# -*- coding: utf-8 -*-
"""
Created on Tue Feb 03 17:07:04 2015

Listing 15.1 : analyse de marches aléatoires

@author: grivet
"""

import numpy as ny
import matplotlib.pyplot as plt

NPMAX = 1000
dm = ny.zeros(NPMAX); sigma_d = ny.zeros(NPMAX)
for np in range(10,NPMAX):
    if np % 10 == 0:
         print("  %d" %np, end = '')
    if (np + 1) % 100 == 0:
         print('\n')
    NR = int(ny.sqrt(np));
    d = ny.zeros(NR); 
    for ir in range(NR):
        x = 0; y = 0;
        for i in range(np):
            dx = ny.random.random()-0.5; dy = ny.random.random()-0.5
#        plot2d([x,x+dx],[y,y+dy], frameflag = 0,style = ir)
            x += dx; y += dy
        d[ir] = ny.sqrt(x*x+y*y)
    dm[np] = ny.sum(d)/NR
    ddm = ny.sum(d*d)/NR
    sigma_d[np] = ny.sqrt(ddm - dm[np]*dm[np])
xx = range(NPMAX)
plt.figure(2)
plt.loglog(xx,dm)
plt.xlabel("$N$")
plt.ylabel("$<d>$")
plt.xlim(10,1000)
plt.figure(3)
plt.plot(ny.sqrt(xx),dm)
plt.xlabel("$N^{1/2}$")
plt.ylabel("$<d>$")
plt.xlim(3,32)