netsyncanalysisv2eigenwigner.py

# -*- coding: utf-8 -*-
"""
Created on Sat Feb 13 13:30:10 2021

@author: cosmi
"""


import matplotlib 
matplotlib.use('TkAgg') 
from pylab import * 
import networkx as nx
from math import pi
import numpy as np


    
import scipy
import numpy as np
from scipy import misc
import numpy as np
import scipy.linalg as la

from matplotlib import pyplot as plt  # For image viewing

from matplotlib import colors
from matplotlib import ticker
from matplotlib.colors import LinearSegmentedColormap

from matplotlib.collections import LineCollection
from matplotlib.colors import ListedColormap, BoundaryNorm



from random import random as rand
from random import uniform

from qutip.visualization import plot_wigner, hinton

#qutip star imports
from qutip import *

from qutip import Qobj, rand_dm, fidelity, displace, qdiags, qeye, expect
from qutip.states import coherent, coherent_dm, thermal_dm, fock_dm
from qutip.wigner import qfunc


from pygsp import graphs

#def gridsize(val):
#    '''
#    Number Of Particles in a Grid Shall Be Entered such that gridsize 4 = 4 x 4 i.e. 16
#    Particles in Total. Note: this can only be changed at the start of a new 
#    Simulation Run - In This Version Do Note Change While Running the Simulation!
#    '''
#    global n

#    n = int(val)
#    return val
    
    

def initialize(): 
    global g, nextg, hilbert_size
    
    

    
    n = 2
    g = nx.grid_graph(dim=[n,n])

    #g = nx.karate_club_graph()
    
    for i in list(g.nodes()):
        g.node[i]['theta'] = 2 * pi * random()
        #rows, cols = (-0.05, 0.05)
        #arr = [[rand.randrange(10) for i in range(int(cols))] for j in range(int(rows))]
        #a = numpy.asarray(arr)
        #g.node[i]['omega'] = 1. + rand.uniform(-0.05, 0.05) 
        g.node[i]['omega'] = 1. + uniform(-0.05, 0.05)        
    nextg = g.copy()     
    
        
    for i in list(g.nodes()):
        g.node[i]['theta'] = random()    
    nextg = g.copy() 
    
    
    
    
    

    
       
    grid2d = graphs.Graph.from_networkx(nextg)
    
    #print(grid2d.W.toarray())
    #print(grid2d.signals)
    #print(grid2d)
    
    grid2d.compute_fourier_basis()
    
    grid2d.set_coordinates()
    




# plot spectrum 
    fig, ax = plt.subplots(1, 1, figsize=(7,7))
    ax.plot(grid2d.e)
    ax.set_xlabel('eigenvalue index (i)')
    ax.set_ylabel('eigenvalue ($\lambda_{i}$)')
    ax.set_title('2D-grid spectrum');
    #fiedler vector highlighted graph 
    grid2d.plot_signal(grid2d.U[:,1])
   
    #plot all eigenvectors as network graph frames
   
    fig, axes = plt.subplots(2, 3, figsize=(10, 6.6))
    count = 0
    for j in range(2):
        for i in range(2):
            grid2d.plot_signal(grid2d.U[:, count*1], ax=axes[j,i],colorbar=False)
            axes[j,i].set_xticks([])
            axes[j,i].set_yticks([])
            axes[j,i].set_title(f'Eigvec {count*1+1}')
            count+=1
            fig.tight_layout()
            
            
    
    #hilbert space must be the same as the network size for this to make sense
    
    
    alphas = grid2d.signals['omega'] 
    

    print(alphas)
    
    betas = grid2d.signals['theta']
    
    print(betas)
    
    hilbert_size = n

    

    
    psi = coherent(hilbert_size, 0)
    
    rho = coherent_dm(hilbert_size, 1-1j)

    d = displace(hilbert_size, 2+2j)
    
    
    
    #psi = sum([coherent_dm(hilbert_size, a) for a in alphas])
    psi = psi.unit()
    rho = psi*psi.dag()

    fig, ax = plt.subplots(1, 4, figsize=(19, 4))
    
    plot_wigner_fock_distribution(psi, fig=fig, axes=[ax[0], ax[1]])
    plot_wigner_fock_distribution(d*psi, fig=fig, axes=[ax[2], ax[3]])
    
    ax[0].set_title(r"Initial state, $\psi_{vac} = |0 \rangle$")
    ax[2].set_title(r"Displaced state, $D(\alpha=2+2i )\psi_{vac}$")
    plt.show()
    
    fig, ax = plot_wigner_fock_distribution(rho, figsize=(9, 4))
    ax[0].set_title("Superposition of three coherent states")
    plt.show()
    
    
    measured_populations = [measure_population(b, rho) for b in betas]

    




        


def observe(): 
    global g, nextg, grid2d
    subplot(1,2,1)
    cla()
    nx.draw(g, cmap = cm.hsv, vmin = -1, vmax = 1, 
            node_color = [np.sin(g.node[i]['theta']) for i in list(g.nodes())], 
            pos = nx.spring_layout(g) )
    axis('image')
    
    subplot(1,2,2)
    cla()
    
    plot([np.cos(g.node[i]['theta']) for i in list(g.nodes())],
        [np.sin(g.node[i]['theta']) for i in list(g.nodes())], '.')
    axis('image')
    
    axis([-1.1,1.1,-1.1,1.1])
    
    
 

   
    
    #subplot(1,2,2)
    #cla()
    #plot(xdata, ydata,'o',alpha = 0.05)
    #axis('image')
    # for space vs time plotting (chimera search)
    


    
alpha = 2 # coupling strength 
beta = 1 # acceleration rate


#beta could a delay for simulating memory.

Dt = 0.01 # Delta t 

#def update(): 
#    global g, nextg 
#    for i in list(g.nodes()): 
#        theta_i = g.node[i]['theta'] 
#        nextg.node[i]['theta'] = theta_i + (beta * theta_i + alpha * (np.sum(sin(g.node[j]['theta'] - theta_i) for j in g.neighbors(i))) * Dt) 
#    g, nextg = nextg, g 

def measure_population(beta, rho):
    """
    Measures the photon number statistics for state rho when displaced
    by angle alpha.
    
    Parameters
    ----------    
    alpha: np.complex
        A complex displacement.

    rho:
        The density matrix as a QuTiP Qobj (`qutip.Qobj`)

    Returns
    -------
    population: ndarray
        A 1D array for the probabilities for populations.
    """
    hilbertsize = rho.shape[0]
    # Apply a displacement to the state and then measure the diagonals.

    D = displace(hilbertsize, beta)
    rho_disp = D*rho*D.dag()
    populations = np.real(np.diagonal(rho_disp.full()))
    return populations





def update(): 
    global g, nextg, eig_values, eig_vectors, rho, grid2d, theta_i
    for i in list(g.nodes()): 
        theta_i = g.node[i]['theta'] 
        omega_i = g.node[i]['omega']
        nextg.node[i]['theta'] = theta_i + (g.node[i]['omega'] + alpha * ( \
           sum(np.sin(g.node[j]['theta'] - theta_i) for j in g.neighbors(i)) \
           / g.degree(i))) * Dt 
    g, nextg = nextg, g 
    
    
    #for i, j in list(g.nodes()):
        #xdata.append(g.degree(i))
        #ccs = nx.connected_components(g)
        #ydata.append(max(len(cc) for cc in ccs))
        #xdata.append(g.degree(i)); ydata.append(g.degree(j))
        #xdata.append(g.degree(j)); ydata.append(g.degree(i))


    A = nx.adjacency_matrix(nextg)
    print(A)
    n, m = A.shape
    diags = A.sum(axis=0)  # 1 = outdegree, 0 = indegree
    D = scipy.sparse.spdiags(diags.flatten(), [0], m, n, format="csr")
    L = (A-D)
    Lap = L.todense()
    print(Lap)
    
    eig_values, eig_vectors = la.eig(Lap)
    fiedler_pos = np.where(eig_values.real == np.sort(eig_values.real)[1])[0][0]
    fiedler_vector = np.transpose(eig_vectors)[fiedler_pos]
    
    #print("Fiedler value: " + str(fiedler_pos.real))

    # this will be an eigenbra version 
    print("Fiedler vector: " + str(fiedler_vector.real))
    
    
    #nx.laplacian_matrix(nextg).toarray()
    
    
    # applying matrix.trace() method
    LTrace = np.matrix.trace(Lap)
    #print(LTrace)
    
    #print density matrix from graph laplacian
    
    rho = np.divide(Lap,LTrace)
    
    #we need to represent this graph density matrix as a cavity reduced density matrix to make physical sense
    
    #print(rho)
    



    
    print(theta_i)
    
    print(omega_i)
 

    

    #note you can calculate the trace faster using the hadamard product (element-wise multiplication)
    # using the fiedler vector as the basis for the emergent density matrix 
    
    


import pycxsimulator 

pycxsimulator.GUI().start(func=[initialize, observe, update]) 



#plt.figure(1)
    #compare red and blue pixel data
#nbins = 20
#plt.hexbin(x=plot_time_stamp, y=plot_agent, gridsize=nbins, cmap=plt.cm.jet)
#plt.xlabel('Blue Reflectance')
#plt.ylabel('NIR Reflectance')
    # Add a title
#plt.title('NIR vs Blue Spectral Data')
#plt.show()