import numpy as np
from scipy.constants import mu_0, pi
from scipy import special

def DCAnalyticHalf(txloc, rxlocs, sigma, flag="wholespace"):
    """
        Analytic solution for electric potential from a postive pole

        Input variables:

            txloc =  a xyz location of A (+) electrode (np.r_[xa, ya, za])

            rxlocs = [M, N]
                M: xyz locations of M (+) electrode (np.c_[xmlocs, ymlocs, zmlocs])
                N: xyz locations of N (-) electrode (np.c_[xnlocs, ynlocs, znlocs])

            sigma = conductivity (either float or complex)
            flag = "wholsespace" or "halfspace"

    """
    M = rxlocs[0]
    N = rxlocs[1]

    rM = np.sqrt( (M[:,0]-txloc[0])**2 + (M[:,1]-txloc[1])**2 + (M[:,2]-txloc[1])**2 )
    rN = np.sqrt( (N[:,0]-txloc[0])**2 + (N[:,1]-txloc[1])**2 + (N[:,2]-txloc[1])**2 )

    phiM = 1./(4*np.pi*rM*sigma)
    phiN = 1./(4*np.pi*rN*sigma)
    phi = phiM - phiN

    if flag == "halfspace":
        phi *= 2

    return phi

deg2rad  = lambda deg: deg/180.*np.pi
rad2deg  = lambda rad: rad*180./np.pi

def DCAnalyticSphere(txloc, rxloc, xc, radius, sigma, sigma1, \
                 flag = "sec", order=12, halfspace=False):
# def DCSpherePointCurrent(txloc, rxloc, xc, radius, rho, rho1, \
#                  flag = "sec", order=12):
    """

        Parameters:

            txloc (array) : current electrode location (x,y,z)
            xc (float)    : x center of depressed sphere
            rxloc (array) : electrode locations
                              (Nx3 array, # of electrodes)
            radius (float): radius of the sphere (m)
            rho (float)   : resistivity of the background (ohm-m)
            rho1 (float)  : resistivity of the sphere
            flag (string) : "sec", "total", "prim"
                              (default="sec")
                              "sec": secondary potential only due to sphere
                              "prim": primary potential from the point source
                              "total": "sec"+"prim"
            order (float) : maximum order of Legendre polynomial
                              (default=12)

        Written by Seogi Kang (skang@eos.ubc.ca)
        Ph.D. Candidate of University of British Columbia, Canada

    """

    Pleg = []
    # Compute Legendre Polynomial
    for i in range(order):
        Pleg.append(special.legendre(i, monic=0))


    rho = 1./sigma
    rho1 = 1./sigma1

    # Center of the sphere should be aligned in txloc in y-direction
    yc = txloc[1]
    xyz = np.c_[rxloc[:,0]-xc, rxloc[:,1]-yc, rxloc[:,2]]
    r = np.sqrt( (xyz**2).sum(axis=1) )

    x0 = abs(txloc[0]-xc)

    costheta = xyz[:,0]/r * (txloc[0]-xc)/x0
    phi = np.zeros_like(r)
    R = (r**2+x0**2.-2.*r*x0*costheta)**0.5
    # primary potential in a whole space
    prim = rho*1./(4*np.pi*R)

    if flag =="prim":
        return prim

    sphind = r < radius
    out = np.zeros_like(r)
    for n in range(order):
        An, Bn = AnBnfun(n, radius, x0, rho, rho1)
        dumout = An*r[~sphind]**(-n-1.)*Pleg[n](costheta[~sphind])
        out[~sphind] += dumout
        dumin = Bn*r[sphind]**(n)*Pleg[n](costheta[sphind])
        out[sphind] += dumin

    out[~sphind] += prim[~sphind]

    if halfspace:
        scale = 2
    else:
        scale = 1

    if flag == "sec":
        return scale*(out-prim)
    elif flag == "total":
        return scale*out

def AnBnfun(n, radius, x0, rho, rho1, I=1.):
    const = I*rho/(4*np.pi)
    bunmo = n*rho + (n+1)*rho1
    An = const * radius**(2*n+1) / x0 ** (n+1.) * n * \
        (rho1-rho) / bunmo
    Bn = const * 1. / x0 ** (n+1.) * (2*n+1) * (rho1) / bunmo
    return An, Bn