import numpy as np
from scipy.special import erf
from scipy import integrate
import matplotlib.pyplot as plt


def VarLgauss(lc,blks,d):

	scl=(blks/lc)**2
	return (scl**-d)*((np.sqrt(2*np.pi*scl)*erf(np.sqrt(scl/2)) +2*np.exp(-0.5*scl)-2)**d)


def VarLgaussSimp(lc,blks,d):

	A=lc/blks  #lc/L
	B=np.sqrt(2*np.pi) # square root of 2*pi
	C=erf((blks/lc)/np.sqrt(8)) # erf( (L/lc) / square root of 2)
	
	return (A*B*C)**d
	




def arg_exp(t,lc,blks,d):

	scl=(blks/lc)**2

	aux1=np.pi*erf(np.sqrt(scl/(4*t)))
	aux2=np.sqrt(np.pi)*(1-np.exp(-scl/(4*t)))*np.sqrt(4*t/scl)
	return t*np.exp(-t)*((aux1-aux2)**d)


def VarLexp3d(lc,blks):	#ic=5.378669493723924333  para lc 16
	d=3
	#a=1/64/np.pi
	t=np.arange(0.000000001,50,0.001)	
	var=np.empty(0)
	for blk in blks:
		y=arg_exp(t,lc,blk,d)
		var=np.append(var,64*np.pi*((lc/(2*np.pi*blk))**d)*np.trapz(y))

	return var

def argVarLexp2d(lc,blk):
	scl=float(blk/(2*lc))
	f = lambda y, x: np.exp(-1*np.sqrt(x**2 +y**2))

	res=integrate.dblquad(f,-scl , scl, lambda x: -scl, lambda x: scl,epsabs=1.49e-8, epsrel=1.49e-8)#0,1,lambda x: 0, lambda x: 1)

	return ((lc/blk)**2)*res[0]

def VarLexp2d(lc,blks):
	#if lc==1.33:
	#	blks=np.append(np.arange(1,2,0.1),blks[1:])
	res=np.empty(0)
	for blk in blks:
		res=np.append(res,argVarLexp2d(lc,blk))

	return res