def dispersion_abtransition_gapbounds(lp, abvals=None):
"""
Parameters
----------
lp
Returns
-------
"""
# prepare the values of inversion symmetry breaking
if abvals is None:
# abvals = np.arange(0, 2.4, 0.1)
abvals = np.arange(0, 1.0, 0.025)
meshfn = le.find_meshfn(lp)
lat = lattice_class.Lattice(lp)
lat.load(check=lp['check'])
lp['ABDelta'] = np.max(abvals)
mglat = MagneticGyroLattice(lat, lp)
outname = dio.prepdir(meshfn) + 'dispersion_abtrans' + mglat.lp[
'meshfn_exten'] + '_gapbounds'
gapbounds_glob = glob.glob(outname + '.txt')
if gapbounds_glob:
# Load the text file and save the image
gapbounds = np.loadtxt(outname + '.txt')
plot_gapbounds(gapbounds[:, 0], gapbounds[:, 1:], outname + '.png', lp)
else:
# Compute the dispersions and save the image (occurs inside dispersion_abtransition
omegas, kx, ky = dispersion_abtransition(lp,
save_plots=False,
return_omegas=True)
def dice_glat(lp, args):
"""make the OmK arrays to load when computing cherns for diced networks
Example usage:
python run_series.py -pro gyro_lattice_class -opts LT/hexagonal/-N/11/-shape/square/-dice_glat/-gridspacing/3.0 -var weakbond_val n1.0:0.1:0.05
Parameters
----------
lp
args
Returns
-------
"""
import lepm.line_segments as lsegs
# Create a glat with bonds that are weakened in a gridlike fashion (bonds crossing gridlines are weak)
meshfn = le.find_meshfn(lp)
lp['meshfn'] = meshfn
lat = lattice_class.Lattice(lp)
lat.load()
# Find where bonds cross gridlines
gridspacing = args.gridspacing
lp['OmKspec'] = 'gridlines{0:0.2f}'.format(gridspacing).replace('.', 'p') + \
'strong{0:0.3f}'.format(lp['Omk']).replace('.', 'p').replace('-', 'n') + \
'weak{0:0.3f}'.format(args.weakbond_val).replace('.', 'p').replace('-', 'n')
maxval = max(np.max(np.abs(lat.xy[:, 0])), np.max(np.abs(lat.xy[:, 1]))) + 1
gridright = np.arange(gridspacing, maxval, gridspacing)
gridleft = -gridright
gridvals = np.hstack((gridleft, 0, gridright))
# Draw grid
gridlinesH = np.array([[-maxval, gridv, maxval, gridv] for gridv in gridvals])
gridlinesV = np.array([[gridv, -maxval, gridv, maxval] for gridv in gridvals])
gridsegs = np.vstack((gridlinesH, gridlinesV))
print 'np.shape(gridlines) = ', np.shape(gridsegs)
# Make the bond linesegments
xy = lat.xy
bondsegs = np.array([[xy[b[0], 0], xy[b[0], 1], xy[b[1], 0], xy[b[1], 1]] for b in lat.BL])
# get crossings
print 'gridsegs = ', gridsegs
does_intersect = lsegs.linesegs_intersect_linesegs(bondsegs, gridsegs)
tmp_glat = GyroLattice(lat, lp)
OmK = copy.deepcopy(tmp_glat.OmK)
print 'Altering weak bonds --> ', args.weakbond_val
for bond in lat.BL[does_intersect]:
OmK[bond[0], np.where(lat.NL[bond[0]] == bond[1])] = args.weakbond_val
glat = GyroLattice(lat, lp, OmK=OmK)
glat.plot_OmK()
if args.dice_eigval:
glat.save_eigval_eigvect()
glat.save_DOSmovie()
def localization(lp, args):
"""Load a periodic lattice from file, provide physics, and seek exponential localization of modes
Example usage:
python run_series.py -pro gyro_lattice_class -opts LT/hucentroid/-periodic/-NP/20/-localization/-save_eig -var AB 0.0:0.05:1.0
python run_series.py -pro gyro_lattice_class -opts LT/hyperuniform/-periodic/-NP/50/-localization/-save_eig -var Vpin 0.1/0.5/1.0/2.0/4.0/6.0
python run_series.py -pro gyro_lattice_class -opts LT/hyperuniform/-periodic/-NP/50/-DOSmovie/-save_eig -var Vpin 0.1/0.5/1.0/2.0/4.0/6.0
"""
meshfn = le.find_meshfn(lp)
lp['meshfn'] = meshfn
lat = lattice_class.Lattice(lp)
lat.load()
extent = 2 * max(np.max(lat.xy[:, 0]), np.max(lat.xy[:, 1]))
glat = GyroLattice(lat, lp)
glat.save_localization(attribute=True, save_images=args.save_images, save_eigvect_eigval=args.save_eig)
glat.plot_ill_dos(vmax=4. / extent, xlim=(0., 14.), ticks=[0, 2. / extent, 4. / extent],
cbar_ticklabels=[0, r'$2/L$', r'$4/L$'], cbar_labelpad=15)
python ./bott/bott_magnetic_gyro_collection_collection.py -ABphase -LT hexagonal -shape square -paramV 0.:0.1:0.9 -N 15 -shortrange -aol 0.6 -Vpin 0.01 -save_as_txt
python ./bott/bott_magnetic_gyro_collection_collection.py -ABphase -LT hexagonal -shape square -paramV 0.:0.1:0.9 -N 11 -shortrange -aol 0.6 -Vpin 0.01 -save_as_txt
python ./bott/bott_magnetic_gyro_collection_collection.py -ABphase -LT hexagonal -shape square -paramV 0.:0.1:0.9 -N 15 -shortrange -aol 0.8 -Vpin 0.01 -save_as_txt
"""
# Collate botts for one lattice with a mgyro_lattice parameter that varies between instances of that lattice
lp_master = copy.deepcopy(lp)
paramV = sf.string_sequence_to_numpy_array(args.paramV, dtype=float)
if args.lpparam == 'delta':
# vary delta between lattices
deltaV = np.arange(0.7, 1.31, 0.1)
deltaV = np.hstack((0.667, deltaV))
bmgcollcoll = BottMagneticGyroCollectionCollection()
for delta in deltaV:
lp = copy.deepcopy(lp_master)
lp['delta_lattice'] = '{0:0.3f}'.format(delta)
meshfn = le.find_meshfn(lp)
lp['meshfn'] = meshfn
print '\n\n\nlp[meshfn] = ', lp['meshfn']
lat = lattice_class.Lattice(lp)
lat.load()
mgc = magnetic_gyro_collection.MagneticGyroCollection()
lp_submaster = copy.deepcopy(lp)
# Need only to add one single mgryo_lattice
# for glatpval in paramV:
# lpii = copy.deepcopy(lp_submaster)
# lpii[args.glatparam] = glatpval
# mglat = magnetic_gyro_lattice_class.MagneticGyroLattice(lat, lpii)
# mglat.load()
# mgc.add_mgyro_lattice(mglat)
lpii = copy.deepcopy(lp_submaster)
lpii[args.glatparam] = paramV[0]
'Ndefects': args.Ndefects,
'Bvec': args.Bvec,
'dislocxy': (args.dislocation_xy.split('/')),
'cutz_method': args.cutz_method,
'origin': np.array([0., 0.]),
'source': 'hexner',
}
if doNP:
print 'check'
lp['NP_load'] = N
else:
lp['NP_load'] = 0
meshfn = le.find_meshfn(args.LatticeTop,
shape,
sourcedir,
NH,
NV,
lattice_params=lp)
print 'found meshfn = ', meshfn
if glob.glob(meshfn + '/harmonic_diffusivity_sigmax.pkl'):
with open(meshfn + '/harmonic_diffusivity_sigma.pkl',
"rb") as input_file:
SS = pickle.load(input_file)
with open(meshfn + '/harmonic_diffusivity_sigmax.pkl',
"rb") as input_file:
SSx = pickle.load(input_file)
with open(meshfn + '/harmonic_diffusivity_sigmay.pkl',
"rb") as input_file:
SSy = pickle.load(input_file)
with open(meshfn + '/eigval_mass.pkl', "rb") as input_file:
def dispersion_abtransition(lp,
save_plots=True,
return_omegas=False,
abvals=None,
fullspectrum=False):
"""
Parameters
----------
lp : dictionary
lattice parameter dictionary
return_omegas : bool
Return a list of the frequencies in the dispersion
abvals : n x 1 float array or list
The Delta_AB values for each spectrum
Returns
-------
"""
# prepare the values of inversion symmetry breaking
if abvals is None:
# abvals = np.arange(0, 2.4, 0.1)
abvals = np.arange(0, 1.0, 0.025)
# Prepare magnetic gyro lattice
meshfn = le.find_meshfn(lp)
lp['meshfn'] = meshfn
lpmaster = copy.deepcopy(lp)
# create a place to put images
outdir = dio.prepdir(
meshfn) + 'dispersion_abtransition_aol' + sf.float2pstr(
lp['aoverl']) + '/'
dio.ensure_dir(outdir)
fs = 20
if return_omegas:
omegas_out = []
kx_out = []
ky_out = []
# go through each ab and make the image
ii = 0
for ab in abvals:
lp = copy.deepcopy(lpmaster)
lp['ABDelta'] = ab
lat = lattice_class.Lattice(lp)
lat.load(check=lp['check'])
glat = MagneticGyroLattice(lat, lp)
# glat.get_eigval_eigvect(attribute=True)
fig, ax = leplt.initialize_portrait(ax_pos=[0.12, 0.2, 0.76, 0.6])
omegas, kx, ky = glat.infinite_dispersion(save=False,
nkxvals=50,
nkyvals=50,
outdir=outdir,
save_plot=False)
if return_omegas:
omegas_out.append(omegas)
kx_out.append(kx)
ky_out.append(ky)
if save_plots:
# plot and save it
title = r'$\Delta_{AB} =$' + '{0:0.2f}'.format(ab)
for jj in range(len(ky)):
for kk in range(len(omegas[0, jj, :])):
ax.plot(kx,
omegas[:, jj, kk],
'k-',
lw=max(0.5, 30. / (len(kx) * len(ky))))
ax.set_title(title, fontsize=fs)
ax.set_xlabel(r'$k$ $[\langle \ell \rangle ^{-1}]$', fontsize=fs)
ax.set_ylabel(r'$\omega$', fontsize=fs)
for tick in ax.xaxis.get_major_ticks():
tick.label.set_fontsize(fs)
for tick in ax.yaxis.get_major_ticks():
tick.label.set_fontsize(fs)
if ii == 0:
ylims = ax.get_ylim()
if fullspectrum:
ax.set_ylim(-ylims[1] * 1.2, ylims[1] * 1.2)
else:
ax.set_ylim(0., ylims[1] * 1.2)
# Save it
name = outdir + 'dispersion{0:04d}'.format(ii)
plt.savefig(name + '.png', dpi=300)
plt.close('all')
ii += 1
# Save a movie of the dispersions
movname = dio.prepdir(
meshfn) + 'dispersion_abtrans' + glat.lp['meshfn_exten']
if save_plots:
# Turn images into a movie
imgname = outdir + 'dispersion'
lemov.make_movie(imgname,
movname,
indexsz='04',
framerate=4,
imgdir=outdir,
rm_images=True,
save_into_subdir=True)
if return_omegas:
# Save the gap bounds and return the arrays of kx, ky, and omega
omegas, kx, ky = np.array(omegas_out), np.array(kx_out), np.array(
ky_out)
# Get gap bounds:
botmin = []
botmax = []
topmin = []
topmax = []
for band in omegas:
botmin.append(np.min(band[:, :, 2]))
botmax.append(np.max(band[:, :, 2]))
topmin.append(np.min(band[:, :, 3]))
topmax.append(np.max(band[:, :, 3]))
botmin = np.array(botmin)
botmax = np.array(botmax)
topmin = np.array(topmin)
topmax = np.array(topmax)
gapbounds = np.dstack((abvals, botmin, botmax, topmin, topmax))[0]
outfn = movname + '_gapbounds.txt'
print 'saving to ', outfn
header = 'Delta_AB, band min frequency, band max frequency, band 2 min, band 2 max...'
np.savetxt(outfn, gapbounds, header=header)
plot_gapbounds(abvals, gapbounds, movname + '_gapbounds.png', lp)
return omegas, kx, ky
else:
return None
def twistbcs(lp):
"""Load a periodic lattice from file, twist the BCs by phases theta_twist and phi_twist with vals finely spaced
between 0 and 2pi. Then compute the berry curvature associated with |alpha(theta, phi)>
Example usage:
python haldane_lattice_class.py -twistbcs -N 3 -LT hexagonal -shape square -periodic
Parameters
----------
lp
Returns
-------
"""
lp['periodicBC'] = True
meshfn = le.find_meshfn(lp)
lp['meshfn'] = meshfn
lat = lattice_class.Lattice(lp)
lat.load()
# Make a big array of the eigvals: N x N x thetav x phiv
# thetav = np.arange(0., 2. * np.pi, 0.5)
# phiv = np.arange(0., 2. * np.pi, 0.5)
# First just test for two values of theta and two of phi
thetav = [0., 0.01]
phiv = [0., 0.01]
eigvects = {}
ii = 0
for theta in thetav:
eigvects[ii] = {}
jj = 0
for phi in phiv:
lpnew = copy.deepcopy(lp)
lpnew['theta_twist'] = theta
lpnew['phi_twist'] = phi
hlat = HaldaneLattice(lat, lpnew)
ev, evec = hlat.get_eigval_eigvect(attribute=True)
if ii == 0 and jj == 0:
eigval = copy.deepcopy(ev)
ill = hlat.get_ill()
eigvects[ii][jj] = evec
jj += 1
ii += 1
# Dot the derivs of eigvects together
# Ensure that there is a nonzero-amplitude wannier with matching phase
dtheta = eigvects[1][0] - eigvects[0][0]
dphi = eigvects[0][1] - eigvects[0][0]
thetamov_fn = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '_dos_ev.mov'
if not glob.glob(thetamov_fn):
# Plot differences
fig, DOS_ax, eig_ax = leplt.initialize_eigvect_DOS_header_plot(
ev,
hlat.lattice.xy,
sim_type='haldane',
colorV=ill,
colormap='viridis',
linewidth=0,
cax_label=r'$\xi^{-1}$',
cbar_nticks=2,
xlabel_pad=10,
ylabel_pad=10,
cbar_tickfmt='%0.3f')
DOS_ax.set_title(r'$\partial_\phi \psi$')
hlat.lattice.plot_BW_lat(fig=fig,
ax=eig_ax,
save=False,
close=False,
axis_off=False,
title='')
outdir = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '/'
dio.ensure_dir(outdir)
for ii in range(len(ev)):
fig, [scat_fg, scat_fg2, p, f_mark, lines_12_st], cw_ccw = \
hlatpfns.construct_haldane_eigvect_DOS_plot(hlat.lattice.xy, fig, DOS_ax, eig_ax, eigval,
dtheta, ii, hlat.lattice.NL, hlat.lattice.KL,
marker_num=0, color_scheme='default', normalization=1.)
print 'saving theta ', ii
plt.savefig(outdir + 'dos_ev' + '{0:05}'.format(ii) + '.png')
scat_fg.remove()
scat_fg2.remove()
p.remove()
f_mark.remove()
lines_12_st.remove()
plt.close('all')
imgname = outdir + 'dos_ev'
movname = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '_dos_ev'
lemov.make_movie(imgname, movname, rm_images=False)
phimov_fn = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '_dos_ev.mov'
if not glob.glob(phimov_fn):
fig, DOS_ax, eig_ax = leplt.initialize_eigvect_DOS_header_plot(
ev,
hlat.lattice.xy,
sim_type='haldane',
colorV=ill,
colormap='viridis',
linewidth=0,
cax_label=r'$\xi^{-1}$',
cbar_nticks=2,
xlabel_pad=10,
ylabel_pad=10,
cbar_tickfmt='%0.3f')
DOS_ax.set_title(r'$\partial_\phi \psi$')
outdir = dio.prepdir(
hlat.lp['meshfn']) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '/'
dio.ensure_dir(outdir)
for ii in range(len(ev)):
fig, [scat_fg, scat_fg2, p, f_mark, lines_12_st], cw_ccw = \
hlatpfns.construct_haldane_eigvect_DOS_plot(hlat.lattice.xy, fig, DOS_ax, eig_ax, eigval,
dphi, ii, hlat.lattice.NL, hlat.lattice.KL,
marker_num=0, color_scheme='default', normalization=1.)
print 'saving phi ', ii
plt.savefig(outdir + 'dos_ev' + '{0:05}'.format(ii) + '.png')
scat_fg.remove()
scat_fg2.remove()
p.remove()
f_mark.remove()
lines_12_st.remove()
plt.close('all')
imgname = outdir + 'dos_ev'
movname = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '_dos_ev'
lemov.make_movie(imgname, movname, rm_images=False)
# Check
# print 'shape(dtheta) = ', np.shape(dtheta)
# print 'shape(dphi) = ', np.shape(dphi)
# le.plot_complex_matrix(dtheta, show=True, name='dtheta')
# le.plot_complex_matrix(dphi, show=True, name='dphi')
fig, ax = leplt.initialize_nxmpanel_fig(4, 1, wsfrac=0.6, x0frac=0.3)
# < dphi | dtheta >
dpdt = np.einsum('ij...,ij...->i...', dtheta, dphi.conj())
# < dtheta | dphi >
dtdp = np.einsum('ij...,ij...->i...', dphi, dtheta.conj())
print 'dtdp = ', dtdp
ax[0].plot(np.arange(len(dtdp)), dtdp, '-')
ax[1].plot(np.arange(len(dpdt)), dpdt, '-')
hc = 2. * np.pi * 1j * (dpdt - dtdp)
ax[2].plot(np.arange(len(lat.xy)), hc, '.-')
# Plot cumulative sum
sumhc = np.cumsum(hc)
ax[3].plot(np.arange(len(lat.xy)), sumhc, '.-')
ax[2].set_xlabel(r'Eigvect number')
ax[0].set_ylabel(
r'$\langle \partial_{\theta} \alpha_i | \partial_{\phi} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[1].set_ylabel(
r'$\langle \partial_{\phi} \alpha_i | \partial_{\theta} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[2].set_ylabel(r'$c_H$')
ax[3].set_xlabel(r'Eigvect number')
ax[3].set_ylabel(r'$\sum_{E_\alpha < E_c} c_H$')
outdir = '/Users/npmitchell/Dropbox/Soft_Matter/GPU/twistbc_test/'
dio.ensure_dir(outdir)
print 'saving ', outdir + 'test' + hlat.lp['meshfn_exten'] + '.png'
plt.savefig(outdir + 'test' + hlat.lp['meshfn_exten'] + '.png')
# ### Now do the same thing but with different values of theta, phi
# First just test for two values of theta and two of phi
thetav = [1., 1.01]
phiv = [1., 1.01]
eigvects = {}
ii = 0
for theta in thetav:
eigvects[ii] = {}
jj = 0
for phi in phiv:
lpnew = copy.deepcopy(lp)
lpnew['theta_twist'] = theta
lpnew['phi_twist'] = phi
hlat = HaldaneLattice(lat, lpnew)
ev, evec = hlat.get_eigval_eigvect(attribute=True)
if ii == 0 and jj == 0:
eigval = copy.deepcopy(ev)
ill = hlat.get_ill()
eigvects[ii][jj] = evec
jj += 1
ii += 1
# Dot the derivs of eigvects together
dtheta = eigvects[1][0] - eigvects[0][0]
dphi = eigvects[0][1] - eigvects[0][0]
# Plot differences
thetamov_fn = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '_dos_ev.mov'
if not glob.glob(thetamov_fn):
fig, DOS_ax, eig_ax = leplt.initialize_eigvect_DOS_header_plot(
ev,
hlat.lattice.xy,
sim_type='haldane',
colorV=ill,
colormap='viridis',
linewidth=0,
cax_label=r'$\xi^{-1}$',
cbar_nticks=2,
xlabel_pad=10,
ylabel_pad=10,
cbar_tickfmt='%0.3f')
DOS_ax.set_title(r'$\partial_\theta \psi$')
hlat.lattice.plot_BW_lat(fig=fig,
ax=eig_ax,
save=False,
close=False,
axis_off=False,
title='')
outdir = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '/'
dio.ensure_dir(outdir)
for ii in range(len(ev)):
fig, [scat_fg, scat_fg2, p, f_mark, lines_12_st], cw_ccw = \
hlatpfns.construct_haldane_eigvect_DOS_plot(hlat.lattice.xy, fig, DOS_ax, eig_ax, eigval,
dtheta, ii, hlat.lattice.NL, hlat.lattice.KL,
marker_num=0, color_scheme='default', normalization=1.)
print 'saving theta ', ii
plt.savefig(outdir + 'dos_ev' + '{0:05}'.format(ii) + '.png')
scat_fg.remove()
scat_fg2.remove()
p.remove()
f_mark.remove()
lines_12_st.remove()
plt.close('all')
imgname = outdir + 'dos_ev'
movname = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_theta' + hlat.lp['meshfn_exten'] + '_dos_ev'
lemov.make_movie(imgname, movname, rm_images=False)
# Now do phi
phimov_fn = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '_dos_ev.mov'
if not glob.glob(phimov_fn):
fig, DOS_ax, eig_ax = leplt.initialize_eigvect_DOS_header_plot(
ev,
hlat.lattice.xy,
sim_type='haldane',
colorV=ill,
colormap='viridis',
linewidth=0,
cax_label=r'$\xi^{-1}$',
cbar_nticks=2,
xlabel_pad=10,
ylabel_pad=10,
cbar_tickfmt='%0.3f')
DOS_ax.set_title(r'$\partial_\phi \psi$')
hlat.lattice.plot_BW_lat(fig=fig,
ax=eig_ax,
save=False,
close=False,
axis_off=False,
title='')
outdir = dio.prepdir(
hlat.lp['meshfn']) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '/'
dio.ensure_dir(outdir)
for ii in range(len(ev)):
fig, [scat_fg, scat_fg2, p, f_mark, lines_12_st], cw_ccw = \
hlatpfns.construct_haldane_eigvect_DOS_plot(hlat.lattice.xy, fig, DOS_ax, eig_ax, eigval,
dphi, ii, hlat.lattice.NL, hlat.lattice.KL,
marker_num=0, color_scheme='default', normalization=1.)
print 'saving phi ', ii
plt.savefig(outdir + 'dos_ev' + '{0:05}'.format(ii) + '.png')
scat_fg.remove()
scat_fg2.remove()
p.remove()
f_mark.remove()
lines_12_st.remove()
plt.close('all')
imgname = outdir + 'dos_ev'
movname = dio.prepdir(
hlat.lp['meshfn']
) + 'twistbc_phi' + hlat.lp['meshfn_exten'] + '_dos_ev'
lemov.make_movie(imgname, movname, rm_images=False)
# Check
# print 'shape(dtheta) = ', np.shape(dtheta)
# print 'shape(dphi) = ', np.shape(dphi)
# le.plot_complex_matrix(dtheta, show=True, name='dtheta')
# le.plot_complex_matrix(dphi, show=True, name='dphi')
fig, ax = leplt.initialize_nxmpanel_fig(4, 1, wsfrac=0.6, x0frac=0.3)
# < dphi | dtheta >
dpdt = np.einsum('ij...,ij...->i...', dtheta, dphi.conj())
# < dtheta | dphi >
dtdp = np.einsum('ij...,ij...->i...', dphi, dtheta.conj())
print 'dtdp = ', dtdp
ax[0].plot(np.arange(len(dtdp)), dtdp, '-')
ax[1].plot(np.arange(len(dpdt)), dpdt, '-')
hc = 2. * np.pi * 1j * (dpdt - dtdp)
ax[2].plot(np.arange(len(lat.xy)), hc, '.-')
# Plot cumulative sum
sumhc = np.cumsum(hc)
ax[3].plot(np.arange(len(lat.xy)), sumhc, '.-')
ax[2].set_xlabel(r'Eigvect number')
ax[0].set_ylabel(
r'$\langle \partial_{\theta} \alpha_i | \partial_{\phi} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[1].set_ylabel(
r'$\langle \partial_{\phi} \alpha_i | \partial_{\theta} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[2].set_ylabel(r'$c_H$')
ax[3].set_xlabel(r'Eigvect number')
ax[3].set_ylabel(r'$\sum_{E_\alpha < E_c} c_H$')
outdir = '/Users/npmitchell/Dropbox/Soft_Matter/GPU/twistbc_test/'
dio.ensure_dir(outdir)
plt.savefig(outdir + 'test' + hlat.lp['meshfn_exten'] + '_theta1p0.png')
sys.exit()
########################################
# Now test for more theta values, more phi values
thetav = np.arange(0., 0.14, 0.1)
phiv = np.arange(0., 0.14, 0.1)
eigvects = np.zeros((len(lat.xy), len(lat.xy), len(thetav), len(phiv)),
dtype=complex)
ii = 0
for theta in thetav:
jj = 0
for phi in phiv:
lpnew = copy.deepcopy(lp)
lpnew['theta_twist'] = theta
lpnew['phi_twist'] = phi
hlat = HaldaneLattice(lat, lpnew)
ev, evec = hlat.get_eigval_eigvect()
eigvects[:, :, ii, jj] = evec
jj += 1
ii += 1
# Dot the derivs of eigvects together
print 'eigvects = ', eigvects
dtheta = np.diff(eigvects, axis=2)
dphi = np.diff(eigvects, axis=3)
print 'dtheta = ', dtheta
print 'shape(dtheta) = ', np.shape(dtheta)
print 'shape(dphi) = ', np.shape(dphi)
le.plot_complex_matrix(dtheta[:, :, 0, 0], show=True)
le.plot_complex_matrix(dphi[:, :, 0, 0], show=True)
dtheta = dtheta[:, :, :, 0:np.shape(dtheta)[3] - 1]
dphi = dphi[:, :, 0:np.shape(dphi)[2] - 1, :]
print 'shape(dtheta) = ', np.shape(dtheta)
print 'shape(dphi) = ', np.shape(dphi)
for ii in range(np.shape(dtheta)[-1]):
le.plot_complex_matrix(dtheta[:, :, ii, 0], show=True)
fig, ax = leplt.initialize_nxmpanel_fig(3, 1)
for ii in range(np.shape(dphi)[-1]):
for jj in range(np.shape(dphi)[-1]):
# < dphi | dtheta >
dpdt = np.dot(dtheta[:, :, ii, jj], dphi[:, :, ii, jj].conj().T)
# < dtheta | dphi >
dtdp = np.dot(dphi[:, :, ii, jj], dtheta[:, :, ii, jj].conj().T)
print 'np.shape(dpdt) = ', np.shape(dpdt)
print 'np.shape(dtdp) = ', np.shape(dtdp)
ax[0].plot(np.arange(len(dtdp)), dtdp, '-')
ax[1].plot(np.arange(len(dpdt)), dpdt, '-')
hc = 2. * np.pi * 1j * (dpdt - dtdp)
ax[2].plot(np.arange(len(lat.xy)), hc, '.-')
ax[0].set_xlabel(r'$\theta$')
ax[0].set_ylabel(
r'$\langle \partial_{\theta} \alpha_i | \partial_{\phi} \alpha_i \rangle$'
)
ax[1].set_xlabel(r'$\phi$')
ax[1].set_ylabel(
r'$\langle \partial_{\phi} \alpha_i | \partial_{\theta} \alpha_i \rangle$'
)
ax[2].set_xlabel(r'Eigvect number')
ax[2].set_ylabel(r'$\partial_{\phi} \alpha_i$')
plt.show()
def dispersion_abtransition(lp, invert_bg=False, color1=None, color2=None, color_thres=None,
nkxvals=50, dab_step=0.005, dpi=100, plot_positive_only=True, ab_max=2.6):
"""
Parameters
----------
lp
Returns
-------
"""
if invert_bg:
plt.style.use('dark_background')
if invert_bg:
if color1 is None:
# blue
color1 = '#70a6ff'
if color2 is None:
# red
color2 = '#ff7777' # '#90354c'
# print 'color1, 2 = ', color1, color2
# sys.exit()
else:
cmap = lecmaps.diverging_cmap(250, 10, l=30)
color1 = cmap(0.)
color2 = cmap(1.)
meshfn = le.find_meshfn(lp)
lp['meshfn'] = meshfn
lpmaster = copy.deepcopy(lp)
ablist = np.arange(0, ab_max + dab_step, dab_step)
# create a place to put images
outdir = dio.prepdir(meshfn) + 'dispersion_abtransition/'
dio.ensure_dir(outdir)
fs = 20
# go through each ab and make the image
ii = 0
for ab in ablist:
print 'ab = ', ab
lp = copy.deepcopy(lpmaster)
lp['ABDelta'] = ab
lat = lattice_class.Lattice(lp)
lat.load(check=lp['check'])
glat = GyroLattice(lat, lp)
# glat.get_eigval_eigvect(attribute=True)
fig, ax = leplt.initialize_portrait(ax_pos=[0.12, 0.2, 0.76, 0.6])
omegas, kx, ky = glat.infinite_dispersion(save=False, nkxvals=nkxvals, nkyvals=50, outdir=outdir, save_plot=False)
# plot and save it
title = r'$\Delta_{AB} =$' + '{0:0.2f}'.format(ab)
for jj in range(len(ky)):
for kk in range(len(omegas[0, jj, :])):
if color_thres is None or ab > 0.26:
if invert_bg:
ax.plot(kx, omegas[:, jj, kk], 'w-', lw=max(1., 30. / (len(kx) * len(ky))))
else:
ax.plot(kx, omegas[:, jj, kk], 'k-', lw=max(1., 30. / (len(kx) * len(ky))))
else:
# if positive frequencies, color top band blue
if len(np.where(omegas[:, jj, kk] > 0)[0]) > 0.5 * len(omegas[:, jj, kk]):
# color top band blue
if len(np.where(np.abs(omegas[:, jj, kk]) > color_thres)[0]) > 0.5 * len(omegas[:, jj, kk]):
ax.plot(kx, omegas[:, jj, kk], '-', lw=max(1., 30. / (len(kx) * len(ky))), color=color1)
else:
ax.plot(kx, omegas[:, jj, kk], '-', lw=max(1., 30. / (len(kx) * len(ky))), color=color2)
# if negative frequencies, color bottom band blue
if len(np.where(omegas[:, jj, kk] < 0)[0]) > 0.5 * len(omegas[:, jj, kk]):
# color bottom band blue
if len(np.where(np.abs(omegas[:, jj, kk]) > color_thres)[0]) > 0.5 * len(omegas[:, jj, kk]):
ax.plot(kx, omegas[:, jj, kk], '-', lw=max(1., 30. / (len(kx) * len(ky))), color=color2)
else:
ax.plot(kx, omegas[:, jj, kk], '-', lw=max(1., 30. / (len(kx) * len(ky))), color=color1)
ax.text(0.5, 1.15, title, fontsize=fs, ha='center', va='center', transform=ax.transAxes)
ax.set_xlim(-np.pi, np.pi)
ax.xaxis.set_ticks([-np.pi, 0, np.pi])
ax.xaxis.set_ticklabels([r'$-\pi$', 0, r'$\pi$'])
ax.set_xlabel(r'$k_x$', fontsize=fs)
ax.set_ylabel(r'$\omega$', fontsize=fs)
for tick in ax.xaxis.get_major_ticks():
tick.label.set_fontsize(fs)
for tick in ax.yaxis.get_major_ticks():
tick.label.set_fontsize(fs)
if ii == 0:
ylims = ax.get_ylim()
if plot_positive_only:
ax.set_ylim(0., ylims[1])
else:
ax.set_ylim(ylims[0], ylims[1])
# Save it
name = outdir + 'dispersion{0:04d}'.format(ii)
plt.savefig(name + '.png', dpi=dpi)
plt.close('all')
ii += 1
# Turn images into a movie
imgname = outdir + 'dispersion'
movname = dio.prepdir(meshfn) + 'dispersion_abtrans' + glat.lp['meshfn_exten']
lemov.make_movie(imgname, movname, indexsz='04', framerate=10, imgdir=outdir, rm_images=True,
save_into_subdir=True)
