def line_plot(carr, ax=None, ylabel=None, figsize=None, title=None, **kwargs):
import matplotlib.pyplot as plt
import numpy as np
# fix missing \text support
from expresso.pycas import latex as rlatex
latex = lambda x: rlatex(x).replace(r'\text', r'\mathrm')
fig = None
if ax == None:
fig, ax = plt.subplots(figsize=figsize)
if title:
ax.set_title(title)
e = get_unitless_bounds(carr)[0]
prefix, factor = get_metric_prefix(e[:2])
lines = ax.plot(
np.linspace(
float(e[0]) / factor,
float(e[1]) / factor, carr.data.shape[0]), carr.data, **kwargs)
ax.set_xlabel("$%s$ [$%s %s$]" %
(latex(carr.axis[0]), prefix, latex(e[2])))
if ylabel: ax.set_ylabel(ylabel)
if fig:
plt.show()
return lines[0]
def line_plot(carr,ax = None,ylabel = None,figsize = None,title = None,**kwargs):
import matplotlib.pyplot as plt
import numpy as np
# fix missing \text support
from expresso.pycas import latex as rlatex
latex = lambda x:rlatex(x).replace(r'\text',r'\mathrm')
fig = None
if ax == None:
fig, ax = plt.subplots(figsize=figsize)
if title:
ax.set_title(title)
e = get_unitless_bounds(carr)[0]
prefix,factor = get_metric_prefix(e[:2])
lines = ax.plot(np.linspace(float(e[0])/factor,float(e[1])/factor,carr.data.shape[0]),carr.data, **kwargs)
ax.set_xlabel("$%s$ [$%s %s$]" % (latex(carr.axis[0]),prefix,latex(e[2])))
if ylabel: ax.set_ylabel(ylabel)
if ax == None:
plt.show()
return lines[0]
def callback(r,m):
from IPython.display import display_latex
print "appy rule: %s" % r
lt = pc.latex(r.search.subs(m,evaluate=False)),\
pc.latex(r.replacement.subs(m,evaluate=False)),\
r"\;\text{ if }\;%s" % pc.latex(r.condition.subs(m,evaluate=False)) if r.condition is not None else ''
display_latex(r"$$%s \rightarrow %s%s$$" % lt,raw=True)
def callback(r,m):
from IPython.display import display_latex
import sys
print("appy rule: %s" % r)
lt = pc.latex(r.search.subs(m,evaluate=False)),\
pc.latex(r.replacement.subs(m,evaluate=False)),\
r"\;\text{ if }\;%s" % pc.latex(r.condition.subs(m,evaluate=False)) if r.condition is not None else ''
display_latex(r"$$%s \rightarrow %s%s$$" % lt,raw=True)
sys.stdout.flush()
def get_plot_coordinates(array):
import numpy as np
from expresso.pycas import latex
e = get_unitless_bounds(array)[0]
prefix, factor = get_metric_prefix(e[:2])
return np.linspace(
float(e[0]) / factor,
float(e[1]) / factor, array.shape[0]), prefix + ' ' + latex(e[2])
def image_plot(carr, ax=None, figsize=None, title=None, **kwargs):
import matplotlib.pyplot as plt
# fix missing \text support
from expresso.pycas import latex as rlatex
latex = lambda x: rlatex(x).replace(r'\text', r'\mathrm')
fig = None
if ax == None:
fig, ax = plt.subplots(figsize=figsize)
if title:
ax.set_title(title)
e = get_unitless_bounds(carr)
xprefix, xfactor = get_metric_prefix(e[1][:2])
yprefix, yfactor = get_metric_prefix(e[0][:2])
extent = [
float(e[1][0]) / xfactor,
float(e[1][1]) / xfactor,
float(e[0][0]) / yfactor,
float(e[0][1]) / yfactor
]
if 'aspect' not in kwargs:
kwargs['aspect'] = 'auto'
if 'origin' not in kwargs:
kwargs['origin'] = 'lower'
image = ax.imshow(carr.data, extent=extent, **kwargs)
ax.set_ylabel("$%s$ [$%s %s$]" %
(latex(carr.axis[0]), yprefix, latex(e[0][2])))
ax.set_xlabel("$%s$ [$%s %s$]" %
(latex(carr.axis[1]), xprefix, latex(e[1][2])))
if fig:
fig.colorbar(image)
plt.show()
return image
def image_plot(carr,ax = None,figsize = None,title = None, **kwargs):
import matplotlib.pyplot as plt
# fix missing \text support
from expresso.pycas import latex as rlatex
latex = lambda x:rlatex(x).replace(r'\text',r'\mathrm')
fig = None
if ax == None:
fig, ax = plt.subplots(figsize=figsize)
if title:
ax.set_title(title)
e = get_unitless_bounds(carr)
xprefix,xfactor = get_metric_prefix(e[1][:2])
yprefix,yfactor = get_metric_prefix(e[0][:2])
extent = [float(e[1][0])/xfactor,float(e[1][1])/xfactor,float(e[0][0])/yfactor,float(e[0][1])/yfactor]
if 'aspect' not in kwargs:
kwargs['aspect'] = 'auto'
if 'origin' not in kwargs:
kwargs['origin'] = 'lower'
image = ax.imshow(carr.data, extent=extent, **kwargs )
ax.set_ylabel("$%s$ [$%s %s$]" % (latex(carr.axis[0]),yprefix,latex(e[0][2])))
ax.set_xlabel("$%s$ [$%s %s$]" % (latex(carr.axis[1]),xprefix,latex(e[1][2])))
if fig:
fig.colorbar(image)
if ax == None:
plt.show()
return image
def poynting_streamplot_with_start_points(carr,
k,
start_points,
color='w',
ax=None,
figsize=None,
title=None,
arrowsize=5,
arrowpositions=[0.1, 0.9],
set_limits=True,
mask=None,
support=None,
settings=None,
dxdy=None,
**kwargs):
import matplotlib.pyplot as plt
import numpy as np
import expresso.pycas as pc
from pypropagate.phase_gradient import phase_gradient
def streamlines(x, y, U, V, start_points):
import scipy as sci
import scipy.integrate
import scipy.interpolate
import numpy as np
N = len(start_points)
flat_start_values = np.array(start_points).flatten()
dt = np.sqrt((x[1] - x[0])**2 + (y[1] - y[0])**2)
NT = max(len(x), len(y))
norm = np.sqrt(U**2 + V**2) * dt
XY = (y, x)
uinterp = sci.interpolate.RegularGridInterpolator(XY,
U / norm,
fill_value=0,
bounds_error=False)
vinterp = sci.interpolate.RegularGridInterpolator(XY,
V / norm,
fill_value=0,
bounds_error=False)
dx = [0]
def interpolated_velocity(t, x):
x = x.reshape((N, 2))
res = np.stack([vinterp(x), uinterp(x)]).transpose().flatten()
dx[0] = res
return res
integrator = sci.integrate.ode(interpolated_velocity).set_integrator(
'dopri5')
integrator.set_initial_value(flat_start_values, 0)
integrated = np.zeros((NT, N, 2), dtype=float)
integrated[0] = start_points
for i in range(1, NT):
if not integrator.successful():
print "error"
break
integrated[i] = integrator.integrate(i * dt).reshape((N, 2))
if np.all(dx[0] == 0):
integrated = integrated[:i + 1]
break
return integrated
e = get_unitless_bounds(carr)
xprefix, xfactor = get_metric_prefix(e[1][:2])
yprefix, yfactor = get_metric_prefix(e[0][:2])
extent = [
float(e[1][0]) / xfactor,
float(e[1][1]) / xfactor,
float(e[0][0]) / yfactor,
float(e[0][1]) / yfactor
]
x = np.linspace(extent[0], extent[1], carr.shape[1])
y = np.linspace(extent[2], extent[3], carr.shape[0])
if dxdy is None:
gx, gy = phase_gradient(carr)
gx /= xfactor * (x[0] - x[1])
gy /= yfactor * (y[0] - y[1])
gx += float(carr.evaluate(k * e[1][2]))
else:
gx, gy = dxdy
gx *= yfactor / xfactor
if support is not None:
if mask is not None:
raise ValueError('provide either support or mask arguments')
if isinstance(support, pc.Expression):
mask = pc.Not(support)
else:
mask = support.copy()
mask.data = np.logical_not(support.data)
if mask is not None:
import expresso.pycas
if isinstance(mask, pc.Expression):
if settings == None:
raise ValueError('no settings argument provided')
mask = expression_for_array(mask, carr, settings)
gx = np.ma.array(gx.data, mask=mask.data)
gy = np.ma.array(gy.data, mask=mask.data)
fig = None
if ax == None:
fig, ax = plt.subplots(figsize=figsize)
if title:
ax.set_title(title)
start_points = [[
float(carr.evaluate(sp[1] / (yfactor * e[0][2]))),
float(carr.evaluate(sp[0] / (xfactor * e[1][2])))
] for sp in start_points]
stream = streamlines(x, y, gx.data, gy.data, start_points)
for i in range(stream.shape[1]):
ax.plot(stream[:, i, 1], stream[:, i, 0], '-', color=color, **kwargs)
import scipy
xmin, xmax = stream[:, i, 1].min(), stream[:, i, 1].max()
dx = (xmax - xmin) / len(stream[:, i, 1]) / 10
xpositions = [xmin + ap * (xmax - xmin) for ap in arrowpositions]
ypositions = scipy.interp(xpositions + [xp - dx for xp in xpositions],
stream[:, i, 1], stream[:, i, 0])
for i in range(len(arrowpositions)):
size = arrowsize
x0, y0, y1 = xpositions[i], ypositions[i], ypositions[
i + len(arrowpositions)]
props = dict(color=color,
width=0,
headwidth=size,
headlength=2 * size,
linewidth=0)
ax.annotate("",
xy=(x0, y0),
xycoords='data',
xytext=(x0 - dx, y1),
textcoords='data',
arrowprops=props)
if set_limits:
ax.set_xlim(extent[0], extent[1])
ax.set_ylim(extent[2], extent[3])
from expresso.pycas import latex as rlatex
latex = lambda x: rlatex(x).replace(r'\text', r'\mathrm')
ax.set_ylabel("$%s$ [$%s %s$]" %
(latex(carr.axis[0]), yprefix, latex(e[0][2])))
ax.set_xlabel("$%s$ [$%s %s$]" %
(latex(carr.axis[1]), xprefix, latex(e[1][2])))
if fig:
plt.show()
return stream
def poynting_streamplot(carr,
k,
ax=None,
figsize=None,
title=None,
set_limits=True,
mask=None,
support=None,
settings=None,
dxdy=None,
**kwargs):
import matplotlib.pyplot as plt
import numpy as np
import expresso.pycas as pc
from .phase_gradient import phase_gradient
e = get_unitless_bounds(carr)
xprefix, xfactor = get_metric_prefix(e[1][:2])
yprefix, yfactor = get_metric_prefix(e[0][:2])
extent = [
float(e[1][0]) / xfactor,
float(e[1][1]) / xfactor,
float(e[0][0]) / yfactor,
float(e[0][1]) / yfactor
]
x = np.linspace(extent[0], extent[1], carr.shape[1])
y = np.linspace(extent[2], extent[3], carr.shape[0])
if dxdy is None:
gx, gy = [g.data for g in phase_gradient(carr)]
gx /= xfactor * (x[0] - x[1])
gy /= yfactor * (y[0] - y[1])
gx += float(carr.evaluate(k * e[1][2]))
else:
gx, gy = dxdy
gx *= yfactor / xfactor
if support is not None:
if mask is not None:
raise ValueError('provide either support or mask arguments')
if isinstance(support, pc.Expression):
mask = pc.Not(support)
else:
mask = support.copy()
mask.data = np.logical_not(support.data)
if mask is not None:
import expresso.pycas
if isinstance(mask, pc.Expression):
if settings == None:
raise ValueError('no settings argument provided')
mask = expression_for_array(mask, carr, settings)
gx = np.ma.array(gx, mask=mask.data)
gy = np.ma.array(gy, mask=mask.data)
fig = None
if ax == None:
fig, ax = plt.subplots(figsize=figsize)
if title:
ax.set_title(title)
stream = ax.streamplot(x, y, gx, gy, **kwargs)
if set_limits:
ax.set_xlim(extent[0], extent[1])
ax.set_ylim(extent[2], extent[3])
from expresso.pycas import latex as rlatex
latex = lambda x: rlatex(x).replace(r'\text', r'\mathrm')
ax.set_ylabel("$%s$ [$%s %s$]" %
(latex(carr.axis[0]), yprefix, latex(e[0][2])))
ax.set_xlabel("$%s$ [$%s %s$]" %
(latex(carr.axis[1]), xprefix, latex(e[1][2])))
if fig:
plt.show()
return stream
def get_plot_coordinates(array):
import numpy as np
from expresso.pycas import latex
e = get_unitless_bounds(array)[0]
prefix,factor = get_metric_prefix(e[:2])
return np.linspace(float(e[0])/factor,float(e[1])/factor,array.shape[0]), prefix + ' ' + latex(e[2])