def _plot_2d(self, cmap='winter', vmin=None, vmax=None):
points = [(m, l, [i,j])
for i, m in enumerate(self._mu2)
for j, l in enumerate(self._lambda)]
result = self._parallel_eval(points)
value_min = vmin if vmin is not None else min(r[2] for r in result)
value_max = vmax if vmax is not None else max(r[2] for r in result)
delta_mu2 = [(self._mu2[i] - self._mu2[i-1])/2.0
for i in range(1, len(self._mu2))]
delta_lambda = [(self._lambda[i] - self._lambda[i-1])/2.0
for i in range(1, len(self._lambda))]
from sage.plot.colors import get_cmap
cmap = get_cmap(cmap)
def tile(i, j, value):
m = self._mu2[i]
if i == 0:
dm = (delta_mu2[0], delta_mu2[0])
elif i == len(delta_mu2):
dm = (delta_mu2[-1], delta_mu2[-1])
else:
dm = (delta_mu2[i-1], delta_mu2[i])
l = self._lambda[j]
if j == 0:
dl = (delta_lambda[0], delta_lambda[0])
elif j == len(delta_lambda):
dl = (delta_lambda[-1], delta_lambda[-1])
else:
dl = (delta_lambda[j-1], delta_lambda[j])
norm_value = (value - value_min) / (value_max - value_min)
print value, norm_value
c = cmap(norm_value)[:3]
v0 = (l-dl[0], m-dm[0])
v1 = (l+dl[1], m-dm[0])
v2 = (l+dl[1], m+dm[1])
v3 = (l-dl[0], m+dm[1])
return polygon2d([v0, v1, v2, v3], rgbcolor=c, fill=True)
g = Graphics()
g.axes_labels([r'$\lambda$', r'$\mu^2$'])
g._set_extra_kwds({
'title': self.title,
'axes_labels': [r'$\lambda$', r'$\mu^2$'],
'title_pos': (0.5, 1.1),
})
for i, j, value in result:
g = tile(i, j, value) + g
return g
def _render_on_subplot(self, subplot):
"""
TESTS:
A somewhat random plot, but fun to look at::
sage: x,y = var('x,y')
sage: density_plot(x^2-y^3+10*sin(x*y), (x, -4, 4), (y, -4, 4),plot_points=121,cmap='hsv')
"""
options = self.options()
cmap = get_cmap(options['cmap'])
x0,x1 = float(self.xrange[0]), float(self.xrange[1])
y0,y1 = float(self.yrange[0]), float(self.yrange[1])
subplot.imshow(self.xy_data_array, origin='lower', cmap=cmap, extent=(x0,x1,y0,y1), interpolation=options['interpolation'])
def _render_on_subplot(self, subplot):
"""
TESTS:
A somewhat random plot, but fun to look at::
sage: x,y = var('x,y')
sage: contour_plot(x^2-y^3+10*sin(x*y), (x, -4, 4), (y, -4, 4),plot_points=121,cmap='hsv')
"""
from sage.rings.integer import Integer
options = self.options()
fill = options['fill']
contours = options['contours']
if options.has_key('cmap'):
cmap = get_cmap(options['cmap'])
elif fill or contours is None:
cmap = get_cmap('gray')
else:
if isinstance(contours, (int, Integer)):
cmap = get_cmap([(i,i,i) for i in xsrange(0,1,1/contours)])
else:
l = Integer(len(contours))
cmap = get_cmap([(i,i,i) for i in xsrange(0,1,1/l)])
x0,x1 = float(self.xrange[0]), float(self.xrange[1])
y0,y1 = float(self.yrange[0]), float(self.yrange[1])
if isinstance(contours, (int, Integer)):
contours = int(contours)
CSF=None
if fill:
if contours is None:
CSF=subplot.contourf(self.xy_data_array, cmap=cmap, extent=(x0,x1,y0,y1), label=options['legend_label'])
else:
CSF=subplot.contourf(self.xy_data_array, contours, cmap=cmap, extent=(x0,x1,y0,y1),extend='both', label=options['legend_label'])
linewidths = options.get('linewidths',None)
if isinstance(linewidths, (int, Integer)):
linewidths = int(linewidths)
elif isinstance(linewidths, (list, tuple)):
linewidths = tuple(int(x) for x in linewidths)
linestyles = options.get('linestyles',None)
if contours is None:
CS = subplot.contour(self.xy_data_array, cmap=cmap, extent=(x0,x1,y0,y1),
linewidths=linewidths, linestyles=linestyles, label=options['legend_label'])
else:
CS = subplot.contour(self.xy_data_array, contours, cmap=cmap, extent=(x0,x1,y0,y1),
linewidths=linewidths, linestyles=linestyles, label=options['legend_label'])
if options.get('labels', False):
label_options = options['label_options']
label_options['fontsize'] = int(label_options['fontsize'])
if fill and label_options is None:
label_options['inline']=False
subplot.clabel(CS, **label_options)
if options.get('colorbar', False):
colorbar_options = options['colorbar_options']
from matplotlib import colorbar
cax,kwds=colorbar.make_axes_gridspec(subplot,**colorbar_options)
if CSF is None:
cb=colorbar.Colorbar(cax,CS, **kwds)
else:
cb=colorbar.Colorbar(cax,CSF, **kwds)
cb.add_lines(CS)
def _render_on_subplot(self, subplot):
"""
TESTS::
sage: matrix_plot(random_matrix(RDF, 50), cmap='jet')
Graphics object consisting of 1 graphics primitive
"""
options = self.options()
cmap = get_cmap(options.pop('cmap',None))
origin=options['origin']
norm=options['norm']
if norm=='value':
import matplotlib
norm=matplotlib.colors.NoNorm()
if options['subdivisions']:
subdiv_options=options['subdivision_options']
if isinstance(subdiv_options['boundaries'], (list, tuple)):
rowsub,colsub=subdiv_options['boundaries']
else:
rowsub=subdiv_options['boundaries']
colsub=subdiv_options['boundaries']
if isinstance(subdiv_options['style'], (list, tuple)):
rowstyle,colstyle=subdiv_options['style']
else:
rowstyle=subdiv_options['style']
colstyle=subdiv_options['style']
if rowstyle is None:
rowstyle=dict()
if colstyle is None:
colstyle=dict()
# Make line objects for subdivisions
from .line import line2d
lim=self.get_minmax_data()
# First draw horizontal lines representing row subdivisions
for y in rowsub:
l=line2d([(lim['xmin'],y-0.5), (lim['xmax'],y-0.5)], **rowstyle)[0]
l._render_on_subplot(subplot)
for x in colsub:
l=line2d([(x-0.5, lim['ymin']), (x-0.5, lim['ymax'])], **colstyle)[0]
l._render_on_subplot(subplot)
if hasattr(self.xy_data_array, 'tocoo'):
# Sparse matrix -- use spy
opts=options.copy()
for opt in ['vmin', 'vmax', 'norm', 'origin','subdivisions','subdivision_options',
'colorbar','colorbar_options']:
del opts[opt]
if origin=='lower':
subplot.spy(self.xy_data_array.tocsr()[::-1], **opts)
else:
subplot.spy(self.xy_data_array, **opts)
else:
opts = dict(cmap=cmap, interpolation='nearest', aspect='equal',
norm=norm, vmin=options['vmin'], vmax=options['vmax'],
origin=origin,zorder=options.get('zorder',None))
image = subplot.imshow(self.xy_data_array, **opts)
if options.get('colorbar', False):
colorbar_options = options['colorbar_options']
from matplotlib import colorbar
cax,kwds=colorbar.make_axes_gridspec(subplot,**colorbar_options)
colorbar.Colorbar(cax, image, **kwds)
if origin == 'upper':
subplot.xaxis.tick_top()
elif origin == 'lower':
subplot.xaxis.tick_bottom()
subplot.xaxis.set_ticks_position('both') #only tick marks, not tick labels
def _render_on_subplot(self, subplot):
"""
TESTS::
sage: matrix_plot(random_matrix(RDF, 50), cmap='jet')
Graphics object consisting of 1 graphics primitive
"""
options = self.options()
cmap = get_cmap(options.pop('cmap',None))
origin=options['origin']
norm=options['norm']
if norm=='value':
import matplotlib
norm=matplotlib.colors.NoNorm()
if options['subdivisions']:
subdiv_options=options['subdivision_options']
if isinstance(subdiv_options['boundaries'], (list, tuple)):
rowsub,colsub=subdiv_options['boundaries']
else:
rowsub=subdiv_options['boundaries']
colsub=subdiv_options['boundaries']
if isinstance(subdiv_options['style'], (list, tuple)):
rowstyle,colstyle=subdiv_options['style']
else:
rowstyle=subdiv_options['style']
colstyle=subdiv_options['style']
if rowstyle is None:
rowstyle=dict()
if colstyle is None:
colstyle=dict()
# Make line objects for subdivisions
from line import line2d
lim=self.get_minmax_data()
# First draw horizontal lines representing row subdivisions
for y in rowsub:
l=line2d([(lim['xmin'],y-0.5), (lim['xmax'],y-0.5)], **rowstyle)[0]
l._render_on_subplot(subplot)
for x in colsub:
l=line2d([(x-0.5, lim['ymin']), (x-0.5, lim['ymax'])], **colstyle)[0]
l._render_on_subplot(subplot)
if hasattr(self.xy_data_array, 'tocoo'):
# Sparse matrix -- use spy
opts=options.copy()
for opt in ['vmin', 'vmax', 'norm', 'origin','subdivisions','subdivision_options',
'colorbar','colorbar_options']:
del opts[opt]
if origin=='lower':
subplot.spy(self.xy_data_array.tocsr()[::-1], **opts)
else:
subplot.spy(self.xy_data_array, **opts)
else:
opts = dict(cmap=cmap, interpolation='nearest', aspect='equal',
norm=norm, vmin=options['vmin'], vmax=options['vmax'],
origin=origin,zorder=options.get('zorder',None))
image=subplot.imshow(self.xy_data_array, **opts)
if options.get('colorbar', False):
colorbar_options = options['colorbar_options']
from matplotlib import colorbar
cax,kwds=colorbar.make_axes_gridspec(subplot,**colorbar_options)
cb=colorbar.Colorbar(cax,image, **kwds)
if origin=='upper':
subplot.xaxis.tick_top()
elif origin=='lower':
subplot.xaxis.tick_bottom()
subplot.xaxis.set_ticks_position('both') #only tick marks, not tick labels
def _render_on_subplot(self, subplot):
"""
TESTS:
A somewhat random plot, but fun to look at::
sage: x,y = var('x,y')
sage: contour_plot(x^2-y^3+10*sin(x*y), (x, -4, 4), (y, -4, 4),plot_points=121,cmap='hsv')
"""
from sage.rings.integer import Integer
options = self.options()
fill = options['fill']
contours = options['contours']
if 'cmap' in options:
cmap = get_cmap(options['cmap'])
elif fill or contours is None:
cmap = get_cmap('gray')
else:
if isinstance(contours, (int, Integer)):
cmap = get_cmap([(i, i, i)
for i in xsrange(0, 1, 1 / contours)])
else:
l = Integer(len(contours))
cmap = get_cmap([(i, i, i) for i in xsrange(0, 1, 1 / l)])
x0, x1 = float(self.xrange[0]), float(self.xrange[1])
y0, y1 = float(self.yrange[0]), float(self.yrange[1])
if isinstance(contours, (int, Integer)):
contours = int(contours)
CSF = None
if fill:
if contours is None:
CSF = subplot.contourf(self.xy_data_array,
cmap=cmap,
extent=(x0, x1, y0, y1),
label=options['legend_label'])
else:
CSF = subplot.contourf(self.xy_data_array,
contours,
cmap=cmap,
extent=(x0, x1, y0, y1),
extend='both',
label=options['legend_label'])
linewidths = options.get('linewidths', None)
if isinstance(linewidths, (int, Integer)):
linewidths = int(linewidths)
elif isinstance(linewidths, (list, tuple)):
linewidths = tuple(int(x) for x in linewidths)
from sage.plot.misc import get_matplotlib_linestyle
linestyles = options.get('linestyles', None)
if isinstance(linestyles, (list, tuple)):
linestyles = [
get_matplotlib_linestyle(l, 'long') for l in linestyles
]
else:
linestyles = get_matplotlib_linestyle(linestyles, 'long')
if contours is None:
CS = subplot.contour(self.xy_data_array,
cmap=cmap,
extent=(x0, x1, y0, y1),
linewidths=linewidths,
linestyles=linestyles,
label=options['legend_label'])
else:
CS = subplot.contour(self.xy_data_array,
contours,
cmap=cmap,
extent=(x0, x1, y0, y1),
linewidths=linewidths,
linestyles=linestyles,
label=options['legend_label'])
if options.get('labels', False):
label_options = options['label_options']
label_options['fontsize'] = int(label_options['fontsize'])
if fill and label_options is None:
label_options['inline'] = False
subplot.clabel(CS, **label_options)
if options.get('colorbar', False):
colorbar_options = options['colorbar_options']
from matplotlib import colorbar
cax, kwds = colorbar.make_axes_gridspec(subplot,
**colorbar_options)
if CSF is None:
cb = colorbar.Colorbar(cax, CS, **kwds)
else:
cb = colorbar.Colorbar(cax, CSF, **kwds)
cb.add_lines(CS)
def _render_on_subplot(self, subplot):
"""
TESTS::
sage: matrix_plot(random_matrix(RDF, 50), cmap='jet')
"""
options = self.options()
cmap = get_cmap(options.pop("cmap", None))
origin = options["origin"]
norm = options["norm"]
if norm == "value":
import matplotlib
norm = matplotlib.colors.NoNorm()
if options["subdivisions"]:
subdiv_options = options["subdivision_options"]
if isinstance(subdiv_options["boundaries"], (list, tuple)):
rowsub, colsub = subdiv_options["boundaries"]
else:
rowsub = subdiv_options["boundaries"]
colsub = subdiv_options["boundaries"]
if isinstance(subdiv_options["style"], (list, tuple)):
rowstyle, colstyle = subdiv_options["style"]
else:
rowstyle = subdiv_options["style"]
colstyle = subdiv_options["style"]
if rowstyle is None:
rowstyle = dict()
if colstyle is None:
colstyle = dict()
# Make line objects for subdivisions
from line import line2d
lim = self.get_minmax_data()
# First draw horizontal lines representing row subdivisions
for y in rowsub:
l = line2d([(lim["xmin"], y - 0.5), (lim["xmax"], y - 0.5)], **rowstyle)[0]
l._render_on_subplot(subplot)
for x in colsub:
l = line2d([(x - 0.5, lim["ymin"]), (x - 0.5, lim["ymax"])], **colstyle)[0]
l._render_on_subplot(subplot)
if hasattr(self.xy_data_array, "tocoo"):
# Sparse matrix -- use spy
opts = options.copy()
for opt in [
"vmin",
"vmax",
"norm",
"origin",
"subdivisions",
"subdivision_options",
"colorbar",
"colorbar_options",
]:
del opts[opt]
if origin == "lower":
subplot.spy(self.xy_data_array.tocsr()[::-1], **opts)
else:
subplot.spy(self.xy_data_array, **opts)
else:
opts = dict(
cmap=cmap,
interpolation="nearest",
aspect="equal",
norm=norm,
vmin=options["vmin"],
vmax=options["vmax"],
origin=origin,
zorder=options.get("zorder", None),
)
image = subplot.imshow(self.xy_data_array, **opts)
if options.get("colorbar", False):
colorbar_options = options["colorbar_options"]
from matplotlib import colorbar
cax, kwds = colorbar.make_axes_gridspec(subplot, **colorbar_options)
cb = colorbar.Colorbar(cax, image, **kwds)
if origin == "upper":
subplot.xaxis.tick_top()
elif origin == "lower":
subplot.xaxis.tick_bottom()
subplot.xaxis.set_ticks_position("both") # only tick marks, not tick labels