import numpy as np
import scipy.sparse as sp
from scipy.constants import pi
from SimPEG.Utils import mkvc, ndgrid, sdiag
from TensorMesh import TensorMesh

class CylMesh(TensorMesh):
    """
        CylMesh is a mesh class for cylindrically problems
    """

    _meshType = 'CYL'

    def __init__(self, h, x0=None):
        assert len(h) == 3, "len(h) must equal 3, for a cylindrically symmetric mesh use [hx, 1, hz]"

        if x0 is not None:
            assert x0.size == 3, "x0.size must equal 1"
        else:
            x0 = np.r_[0, 0, 0]

        for i, h_i in enumerate(h):
            if type(h_i) in [int, long, float]:
                # This gives you something over the unit cylinder.
                h_i = (2*np.pi if i==1 else 1.)*np.ones(int(h_i))/int(h_i)
            assert type(h_i) == np.ndarray, ("h[%i] is not a numpy array." % i)
            assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
            h[i] = h_i[:] # make a copy.

        assert h[1].sum() == 2*np.pi, "The 2nd dimension must sum to 2*pi"

        TensorMesh.__init__(self, h, x0)

    @property
    def nNx(self):
        """
        Number of nodes in the x-direction

        :rtype: int
        :return: nNx
        """
        return self.nCx

    @property
    def nNy(self):
        """
        Number of nodes in the y-direction

        :rtype: int
        :return: nNy
        """
        return self.nCy - 1

    @property
    def nN(self):
        """
        Total number of nodes

        :rtype: int
        :return: nN
        """
        return (np.r_[self.nNx, self.nNy, self.nNz]).prod()

    @property
    def nFx(self):
        """
        Number of x-faces

        :rtype: int
        :return: nFx
        """
        return self.nC

    @property
    def vnFx(self):
        """
        Number of x-faces in each direction

        :rtype: numpy.array (dim, )
        :return: vnFx
        """
        return self.vnC

    @property
    def nFy(self):
        """
        Number of y-faces

        :rtype: int
        :return: nFy
        """
        return (self.vnC + np.r_[0,-1,0][:self.dim]).prod()

    @property
    def nEx(self):
        """
        Number of x-edges

        :rtype: int
        :return: nEx
        """
        return (self._n + np.r_[0,-1,1]).prod()

    @property
    def nEy(self):
        """
        Number of y-edges

        :rtype: int
        :return: nEy
        """
        return (self._n + np.r_[0,0,1]).prod()

    @property
    def nEz(self):
        """
        Number of z-edges

        :rtype: int
        :return: nEz
        """
        return (self._n + np.r_[0,-1,0]).prod()

    @property
    def vectorNx(self):
        """Nodal grid vector (1D) in the r direction"""
        return self.hr.cumsum()

    @property
    def edge(self):
        """Edge lengths"""
        if getattr(self, '_edge', None) is None:
            self._edge = 2*pi*self.gridN[:,0]
        return self._edge

    @property
    def area(self):
        """Face areas"""
        if getattr(self, '_area', None) is None:
            areaR = np.kron(self.hz, 2*pi*self.vectorNr)
            areaZ = np.kron(np.ones_like(self.vectorNz),pi*(self.vectorNr**2 - np.r_[0, self.vectorNr[:-1]]**2))
            self._area = np.r_[areaR, areaZ]
        return self._area

    @property
    def vol(self):
        """Volume of each cell"""
        if getattr(self, '_vol', None) is None:
            az = pi*(self.vectorNr**2 - np.r_[0, self.vectorNr[:-1]]**2)
            self._vol = np.kron(self.hz,az)
        return self._vol

    ####################################################
    # Operators
    ####################################################

    @property
    def edgeCurl(self):
        """The edgeCurl property."""
        if getattr(self, '_edgeCurl', None) is None:
            #1D Difference matricies
            dr = sp.spdiags((np.ones((self.nCx+1, 1))*[-1, 1]).T, [-1,0], self.nCx, self.nCx, format="csr")
            dz = sp.spdiags((np.ones((self.nCz+1, 1))*[-1, 1]).T, [0,1], self.nCz, self.nCz+1, format="csr")

            #2D Difference matricies
            Dr = sp.kron(sp.eye(self.nNz), dr)
            Dz = -sp.kron(dz, sp.eye(self.nCx))  #Not sure about this negative

            #Edge curl operator
            self._edgeCurl = sp.diags(1/self.area,0)*sp.vstack((Dz, Dr))*sp.diags(self.edge,0)
        return self._edgeCurl

    @property
    def aveE2CC(self):
        """Averaging operator from cell edges to cell centres"""
        if getattr(self, '_aveE2CC', None) is None:
            az = sp.spdiags(0.5*np.ones((2, self.nNz)), [-1,0], self.nNz, self.nCz, format='csr')
            ar = sp.spdiags(0.5*np.ones((2, self.nCx)), [0, 1], self.nCx, self.nCx, format='csr')
            ar[0,0] = 1
            self._aveE2CC = sp.kron(az, ar).T
        return self._aveE2CC

    @property
    def aveF2CC(self):
        """Averaging operator from cell faces to cell centres"""
        if getattr(self, '_aveF2CC', None) is None:
            az = sp.spdiags(0.5*np.ones((2, self.nNz)), [-1,0], self.nNz, self.nCz, format='csr')
            ar = sp.spdiags(0.5*np.ones((2, self.nCx)), [0, 1], self.nCx, self.nCx, format='csr')
            ar[0,0] = 1
            Afr = sp.kron(sp.eye(self.nCz),ar)
            Afz = sp.kron(az,sp.eye(self.nCx))
            self._aveF2CC = sp.vstack((Afr,Afz)).T
        return self._aveF2CC

    def getFaceMassDeriv(self):
        Av = self.aveF2CC
        return Av.T * sdiag(self.vol)

    def getEdgeMassDeriv(self):
        Av = self.aveE2CC
        return Av.T * sdiag(self.vol)


    ####################################################
    # Methods
    ####################################################


    def getMass(self, materialProp=None, loc='e'):
        """ Produces mass matricies.

        :param None,float,numpy.ndarray materialProp: property to be averaged (see below)
        :param str loc: Average to location: 'e'-edges, 'f'-faces
        :rtype: scipy.sparse.csr.csr_matrix
        :return: M, the mass matrix

        materialProp can be::

            None            -> takes materialProp = 1 (default)
            float           -> a constant value for entire domain
            numpy.ndarray   -> if materialProp.size == self.nC
                                    3D property model
                               if materialProp.size = self.nCz
                                    1D (layered eath) property model
        """
        if materialProp is None:
            materialProp = np.ones(self.nC)
        elif type(materialProp) is float:
            materialProp = np.ones(self.nC)*materialProp
        elif materialProp.shape == (self.nCz,):
            materialProp = materialProp.repeat(self.nCx)
        materialProp = mkvc(materialProp)
        assert materialProp.shape == (self.nC,), "materialProp incorrect shape"

        if loc=='e':
            Av = self.aveE2CC
        elif loc=='f':
            Av = self.aveF2CC
        else:
            raise ValueError('Invalid loc')

        diag = Av.T * (self.vol * mkvc(materialProp))

        return sdiag(diag)

    def getEdgeMass(self, materialProp=None):
        """mass matrix for products of edge functions w'*M(materialProp)*e"""
        return self.getMass(loc='e', materialProp=materialProp)

    def getFaceMass(self, materialProp=None):
        """mass matrix for products of face functions w'*M(materialProp)*f"""
        return self.getMass(loc='f', materialProp=materialProp)

    def getInterpolationMat(self, loc, locType='fz'):
        """ Produces intrpolation matrix

        :param numpy.ndarray loc: Location of points to interpolate to
        :param str locType: What to interpolate (see below)
        :rtype: scipy.sparse.csr.csr_matrix
        :return: M, the intrpolation matrix

        locType can be::

            'fz'    -> z-component of field defined on faces
            'fr'    -> r-component of field defined on faces
            'et'    -> theta-component of field defined on edges
        """

        loc = np.atleast_2d(loc)

        assert np.all(loc[:,0]<=self.vectorNr.max()) & \
               np.all(loc[:,1]>=self.vectorNz.min()) & \
               np.all(loc[:,1]<=self.vectorNz.max()), \
               "Points outside of mesh"


        if locType=='fz':
            Q = sp.lil_matrix((loc.shape[0], self.nF), dtype=float)

            for i, iloc in enumerate(loc):
                # Point is on a z-interface
                if np.any(np.abs(self.vectorNz-iloc[1])<0.001):
                    dFz = self.gridFz-iloc          #Distance to z faces
                    dFz[dFz[:,0]>0,:] = np.inf      #Looking for next face to the left...
                    indL = np.argmin(np.sum(dFz**2, axis=1))  #Closest one
                    if self.gridFz[indL,0] == self.vectorCCr.max(): #Point in outer half cell (linear extrapolation)
                        zFL = self.gridFz[indL,:]
                        zFLL = self.gridFz[indL-1,:]
                        Q[i, indL+self.nFr] = (iloc[0] - zFLL[0])/(zFL[0] - zFLL[0])
                        Q[i, indL+self.nFr-1] = -(iloc[0] - zFL[0])/(zFL[0] - zFLL[0])
                    else:
                        zFL = self.gridFz[indL,:]
                        zFR = self.gridFz[indL+1,:]
                        Q[i,indL+self.nFr] = (zFR[0] - iloc[0])/(zFR[0] - zFL[0])
                        Q[i,indL+self.nFr+1] = (iloc[0] - zFL[0])/(zFR[0] - zFL[0])
                # Point is in a cell
                else:
                    dFz = self.gridFz-iloc
                    dFz[dFz>0] = np.inf
                    dFz = np.sum(dFz**2, axis=1)

                    indBL = np.argmin(dFz)         # Face below and to the left
                    indAL = indBL + self.nCx        # Face above and to the left

                    zF_BL = self.gridFz[indBL,:]
                    zF_AL = self.gridFz[indAL,:]

                    dzB = iloc[1] - zF_BL[1]         # z-distance to face below
                    dzA = zF_AL[1] - iloc[1]         # z-distance to face above

                    if self.gridFz[indBL,0] == self.vectorCCr.max(): #Point in outer half cell (linear extrapolation)
                        zF_BLL = self.gridFz[indBL-1,:]
                        zF_ALL = self.gridFz[indAL-1,:]

                        DZ = zF_AL[1] - zF_BL[1]
                        DR = zF_AL[0] - zF_ALL[0]

                        drL = iloc[0] - zF_AL[0]
                        drLL = iloc[0] - zF_ALL[0]

                        Q[i, indBL+self.nFr-1] = -(1 - dzB/DZ)*(drL/DR)
                        Q[i, indBL+self.nFr] = (1 - dzB/DZ)*(drLL/DR)
                        Q[i, indAL+self.nFr-1] = -(dzB/DZ)*(drL/DR)
                        Q[i, indAL+self.nFr] = (dzB/DZ)*(drLL/DR)
                    else:
                        indBR = indBL+1                 # Face below and to the right
                        indAR = indAL + 1               # Face above and to the right
                        zF_BR = self.gridFz[indBR,:]

                        drL = iloc[0] - zF_BL[0]         # r-distance to face on left
                        drR = zF_BR[0] - iloc[0]         # r-distance to face on right

                        drz = (drL + drR)*(dzB + dzA)
                        Q[i,indBL+self.nFr] = drR*dzA/drz
                        Q[i,indBR+self.nFr] = drL*dzA/drz
                        Q[i,indAL+self.nFr] = drR*dzB/drz
                        Q[i,indAR+self.nFr] = drL*dzB/drz

        elif locType=='fr':
            raise NotImplementedError('locType==fr')
        elif locType=='et':
            raise NotImplementedError('locType==et')
        else:
            raise ValueError('Invalid locType')
        return Q.tocsr()

    def getNearest(self, loc, locType):
        """ Returns the index of the closest face or edge to a given location

        :param numpy.ndarray loc: Test point
        :param str locType: Type of location desired (see below)
        :rtype: int
        :return: ind:

        locType can be::

            'fz'    -> location of nearest z-face
            'fr'    -> location of nearest r-face
            'et'    -> location of nearest edge
        """

        if locType=='et':
            dr = self.gridN[:,0] - loc[0]
            dz = self.gridN[:,1] - loc[1]
        elif locType=='fz':
            dr = self.gridFz[:,0] - loc[0]
            dz = self.gridFz[:,1] - loc[1]
        elif locType=='fr':
            dr = self.gridFr[:,0] - loc[0]
            dz = self.gridFr[:,1] - loc[1]
        else:
            raise ValueError('Invalid locType')
        R = np.sqrt(dr**2 + dz**2)
        ind = np.argmin(R)
        return ind