def Histo(x, mean, sigma_mean, std, stderr, P, orient='horizontal', xlabel='', ylabel=''):
'''
Function that plot the histogramm of the distribution given in x
imputs:
-x is the distrib itself (array)
-mean is the mean of the distrib (float)
-sigma_mean : the error on the average (float)
-std : the standard deviation (RMS) of the distribution (float)
-stderr : the errot on the RMS (float)
-P is the figure where the histogram will be plotted.
-xylabel and y label are the name ofthe axis.
'''
numBins = 20
P.hist(x, numBins, color='blue', alpha=0.8, orientation=orient, label='average = ' + str("%.5f" % mean) +
'$\pm$' + str("%.5f" % sigma_mean) + '\n' + 'rms =' + str("%.5f" % std) + '$\pm$' + str("%.5f" % stderr))
if xlabel == '':
P.set_xlabel('number of SNe')
else:
P.set_xlabel(xlabel)
if ylabel == '':
P.set_ylabel('number of SNe')
else:
P.set_ylabel(ylabel)
P.set_title('Residuals')
P.legend(bbox_to_anchor=(0.95, 1.0), prop={'size': 10})
def image(sim, qty='rho', width="10 kpc", resolution=500, units=None, log=True,
vmin=None, vmax=None, av_z=False, filename=None,
z_camera=None, clear=True, cmap=None,
title=None, qtytitle=None, show_cbar=True, subplot=False,
noplot=False, ret_im=False, fill_nan=True, fill_val=0.0, linthresh=None,
**kwargs):
"""
Make an SPH image of the given simulation.
**Keyword arguments:**
*qty* (rho): The name of the array to interpolate
*width* (10 kpc): The overall width and height of the plot. If
``width`` is a float or an int, then it is assumed to be in units
of ``sim['pos']``. It can also be passed in as a string
indicating the units, i.e. '10 kpc', in which case it is
converted to units of ``sim['pos']``.
*resolution* (500): The number of pixels wide and tall
*units* (None): The units of the output
*av_z* (False): If True, the requested quantity is averaged down
the line of sight (default False: image is generated in
the thin plane z=0, unless output units imply an integral
down the line of sight). If a string, the requested quantity
is averaged down the line of sight weighted by the av_z
array (e.g. use 'rho' for density-weighted quantity;
the default results when av_z=True are volume-weighted).
*z_camera* (None): If set, a perspective image is rendered. See
:func:`pynbody.sph.image` for more details.
*filename* (None): if set, the image will be saved in a file
*clear* (True): whether to call clf() on the axes first
*cmap* (None): user-supplied colormap instance
*title* (None): plot title
*qtytitle* (None): colorbar quantity title
*show_cbar* (True): whether to plot the colorbar
*subplot* (False): the user can supply a AxesSubPlot instance on
which the image will be shown
*noplot* (False): do not display the image, just return the image array
*ret_im* (False): return the image instance returned by imshow
*num_threads* (None) : if set, specify the number of threads for
the multi-threaded routines; otherwise the pynbody.config default is used
*fill_nan* (True): if any of the image values are NaN, replace with fill_val
*fill_val* (0.0): the fill value to use when replacing NaNs
*linthresh* (None): if the image has negative and positive values
and a log scaling is requested, the part between `-linthresh` and
`linthresh` is shown on a linear scale to avoid divergence at 0
"""
if not noplot:
import matplotlib.pylab as plt
global config
if not noplot:
if subplot:
p = subplot
else:
p = plt
if isinstance(units, str):
units = _units.Unit(units)
if isinstance(width, str) or issubclass(width.__class__, _units.UnitBase):
if isinstance(width, str):
width = _units.Unit(width)
width = width.in_units(sim['pos'].units, **sim.conversion_context())
width = float(width)
kernel = sph.Kernel()
perspective = z_camera is not None
if perspective and not av_z:
kernel = sph.Kernel2D()
if units is not None:
try:
sim[qty].units.ratio(units, **sim[qty].conversion_context())
# if this fails, perhaps we're requesting a projected image?
except _units.UnitsException:
# if the following fails, there's no interpretation this routine
# can cope with
sim[qty].units.ratio(
units / (sim['x'].units), **sim[qty].conversion_context())
# if we get to this point, we want a projected image
kernel = sph.Kernel2D()
if av_z:
if isinstance(kernel, sph.Kernel2D):
raise _units.UnitsException(
"Units already imply projected image; can't also average over line-of-sight!")
else:
kernel = sph.Kernel2D()
if units is not None:
aunits = units * sim['z'].units
else:
aunits = None
if isinstance(av_z, str):
if units is not None:
aunits = units * sim[av_z].units * sim['z'].units
sim["__prod"] = sim[av_z] * sim[qty]
qty = "__prod"
else:
av_z = "__one"
sim["__one"] = np.ones_like(sim[qty])
sim["__one"].units = "1"
im = sph.render_image(sim, qty, width / 2, resolution, out_units=aunits, kernel=kernel,
z_camera=z_camera, **kwargs)
im2 = sph.render_image(sim, av_z, width / 2, resolution, kernel=kernel,
z_camera=z_camera, **kwargs)
top = sim.ancestor
try:
del top["__one"]
except KeyError:
pass
try:
del top["__prod"]
except KeyError:
pass
im = im / im2
else:
im = sph.render_image(sim, qty, width / 2, resolution, out_units=units,
kernel=kernel, z_camera=z_camera, **kwargs)
if fill_nan:
im[np.isnan(im)] = fill_val
if not noplot:
# set the log or linear normalizations
if log:
try:
im[np.where(im == 0)] = abs(im[np.where(abs(im != 0))]).min()
except ValueError:
raise ValueError, "Failed to make a sensible logarithmic image. This probably means there are no particles in the view."
# check if there are negative values -- if so, use the symmetric
# log normalization
if (im < 0).any():
# need to set the linear regime around zero -- set to by
# default start at 1/1000 of the log range
if linthresh is None:
linthresh = np.nanmax(abs(im)) / 1000.
norm = matplotlib.colors.SymLogNorm(
linthresh, vmin=vmin, vmax=vmax)
else:
norm = matplotlib.colors.LogNorm(vmin=vmin, vmax=vmax)
else:
norm = matplotlib.colors.Normalize(vmin=vmin, vmax=vmax)
#
# do the actual plotting
#
if clear and not subplot:
p.clf()
if ret_im:
return p.imshow(im[::-1, :].view(np.ndarray), extent=(-width / 2, width / 2, -width / 2, width / 2),
vmin=vmin, vmax=vmax, cmap=cmap, norm = norm)
ims = p.imshow(im[::-1, :].view(np.ndarray), extent=(-width / 2, width / 2, -width / 2, width / 2),
vmin=vmin, vmax=vmax, cmap=cmap, norm = norm)
u_st = sim['pos'].units.latex()
if not subplot:
plt.xlabel("$x/%s$" % u_st)
plt.ylabel("$y/%s$" % u_st)
else:
p.set_xlabel("$x/%s$" % u_st)
p.set_ylabel("$y/%s$" % u_st)
if units is None:
units = im.units
if log :
units = r"$\log_{10}\,"+units.latex()+"$"
else :
if units.latex() is "":
units=""
else:
units = "$"+units.latex()+"$"
if show_cbar:
if log:
custom_formatter = FuncFormatter(fmt)
## l_f = LogFormatterExponent() # sometimes tacks 'e' on value...???
l_f = custom_formatter
else:
l_f = ScalarFormatter()
if qtytitle is not None:
plt.colorbar(ims,format=l_f).set_label(qtytitle)
else:
plt.colorbar(ims,format=l_f).set_label(units)
# colorbar doesn't work wtih subplot: mappable is NoneType
# elif show_cbar:
# import matplotlib.pyplot as mpl
# if qtytitle: mpl.colorbar().set_label(qtytitle)
# else: mpl.colorbar().set_label(units)
if title is not None:
if not subplot:
p.title(title)
else:
p.set_title(title)
if filename is not None:
p.savefig(filename)
plt.draw()
# plt.show() - removed by AP on 30/01/2013 - this should not be here as
# for some systems you don't get back to the command prompt
return im
def image(sim,
qty='rho',
width="10 kpc",
resolution=500,
units=None,
log=True,
vmin=None,
vmax=None,
av_z=False,
filename=None,
z_camera=None,
clear=True,
cmap=None,
title=None,
qtytitle=None,
show_cbar=True,
subplot=False,
noplot=False,
ret_im=False,
fill_nan=True,
fill_val=0.0,
linthresh=None,
**kwargs):
"""
Make an SPH image of the given simulation.
**Keyword arguments:**
*qty* (rho): The name of the array to interpolate
*width* (10 kpc): The overall width and height of the plot. If
``width`` is a float or an int, then it is assumed to be in units
of ``sim['pos']``. It can also be passed in as a string
indicating the units, i.e. '10 kpc', in which case it is
converted to units of ``sim['pos']``.
*resolution* (500): The number of pixels wide and tall
*units* (None): The units of the output
*av_z* (False): If True, the requested quantity is averaged down
the line of sight (default False: image is generated in
the thin plane z=0, unless output units imply an integral
down the line of sight). If a string, the requested quantity
is averaged down the line of sight weighted by the av_z
array (e.g. use 'rho' for density-weighted quantity;
the default results when av_z=True are volume-weighted).
*z_camera* (None): If set, a perspective image is rendered. See
:func:`pynbody.sph.image` for more details.
*filename* (None): if set, the image will be saved in a file
*clear* (True): whether to call clf() on the axes first
*cmap* (None): user-supplied colormap instance
*title* (None): plot title
*qtytitle* (None): colorbar quantity title
*show_cbar* (True): whether to plot the colorbar
*subplot* (False): the user can supply a AxesSubPlot instance on
which the image will be shown
*noplot* (False): do not display the image, just return the image array
*ret_im* (False): return the image instance returned by imshow
*num_threads* (None) : if set, specify the number of threads for
the multi-threaded routines; otherwise the pynbody.config default is used
*fill_nan* (True): if any of the image values are NaN, replace with fill_val
*fill_val* (0.0): the fill value to use when replacing NaNs
*linthresh* (None): if the image has negative and positive values
and a log scaling is requested, the part between `-linthresh` and
`linthresh` is shown on a linear scale to avoid divergence at 0
"""
if not noplot:
import matplotlib.pylab as plt
global config
if not noplot:
if subplot:
p = subplot
else:
p = plt
if isinstance(units, str):
units = _units.Unit(units)
if isinstance(width, str) or issubclass(width.__class__, _units.UnitBase):
if isinstance(width, str):
width = _units.Unit(width)
width = width.in_units(sim['pos'].units, **sim.conversion_context())
width = float(width)
kernel = sph.Kernel()
perspective = z_camera is not None
if perspective and not av_z:
kernel = sph.Kernel2D()
if units is not None:
try:
sim[qty].units.ratio(units, **sim[qty].conversion_context())
# if this fails, perhaps we're requesting a projected image?
except _units.UnitsException:
# if the following fails, there's no interpretation this routine
# can cope with
sim[qty].units.ratio(units / (sim['x'].units),
**sim[qty].conversion_context())
# if we get to this point, we want a projected image
kernel = sph.Kernel2D()
if av_z:
if isinstance(kernel, sph.Kernel2D):
raise _units.UnitsException(
"Units already imply projected image; can't also average over line-of-sight!"
)
else:
kernel = sph.Kernel2D()
if units is not None:
aunits = units * sim['z'].units
else:
aunits = None
if isinstance(av_z, str):
if units is not None:
aunits = units * sim[av_z].units * sim['z'].units
sim["__prod"] = sim[av_z] * sim[qty]
qty = "__prod"
else:
av_z = "__one"
sim["__one"] = np.ones_like(sim[qty])
sim["__one"].units = "1"
im = sph.render_image(sim,
qty,
width / 2,
resolution,
out_units=aunits,
kernel=kernel,
z_camera=z_camera,
**kwargs)
im2 = sph.render_image(sim,
av_z,
width / 2,
resolution,
kernel=kernel,
z_camera=z_camera,
**kwargs)
top = sim.ancestor
try:
del top["__one"]
except KeyError:
pass
try:
del top["__prod"]
except KeyError:
pass
im = im / im2
else:
im = sph.render_image(sim,
qty,
width / 2,
resolution,
out_units=units,
kernel=kernel,
z_camera=z_camera,
**kwargs)
if fill_nan:
im[np.isnan(im)] = fill_val
if not noplot:
# set the log or linear normalizations
if log:
try:
im[np.where(im == 0)] = abs(im[np.where(abs(im != 0))]).min()
except ValueError:
raise ValueError, "Failed to make a sensible logarithmic image. This probably means there are no particles in the view."
# check if there are negative values -- if so, use the symmetric
# log normalization
if (im < 0).any():
# need to set the linear regime around zero -- set to by
# default start at 1/1000 of the log range
if linthresh is None:
linthresh = np.nanmax(abs(im)) / 1000.
norm = matplotlib.colors.SymLogNorm(linthresh,
vmin=vmin,
vmax=vmax)
else:
norm = matplotlib.colors.LogNorm(vmin=vmin, vmax=vmax)
else:
norm = matplotlib.colors.Normalize(vmin=vmin, vmax=vmax)
#
# do the actual plotting
#
if clear and not subplot:
p.clf()
if ret_im:
return p.imshow(im[::-1, :].view(np.ndarray),
extent=(-width / 2, width / 2, -width / 2,
width / 2),
vmin=vmin,
vmax=vmax,
cmap=cmap,
norm=norm)
ims = p.imshow(im[::-1, :].view(np.ndarray),
extent=(-width / 2, width / 2, -width / 2, width / 2),
vmin=vmin,
vmax=vmax,
cmap=cmap,
norm=norm)
u_st = sim['pos'].units.latex()
if not subplot:
plt.xlabel("$x/%s$" % u_st)
plt.ylabel("$y/%s$" % u_st)
else:
p.set_xlabel("$x/%s$" % u_st)
p.set_ylabel("$y/%s$" % u_st)
if units is None:
units = im.units
if log:
units = r"$\log_{10}\," + units.latex() + "$"
else:
if units.latex() is "":
units = ""
else:
units = "$" + units.latex() + "$"
if show_cbar:
if qtytitle is not None:
plt.colorbar(ims).set_label(qtytitle)
else:
plt.colorbar(ims).set_label(units)
# colorbar doesn't work wtih subplot: mappable is NoneType
# elif show_cbar:
# import matplotlib.pyplot as mpl
# if qtytitle: mpl.colorbar().set_label(qtytitle)
# else: mpl.colorbar().set_label(units)
if title is not None:
if not subplot:
p.title(title)
else:
p.set_title(title)
if filename is not None:
p.savefig(filename)
plt.draw()
# plt.show() - removed by AP on 30/01/2013 - this should not be here as
# for some systems you don't get back to the command prompt
return im
self.F_D * math.sin(ou_D * self.t[-1])) * self.dt
self.omiga.append(omiga_new)
sita_new = self.sita[-1] + self.omiga[-1] * self.dt
t_new = self.t[-1] + self.dt
while sita_new > math.pi:
sita_new -= 2 * (math.pi)
while sita_new < -math.pi:
sita_new += 2 * (math.pi)
self.sita.append(sita_new)
self.t.append(t_new)
F_D2 = [1.35] * 128
sita3 = []
while F_D2[-1] < 1.5:
A = pendulum0(F_D2[-1], 0.2)
A.calculate()
sita2 = []
for i in range(301, 429):
A.sita2.append(A.sita[1000 * i])
sita3 = sita3 + A.sita2
F_Dnew = [F_D2[-1] + 0.00005] * 128
F_D2 = F_D2 + F_Dnew
py.plot(F_D2[0:-128], sita3, 'g.')
py.set_title('$\omega$ versus $\\theta$')
py.xlabel('$\\theta$(radians)')
py.ylabel('$\omega$(radians/s)')
py.show()
def image(sim, qty='rho', width=10, resolution=500, units=None, log=True,
vmin=None, vmax=None, av_z = False, filename=None,
z_camera=None, clear = True, cmap=None, center=False,
title=None, qtytitle=None, show_cbar=True, subplot=False,
noplot = False, ret_im=False, fill_nan = True, fill_val=0.0,
**kwargs) :
"""
Make an SPH image of the given simulation.
**Keyword arguments:**
*qty* (rho): The name of the array to interpolate
*width* (10): The overall width and height of the plot in sim['pos'] units
*resolution* (500): The number of pixels wide and tall
*units* (None): The units of the output
*av_z* (False): If True, the requested quantity is averaged down
the line of sight (default False: image is generated in
the thin plane z=0, unless output units imply an integral
down the line of sight). If a string, the requested quantity
is averaged down the line of sight weighted by the av_z
array (e.g. use 'rho' for density-weighted quantity;
the default results when av_z=True are volume-weighted).
*z_camera* (None): If set, a perspective image is rendered. See
:func:`pynbody.sph.image` for more details.
*filename* (None): if set, the image will be saved in a file
*clear* (True): whether to call clf() on the axes first
*cmap* (None): user-supplied colormap instance
*title* (None): plot title
*qtytitle* (None): colorbar quantity title
*show_cbar* (True): whether to plot the colorbar
*subplot* (False): the user can supply a AxesSubPlot instance on
which the image will be shown
*noplot* (False): do not display the image, just return the image array
*ret_im* (False): return the image instance returned by imshow
*num_threads* (None) : if set, specify the number of threads for
the multi-threaded routines; otherwise the pynbody.config default is used
*fill_nan* (True): if any of the image values are NaN, replace with fill_val
*fill_val* (0.0): the fill value to use when replacing NaNs
"""
import matplotlib.pylab as plt
global config
if subplot:
p = subplot
else :
p = plt
if isinstance(units, str) :
units = _units.Unit(units)
width = float(width)
kernel = sph.Kernel()
perspective = z_camera is not None
if perspective and not av_z: kernel = sph.Kernel2D()
if units is not None :
try :
sim[qty].units.ratio(units, **sim[qty].conversion_context())
# if this fails, perhaps we're requesting a projected image?
except _units.UnitsException :
# if the following fails, there's no interpretation this routine can cope with
sim[qty].units.ratio(units/(sim['x'].units), **sim[qty].conversion_context())
kernel = sph.Kernel2D() # if we get to this point, we want a projected image
if av_z :
if isinstance(kernel, sph.Kernel2D) :
raise _units.UnitsException("Units already imply projected image; can't also average over line-of-sight!")
else :
kernel = sph.Kernel2D()
if units is not None :
aunits = units*sim['z'].units
else :
aunits = None
if isinstance(av_z, str) :
if units is not None:
aunits = units*sim[av_z].units*sim['z'].units
sim["__prod"] = sim[av_z]*sim[qty]
qty = "__prod"
else :
av_z = "__one"
sim["__one"]=np.ones_like(sim[qty])
sim["__one"].units="1"
im = sph.render_image(sim,qty,width/2,resolution,out_units=aunits, kernel = kernel,
z_camera=z_camera, **kwargs)
im2 = sph.render_image(sim, av_z, width/2, resolution, kernel=kernel,
z_camera=z_camera, **kwargs)
top = sim.ancestor
try:
del top["__one"]
except KeyError :
pass
try:
del top["__prod"]
except KeyError :
pass
im = im/im2
else :
im = sph.render_image(sim,qty,width/2,resolution,out_units=units,
kernel = kernel, z_camera = z_camera, **kwargs)
if fill_nan :
im[np.isnan(im)] = fill_val
if log :
im[np.where(im==0)] = abs(im[np.where(im!=0)]).min()
im = np.log10(im)
if clear and not subplot : p.clf()
if ret_im:
return plt.imshow(im[::-1,:],extent=(-width/2,width/2,-width/2,width/2),
vmin=vmin, vmax=vmax, cmap=cmap)
ims = p.imshow(im[::-1,:],extent=(-width/2,width/2,-width/2,width/2),
vmin=vmin, vmax=vmax, cmap=cmap)
u_st = sim['pos'].units.latex()
if not subplot:
plt.xlabel("$x/%s$"%u_st)
plt.ylabel("$y/%s$"%u_st)
else :
p.set_xlabel("$x/%s$"%u_st)
p.set_ylabel("$y/%s$"%u_st)
if units is None :
units = im.units
if log :
units = r"$\log_{10}\,"+units.latex()+"$"
else :
units = "$"+units.latex()+"$"
if show_cbar:
if qtytitle is not None: plt.colorbar(ims).set_label(qtytitle)
else: plt.colorbar(ims).set_label(units)
# colorbar doesn't work wtih subplot: mappable is NoneType
#elif show_cbar:
# import matplotlib.pyplot as mpl
# if qtytitle: mpl.colorbar().set_label(qtytitle)
# else: mpl.colorbar().set_label(units)
if title is not None:
p.set_title(title)
if filename is not None:
p.savefig(filename)
plt.draw()
plt.show()
return im