def plotSolution(path, error):
"""
Definition space of the solution is assumed to be [0, 1)
Length of loaded array is assumed to be N = N_sim+2, where 2 comes
from adding the boundaries after calculations.
h = 1/(N_sim+1) = 1/(N-1)
Plotting only solutions with high steplength to avoid crash of gnuplot
"""
dataSolution = np.fromfile(path, dtype=np.float64)
N = len(dataSolution)
h = 1.0 / (N - 1)
x = np.linspace(0, 1, N)
solution = analytic_solution(x)
if N < 10000:
figure()
plot(x, dataSolution, 'o')
hold('on')
plot(x, solution)
title('Solution to -u\'\'=f(x), h=%6.2g' % h)
xlabel('x')
ylabel('u(x)')
legend('Approximation', 'Analytic solution')
error_array = solution - dataSolution
error_array = np.abs(error_array / solution)
error_array[0] = 0
error_array[len(error_array) - 1] = 0
error.append([h, np.max(error_array)])
def plot_absmag(self, N):
figure()
for i in N:
T_list = []
absM_list = []
for sim in self.simulations:
if sim.N == i:
absM_list.append(sim.absM_end)
T_list.append(sim.T)
T_diff = []
T_list, absM_list = zip(*sorted(zip(T_list, absM_list)))
for j in range(len(T_list)-1):
T_diff.append((absM_list[j+1]-absM_list[j])/(T_list[j+1]-T_list[j-1]))
T_diff = abs(np.asarray(T_diff))
index = T_diff.argmax()
self.Tc.append((T_list[index+1]+T_list[index])/2.0)
self.L.append(1./i)
plot(T_list, absM_list, '-*', legend="N = %d" % i)
title("Absolute magnetic moment as a function of temperature")
xlabel("$kT/J$")
ylabel("$|\mathcal{M}|$")
hold('on')
hardcopy(self.figurepath + "absmag.png")
slope, intercept, tmp1, tmp2, tmp3 = stats.linregress(self.L, self.Tc)
x = np.linspace(0, 0.05, 20)
y = intercept + slope*x
hold("off")
figure()
plot(self.L, self.Tc, '*', legend="Data points")
hold("on")
plot(x, y, legend="%f $L^{-1}$ + %f" %(slope, intercept))
xlabel("$1/L$")
ylabel("$kT_c/J$")
title("Calculated critical temperature")
hardcopy(self.figurepath + "calctc.png")
def plotSolution(path, error):
"""
Definition space of the solution is assumed to be [0, 1)
Length of loaded array is assumed to be N = N_sim+2, where 2 comes
from adding the boundaries after calculations.
h = 1/(N_sim+1) = 1/(N-1)
Plotting only solutions with high steplength to avoid crash of gnuplot
"""
dataSolution = np.fromfile(path, dtype=np.float64);
N = len(dataSolution);
h = 1.0/(N-1);
x = np.linspace(0, 1, N);
solution = analytic_solution(x);
if N<10000:
figure()
plot(x, dataSolution, 'o');
hold('on');
plot(x, solution);
title('Solution to -u\'\'=f(x), h=%6.2g' %h)
xlabel('x')
ylabel('u(x)')
legend('Approximation', 'Analytic solution')
error_array = solution-dataSolution
error_array = np.abs(error_array/solution)
error_array[0] = 0;
error_array[len(error_array)-1] =0;
error.append([h, np.max(error_array)])
def plot_velocities(self):
figure();
if not self.velocities:
self.calculate_velocities();
plot(self.t, self.velocities);
title(self.filename + ' Velocities');
xlabel('t[s]');
ylabel('radial velocity [m/s]');
def plot_velocities(self):
figure()
if not self.velocities:
self.calculate_velocities()
plot(self.t, self.velocities)
title(self.filename + ' Velocities')
xlabel('t[s]')
ylabel('radial velocity [m/s]')
def plotBySimulation(self):
for i in range(len(self.simulations)):
sim = self.simulations[i];
figure(i);
for j in range(len(sim.states)):
plot(sim.rho, sim.states[j]**2, legend=r"$\psi_{%d}, \lambda= %g$" % (j, sim.eigenvalues[j]), xlabel=r'$\frac{1}{\alpha}r$', ylabel=r'$\alpha|\psi_n|^2$')
title("$\omega = %g$" %sim.omega)
hold('on')
raw_input("press enter")
closefigs()
def plotByOmega(self, omegalimit=0.1):
for sim in self.simulations:
for i in range(len(sim.states)):
if sim.omega >= omegalimit:
figure(i)
plot(sim.rho, sim.states[i]**2, legend="$\omega= %g, \lambda= %g$" % (sim.omega, sim.eigenvalues[i]), xlabel=r'$\frac{1}{\alpha}r$', \
ylabel=r'$\alpha|\psi_n|^2$')
title(r"$\psi_{%d}$" % i)
hold('on')
raw_input("press enter")
closefigs()
def plotByOmega(self, omegalimit = 0.1):
for sim in self.simulations:
for i in range(len(sim.states)):
if sim.omega >= omegalimit:
figure(i);
plot(sim.rho, sim.states[i]**2, legend="$\omega= %g, \lambda= %g$" % (sim.omega, sim.eigenvalues[i]), xlabel=r'$\frac{1}{\alpha}r$', \
ylabel=r'$\alpha|\psi_n|^2$')
title(r"$\psi_{%d}$" % i);
hold('on')
raw_input("press enter")
closefigs();
def plot_fitted_velocities(self, destination = False):
if self.P == 0:
self.fit_velocities();
data = self.model.modelFunction([self.v_mean, self.v_r, self.P, self.t_0], self.t);
figure();
plot(self.t, self.velocities, '--r');
hold('on');
plot(self.t, data, '-b')
title("Least square modeled velocities");
xlabel('t [s]');
ylabel('v [m/s]');
legend('v_mean=%g \n v_r=%g \n P=%g \n t_0=%g' % (self.v_mean, self.v_r, self.P, self.t_0));
if destination:
hardcopy(destination);
def plotBySimulation(self):
for i in range(len(self.simulations)):
sim = self.simulations[i]
figure(i)
for j in range(len(sim.states)):
plot(sim.rho,
sim.states[j]**2,
legend=r"$\psi_{%d}, \lambda= %g$" %
(j, sim.eigenvalues[j]),
xlabel=r'$\frac{1}{\alpha}r$',
ylabel=r'$\alpha|\psi_n|^2$')
title("$\omega = %g$" % sim.omega)
hold('on')
raw_input("press enter")
closefigs()
def plot_heat_capacity(self, N):
figure()
for i in N:
T_list = []
hc_list = []
for sim in self.simulations:
if sim.N == i:
hc_list.append(sim.heat_capacity)
T_list.append(sim.T)
T_list, hc_list = zip(*sorted(zip(T_list, hc_list)))
plot(T_list, hc_list, '-*', legend="N = %d" % i)
xlabel("$kT/J$")
ylabel("$C_V/k$")
title("Heat capacity as a function of temperature")
hold('on')
hardcopy(self.figurepath + "heat_capacity.png")
def plot_energies(self, N):
figure()
for i in N:
T_list = []
E_list = []
for sim in self.simulations:
if sim.N == i:
E_list.append(sim.E_end)
T_list.append(sim.T)
T_list, E_list = zip(*sorted(zip(T_list, E_list)))
plot(T_list, E_list, '-*', legend="N = %d" % i)
title("Energy as a function of temperature")
xlabel("$kT/J$")
ylabel("$E/J$")
hold('on')
hardcopy(self.figurepath + "energy.png")
def plot_energies(self, N):
figure()
for i in N:
T_list = []
E_list = []
for sim in self.simulations:
if sim.N == i:
E_list.append(sim.E_end)
T_list.append(sim.T)
T_list, E_list = zip(*sorted(zip(T_list, E_list)))
plot(T_list, E_list, '-*', legend="N = %d" % i)
title("Energy as a function of temperature")
xlabel("$kT/J$")
ylabel("$E/J$")
hold('on')
hardcopy(self.figurepath + "energy.png")
def plot_fitted_velocities(self, destination=False):
if self.P == 0:
self.fit_velocities()
data = self.model.modelFunction(
[self.v_mean, self.v_r, self.P, self.t_0], self.t)
figure()
plot(self.t, self.velocities, '--r')
hold('on')
plot(self.t, data, '-b')
title("Least square modeled velocities")
xlabel('t [s]')
ylabel('v [m/s]')
legend('v_mean=%g \n v_r=%g \n P=%g \n t_0=%g' %
(self.v_mean, self.v_r, self.P, self.t_0))
if destination:
hardcopy(destination)
def plot_heat_capacity(self, N):
figure()
for i in N:
T_list = []
hc_list = []
for sim in self.simulations:
if sim.N == i:
hc_list.append(sim.heat_capacity)
T_list.append(sim.T)
T_list, hc_list = zip(*sorted(zip(T_list, hc_list)))
plot(T_list, hc_list, '-*', legend="N = %d" % i)
xlabel("$kT/J$")
ylabel("$C_V/k$")
title("Heat capacity as a function of temperature")
hold('on')
hardcopy(self.figurepath + "heat_capacity.png")
def plot_susceptibility(self, N):
figure()
legends = []
for i in N:
T_list = []
su_list = []
#legends.append("N = %d" % i)
for sim in self.simulations:
if sim.N == i:
su_list.append(sim.susceptibility)
T_list.append(sim.T)
T_list, su_list = zip(*sorted(zip(T_list, su_list)))
plot(T_list, su_list, '-*', legend="N = %d" % i)
title("Susceptibility as a function of temperature")
xlabel("$kT/J$")
ylabel("$\chi J$")
hold('on')
hardcopy(self.figurepath + "susceptibility.png")
def plot_susceptibility(self, N):
figure()
legends = []
for i in N:
T_list = []
su_list = []
#legends.append("N = %d" % i)
for sim in self.simulations:
if sim.N == i:
su_list.append(sim.susceptibility)
T_list.append(sim.T)
T_list, su_list = zip(*sorted(zip(T_list, su_list)))
plot(T_list, su_list, '-*', legend="N = %d" % i)
title("Susceptibility as a function of temperature")
xlabel("$kT/J$")
ylabel("$\chi J$")
hold('on')
hardcopy(self.figurepath + "susceptibility.png")
def plotSolution(path, name, rho, eigenvalues):
dataSolution = np.fromfile(path + name, dtype=np.float64)
N = len(dataSolution)
x = rho
dataSolution = dataSolution / np.sqrt(trapz(dataSolution ** 2 / x ** 2, x))
state_number = round(float((name.strip(".bin").strip("state"))))
integral = trapz(dataSolution ** 2 / x ** 2, x)
print state_number
if N < 10000:
figure()
plot(x, dataSolution ** 2 / x ** 2)
hold("on")
xlabel(r"$\rho$")
ylabel(r"$R^2(\rho)$")
title(name.strip(".bin") + ", " + "$\lambda =$ %g" % eigenvalues[state_number])
legend("integral = %g" % integral)
else:
print "Stopped plot, N>10000"
def plotSolution(path, name, rho, eigenvalues):
dataSolution = np.fromfile(path + name, dtype=np.float64)
N = len(dataSolution)
x = rho
dataSolution = dataSolution / np.sqrt(trapz(dataSolution**2 / x**2, x))
state_number = round(float((name.strip(".bin").strip("state"))))
integral = trapz(dataSolution**2 / x**2, x)
print state_number
if N < 10000:
figure()
plot(x, dataSolution**2 / x**2)
hold('on')
xlabel(r'$\rho$')
ylabel(r'$R^2(\rho)$')
title(
name.strip('.bin') + ", " +
'$\lambda =$ %g' % eigenvalues[state_number])
legend("integral = %g" % integral)
else:
print "Stopped plot, N>10000"
def plot_absmag(self, N):
figure()
for i in N:
T_list = []
absM_list = []
for sim in self.simulations:
if sim.N == i:
absM_list.append(sim.absM_end)
T_list.append(sim.T)
T_diff = []
T_list, absM_list = zip(*sorted(zip(T_list, absM_list)))
for j in range(len(T_list) - 1):
T_diff.append((absM_list[j + 1] - absM_list[j]) /
(T_list[j + 1] - T_list[j - 1]))
T_diff = abs(np.asarray(T_diff))
index = T_diff.argmax()
self.Tc.append((T_list[index + 1] + T_list[index]) / 2.0)
self.L.append(1. / i)
plot(T_list, absM_list, '-*', legend="N = %d" % i)
title("Absolute magnetic moment as a function of temperature")
xlabel("$kT/J$")
ylabel("$|\mathcal{M}|$")
hold('on')
hardcopy(self.figurepath + "absmag.png")
slope, intercept, tmp1, tmp2, tmp3 = stats.linregress(self.L, self.Tc)
x = np.linspace(0, 0.05, 20)
y = intercept + slope * x
hold("off")
figure()
plot(self.L, self.Tc, '*', legend="Data points")
hold("on")
plot(x, y, legend="%f $L^{-1}$ + %f" % (slope, intercept))
xlabel("$1/L$")
ylabel("$kT_c/J$")
title("Calculated critical temperature")
hardcopy(self.figurepath + "calctc.png")
eigenvalues = None
rho = None
sqsum = None
for name in os.listdir(path):
if "eigenvalues" in name:
eigenvalues = np.fromfile(path + name, dtype=np.float64)
print eigenvalues
if "grid" in name:
print path + name
rho = np.fromfile(path + name, dtype=np.float64)
print rho
if "sqsum" in name:
sqsum = []
fileInput = open(path + name)
for line in fileInput:
sqsum.append(float(eval(line)))
sqsum = np.asarray(sqsum)
figure()
semilogy(sqsum)
title("Sum of squared off-diagonal elements")
for name in os.listdir(path):
if "state" in name:
plotSolution(path, name, rho, eigenvalues)
raw_input("press enter")
def plot_intensities(self):
figure();
plot(self.t, self.intensities);
xlabel('t[s]');
ylabel('Relative intensity')
title(self.filename + ' intensity');
sims.load_tree()
N = [20, 30, 40, 60, 80, 100]
sims.plot_heat_capacity(N)#, 40, 60, 80, 100])
sims.plot_susceptibility(N)
sims.plot_absmag(N)
sims.plot_energies(N)
"""
###########################
# Plotting P(E) for L=20 an T = [1, 2.4]
###########################
sim = Simulation(20, 2.4, "/scratch/henriasv/FYS3150/IsingModel_once/N20/T2.4")
sim.set_thermalization(0.2)
sim.calculate_properties()
sim.plot_pe()
title("Probability density function for the energy at T=2.4 (not normalized)")
xlabel("E")
ylabel("Count")
variance = stats.var(sim.e_array)
print "variance = %f" % variance, sim.var_E
hold("on")
sim = Simulation(20, 1, "/scratch/henriasv/FYS3150/IsingModel_once/N20/T1")
sim.set_thermalization(0.2)
sim.calculate_properties()
sim.plot_pe()
title("Probability density function for the energy at T=1 (not normalized)")
xlabel("E")
ylabel("Count")
"""
###########################
# Plotting convergence with ordered or random initialization for T = [1, 2.4]
def plot_frequencies(self):
figure();
plot(self.t, self.frequencies);
xlabel('t[s]');
ylabel('Wavelength [nm]');
title(self.filename + ' Wavelength');
plot(x, dataSolution, 'o')
hold('on')
plot(x, solution)
title('Solution to -u\'\'=f(x), h=%6.2g' % h)
xlabel('x')
ylabel('u(x)')
legend('Approximation', 'Analytic solution')
error_array = solution - dataSolution
error_array = np.abs(error_array / solution)
error_array[0] = 0
error_array[len(error_array) - 1] = 0
error.append([h, np.max(error_array)])
path = "/scratch/henriasv/FYS3150/project1/"
error = []
for name in os.listdir(path):
if not name.endswith('.txt'):
plotSolution(path + name, error)
error = np.asarray(error)
error = np.log10(error)
figure()
plot(error[:, 0], error[:, 1], '*')
title('maximum relative error with different step lengths')
xlabel('log(h)')
ylabel('log($\epsilon$)')
raw_input("press enter")
sims.load_tree()
N = [20, 30, 40, 60, 80, 100]
sims.plot_heat_capacity(N)#, 40, 60, 80, 100])
sims.plot_susceptibility(N)
sims.plot_absmag(N)
sims.plot_energies(N)
"""
###########################
# Plotting P(E) for L=20 an T = [1, 2.4]
###########################
sim = Simulation(20, 2.4, "/scratch/henriasv/FYS3150/IsingModel_once/N20/T2.4")
sim.set_thermalization(0.2)
sim.calculate_properties()
sim.plot_pe()
title("Probability density function for the energy at T=2.4 (not normalized)")
xlabel("E")
ylabel("Count")
variance = stats.var(sim.e_array)
print "variance = %f" % variance, sim.var_E
hold("on")
sim = Simulation(20, 1, "/scratch/henriasv/FYS3150/IsingModel_once/N20/T1")
sim.set_thermalization(0.2)
sim.calculate_properties()
sim.plot_pe()
title("Probability density function for the energy at T=1 (not normalized)")
xlabel("E")
ylabel("Count")
"""
###########################
path = "/scratch/henriasv/FYS3150/project2/" + sys.argv[1]
eigenvalues = None
rho = None
sqsum = None
for name in os.listdir(path):
if "eigenvalues" in name:
eigenvalues = np.fromfile(path + name, dtype=np.float64)
print eigenvalues
if "grid" in name:
print path + name
rho = np.fromfile(path + name, dtype=np.float64)
print rho
if "sqsum" in name:
sqsum = []
fileInput = open(path + name)
for line in fileInput:
sqsum.append(float(eval(line)))
sqsum = np.asarray(sqsum)
figure()
semilogy(sqsum)
title("Sum of squared off-diagonal elements")
for name in os.listdir(path):
if "state" in name:
plotSolution(path, name, rho, eigenvalues)
raw_input("press enter")
def plot_intensities(self):
figure()
plot(self.t, self.intensities)
xlabel('t[s]')
ylabel('Relative intensity')
title(self.filename + ' intensity')
plot(x, dataSolution, 'o');
hold('on');
plot(x, solution);
title('Solution to -u\'\'=f(x), h=%6.2g' %h)
xlabel('x')
ylabel('u(x)')
legend('Approximation', 'Analytic solution')
error_array = solution-dataSolution
error_array = np.abs(error_array/solution)
error_array[0] = 0;
error_array[len(error_array)-1] =0;
error.append([h, np.max(error_array)])
path = "/scratch/henriasv/FYS3150/project1/"
error = [];
for name in os.listdir(path):
if not name.endswith('.txt'):
plotSolution(path+name, error)
error = np.asarray(error)
error = np.log10(error)
figure()
plot(error[:, 0], error[:, 1], '*')
title('maximum relative error with different step lengths')
xlabel('log(h)')
ylabel('log($\epsilon$)')
raw_input("press enter")
sort_data(prec_gaulag)
sort_data(prec_gauleg)
sort_data(prec_is_mc)
sort_data(prec_bf_mc)
figure()
loglog(prec_gaulag[:,0], prec_gaulag[:,1])
hold("all")
loglog(prec_gauleg[:,0], prec_gauleg[:,1])
loglog(prec_bf_mc[:,0], prec_bf_mc[:,1])
loglog(prec_is_mc[:,0], prec_is_mc[:,1])
legend("Gauss Laguerre", "Gauss Legendre", "Brute force Monte Carlo", "Importance sampling Monte Carlo")
xlabel("Number of function evaluations")
ylabel("Relative error")
title("Relative error vs number of calculations for different methods")
hold("off")
# Plotting function evaluations and cpu_time
prec_gaulag = []
prec_gauleg = []
prec_is_mc = []
prec_bf_mc = []
for sim in simulations:
if sim.ID == "gaulag":
prec_gaulag.append([sim.N, sim.cpu_time])
if sim.ID == "gauleg":
prec_gauleg.append([sim.N, sim.cpu_time])
if sim.ID == "bf_mc":
prec_bf_mc.append([sim.N, sim.cpu_time])
def plot_frequencies(self):
figure()
plot(self.t, self.frequencies)
xlabel('t[s]')
ylabel('Wavelength [nm]')
title(self.filename + ' Wavelength')