def plot_components(eigvec_file, eigval_file, bas_state_index, majorX = 50, majorY = 0.02, col="b-o"):
###
'''LDOS Plots function
Plot squared components in all eigenvectors of a bas_state_index basis element (min bas_state_index = 0) as a function of the state energy.'''
###
import numpy as np
from matplotlib import pyplot
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
#
from survival_probability_basis import read_energy_data, read_eigenstates
#
#
eigstates=read_eigenstates(eigvec_file)
eigvals= read_energy_data(eigval_file)
#
#
majorXLocator = MultipleLocator(majorX)
majorYLocator = MultipleLocator(majorY)
#
## for bas_state in range(0,4):
components = eigstates[bas_state_index,:] ## Components of a given basis element in all eigenstates
##
panel = pyplot.subplot(1, 1, 1)
panel.tick_params(axis='both', which='major', labelsize=14)
pyplot.plot(eigvals,components**2,col)
##
panel.xaxis.set_major_locator(majorXLocator)
panel.yaxis.set_major_locator(majorYLocator)
##
##
## pyplot.annotate(bas_state, xy=(30, 0.07))
pyplot.xlabel("Energy")
pyplot.ylabel("Squared Eigenvector Components")
panel.xaxis.label.set_fontsize(18)
panel.yaxis.label.set_fontsize(18)
def hist_components(eigvec_file, basis_index, energy_file, N_value = 1, bins = 20, fig=False):
###
'''Histogram of the squared components of the index-th basis state in the system eigenvectors
(min value = 0) as a function of the system eigenvalues.
Options:
bins : number of bins in the histogram
N_value : renormalize by the system size
fig : plot bar fig
'''
#
import numpy as np
from matplotlib import pyplot
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
#
from survival_probability_basis import read_eigenstates, read_energy_data
#
#
eigstates=read_eigenstates(eigvec_file)
##
eigenvalues = read_energy_data(energy_file)/N_value
#
## Energy bins
energy_bins=np.linspace(eigenvalues[0], eigenvalues[-1],num = bins)
col_values = np.zeros(len(energy_bins)) # Initialize histogram values
#
## Basis state components
components = eigstates[basis_index,:]**2
#
columns = np.zeros(bins)
###
idx = 0
for index_bin in range(1,bins):
#
for aval_index in range(idx, len(eigenvalues)+1):
#
energy = eigenvalues[aval_index]
#
if (energy < energy_bins[index_bin]):
columns[index_bin] = columns[index_bin] + components[aval_index]
idx = idx + 1
else:
break
#
# Define bar centroids
wdth = (energy_bins[1]-energy_bins[0])
lngth = bins - 1
centroids = energy_bins + wdth/2
##
if (fig):
figure = pyplot.figure()
ax = pyplot.subplot(111)
ax.bar(centroids[:lngth], columns[:lngth],width=wdth,alpha=0.5)
##
return centroids[:lngth], columns[:lngth]
def plot_components_grid(eigvec_file, min_eigstate_index, state_step, num_rows, num_cols, X_vector = 0, majorX = 50, majorY = 0.02, col="b-o"):
###
'''Plot in a num_rows x num_cols grid squared components of eigstates
from min_eigenstate_index-th eigenvector (min value = 0) adding state_step.
'''
#
import numpy as np
from matplotlib import pyplot
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
#
from survival_probability_basis import read_eigenstates
#
#
eigstates=read_eigenstates(eigvec_file)
#
#
fig,axes = pyplot.subplots(num_rows,num_cols,sharex=True,sharey=True)
##
# if (not isinstance(X_vector,np.ndarray)):
# majorXLocator = MultipleLocator(majorX)
# majorXFormatter = FormatStrFormatter('%d')
# else:
# axes.tick_params(axis='both', which='major', labelsize=12)
##
# majorYLocator = MultipleLocator(majorY)
#
##pyplot.xlim(-5,240)
#
index_plot = min_eigstate_index
#
for index_row in range(0,num_rows):
for index_col in range(0,num_cols):
##
components = eigstates[:,index_plot] ## Eigenstate's components
##
axes[index_row,index_col].tick_params(axis='both', which='major', labelsize=12)
##
if (not isinstance(X_vector,np.ndarray)):
axes[index_row,index_col].plot(components**2,col)
# axes[index_row,index_col].xaxis.set_major_formatter(majorXFormatter)
else:
axes[index_row,index_col].plot(X_vector, components**2, col, markersize = 6)
string_label = "$k = " + str(index_plot) + "$"
axes[index_row,index_col].text(0.6, 0.05, string_label, fontsize=12)
##
## axes[index_row,index_col].annotate(min_eigstate_index+index_row+index_col+1, xy=(11, 0.75))
##
# axes[index_row,index_col].xaxis.set_major_locator(majorXLocator)
# axes[index_row,index_col].tick_params(axis='both', which='major', labelsize=9)
# axes[index_row,index_col].annotate(eigstate_index, xy=(150, 0.2))
##
index_plot = index_plot + state_step
pyplot.subplots_adjust(wspace=0,hspace=0)
def plot_components(eigvec_file,
eigval_file,
bas_state_index,
majorX=50,
majorY=0.02,
col="b-o"):
###
'''LDOS Plots function
Plot squared components in all eigenvectors of a bas_state_index basis element (min bas_state_index = 0) as a function of the state energy.'''
###
import numpy as np
from matplotlib import pyplot
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
#
from survival_probability_basis import read_energy_data, read_eigenstates
#
#
eigstates = read_eigenstates(eigvec_file)
eigvals = read_energy_data(eigval_file)
#
#
majorXLocator = MultipleLocator(majorX)
majorYLocator = MultipleLocator(majorY)
#
## for bas_state in range(0,4):
components = eigstates[
bas_state_index, :] ## Components of a given basis element in all eigenstates
##
panel = pyplot.subplot(1, 1, 1)
panel.tick_params(axis='both', which='major', labelsize=14)
pyplot.plot(eigvals, components**2, col)
##
panel.xaxis.set_major_locator(majorXLocator)
panel.yaxis.set_major_locator(majorYLocator)
##
##
## pyplot.annotate(bas_state, xy=(30, 0.07))
pyplot.xlabel("Energy")
pyplot.ylabel("Squared Eigenvector Components")
panel.xaxis.label.set_fontsize(18)
panel.yaxis.label.set_fontsize(18)
def plot_components(eigvec_file, eigstate_index, save_data = False, X_vector = 0, file_name = "sqrd_component_out.dat", majorX = 50, majorY = 0.02, col="b-o"):
###
'''Plot or save the squared components of the eigstate_index-th eigenvector (min value = 0).
Options:
save_data : if True do no plot the data but save them.
X_vector : plot as a function of the X_vector instead of simple indices.
file_name : squared component filename if save_data = True
'''
#
import numpy as np
from matplotlib import pyplot
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
#
from survival_probability_basis import read_eigenstates
#
#
eigstates=read_eigenstates(eigvec_file)
#
#
majorYLocator = MultipleLocator(majorY)
#
components = eigstates[:,eigstate_index]**2 ## Eigenstate's squared components
##
if (save_data):
# Saving data
if (isinstance(X_vector,np.ndarray)):
data_save = np.transpose(np.array([X_vector,components]))
else:
data_save = np.transpose(np.array([range(len(components)),components]))
##
np.savetxt(file_name, data_save)
else:
# Plot data
panel = pyplot.subplot(1, 1, 1)
##
##
if (not isinstance(X_vector,np.ndarray)):
majorXLocator = MultipleLocator(majorX)
majorXFormatter = FormatStrFormatter('%d')
panel.tick_params(axis='both', which='major', labelsize=12)
pyplot.plot(components, col)
panel.xaxis.set_major_locator(majorXLocator)
panel.xaxis.set_major_formatter(majorXFormatter)
else:
panel.tick_params(axis='both', which='major', labelsize=12)
pyplot.plot(X_vector, components, col, markersize = 6)
##
panel.yaxis.set_major_locator(majorYLocator)
##
##
panel.text(0.7, 0.03, r'$k = 49$', fontsize=15)
pyplot.plot([0.4166666666666667, 0.4166666666666667], [0, 0.039], 'k-.', lw=2)
## pyplot.annotate("$k = 148$", xy=(0.1, 0.025))
## pyplot.xlabel("Normalized Basis State Energy $e_\omega$") ## SO(4) basis
pyplot.xlabel("Normalized Basis State Energy $e_n$") ## U(3) basis
## pyplot.ylabel("$|C_\omega^{(k)}|^2$") ## SO(4) basis
pyplot.ylabel("$|C_n^{(k)}|^2$") ## U(3) basis
panel.xaxis.label.set_fontsize(18)
panel.yaxis.label.set_fontsize(18)
return
def plot_components(eigvec_file, eigstate_index, save_data = False, X_vector = 0, file_name = "sqrd_component_out.dat", majorX = 50, majorY = 0.02, col="b-o"):
###
'''Plot or save the squared components of the eigstate_index-th eigenvector (min value = 0).
Options:
save_data : if True do no plot the data but save them.
X_vector : plot as a function of the X_vector instead of simple indices.
file_name : squared component filename if save_data = True
'''
#
import numpy as np
from matplotlib import pyplot
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
#
from survival_probability_basis import read_eigenstates
#
#
eigstates=read_eigenstates(eigvec_file)
#
#
majorYLocator = MultipleLocator(majorY)
#
components = eigstates[:,eigstate_index]**2 ## Eigenstate's squared components
##
if (save_data):
# Saving data
if (isinstance(X_vector,np.ndarray)):
data_save = np.transpose(np.array([X_vector,components]))
else:
data_save = np.transpose(np.array([range(len(components)),components]))
##
np.savetxt(file_name, data_save)
else:
# Plot data
panel = pyplot.subplot(1, 1, 1)
##
##
if (not isinstance(X_vector,np.ndarray)):
majorXLocator = MultipleLocator(majorX)
majorXFormatter = FormatStrFormatter('%d')
panel.tick_params(axis='both', which='major', labelsize=12)
pyplot.plot(components, col)
panel.xaxis.set_major_locator(majorXLocator)
panel.xaxis.set_major_formatter(majorXFormatter)
else:
panel.tick_params(axis='both', which='major', labelsize=12)
pyplot.plot(X_vector, components, col, markersize = 6)
##
panel.yaxis.set_major_locator(majorYLocator)
##
##
panel.text(0.7, 0.03, r'$k = 49$', fontsize=15)
pyplot.plot([0.4166666666666667, 0.4166666666666667], [0, 0.039], 'k-.', lw=2)
## pyplot.annotate("$k = 148$", xy=(0.1, 0.025))
## pyplot.xlabel("Normalized Basis State Energy $e_\omega$") ## SO(4) basis
pyplot.xlabel("Normalized Basis State Energy $e_n$") ## U(3) basis
## pyplot.ylabel("$|C_\omega^{(k)}|^2$") ## SO(4) basis
pyplot.ylabel("$|C_n^{(k)}|^2$") ## U(3) basis
panel.xaxis.label.set_fontsize(18)
panel.yaxis.label.set_fontsize(18)
return
## Variable length grids
t_max = 60.;dim_t = 5000
time_grid = np.zeros(dim_t+1)
for index in np.arange(0,dim_t+1):
time_grid[index] = t_max*index**3/dim_t**3
# Basis states indexes (start in 1) -1 --> Closest to separatrix
basis_states_indexes = [-1]
###########################################
# End of Defs ## Edit only this section #
###########################################
#
print "N = ", Nval, ", L = ", Lval, ", xi = ", xi
## Read eigenvalues (absolute eigenvalues) and eigenvectors
Eigenvalues = read_energy_data("../../test/eigval_"+basis+"_N"+str(Nval)+"_L"+str(Lval)+".dat")
Eigenstates = read_eigenstates("../../test/eigvec_"+basis+"_N"+str(Nval)+"_L"+str(Lval)+".dat")
E0 = Eigenvalues[0]
Eigenvalues = Eigenvalues - E0 # Escitation energies
# Computing survival probability
print "Computing survival probability ... "
#
sp=np.zeros((time_grid.shape[0],len(basis_states_indexes)+1),order="F") # +1 for the abscyssa values
#
for index, index_state in enumerate(basis_states_indexes):
if (index == -1):
# Find basis state close to separatrix
if basis is "u3":
basisen = energy_basis_I(Nval,np.arange(0,Nval+1,2), Lval, xi)
else:
basisen = energy_basis_II(Nval,np.arange(0,Nval+1,2), Lval, xi)
#
#
N_value = 500
l_value = 0
xi_value = 0.4
##eigenvectors = "../test/eigvec_so3_xi04_N500_L0.dat"
eigenvectors = "../test/eigvec_u2_xi04_N500_L0.dat"
##eigenvalues = "../test/energy_so3_xi_04_N500_L0.dat"
eigenvalues = "../test/energy_u2_xi_04_N500_L0.dat"
#
## time_max = 16
## time_points = 300
time_max = 0.5
time_points = 200
nvals = np.arange(0, N_value + 2, 2)
#
eigstates = read_eigenstates(eigenvectors)
eigvals = read_energy_data(eigenvalues)
#
time_grid = np.linspace(0.0, time_max, time_points)
spb = survival_probability_basis_states(eigvals,
eigstates,
1,
N_value / 2 + 1,
t_max=time_max,
dim_t=time_points)
#
##majorXLocator = MultipleLocator(5)
##majorXFormatter = FormatStrFormatter('%d')
majorXLocator = MultipleLocator(0.2)
majorXFormatter = FormatStrFormatter('%3.1f')
#
#t_max = 5.;dim_t = 5000
#time_grid = np.zeros(dim_t+1)
#for index in np.arange(0,dim_t+1):
# time_grid[index] = (t_max*index**3/dim_t**3)
# Basis states indexes (start in 1) -1 --> Closest to separatrix
basis_states_indexes = [-1]
###########################################
# End of Defs ## Edit only this section #
###########################################
#
print "N = ", Nval, ", L = ", Lval, ", xi = ", xi
## Read eigenvalues (absolute eigenvalues) and eigenvectors
Eigenvalues = read_energy_data("../test/eigval_" + basis + "_N" + str(Nval) +
"_L" + str(Lval) + ".dat")
Eigenstates = read_eigenstates("../test/eigvec_" + basis + "_N" + str(Nval) +
"_L" + str(Lval) + ".dat")
E0 = Eigenvalues[0]
Eigenvalues = Eigenvalues - E0 # Excitation energies
# Computing survival probability
print "Computing survival probability ... "
#
sp = np.zeros((time_grid.shape[0], len(basis_states_indexes) + 1),
order="F") # +1 for the abscyssa values
#
for index, index_state in enumerate(basis_states_indexes):
if (index_state == -1):
# Find basis state close to separatrix
if basis is "u2":
basisen = energy_basis_u2(Nval, np.arange(Lval, Nval + 1, 2), Lval,
xi)
else:
#
N_value = 500
l_value = 0
xi_value = 0.4
##eigenvectors = "../test/eigvec_so3_xi04_N500_L0.dat"
eigenvectors = "../test/eigvec_u2_xi04_N500_L0.dat"
##eigenvalues = "../test/energy_so3_xi_04_N500_L0.dat"
eigenvalues = "../test/energy_u2_xi_04_N500_L0.dat"
#
## time_max = 16
## time_points = 300
time_max = 0.5
time_points = 200
nvals = np.arange(0, N_value + 2, 2)
#
eigstates=read_eigenstates(eigenvectors)
eigvals= read_energy_data(eigenvalues)
#
time_grid = np.linspace( 0.0, time_max, time_points)
spb = survival_probability_basis_states(eigvals, eigstates, 1, N_value/2 + 1, t_max = time_max, dim_t = time_points)
#
##majorXLocator = MultipleLocator(5)
##majorXFormatter = FormatStrFormatter('%d')
majorXLocator = MultipleLocator(0.2)
majorXFormatter = FormatStrFormatter('%3.1f')
#
fig,axes = pyplot.subplots(5,5,sharex=True,sharey=True)
#
pyplot.xlim(0,time_max)
pyplot.ylim(0,1)
#
def hist_components_LDOS(eigvec_file, basis_state, energy_file, ExcE = True, N_value = 1, bins = 20, OutputCentroid = False, fig=False, iprint=0):
###
'''LDOS Plot: Histogram of the squared components of a basis state as a function of
the system eigenvectors (min basis state value = 0) and as a function of the system eigenvalues.
Options:
ExcE : Transform energy_file to excitation energies. Default value True
N_value : renormalize by the system size (N_value = N)
bins : number of bins in the histogram
OutputCentroid : If True outputs the centroid value for the bardiagram.
fig : plot bar fig (pyplot.show())
iprint : control verbosity
'''
#
import numpy as np
from matplotlib import pyplot
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
#
from survival_probability_basis import read_eigenstates, read_energy_data
#
#
eigstates=read_eigenstates(eigvec_file)
##
eigenvalues = read_energy_data(energy_file)
if (ExcE):
E0 = eigenvalues[0]
eigenvalues = eigenvalues - E0
#
eigenvalues = eigenvalues/N_value
## Energy bins
energy_bins=np.linspace(eigenvalues[0], eigenvalues[-1],num = bins+1)
if (iprint > 0):
print "Energy bins = ", energy_bins
#
## Basis state components
components = eigstates[basis_state,:]**2
#
columns = np.zeros(bins)
###
idx = 0
for index_bin in range(1,bins+1):
#
if (iprint > 0):
print "bin index = ", index_bin, " of ", bins
for aval_index in range(idx, len(eigenvalues)+1):
#
energy = eigenvalues[aval_index]
if (iprint > 0):
print "aval_index, energy = ", aval_index, energy
#
if (energy < energy_bins[index_bin]):
columns[index_bin-1] = columns[index_bin-1] + components[aval_index]
idx = idx + 1
if (iprint > 0):
print "idx = ", idx, "col = ", columns[index_bin-1]
else:
if (iprint > 0):
print "BREAK", index_bin, aval_index
break
# Sum last component
columns[index_bin-1] = columns[index_bin-1] + components[aval_index]
if (iprint > 0):
print "Columns = ", columns
# Define bar centroids
wdth = (energy_bins[1]-energy_bins[0])
lngth = bins
centroids = energy_bins + wdth/2.
##
if (fig):
figure = pyplot.figure()
ax = pyplot.subplot(111)
ax.bar(centroids[:lngth], columns[:lngth],width=wdth,alpha=0.5)
##
if (OutputCentroid):
return centroids[:lngth], columns[:lngth]
else:
output_data = np.zeros([2*bins+1,2]) # +1 to close the block diagram
output_data[0,0] = energy_bins[0]
output_data[0,1] = columns[0]
#
icount = 1
for index_bin in range(1,bins):
output_data[icount,0] = energy_bins[index_bin]
output_data[icount,1] = columns[index_bin-1]
output_data[icount+1,0] = energy_bins[index_bin]
output_data[icount+1,1] = columns[index_bin]
icount = icount + 2
#
output_data[icount,0] = energy_bins[-1]
output_data[icount,1] = columns[-1]
output_data[icount+1,0] = energy_bins[-1]
output_data[icount+1,1] = 0.0
return output_data