import numpy as np
from scipy.constants import mu_0, epsilon_0

# useful params
def omega(freq):
    """Angular frequency, omega"""
    return 2.*np.pi*freq

def k(freq, sigma, mu=mu_0, eps=epsilon_0):
    """ Eq 1.47 - 1.49 in Ward and Hohmann """
    w = omega(freq)
    alp  = w * np.sqrt( mu*eps/2 * ( np.sqrt(1. + (sigma / (eps*w))**2 ) + 1) ) 
    beta = w * np.sqrt( mu*eps/2 * ( np.sqrt(1. + (sigma / (eps*w))**2 ) - 1) ) 
    return alp - 1j*beta

# Constitutive relations
def e_from_j(prob,j):
    eqLocs = prob._eqLocs
    if eqLocs is 'FE':
        MSigmaI = prob.MeSigmaI
    elif eqLocs is 'EF':
        MSigmaI = prob.MfRho
    return MSigmaI*j

def j_from_e(prob,e):
    eqLocs = prob._eqLocs
    if eqLocs is 'FE':
        MSigma = prob.MeSigma
    elif eqLocs is 'EF':
        MSigma = prob.MfRhoI
    return MSigma*e

def b_from_h(prob,h):
    eqLocs = prob._eqLocs
    if eqLocs is 'FE':
        MMu = prob.MfMuiI
    elif eqLocs is 'EF':
        MMu = prob.MeMu
    return MMu*h

def h_from_b(prob,b):
    eqLocs = prob._eqLocs
    if eqLocs is 'FE':
        MMuI = prob.MfMui
    elif eqLocs is 'EF':
        MMuI = prob.MeMuI
    return MMuI*b