"""
Functions for visualizing results of quantum dynamics simulations,
visualizations of quantum states and processes.
"""
__all__ = ['plot_wigner_sphere', 'hinton', 'sphereplot',
'matrix_histogram', 'plot_energy_levels', 'plot_fock_distribution',
'plot_wigner', 'plot_expectation_values',
'plot_spin_distribution', 'complex_array_to_rgb',
'plot_qubism', 'plot_schmidt']
import warnings
import itertools as it
import numpy as np
from numpy import pi, array, sin, cos, angle, log2, sqrt
from packaging.version import parse as parse_version
from . import (
Qobj, isket, ket2dm, tensor, vector_to_operator, to_super, settings
)
from .core.dimensions import flatten
from .core.superop_reps import _to_superpauli, isqubitdims
from .wigner import wigner
from .matplotlib_utilities import complex_phase_cmap
try:
import matplotlib.pyplot as plt
import matplotlib as mpl
import matplotlib.animation as animation
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
# Define a custom _axes3D function based on the matplotlib version.
# The auto_add_to_figure keyword is new for matplotlib>=3.4.
if parse_version(mpl.__version__) >= parse_version('3.4'):
def _axes3D(fig, *args, **kwargs):
ax = Axes3D(fig, *args, auto_add_to_figure=False, **kwargs)
return fig.add_axes(ax)
else:
def _axes3D(*args, **kwargs):
return Axes3D(*args, **kwargs)
except:
pass
def _cyclic_cmap():
if settings.colorblind_safe:
return cm.twilight
else:
return complex_phase_cmap()
def _diverging_cmap():
if settings.colorblind_safe:
return cm.seismic
else:
return cm.RdBu
def _sequential_cmap():
if settings.colorblind_safe:
return cm.cividis
else:
return cm.jet
def _is_fig_and_ax(fig, ax, projection='2d'):
if fig is None:
if ax is None:
fig = plt.figure()
if projection == '2d':
ax = fig.add_subplot(1, 1, 1)
else:
ax = _axes3D(fig)
else:
fig = ax.get_figure()
else:
if ax is None:
if projection == '2d':
ax = fig.add_subplot(1, 1, 1)
else:
ax = _axes3D(fig)
return fig, ax
def _set_ticklabels(ax, ticklabels, ticks, axis, fontsize=14):
if len(ticks) != len(ticklabels):
raise ValueError(
f"got {len(ticklabels)} ticklabels but needed {len(ticks)}"
)
if axis == 'x':
ax.set_xticks(ticks)
ax.set_xticklabels(ticklabels, fontsize=fontsize)
elif axis == 'y':
ax.set_yticks(ticks)
ax.set_yticklabels(ticklabels, fontsize=fontsize)
else:
raise ValueError(
"axis must be either 'x' or 'y'"
)
def _equal_shape(matrices):
first_shape = matrices[0].shape
text = "All inputs should have the same shape."
if not all(matrix.shape == first_shape for matrix in matrices):
raise ValueError(text)
[docs]def plot_wigner_sphere(wigner, reflections=False, *, cmap=None,
colorbar=True, fig=None, ax=None):
"""Plots a coloured Bloch sphere.
Parameters
----------
wigner : a wigner transformation
The wigner transformation at `steps` different theta and phi.
reflections : bool, default: False
If the reflections of the sphere should be plotted as well.
cmap : a matplotlib colormap instance, optional
Color map to use when plotting.
colorbar : bool, default: True
Whether (True) or not (False) a colorbar should be attached.
fig : a matplotlib Figure instance, optional
The Figure canvas in which the plot will be drawn.
ax : a matplotlib axes instance, optional
The ax context in which the plot will be drawn.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
Notes
-----
Special thanks to Russell P Rundle for writing this function.
"""
fig, ax = _is_fig_and_ax(fig, ax, projection='3d')
if not isinstance(wigner, list):
wigners = [wigner]
else:
wigners = wigner
_equal_shape(wigners)
wigner_max = np.real(np.amax(np.abs(wigners[0])))
for wigner in wigners:
wigner_max = max(np.real(np.amax(np.abs(wigner))), wigner_max)
norm = mpl.colors.Normalize(-wigner_max, wigner_max)
if cmap is None:
cmap = _diverging_cmap()
artist_list = list()
for wigner in wigners:
steps = len(wigner)
theta = np.linspace(0, np.pi, steps)
phi = np.linspace(0, 2 * np.pi, steps)
x = np.outer(np.sin(theta), np.cos(phi))
y = np.outer(np.sin(theta), np.sin(phi))
z = np.outer(np.cos(theta), np.ones(steps))
wigner = np.real(wigner)
artist = list()
# Plot coloured Bloch sphere:
artist.append(ax.plot_surface(x, y, z, facecolors=cmap(norm(wigner)),
rcount=steps, ccount=steps, linewidth=0,
zorder=0.5, antialiased=None))
if reflections:
side_color = cmap(norm(wigner[0:steps, 0:steps]))
# Plot bottom reflection:
artist.append(ax.plot_surface(x[0:steps, 0:steps],
y[0:steps, 0:steps],
-1.5*np.ones((steps, steps)),
facecolors=side_color,
rcount=steps/2, ccount=steps/2,
linewidth=0, zorder=0.5,
antialiased=False))
# Plot side reflection:
artist.append(ax.plot_surface(-1.5*np.ones((steps, steps)),
y[0:steps, 0:steps],
z[0:steps, 0:steps],
facecolors=side_color,
rcount=steps/2, ccount=steps/2,
linewidth=0, zorder=0.5,
antialiased=False))
# Plot back reflection:
artist.append(ax.plot_surface(x[0:steps, 0:steps],
1.5*np.ones((steps, steps)),
z[0:steps, 0:steps],
facecolors=side_color,
rcount=steps/2, ccount=steps/2,
linewidth=0, zorder=0.5,
antialiased=False))
artist_list.append(artist)
if len(wigners) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
# Create colourbar:
if colorbar:
cax, kw = mpl.colorbar.make_axes(ax, shrink=0.75, pad=.1)
mpl.colorbar.ColorbarBase(cax, norm=norm, cmap=cmap)
return fig, output
# Adopted from the SciPy Cookbook.
def _blob(x, y, w, w_max, area, color_fn, ax=None):
"""
Draws a square-shaped blob with the given area (< 1) at
the given coordinates.
"""
hs = np.sqrt(area) / 2
xcorners = array([x - hs, x + hs, x + hs, x - hs])
ycorners = array([y - hs, y - hs, y + hs, y + hs])
if ax is not None:
handle = ax
else:
handle = plt
return handle.fill(xcorners, ycorners, color=color_fn(w))
def _cb_labels(left_dims):
"""Creates plot labels for matrix elements in the computational basis.
Parameters
----------
left_dims : flat list of ints
Dimensions of the left index of a density operator. E. g.
[2, 3] for a qubit tensored with a qutrit.
Returns
-------
left_labels, right_labels : lists of strings
Labels for the left and right indices of a density operator
(kets and bras, respectively).
"""
# FIXME: assumes dims, such that we only need left_dims == dims[0].
basis_labels = list(map(",".join, it.product(*[
map(str, range(dim))
for dim in left_dims
])))
return [
map(fmt.format, basis_labels) for fmt in
(
r"$\langle{}|$",
r"$|{}\rangle$",
)
]
# Adopted from the SciPy Cookbook.
[docs]def hinton(rho, x_basis=None, y_basis=None, color_style="scaled",
label_top=True, *, cmap=None, colorbar=True, fig=None, ax=None):
"""Draws a Hinton diagram to visualize a density matrix or superoperator.
Parameters
----------
rho : qobj
Input density matrix or superoperator.
.. note::
Hinton plots of superoperators are currently only
supported for qubits.
x_basis : list of strings, optional
list of x ticklabels to represent x basis of the input.
y_basis : list of strings, optional
list of y ticklabels to represent y basis of the input.
color_style : str, {"scaled", "threshold", "phase"}, default: "scaled"
Determines how colors are assigned to each square:
- If set to ``"scaled"`` (default), each color is chosen by
passing the absolute value of the corresponding matrix
element into `cmap` with the sign of the real part.
- If set to ``"threshold"``, each square is plotted as
the maximum of `cmap` for the positive real part and as
the minimum for the negative part of the matrix element;
note that this generalizes `"threshold"` to complex numbers.
- If set to ``"phase"``, each color is chosen according to
the angle of the corresponding matrix element.
label_top : bool, default: True
If True, x ticklabels will be placed on top, otherwise
they will appear below the plot.
cmap : a matplotlib colormap instance, optional
Color map to use when plotting.
colorbar : bool, default: True
Whether (True) or not (False) a colorbar should be attached.
fig : a matplotlib Figure instance, optional
The Figure canvas in which the plot will be drawn.
ax : a matplotlib axes instance, optional
The ax context in which the plot will be drawn.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
Raises
------
ValueError
Input argument is not a quantum object.
Examples
--------
>>> import qutip
>>> dm = qutip.rand_dm(4)
>>> fig, ax = qutip.hinton(dm)
>>> fig.show()
>>> qutip.settings.colorblind_safe = True
>>> fig, ax = qutip.hinton(dm, color_style="threshold")
>>> fig.show()
>>> qutip.settings.colorblind_safe = False
>>> fig, ax = qutip.hinton(dm, color_style="phase")
>>> fig.show()
"""
fig, ax = _is_fig_and_ax(fig, ax)
if not isinstance(rho, list):
rhos = [rho]
else:
rhos = rho
_equal_shape(rhos)
Ws = list()
w_max = 0
for rho in rhos:
# Extract plotting data W from the input.
if isinstance(rho, Qobj):
if rho.isoper or rho.isoperket or rho.isoperbra:
if rho.isoperket:
rho = vector_to_operator(rho)
elif rho.isoperbra:
rho = vector_to_operator(rho.dag())
W = rho.full()
# Create default labels if none are given.
labels = _cb_labels(rho.dims[0])
if x_basis is None:
x_basis = list(labels[0])
if y_basis is None:
y_basis = list(labels[1])
elif rho.issuper:
if not isqubitdims(rho.dims):
raise ValueError("Hinton plots of superoperators are "
"currently only supported for qubits.")
# Convert to a superoperator in the Pauli basis,
# so that all the elements are real.
sqobj = _to_superpauli(rho)
nq = int(log2(sqobj.shape[0]) / 2)
W = sqobj.full().T
# Create default labels, too.
labels = list(map("".join, it.product("IXYZ", repeat=nq)))
if x_basis is None:
x_basis = labels
if y_basis is None:
y_basis = labels
else:
raise ValueError(
"Input quantum object must be "
"an operator or superoperator.")
else:
W = rho
Ws.append(W)
height, width = W.shape
w_max = max(1.25 * max(abs(np.array(W)).flatten()), w_max)
if w_max <= 0.0:
w_max = 1.0
# Set color_fn here.
if color_style == "scaled":
if cmap is None:
cmap = _diverging_cmap()
def color_fn(w):
w = np.abs(w) * np.sign(np.real(w))
return cmap(int((w + w_max) * 256 / (2 * w_max)))
elif color_style == "threshold":
if cmap is None:
cmap = _diverging_cmap()
def color_fn(w):
w = np.real(w)
return cmap(255 if w > 0 else 0)
elif color_style == "phase":
if cmap is None:
cmap = _cyclic_cmap()
def color_fn(w):
return cmap(int(255 * (np.angle(w) / 2 / np.pi + 0.5)))
else:
raise ValueError(
"Unknown color style {} for Hinton diagrams.".format(color_style)
)
artist_list = list()
ax.fill(array([0, width, width, 0]), array([0, 0, height, height]),
color=cmap(128))
for W in Ws:
artist = list()
for x in range(width):
for y in range(height):
_x = x + 1
_y = y + 1
artist += _blob(_x - 0.5, height - _y + 0.5, W[y, x],
w_max, min(1, abs(W[y, x]) / w_max),
color_fn=color_fn, ax=ax)
artist_list.append(artist)
if len(rhos) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
# axis
if not (x_basis or y_basis):
ax.axis('off')
ax.axis('equal')
ax.set_frame_on(False)
# x axis
xticks = 0.5 + np.arange(width)
if x_basis:
_set_ticklabels(ax, x_basis, xticks, 'x')
if label_top:
ax.xaxis.tick_top()
# y axis
yticks = 0.5 + np.arange(height)
if y_basis:
_set_ticklabels(ax, list(reversed(y_basis)), yticks, 'y')
if colorbar:
vmax = np.pi if color_style == "phase" else w_max
norm = mpl.colors.Normalize(-vmax, vmax)
cax, kw = mpl.colorbar.make_axes(ax, shrink=0.75, pad=.1)
mpl.colorbar.ColorbarBase(cax, norm=norm, cmap=cmap)
return fig, output
[docs]def sphereplot(values, theta, phi, *,
cmap=None, colorbar=True, fig=None, ax=None):
"""Plots a matrix of values on a sphere
Parameters
----------
values : array
Data set to be plotted
theta : float
Angle with respect to z-axis. Its range is between 0 and pi
phi : float
Angle in x-y plane. Its range is between 0 and 2*pi
cmap : a matplotlib colormap instance, optional
Color map to use when plotting.
colorbar : bool, default: True
Whether (True) or not (False) a colorbar should be attached.
fig : a matplotlib Figure instance, optional
The Figure canvas in which the plot will be drawn.
ax : a matplotlib axes instance, optional
The axes context in which the plot will be drawn.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
"""
fig, ax = _is_fig_and_ax(fig, ax, projection='3d')
if not isinstance(values, list):
V = [values]
else:
V = values
_equal_shape(V)
r_and_ph = list()
min_ph = pi
max_ph = -pi
for values in V:
r = array(abs(values))
ph = angle(values)
min_ph = min(min_ph, ph.min())
max_ph = max(max_ph, ph.max())
r_and_ph.append((r, ph))
# normalize color range based on phase angles in list ph
norm = mpl.colors.Normalize(min_ph, max_ph)
if cmap is None:
cmap = _sequential_cmap()
# plot with facecolors set to cm.jet colormap normalized to nrm
thetam, phim = np.meshgrid(theta, phi)
xx = sin(thetam) * cos(phim)
yy = sin(thetam) * sin(phim)
zz = cos(thetam)
artist_list = list()
for r, ph in r_and_ph:
artist = [ax.plot_surface(r * xx, r * yy, r * zz, rstride=1, cstride=1,
facecolors=cmap(norm(ph)), linewidth=0,)]
artist_list.append(artist)
if len(V) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
if colorbar:
# create new axes on plot for colorbar and shrink it a bit.
# pad shifts location of bar with repsect to the main plot
cax, kw = mpl.colorbar.make_axes(ax, shrink=.66, pad=.05)
# create new colorbar in axes cax with cmap and normalized to nrm like
# our facecolors
cb1 = mpl.colorbar.ColorbarBase(cax, cmap=cmap, norm=norm)
# add our colorbar label
cb1.set_label('Angle')
return fig, output
def _remove_margins(axis):
"""
removes margins about z = 0 and improves the style
by monkey patching
"""
def _get_coord_info_new(renderer):
mins, maxs, centers, deltas, tc, highs = \
_get_coord_info_old(renderer)
mins += deltas / 4
maxs -= deltas / 4
return mins, maxs, centers, deltas, tc, highs
_get_coord_info_old = axis._get_coord_info
axis._get_coord_info = _get_coord_info_new
def _stick_to_planes(stick, azim, ax, M, spacing):
"""adjusts xlim and ylim in way that bars will
stick to xz and yz planes
"""
if stick is True:
azim = azim % 360
if 0 <= azim <= 90:
ax.set_ylim(1 - .5,)
ax.set_xlim(1 - .5,)
elif 90 < azim <= 180:
ax.set_ylim(1 - .5,)
ax.set_xlim(0, M.shape[0] + (.5 - spacing))
elif 180 < azim <= 270:
ax.set_ylim(0, M.shape[1] + (.5 - spacing))
ax.set_xlim(0, M.shape[0] + (.5 - spacing))
elif 270 < azim < 360:
ax.set_ylim(0, M.shape[1] + (.5 - spacing))
ax.set_xlim(1 - .5,)
def _update_yaxis(spacing, M, ax, ylabels):
"""
updates the y-axis
"""
ytics = [y + (1 - (spacing / 2)) for y in range(M.shape[1])]
ax.yaxis.set_major_locator(plt.FixedLocator(ytics))
if ylabels:
nylabels = len(ylabels)
if nylabels != len(ytics):
raise ValueError(f"got {nylabels} ylabels but needed {len(ytics)}")
ax.set_yticklabels(ylabels)
else:
ax.set_yticklabels([str(y + 1) for y in range(M.shape[1])])
ax.set_yticklabels([str(i) for i in range(M.shape[1])])
ax.tick_params(axis='y', labelsize=14)
ax.set_yticks([y + (1 - (spacing / 2)) for y in range(M.shape[1])])
def _update_xaxis(spacing, M, ax, xlabels):
"""
updates the x-axis
"""
xtics = [x + (1 - (spacing / 2)) for x in range(M.shape[0])]
ax.xaxis.set_major_locator(plt.FixedLocator(xtics))
if xlabels:
nxlabels = len(xlabels)
if nxlabels != len(xtics):
raise ValueError(f"got {nxlabels} xlabels but needed {len(xtics)}")
ax.set_xticklabels(xlabels)
else:
ax.set_xticklabels([str(x + 1) for x in range(M.shape[0])])
ax.set_xticklabels([str(i) for i in range(M.shape[0])])
ax.tick_params(axis='x', labelsize=14)
ax.set_xticks([x + (1 - (spacing / 2)) for x in range(M.shape[0])])
def _update_zaxis(ax, z_min, z_max, zticks):
"""
updates the z-axis
"""
ax.zaxis.set_major_locator(plt.IndexLocator(1, 0.5))
if isinstance(zticks, list):
ax.set_zticks(zticks)
ax.set_zlim3d([min(z_min, 0), z_max])
def _get_matrix_components(option, M, argument):
if option == 'real':
return np.real(M.flatten())
elif option == 'img':
return np.imag(M.flatten())
elif option == 'abs':
return np.abs(M.flatten())
elif option == 'phase':
return angle(M.flatten())
else:
raise ValueError("got an unexpected argument, "
f"{option} for {argument}")
[docs]def matrix_histogram(M, x_basis=None, y_basis=None, limits=None,
bar_style='real', color_limits=None, color_style='real',
options=None, *, cmap=None, colorbar=True,
fig=None, ax=None):
"""
Draw a histogram for the matrix M, with the given x and y labels and title.
Parameters
----------
M : Matrix of Qobj
The matrix to visualize
x_basis : list of strings, optional
list of x ticklabels
y_basis : list of strings, optional
list of y ticklabels
limits : list/array with two float numbers, optional
The z-axis limits [min, max]
bar_style : str, {"real", "img", "abs", "phase"}, default: "real"
- If set to ``"real"`` (default), each bar is plotted
as the real part of the corresponding matrix element
- If set to ``"img"``, each bar is plotted
as the imaginary part of the corresponding matrix element
- If set to ``"abs"``, each bar is plotted
as the absolute value of the corresponding matrix element
- If set to ``"phase"`` (default), each bar is plotted
as the angle of the corresponding matrix element
color_limits : list/array with two float numbers, optional
The limits of colorbar [min, max]
color_style : str, {"real", "img", "abs", "phase"}, default: "real"
Determines how colors are assigned to each square:
- If set to ``"real"`` (default), each color is chosen
according to the real part of the corresponding matrix element.
- If set to ``"img"``, each color is chosen according to
the imaginary part of the corresponding matrix element.
- If set to ``"abs"``, each color is chosen according to
the absolute value of the corresponding matrix element.
- If set to ``"phase"``, each color is chosen according to
the angle of the corresponding matrix element.
cmap : a matplotlib colormap instance, optional
Color map to use when plotting.
colorbar : bool, default: True
show colorbar
fig : a matplotlib Figure instance, optional
The Figure canvas in which the plot will be drawn.
ax : a matplotlib axes instance, optional
The axes context in which the plot will be drawn.
options : dict, optional
A dictionary containing extra options for the plot.
The names (keys) and values of the options are
described below:
'zticks' : list of numbers, optional
A list of z-axis tick locations.
'bars_spacing' : float, default: 0.1
spacing between bars.
'bars_alpha' : float, default: 1.
transparency of bars, should be in range 0 - 1
'bars_lw' : float, default: 0.5
linewidth of bars' edges.
'bars_edgecolor' : color, default: 'k'
The colors of the bars' edges.
Examples: 'k', (0.1, 0.2, 0.5) or '#0f0f0f80'.
'shade' : bool, default: True
Whether to shade the dark sides of the bars (True) or not (False).
The shading is relative to plot's source of light.
'azim' : float, default: -35
The azimuthal viewing angle.
'elev' : float, default: 35
The elevation viewing angle.
'stick' : bool, default: False
Changes xlim and ylim in such a way that bars next to
XZ and YZ planes will stick to those planes.
This option has no effect if ``ax`` is passed as a parameter.
'cbar_pad' : float, default: 0.04
The fraction of the original axes between the colorbar
and the new image axes.
(i.e. the padding between the 3D figure and the colorbar).
'cbar_to_z' : bool, default: False
Whether to set the color of maximum and minimum z-values to the
maximum and minimum colors in the colorbar (True) or not (False).
'threshold': float, optional
Threshold for when bars of smaller height should be transparent. If
not set, all bars are colored according to the color map.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
Raises
------
ValueError
Input argument is not valid.
"""
# default options
default_opts = {'zticks': None, 'bars_spacing': 0.2,
'bars_alpha': 1., 'bars_lw': 0.5, 'bars_edgecolor': 'k',
'shade': True, 'azim': -35, 'elev': 35, 'stick': False,
'cbar_pad': 0.04, 'cbar_to_z': False, 'threshold': None}
# update default_opts from input options
if options is None:
options = dict()
if isinstance(options, dict):
# check if keys in options dict are valid
if set(options) - set(default_opts):
raise ValueError("invalid key(s) found in options: "
f"{', '.join(set(options) - set(default_opts))}")
else:
# updating default options
default_opts.update(options)
options = default_opts
else:
raise ValueError("options must be a dictionary")
fig, ax = _is_fig_and_ax(fig, ax, projection='3d')
if not isinstance(M, list):
Ms = [M]
else:
Ms = M
_equal_shape(Ms)
for i in range(len(Ms)):
M = Ms[i]
if isinstance(M, Qobj):
if x_basis is None:
x_basis = list(_cb_labels([M.shape[0]])[0])
if y_basis is None:
y_basis = list(_cb_labels([M.shape[1]])[1])
# extract matrix data from Qobj
M = M.full()
bar_M = _get_matrix_components(bar_style, M, 'bar_style')
if isinstance(limits, list) and \
len(limits) == 2:
z_min = limits[0]
z_max = limits[1]
else:
z_min = min(bar_M) if i == 0 else min(min(bar_M), z_min)
z_max = max(bar_M) if i == 0 else max(max(bar_M), z_max)
if z_min == z_max:
z_min -= 0.1
z_max += 0.1
color_M = _get_matrix_components(color_style, M, 'color_style')
if isinstance(color_limits, list) and \
len(color_limits) == 2:
c_min = color_limits[0]
c_max = color_limits[1]
else:
if color_style == 'phase':
c_min = -pi
c_max = pi
else:
c_min = min(color_M) if i == 0 else min(min(color_M), c_min)
c_max = min(color_M) if i == 0 else max(max(color_M), c_max)
if c_min == c_max:
c_min -= 0.1
c_max += 0.1
norm = mpl.colors.Normalize(c_min, c_max)
if cmap is None:
# change later
if color_style == 'phase':
cmap = _cyclic_cmap()
else:
cmap = _sequential_cmap()
artist_list = list()
for M in Ms:
if isinstance(M, Qobj):
M = M.full()
bar_M = _get_matrix_components(bar_style, M, 'bar_style')
color_M = _get_matrix_components(color_style, M, 'color_style')
n = np.size(M)
xpos, ypos = np.meshgrid(range(M.shape[0]), range(M.shape[1]))
xpos = xpos.T.flatten() + 0.5
ypos = ypos.T.flatten() + 0.5
zpos = np.zeros(n)
dx = dy = (1 - options['bars_spacing']) * np.ones(n)
colors = cmap(norm(color_M))
colors[:, 3] = options['bars_alpha']
if options['threshold'] is not None:
colors[:, 3] *= 1 * (bar_M >= options['threshold'])
idx, = np.where(bar_M < options['threshold'])
bar_M[idx] = 0
artist = ax.bar3d(xpos, ypos, zpos, dx, dy, bar_M, color=colors,
edgecolors=options['bars_edgecolor'],
linewidths=options['bars_lw'],
shade=options['shade'])
artist_list.append([artist])
if len(Ms) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
# remove vertical lines on xz and yz plane
ax.yaxis._axinfo["grid"]['linewidth'] = 0
ax.xaxis._axinfo["grid"]['linewidth'] = 0
# x axis
_update_xaxis(options['bars_spacing'], M, ax, x_basis)
# y axis
_update_yaxis(options['bars_spacing'], M, ax, y_basis)
# z axis
_update_zaxis(ax, z_min, z_max, options['zticks'])
# stick to xz and yz plane
_stick_to_planes(options['stick'],
options['azim'], ax, M,
options['bars_spacing'])
ax.view_init(azim=options['azim'], elev=options['elev'])
# removing margins
_remove_margins(ax.xaxis)
_remove_margins(ax.yaxis)
_remove_margins(ax.zaxis)
# color axis
if colorbar:
cax, kw = mpl.colorbar.make_axes(ax, shrink=.75,
pad=options['cbar_pad'])
cb = mpl.colorbar.ColorbarBase(cax, cmap=cmap, norm=norm)
if color_style == 'real':
cb.set_label('real')
elif color_style == 'img':
cb.set_label('imaginary')
elif color_style == 'abs':
cb.set_label('absolute')
else:
cb.set_label('arg')
if color_limits is None:
cb.set_ticks([-pi, -pi / 2, 0, pi / 2, pi])
cb.set_ticklabels(
(r'$-\pi$', r'$-\pi/2$', r'$0$', r'$\pi/2$', r'$\pi$'))
return fig, output
[docs]def plot_energy_levels(H_list, h_labels=None, energy_levels=None, N=0, *,
fig=None, ax=None):
"""
Plot the energy level diagrams for a list of Hamiltonians. Include
up to N energy levels. For each element in H_list, the energy
levels diagram for the cummulative Hamiltonian sum(H_list[0:n]) is plotted,
where n is the index of an element in H_list.
Parameters
----------
H_list : List of Qobj
A list of Hamiltonians.
h_lables : List of string, optional
A list of xticklabels for each Hamiltonian
energy_levels : List of string, optional
A list of yticklabels to the left of energy levels of the initial
Hamiltonian.
N : int, default: 0
The number of energy levels to plot
fig : a matplotlib Figure instance, optional
The Figure canvas in which the plot will be drawn.
ax : a matplotlib axes instance, optional
The axes context in which the plot will be drawn.
Returns
-------
fig, ax : tuple
A tuple of the matplotlib figure and axes instances used to produce
the figure.
Raises
------
ValueError
Input argument is not valid.
"""
if not isinstance(H_list, list):
raise ValueError("H_list must be a list of Qobj instances")
fig, ax = _is_fig_and_ax(fig, ax)
H = H_list[0]
N = H.shape[0] if N == 0 else min(H.shape[0], N)
xticks = []
yticks = []
x = 0
evals0 = H.eigenenergies(eigvals=N)
for e_idx, e in enumerate(evals0[:N]):
ax.plot([x, x + 2], np.array([1, 1]) * e, 'b', linewidth=2)
yticks.append(e)
xticks.append(x + 1)
x += 2
for H1 in H_list[1:]:
H = H + H1
evals1 = H.eigenenergies()
for e_idx, e in enumerate(evals1[:N]):
ax.plot([x, x + 1], np.array([evals0[e_idx], e]), 'k:')
x += 1
for e_idx, e in enumerate(evals1[:N]):
ax.plot([x, x + 2], np.array([1, 1]) * e, 'b', linewidth=2)
xticks.append(x + 1)
x += 2
evals0 = evals1
ax.set_frame_on(False)
if energy_levels:
yticks = np.unique(np.around(yticks, 1))
_set_ticklabels(ax, energy_levels, yticks, 'y')
else:
# show eigenenergies
yticks = np.unique(np.around(yticks, 1))
ax.set_yticks(yticks)
if h_labels:
ax.get_xaxis().tick_bottom()
_set_ticklabels(ax, h_labels, xticks, 'x')
else:
# hide xtick
ax.tick_params(axis='x', which='both',
bottom=False, labelbottom=False)
return fig, ax
[docs]def plot_fock_distribution(rho, fock_numbers=None, color="green",
unit_y_range=True, *, fig=None, ax=None):
"""
Plot the Fock distribution for a density matrix (or ket) that describes
an oscillator mode.
Parameters
----------
rho : :obj:`.Qobj`
The density matrix (or ket) of the state to visualize.
fock_numbers : list of strings, optional
list of x ticklabels to represent fock numbers
color : color or list of colors, default: "green"
The colors of the bar faces.
unit_y_range : bool, default: True
Set y-axis limits [0, 1] or not
fig : a matplotlib Figure instance, optional
The Figure canvas in which the plot will be drawn.
ax : a matplotlib axes instance, optional
The axes context in which the plot will be drawn.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
"""
fig, ax = _is_fig_and_ax(fig, ax)
if not isinstance(rho, list):
rhos = [rho]
else:
rhos = rho
_equal_shape(rhos)
artist_list = list()
for rho in rhos:
if isket(rho):
rho = ket2dm(rho)
N = rho.shape[0]
artist = ax.bar(np.arange(N), np.real(rho.diag()),
color=color, alpha=0.6, width=0.8).patches
artist_list.append(artist)
if len(rhos) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
if fock_numbers:
_set_ticklabels(ax, fock_numbers, np.arange(N), 'x', fontsize=12)
if unit_y_range:
ax.set_ylim(0, 1)
ax.set_xlim(-.5, N)
ax.set_xlabel('Fock number', fontsize=12)
ax.set_ylabel('Occupation probability', fontsize=12)
return fig, output
[docs]def plot_wigner(rho, xvec=None, yvec=None, method='clenshaw', projection='2d',
g=sqrt(2), sparse=False, parfor=False, *,
cmap=None, colorbar=False, fig=None, ax=None):
"""
Plot the the Wigner function for a density matrix (or ket) that describes
an oscillator mode.
Parameters
----------
rho : :obj:`.Qobj`
The density matrix (or ket) of the state to visualize.
xvec : array_like, optional
x-coordinates at which to calculate the Wigner function.
yvec : array_like, optional
y-coordinates at which to calculate the Wigner function. Does not
apply to the 'fft' method.
method : str {'clenshaw', 'iterative', 'laguerre', 'fft'}, default: 'clenshaw'
The method used for calculating the wigner function. See the
documentation for qutip.wigner for details.
projection: str {'2d', '3d'}, default: '2d'
Specify whether the Wigner function is to be plotted as a
contour graph ('2d') or surface plot ('3d').
g : float
Scaling factor for `a = 0.5 * g * (x + iy)`, default `g = sqrt(2)`.
See the documentation for qutip.wigner for details.
sparse : bool {False, True}
Flag for sparse format.
See the documentation for qutip.wigner for details.
parfor : bool {False, True}
Flag for parallel calculation.
See the documentation for qutip.wigner for details.
cmap : a matplotlib cmap instance, optional
The colormap.
colorbar : bool, default: False
Whether (True) or not (False) a colorbar should be attached to the
Wigner function graph.
fig : a matplotlib Figure instance, optional
The Figure canvas in which the plot will be drawn.
ax : a matplotlib axes instance, optional
The axes context in which the plot will be drawn.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
"""
if projection not in ('2d', '3d'):
raise ValueError('Unexpected value of projection keyword argument')
fig, ax = _is_fig_and_ax(fig, ax, projection)
if not isinstance(rho, list):
rhos = [rho]
else:
rhos = rho
_equal_shape(rhos)
wlim = 0
Ws = list()
xvec = np.linspace(-7.5, 7.5, 200) if xvec is None else xvec
yvec = np.linspace(-7.5, 7.5, 200) if yvec is None else yvec
for rho in rhos:
if isket(rho):
rho = ket2dm(rho)
W0 = wigner(
rho, xvec, yvec, method=method,
g=g, sparse=sparse, parfor=parfor
)
W, yvec = W0 if isinstance(W0, tuple) else (W0, yvec)
Ws.append(W)
wlim = max(abs(W).max(), wlim)
norm = mpl.colors.Normalize(-wlim, wlim)
if cmap is None:
cmap = _diverging_cmap()
artist_list = list()
for W in Ws:
if projection == '2d':
if parse_version(mpl.__version__) >= parse_version('3.8'):
cf = [ax.contourf(xvec, yvec, W, 100, norm=norm, cmap=cmap)]
else:
cf = ax.contourf(xvec, yvec, W, 100, norm=norm,
cmap=cmap).collections
else:
X, Y = np.meshgrid(xvec, yvec)
cf = [ax.plot_surface(X, Y, W, rstride=5, cstride=5, linewidth=0.5,
norm=norm, cmap=cmap)]
artist_list.append(cf)
if len(rhos) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
ax.set_xlabel(r'$\rm{Re}(\alpha)$', fontsize=12)
ax.set_ylabel(r'$\rm{Im}(\alpha)$', fontsize=12)
if colorbar:
if projection == '2d':
shrink = 1
else:
shrink = .75
cax, kw = mpl.colorbar.make_axes(ax, shrink=shrink, pad=.1)
cbar = mpl.colorbar.ColorbarBase(cax, cmap=cmap, norm=norm)
return fig, output
[docs]def plot_expectation_values(results, ylabels=None, *,
fig=None, axes=None):
"""
Visualize the results (expectation values) for an evolution solver.
`results` is assumed to be an instance of Result, or a list of Result
instances.
Parameters
----------
results : (list of) :class:`.Result`
List of results objects returned by any of the QuTiP evolution solvers.
ylabels : list of strings, optional
The y-axis labels. List should be of the same length as `results`.
fig : a matplotlib Figure instance, optional
The Figure canvas in which the plot will be drawn.
axes : (list of) axes instances, optional
The axes context in which the plot will be drawn.
Returns
-------
fig, axes : tuple
A tuple of the matplotlib figure and array of axes instances
used to produce the figure.
"""
if not isinstance(results, list):
results = [results]
n_e_ops = max([len(result.expect) for result in results])
if axes is None:
if fig is None:
fig = plt.figure()
axes = np.array([fig.add_subplot(n_e_ops, 1, i+1)
for i in range(n_e_ops)])
# create np.ndarray if axes is one axes object or list
if not isinstance(axes, np.ndarray):
if not isinstance(axes, list):
axes = [axes]
axes = np.array(axes)
for _, result in enumerate(results):
for e_idx, e in enumerate(result.expect):
axes[e_idx].plot(result.times, e,
label="%s [%d]" % (result.solver, e_idx))
axes[n_e_ops - 1].set_xlabel("time", fontsize=12)
for n in range(n_e_ops):
if ylabels:
axes[n].set_ylabel(ylabels[n], fontsize=12)
return fig, axes
[docs]def plot_spin_distribution(P, THETA, PHI, projection='2d', *,
cmap=None, colorbar=False, fig=None, ax=None):
"""
Plots a spin distribution (given as meshgrid data).
Parameters
----------
P : matrix
Distribution values as a meshgrid matrix.
THETA : matrix
Meshgrid matrix for the theta coordinate. Its range is between 0 and pi
PHI : matrix
Meshgrid matrix for the phi coordinate. Its range is between 0 and 2*pi
projection: str {'2d', '3d'}, default: '2d'
Specify whether the spin distribution function is to be plotted as a 2D
projection where the surface of the unit sphere is mapped on
the unit disk ('2d') or surface plot ('3d').
cmap : a matplotlib cmap instance, optional
The colormap.
colorbar : bool, default: False
Whether (True) or not (False) a colorbar should be attached to the
Wigner function graph.
fig : a matplotlib figure instance, optional
The figure canvas on which the plot will be drawn.
ax : a matplotlib axis instance, optional
The axis context in which the plot will be drawn.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
"""
if projection in ('2d', '3d'):
fig, ax = _is_fig_and_ax(fig, ax, projection)
else:
raise ValueError('Unexpected value of projection keyword argument')
if not isinstance(P, list):
Ps = [P]
else:
Ps = P
_equal_shape(Ps)
min_P = Ps[0].min()
max_P = Ps[0].max()
for P in Ps:
min_P = min(min_P, P.min())
max_P = max(max_P, P.max())
if cmap is None:
if min_P < -1e12:
cmap = _diverging_cmap()
norm = mpl.colors.Normalize(-max_P, max_P)
else:
cmap = _sequential_cmap()
norm = mpl.colors.Normalize(min_P, max_P)
artist_list = list()
if projection == '2d':
Y = (THETA - pi / 2) / (pi / 2)
X = (pi - PHI) / pi * np.sqrt(cos(THETA - pi / 2))
for P in Ps:
artist_list.append([ax.pcolor(X, Y, P.real, cmap=cmap)])
ax.set_xlabel(r'$\varphi$', fontsize=18)
ax.set_ylabel(r'$\theta$', fontsize=18)
ax.axis('equal')
ax.set_xticks([-1, 0, 1])
ax.set_xticklabels([r'$0$', r'$\pi$', r'$2\pi$'], fontsize=18)
ax.set_yticks([-1, 0, 1])
ax.set_yticklabels([r'$\pi$', r'$\pi/2$', r'$0$'], fontsize=18)
else:
xx = sin(THETA) * cos(PHI)
yy = sin(THETA) * sin(PHI)
zz = cos(THETA)
for P in Ps:
artist = [ax.plot_surface(xx, yy, zz, rstride=1, cstride=1,
facecolors=cmap(norm(P)), linewidth=0)]
artist_list.append(artist)
ax.view_init(azim=-35, elev=35)
if len(Ps) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
if colorbar:
cax, _ = mpl.colorbar.make_axes(ax, shrink=.66, pad=.1)
cb1 = mpl.colorbar.ColorbarBase(cax, cmap=cmap, norm=norm)
cb1.set_label('magnitude')
return fig, output
#
# Qubism and other qubistic visualizations
#
def complex_array_to_rgb(X, theme='light', rmax=None):
"""
Makes an array of complex number and converts it to an array of [r, g, b],
where phase gives hue and saturation/value are given by the absolute value.
Especially for use with imshow for complex plots.
For more info on coloring, see:
Emilia Petrisor,
Visualizing complex-valued functions with Matplotlib and Mayavi
https://nbviewer.ipython.org/github/empet/Math/blob/master/DomainColoring.ipynb
Parameters
----------
X : array
Array (of any dimension) of complex numbers.
theme : str {'light', 'dark'}, default: 'light'
Set coloring theme for mapping complex values into colors.
rmax : float, optional
Maximal abs value for color normalization.
If None (default), uses np.abs(X).max().
Returns
-------
Y : array
Array of colors (of shape X.shape + (3,)).
"""
absmax = rmax or np.abs(X).max()
if absmax == 0.:
absmax = 1.
Y = np.zeros(X.shape + (3,), dtype='float')
Y[..., 0] = np.angle(X) / (2 * pi) % 1
if theme == 'light':
Y[..., 1] = np.clip(np.abs(X) / absmax, 0, 1)
Y[..., 2] = 1
elif theme == 'dark':
Y[..., 1] = 1
Y[..., 2] = np.clip(np.abs(X) / absmax, 0, 1)
Y = mpl.colors.hsv_to_rgb(Y)
return Y
def _index_to_sequence(i, dim_list):
"""
For a matrix entry with index i it returns state it corresponds to.
In particular, for dim_list=[2]*n it returns i written as a binary number.
Parameters
----------
i : int
Index in a matrix.
dim_list : list of int
List of dimensions of consecutive particles.
Returns
-------
seq : list
List of coordinates for each particle.
"""
res = []
j = i
for d in reversed(dim_list):
j, s = divmod(j, d)
res.append(s)
return list(reversed(res))
def _sequence_to_index(seq, dim_list):
"""
Inverse of _index_to_sequence.
Parameters
----------
seq : list of ints
List of coordinates for each particle.
dim_list : list of int
List of dimensions of consecutive particles.
Returns
-------
i : list
Index in a matrix.
"""
i = 0
for s, d in zip(seq, dim_list):
i *= d
i += s
return i
def _to_qubism_index_pair(i, dim_list, how='pairs'):
"""
For a matrix entry with index i
it returns x, y coordinates in qubism mapping.
Parameters
----------
i : int
Index in a matrix.
dim_list : list of int
List of dimensions of consecutive particles.
how : 'pairs' ('default'), 'pairs_skewed' or 'before_after'
Type of qubistic plot.
Returns
-------
x, y : tuple of ints
List of coordinates for each particle.
"""
seq = _index_to_sequence(i, dim_list)
if how == 'pairs':
y = _sequence_to_index(seq[::2], dim_list[::2])
x = _sequence_to_index(seq[1::2], dim_list[1::2])
elif how == 'pairs_skewed':
dim_list2 = dim_list[::2]
y = _sequence_to_index(seq[::2], dim_list2)
seq2 = [(b - a) % d for a, b, d in zip(seq[::2], seq[1::2], dim_list2)]
x = _sequence_to_index(seq2, dim_list2)
elif how == 'before_after':
# https://en.wikipedia.org/wiki/File:Ising-tartan.png
n = len(dim_list)
y = _sequence_to_index(reversed(seq[:(n // 2)]),
reversed(dim_list[:(n // 2)]))
x = _sequence_to_index(seq[(n // 2):], dim_list[(n // 2):])
else:
raise Exception("No such 'how'.")
return x, y
def _sequence_to_latex(seq, style='ket'):
"""
For a sequence of particle states generate LaTeX code.
Parameters
----------
seq : list of ints
List of coordinates for each particle.
style : 'ket' (default), 'bra' or 'bare'
Style of LaTeX (i.e. |01> or <01| or 01, respectively).
Returns
-------
latex : str
LaTeX output.
"""
if style == 'ket':
latex = "$\\left|{0}\\right\\rangle$"
elif style == 'bra':
latex = "$\\left\\langle{0}\\right|$"
elif style == 'bare':
latex = "${0}$"
else:
raise Exception("No such style.")
return latex.format("".join(map(str, seq)))
[docs]def plot_qubism(ket, theme='light', how='pairs', grid_iteration=1,
legend_iteration=0, *, fig=None, ax=None):
"""
Qubism plot for pure states of many qudits. Works best for spin chains,
especially with even number of particles of the same dimension. Allows to
see entanglement between first 2k particles and the rest.
.. note::
colorblind_safe does not apply because of its unique colormap
Parameters
----------
ket : Qobj
Pure state for plotting.
theme : str {'light', 'dark'}, default: 'light'
Set coloring theme for mapping complex values into colors.
See: complex_array_to_rgb.
how : str {'pairs', 'pairs_skewed' or 'before_after'}, default: 'pairs'
Type of Qubism plotting. Options:
- 'pairs' - typical coordinates,
- 'pairs_skewed' - for ferromagnetic/antriferromagnetic plots,
- 'before_after' - related to Schmidt plot (see also: plot_schmidt).
grid_iteration : int, default: 1
Helper lines to be drawn on plot.
Show tiles for 2*grid_iteration particles vs all others.
legend_iteration : int or 'grid_iteration' or 'all', default: 0
Show labels for first ``2*legend_iteration`` particles. Option
'grid_iteration' sets the same number of particles as for
grid_iteration. Option 'all' makes label for all particles. Typically
it should be 0, 1, 2 or perhaps 3.
fig : a matplotlib figure instance, optional
The figure canvas on which the plot will be drawn.
ax : a matplotlib axis instance, optional
The axis context in which the plot will be drawn.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
Notes
-----
See also [1]_.
References
----------
.. [1] J. Rodriguez-Laguna, P. Migdal, M. Ibanez Berganza, M. Lewenstein
and G. Sierra, *Qubism: self-similar visualization of many-body
wavefunctions*, `New J. Phys. 14 053028
<https://dx.doi.org/10.1088/1367-2630/14/5/053028>`_, arXiv:1112.3560
(2012), open access.
"""
fig, ax = _is_fig_and_ax(fig, ax)
if not isinstance(ket, list):
kets = [ket]
else:
kets = ket
_equal_shape(kets)
artist_list = list()
for ket in kets:
if not isket(ket):
raise Exception("Qubism works only for pure states, i.e. kets.")
# add for dm? (perhaps a separate function, plot_qubism_dm)
dim_list = ket.dims[0]
n = len(dim_list)
# for odd number of particles - pixels are rectangular
if n % 2 == 1:
ket = tensor(ket, Qobj([1] * dim_list[-1]))
dim_list = ket.dims[0]
n += 1
ketdata = ket.full()
if how == 'pairs':
dim_list_y = dim_list[::2]
dim_list_x = dim_list[1::2]
elif how == 'pairs_skewed':
dim_list_y = dim_list[::2]
dim_list_x = dim_list[1::2]
if dim_list_x != dim_list_y:
raise Exception("For 'pairs_skewed' pairs " +
"of dimensions need to be the same.")
elif how == 'before_after':
dim_list_y = list(reversed(dim_list[:(n // 2)]))
dim_list_x = dim_list[(n // 2):]
else:
raise Exception("No such 'how'.")
size_x = np.prod(dim_list_x)
size_y = np.prod(dim_list_y)
qub = np.zeros([size_x, size_y], dtype=complex)
for i in range(ketdata.size):
qub[_to_qubism_index_pair(i, dim_list, how=how)] = ketdata[i, 0]
qub = qub.transpose()
artist = [ax.imshow(complex_array_to_rgb(qub, theme=theme),
interpolation="none",
extent=(0, size_x, 0, size_y))]
artist_list.append(artist)
if len(kets) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
quadrants_x = np.prod(dim_list_x[:grid_iteration])
quadrants_y = np.prod(dim_list_y[:grid_iteration])
ticks_x = [size_x // quadrants_x * i for i in range(1, quadrants_x)]
ticks_y = [size_y // quadrants_y * i for i in range(1, quadrants_y)]
ax.set_xticks(ticks_x)
ax.set_xticklabels([""] * (quadrants_x - 1))
ax.set_yticks(ticks_y)
ax.set_yticklabels([""] * (quadrants_y - 1))
theme2color_of_lines = {'light': '#000000',
'dark': '#FFFFFF'}
ax.grid(True, color=theme2color_of_lines[theme])
if legend_iteration == 'all':
label_n = n // 2
elif legend_iteration == 'grid_iteration':
label_n = grid_iteration
else:
try:
label_n = int(legend_iteration)
except:
raise Exception("No such option for legend_iteration keyword " +
"argument. Use 'all', 'grid_iteration' or an " +
"integer.")
if label_n:
if how == 'before_after':
dim_list_small = list(reversed(dim_list_y[-label_n:])) \
+ dim_list_x[:label_n]
else:
dim_list_small = []
for j in range(label_n):
dim_list_small.append(dim_list_y[j])
dim_list_small.append(dim_list_x[j])
scale_x = float(size_x) / np.prod(dim_list_x[:label_n])
shift_x = 0.5 * scale_x
scale_y = float(size_y) / np.prod(dim_list_y[:label_n])
shift_y = 0.5 * scale_y
bbox = ax.get_window_extent().transformed(
fig.dpi_scale_trans.inverted())
fontsize = 35 * bbox.width / np.prod(dim_list_x[:label_n]) / label_n
opts = {'fontsize': fontsize,
'color': theme2color_of_lines[theme],
'horizontalalignment': 'center',
'verticalalignment': 'center'}
for i in range(np.prod(dim_list_small)):
x, y = _to_qubism_index_pair(i, dim_list_small, how=how)
seq = _index_to_sequence(i, dim_list=dim_list_small)
ax.text(scale_x * x + shift_x,
size_y - (scale_y * y + shift_y),
_sequence_to_latex(seq),
**opts)
return fig, output
[docs]def plot_schmidt(ket, theme='light', splitting=None,
labels_iteration=(3, 2), *, fig=None, ax=None):
"""
Plotting scheme related to Schmidt decomposition.
Converts a state into a matrix (A_ij -> A_i^j),
where rows are first particles and columns - last.
See also: plot_qubism with how='before_after' for a similar plot.
.. note::
colorblind_safe does not apply because of its unique colormap
Parameters
----------
ket : Qobj
Pure state for plotting.
theme : str {'light', 'dark'}, default: 'light'
Set coloring theme for mapping complex values into colors.
See: complex_array_to_rgb.
splitting : int, optional
Plot for a number of first particles versus the rest.
If not given, it is (number of particles + 1) // 2.
labels_iteration : int or pair of ints, default: (3, 2)
Number of particles to be shown as tick labels,
for first (vertical) and last (horizontal) particles, respectively.
fig : a matplotlib figure instance, optional
The figure canvas on which the plot will be drawn.
ax : a matplotlib axis instance, optional
The axis context in which the plot will be drawn.
Returns
-------
fig, output : tuple
A tuple of the matplotlib figure and the axes instance or animation
instance used to produce the figure.
"""
fig, ax = _is_fig_and_ax(fig, ax)
if not isinstance(ket, list):
kets = [ket]
else:
kets = ket
_equal_shape(kets)
artist_list = list()
for ket in kets:
if not isket(ket):
err = "Schmidt plot works only for pure states, i.e. kets."
raise Exception(err)
dim_list = ket.dims[0]
if splitting is None:
splitting = (len(dim_list) + 1) // 2
if isinstance(labels_iteration, int):
labels_iteration = labels_iteration, labels_iteration
ketdata = ket.full()
dim_list_y = dim_list[:splitting]
dim_list_x = dim_list[splitting:]
size_x = np.prod(dim_list_x)
size_y = np.prod(dim_list_y)
ketdata = ketdata.reshape((size_y, size_x))
artist = [ax.imshow(complex_array_to_rgb(ketdata, theme=theme),
interpolation="none",
extent=(0, size_x, 0, size_y))]
artist_list.append(artist)
if len(kets) == 1:
output = ax
else:
output = animation.ArtistAnimation(fig, artist_list, interval=50,
blit=True, repeat_delay=1000)
dim_list_small_x = dim_list_x[:labels_iteration[1]]
dim_list_small_y = dim_list_y[:labels_iteration[0]]
quadrants_x = np.prod(dim_list_small_x)
quadrants_y = np.prod(dim_list_small_y)
ticks_x = [size_x / quadrants_x * (i + 0.5)
for i in range(quadrants_x)]
ticks_y = [size_y / quadrants_y * (quadrants_y - i - 0.5)
for i in range(quadrants_y)]
labels_x = [_sequence_to_latex(_index_to_sequence(i*size_x // quadrants_x,
dim_list=dim_list_x))
for i in range(quadrants_x)]
labels_y = [_sequence_to_latex(_index_to_sequence(i*size_y // quadrants_y,
dim_list=dim_list_y))
for i in range(quadrants_y)]
ax.set_xticks(ticks_x)
ax.set_xticklabels(labels_x)
ax.set_yticks(ticks_y)
ax.set_yticklabels(labels_y)
ax.set_xlabel("last particles")
ax.set_ylabel("first particles")
return fig, output