print "start approaching target density", targetDensity
while density < targetDensity:
#deltaDensity /= decayFactor
density += deltaDensity
print "current density", density
solver.setVolumeDensity(density)
solver.solve()
g = solver.getRDF()
solver.setStartValue(g)
#Direct calculation
print "Directly calculating RDF for target density", targetDensity
solver.setStartValue(np.zeros(solver.getNumberOfRadialSamplingPoints()) )
solver.setVolumeDensity(targetDensity)
solver.solve()
g_direct = solver.getRDF()
#Plot results
r = np.arange(solver.getNumberOfRadialSamplingPoints() ).astype('float') + 1.0
r *= solver.getDelta_r()/solver.getHardSphereRadius()
pl.plot(r, g, label = 'RDF obtained by iterating over densities' );
pl.plot(r, g_direct, label = 'RDF obtained directly' );
pl.xlabel('r/sigma'); pl.ylabel('g(r)')
pl.legend(loc = 'upper right')
pl.show()
#now GCE limit version
solver.doEnforceGrandCanonicalZeroQlimit()
#solver is in desired state.
solver.solve()
#Get GCE structure factor
Sq_GCE = solver.getSq()
print "reference Sq(0)", Sq_default[0]
print "GCE Sq(0)", Sq_GCE[0]
print "Analytical Sq(0)", (1.0 - volumeDensity)**4/(1.0 + 2.0*volumeDensity)**2
#Even though the enforcement only affects one point in Fourier space,
#the impact will be global, hence we plot the functions. (But real analyis must be done numerically)
#Plot results
Delta_r = solver.getDelta_r()
numberOfRadialSamplingPoints = solver.getNumberOfRadialSamplingPoints()
sigma = solver.getHardSphereRadius()
Delta_q = np.pi/((numberOfRadialSamplingPoints + 1.0)*Delta_r)
q = Delta_q*((np.arange(numberOfRadialSamplingPoints) + 1.0).astype('float'))
plt.plot(np.arcsinh(q*sigma), Sq_default, label = 'Sq_default(q)');
plt.xlabel('arcsinh(q*sigma)'); plt.ylabel('Sq_default(q)')
plt.plot(np.arcsinh(q*sigma), Sq_GCE, label = 'Sq_GCE(q)');
plt.xlabel('arcsinh(q*sigma)'); plt.ylabel('Sq_GCE(q)')
plt.legend(loc = 'upper right')
plt.show()
#densityRange = np.asarray([0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5])
densityRDFdictionary = {}
#Start loop over densities and measure wall clock time
t_start = time.time()
for d in densityRange:
s.setVolumeDensity(float(d))
s.solve()
g = s.getRDF()
densityRDFdictionary[d] = g
t_stop = time.time()
#Print out benchmark
print "time used for", densityRange.size, "density parameters:", t_stop - t_start, " sec"
print "time used for one OZ run:", (t_stop - t_start)/float(densityRange.size), "seconds"
#Plot results
r = np.arange(s.getNumberOfRadialSamplingPoints() ).astype('float') + 1.0
r *= s.getDelta_r()/s.getHardSphereRadius()
for densityKey in densityRDFdictionary:
pl.plot(r, densityRDFdictionary[densityKey], label = 'RDF for d=' + str(densityKey));
pl.xlabel('r/sigma'); pl.ylabel('g(r)')
pl.legend(loc = 'upper right')
pl.show()
#solver is in desired state.
solver.solve()
#Get GCE structure factor
Sq_GCE = solver.getSq()
print "reference Sq(0)", Sq_default[0]
print "GCE Sq(0)", Sq_GCE[0]
print "Analytical Sq(0)", (1.0 - volumeDensity)**4 / (
1.0 + 2.0 * volumeDensity)**2
#Even though the enforcement only affects one point in Fourier space,
#the impact will be global, hence we plot the functions. (But real analyis must be done numerically)
#Plot results
Delta_r = solver.getDelta_r()
numberOfRadialSamplingPoints = solver.getNumberOfRadialSamplingPoints()
sigma = solver.getHardSphereRadius()
Delta_q = np.pi / ((numberOfRadialSamplingPoints + 1.0) * Delta_r)
q = Delta_q * (
(np.arange(numberOfRadialSamplingPoints) + 1.0).astype('float'))
plt.plot(np.arcsinh(q * sigma), Sq_default, label='Sq_default(q)')
plt.xlabel('arcsinh(q*sigma)')
plt.ylabel('Sq_default(q)')
plt.plot(np.arcsinh(q * sigma), Sq_GCE, label='Sq_GCE(q)')
plt.xlabel('arcsinh(q*sigma)')
plt.ylabel('Sq_GCE(q)')
plt.legend(loc='upper right')
plt.show()
