
        return e_pySolution

    def _e_px(self, e_pxSolution, srcList):
        return self._e_pxPrimary(e_pxSolution,srcList) + self._e_pxSecondary(e_pxSolution,srcList)

    def _e_py(self, e_pySolution, srcList):
        return self._e_pyPrimary(e_pySolution,srcList) + self._e_pySecondary(e_pySolution,srcList)

    #NOTE: For e_p?Deriv_u,
    # v has to be u(2*nE) long for the not adjoint and nE long for adjoint.
    # Returns nE long for not adjoint and 2*nE long for adjoint
    def _e_pxDeriv_u(self, src, v, adjoint = False):
        '''
        Takes the derivative of e_px wrt u
        '''
        if adjoint:
            # adjoint: returns a 2*nE long vector with zero's for py
            return np.vstack((v,np.zeros_like(v)))
        # Not adjoint: return only the px part of the vector
        return v[:len(v)//2]

    def _e_pyDeriv_u(self, src, v, adjoint = False):
        '''
        Takes the derivative of e_py wrt u
        '''
        if adjoint:
            # adjoint: returns a 2*nE long vector with zero's for px
            return np.vstack((np.zeros_like(v),v))
        # Not adjoint: return only the px part of the vector
        return v[len(v)//2::]

    def _e_pxDeriv_m(self, src, v, adjoint = False):
        # assuming primary does not depend on the model
        return None
    def _e_pyDeriv_m(self, src, v, adjoint = False):
        # assuming primary does not depend on the model
        return None

    def _b_pxPrimary(self, e_pxSolution, srcList):
        b_pxPrimary = np.zeros([self.survey.mesh.nF,e_pxSolution.shape[1]], dtype = complex)
        for i, src in enumerate(srcList):
            bp = src.bPrimary(self.survey.prob)
            if bp is not None:
                b_pxPrimary[:,i] += bp[:,0]
        return b_pxPrimary

    def _b_pyPrimary(self, e_pySolution, srcList):
        b_pyPrimary = np.zeros([self.survey.mesh.nF,e_pySolution.shape[1]], dtype = complex)
        for i, src in enumerate(srcList):
            bp = src.bPrimary(self.survey.prob)
            if bp is not None:
                b_pyPrimary[:,i] += bp[:,1]
        return b_pyPrimary

    def _b_pxSecondary(self, e_pxSolution, srcList):
        C = self.mesh.edgeCurl
        b = (C * e_pxSolution)
        for i, src in enumerate(srcList):
            b[:,i] *= -1./(1j*omega(src.freq))
            # There is no magnetic source in the MT problem
            # S_m, _ = src.eval(self.survey.prob)
            # if S_m is not None:
            #     b[:,i] += 1./(1j*omega(src.freq)) * S_m
        return b

    def _b_pySecondary(self, e_pySolution, srcList):
        C = self.mesh.edgeCurl
        b = (C * e_pySolution)
        for i, src in enumerate(srcList):
            b[:,i] *= -1./(1j*omega(src.freq))
            # There is no magnetic source in the MT problem
            # S_m, _ = src.eval(self.survey.prob)
            # if S_m is not None:
            #     b[:,i] += 1./(1j*omega(src.freq)) * S_m
        return b

    def _b_px(self, eSolution, srcList):
        return self._b_pxPrimary(eSolution, srcList) + self._b_pxSecondary(eSolution, srcList)

    def _b_py(self, eSolution, srcList):
        return self._b_pyPrimary(eSolution, srcList) + self._b_pySecondary(eSolution, srcList)

    # NOTE: v needs to be length 2*nE to account for both polarizations
    def _b_pxSecondaryDeriv_u(self, src, v, adjoint = False):
        # C = sp.kron(self.mesh.edgeCurl,[[1,0],[0,0]])
        C = sp.hstack((self.mesh.edgeCurl,Utils.spzeros(self.mesh.nF,self.mesh.nE))) # This works for adjoint = None
        if adjoint:
            return - 1./(1j*omega(src.freq)) * (C.T * v)
        return - 1./(1j*omega(src.freq)) * (C * v)

    def _b_pySecondaryDeriv_u(self, src, v, adjoint = False):
        # C = sp.kron(self.mesh.edgeCurl,[[0,0],[0,1]])
        C = sp.hstack((Utils.spzeros(self.mesh.nF,self.mesh.nE),self.mesh.edgeCurl)) # This works for adjoint = None
        if adjoint:
            return - 1./(1j*omega(src.freq)) * (C.T * v)
        return - 1./(1j*omega(src.freq)) * (C * v)

    def _b_pxSecondaryDeriv_m(self, src, v, adjoint = False):
        # Doesn't depend on m
        # _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
        # S_eDeriv = S_eDeriv(v)
        # if S_eDeriv is not None:
        #     return 1./(1j * omega(src.freq)) * S_eDeriv
        return None

    def _b_pySecondaryDeriv_m(self, src, v, adjoint = False):
        # Doesn't depend on m
        # _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
        # S_eDeriv = S_eDeriv(v)
        # if S_eDeriv is not None:
        #     return 1./(1j * omega(src.freq)) * S_eDeriv
        return None

    def _b_pxDeriv_u(self, src, v, adjoint=False):
        # Primary does not depend on u
        return self._b_pxSecondaryDeriv_u(src, v, adjoint)

    def _b_pyDeriv_u(self, src, v, adjoint=False):
        # Primary does not depend on u
        return self._b_pySecondaryDeriv_u(src, v, adjoint)

    def _b_pxDeriv_m(self, src, v, adjoint=False):
        # Assuming the primary does not depend on the model
        return self._b_pxSecondaryDeriv_m(src, v, adjoint)

    def _b_pyDeriv_m(self, src, v, adjoint=False):
        # Assuming the primary does not depend on the model
        return self._b_pySecondaryDeriv_m(src, v, adjoint)

    def _f_pxDeriv_u(self, src, v, adjoint=False):
        """
        Derivative of the fields object wrt u.

        :param MTsrc src: MT source
        :param numpy.ndarray v: random vector of f_sol.size
        This function stacks the fields derivatives appropriately

        return a vector of size (nreEle+nrbEle)
        """

        de_du = v #Utils.spdiag(np.ones((self.nF,)))
        db_du = self._b_pxDeriv_u(src, v, adjoint)
        # Return the stack
        # This doesn't work...
        return np.vstack((de_du,db_du))

    def _f_pyDeriv_u(self, src, v, adjoint=False):
        """
        Derivative of the fields object wrt u.

        :param MTsrc src: MT source
        :param numpy.ndarray v: random vector of f_sol.size
        This function stacks the fields derivatives appropriately

        return a vector of size (nreEle+nrbEle)
        """

        de_du = v #Utils.spdiag(np.ones((self.nF,)))
        db_du = self._b_pyDeriv_u(src, v, adjoint)
        # Return the stack
        # This doesn't work...
        return np.vstack((de_du,db_du))

    def _f_pxDeriv_m(self, src, v, adjoint=False):
        """
        Derivative of the fields object wrt m.

        This function stacks the fields derivatives appropriately
        """
        # The fields have no dependance to the model.
        return None

    def _f_pyDeriv_m(self, src, v, adjoint=False):
        """
        Derivative of the fields object wrt m.

        This function stacks the fields derivatives appropriately
        """
        # The fields have no dependance to the model.
        return None