Coverage for local/lib/python2.7/site-packages/sage/plot/animate.py : 48%

r""" 

Animated plots 

Animations are generated from a list (or other iterable) of graphics 

objects. 

Images are produced by calling the ``save_image`` method on each input 

object, creating a sequence of PNG files. 

These are then assembled to various target formats using different 

tools. 

In particular, the ``convert`` program from ImageMagick_ can be used to 

generate an animated GIF file. 

FFmpeg_ (with the command line program ``ffmpeg``) provides support for 

various video formats, but also an alternative method of generating 

animated GIFs. 

For `browsers which support it`_, APNG_ can be used as another 

alternative which works without any extra dependencies. 

.. WARNING:: 

Note that ImageMagick and FFmpeg are not included with Sage, and 

must be installed by the user. On unix systems, type ``which 

convert`` at a command prompt to see if ``convert`` (part of the 

ImageMagick suite) is installed. If it is, you will be given its 

location. Similarly, you can check for ``ffmpeg`` with ``which 

ffmpeg``. See the websites of ImageMagick_ or FFmpeg_ for 

installation instructions. 

EXAMPLES: 

The sine function:: 

sage: sines = [plot(c*sin(x), (-2*pi,2*pi), color=Color(c,0,0), ymin=-1, ymax=1) for c in sxrange(0,1,.2)] 

sage: a = animate(sines) 

sage: a # optional -- ImageMagick 

Animation with 5 frames 

sage: a.show() # optional -- ImageMagick 

Animate using FFmpeg_ instead of ImageMagick:: 

sage: f = tmp_filename(ext='.gif') 

sage: a.save(filename=f, use_ffmpeg=True) # optional -- ffmpeg 

Animate as an APNG_:: 

sage: a.apng() # long time 

doctest:...: DeprecationWarning: use tmp_filename instead 

See http://trac.sagemath.org/17234 for details. 

An animated :class:`sage.plot.graphics.GraphicsArray` of rotating ellipses:: 

sage: E = animate((graphics_array([[ellipse((0,0),a,b,angle=t,xmin=-3,xmax=3)+circle((0,0),3,color='blue') for a in range(1,3)] for b in range(2,4)]) for t in sxrange(0,pi/4,.15))) 

sage: str(E) # animations produced from a generator do not have a known length 

'Animation with unknown number of frames' 

sage: E.show() # optional -- ImageMagick 

A simple animation of a circle shooting up to the right:: 

sage: c = animate([circle((i,i), 1-1/(i+1), hue=i/10) for i in srange(0,2,0.2)], 

....: xmin=0,ymin=0,xmax=2,ymax=2,figsize=[2,2]) 

sage: c.show() # optional -- ImageMagick 

Animations of 3d objects:: 

sage: var('s,t') 

(s, t) 

sage: def sphere_and_plane(x): 

....: return sphere((0,0,0),1,color='red',opacity=.5)+parametric_plot3d([t,x,s],(s,-1,1),(t,-1,1),color='green',opacity=.7) 

sage: sp = animate([sphere_and_plane(x) for x in sxrange(-1,1,.3)]) 

sage: sp[0] # first frame 

Graphics3d Object 

sage: sp[-1] # last frame 

Graphics3d Object 

sage: sp.show() # optional -- ImageMagick 

sage: (x,y,z) = var('x,y,z') 

sage: def frame(t): 

....: return implicit_plot3d((x^2 + y^2 + z^2), (x, -2, 2), (y, -2, 2), (z, -2, 2), plot_points=60, contour=[1,3,5], region=lambda x,y,z: x<=t or y>=t or z<=t) 

sage: a = animate([frame(t) for t in srange(.01,1.5,.2)]) 

sage: a[0] # long time 

Graphics3d Object 

sage: a.show() # optional -- ImageMagick 

If the input objects do not have a ``save_image`` method, then the 

animation object attempts to make an image by calling its internal 

method :meth:`sage.plot.animate.Animation.make_image`. This is 

illustrated by the following example:: 

sage: t = var('t') 

sage: a = animate((sin(c*pi*t) for c in sxrange(1,2,.2))) 

sage: a.show() # optional -- ImageMagick 

AUTHORS: 

- William Stein 

- John Palmieri 

- Niles Johnson (2013-12): Expand to animate more graphics objects 

- Martin von Gagern (2014-12): Added APNG support 

REFERENCES: 

- `ImageMagick <http://www.imagemagick.org>`_ 

- `FFmpeg <http://www.ffmpeg.org>`_ 

- `APNG <https://wiki.mozilla.org/APNG_Specification>`_ 

- `browsers which support it <http://caniuse.com/#feat=apng>`_ 

""" 

############################################################################ 

# Copyright (C) 2007 William Stein <wstein@gmail.com> 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

############################################################################ 

from __future__ import print_function, absolute_import 

import os 

import struct 

import zlib 

from sage.misc.fast_methods import WithEqualityById 

from sage.structure.sage_object import SageObject 

from sage.misc.temporary_file import tmp_dir, tmp_filename, graphics_filename 

from . import plot 

import sage.misc.misc 

import sage.misc.viewer 

def animate(frames, **kwds): 

r""" 

Animate a list of frames by creating a 

:class:`sage.plot.animate.Animation` object. 

EXAMPLES:: 

sage: t = var('t') 

sage: a = animate((cos(c*pi*t) for c in sxrange(1,2,.2))) 

sage: a.show() # optional -- ImageMagick 

See also :mod:`sage.plot.animate` for more examples. 

""" 

return Animation(frames, **kwds) 

class Animation(WithEqualityById, SageObject): 

r""" 

Return an animation of a sequence of plots of objects. 

INPUT: 

- ``v`` - iterable of Sage objects. These should preferably be 

graphics objects, but if they aren't then :meth:`make_image` is 

called on them. 

- ``xmin, xmax, ymin, ymax`` - the ranges of the x and y axes. 

- ``**kwds`` - all additional inputs are passed onto the rendering 

command. E.g., use figsize to adjust the resolution and aspect 

ratio. 

EXAMPLES:: 

sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.3)], 

....: xmin=0, xmax=2*pi, figsize=[2,1]) 

sage: a # optional -- ImageMagick 

Animation with 21 frames 

sage: a[:5] # optional -- ImageMagick 

Animation with 5 frames 

sage: a.show() # optional -- ImageMagick 

sage: a[:5].show() # optional -- ImageMagick 

The :meth:`show` method takes arguments to specify the 

delay between frames (measured in hundredths of a second, default 

value 20) and the number of iterations (default value 0, which 

means to iterate forever). To iterate 4 times with half a second 

between each frame:: 

sage: a.show(delay=50, iterations=4) # optional -- ImageMagick 

An animation of drawing a parabola:: 

sage: step = 0.1 

sage: L = Graphics() 

sage: v = [] 

sage: for i in srange(0,1,step): 

....: L += line([(i,i^2),(i+step,(i+step)^2)], rgbcolor=(1,0,0), thickness=2) 

....: v.append(L) 

sage: a = animate(v, xmin=0, ymin=0) 

sage: a.show() # optional -- ImageMagick 

sage: show(L) 

TESTS: 

This illustrates that :trac:`2066` is fixed (setting axes 

ranges when an endpoint is 0):: 

sage: animate([plot(sin, -1,1)], xmin=0, ymin=0)._kwds['xmin'] 

0 

We check that :trac:`7981` is fixed:: 

sage: a = animate([plot(sin(x + float(k)), (0, 2*pi), ymin=-5, ymax=5) 

....: for k in srange(0,2*pi,0.3)]) 

sage: a.show() # optional -- ImageMagick 

Do not convert input iterator to a list, but ensure that 

the frame count is known after rendering the frames:: 

sage: a = animate((plot(x^p, (x,0,2)) for p in sxrange(1,2,.1))) 

sage: str(a) 

'Animation with unknown number of frames' 

sage: a.png() # long time 

'.../' 

sage: len(a) # long time 

10 

sage: a._frames 

<generator object ... 

sage: from sage.plot.animate import Animation 

sage: hash(Animation()) # random 

140658972348064 

""" 

def __init__(self, v=None, **kwds): 

r""" 

Return an animation of a sequence of plots of objects. See 

documentation of :func:`animate` for more details and 

examples. 

EXAMPLES:: 

sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.3)], 

....: xmin=0, xmax=2*pi, figsize=[2,1]) # indirect doctest 

sage: a # optional -- ImageMagick 

Animation with 21 frames 

""" 

self._frames = v 

self._kwds = kwds 

def _combine_kwds(self, *kwds_tuple): 

""" 

Returns a dictionary which is a combination of the all the 

dictionaries in kwds_tuple. This also does the appropriate thing 

for taking the mins and maxes of all of the x/y mins/maxes. 

EXAMPLES:: 

sage: a = animate([plot(sin, -1,1)], xmin=0, ymin=0) 

sage: kwds1 = {'a':1, 'b':2, 'xmin':2, 'xmax':5} 

sage: kwds2 = {'b':3, 'xmin':0, 'xmax':4} 

sage: kwds = a._combine_kwds(kwds1, kwds2) 

sage: list(sorted(kwds.items())) 

[('a', 1), ('b', 3), ('xmax', 5), ('xmin', 0)] 

Test that the bug reported in :trac:`12107` has been fixed:: 

sage: kwds3 = {} 

sage: kwds4 = {'b':3, 'xmin':0, 'xmax':4} 

sage: a._combine_kwds(kwds3, kwds4)['xmin'] 

0 

""" 

new_kwds = {} 

for kwds in kwds_tuple: 

new_kwds.update(kwds) 

from six.moves import builtins 

for name in ['xmin', 'xmax', 'ymin', 'ymax']: 

values = [v for v in [kwds.get(name, None) for kwds in kwds_tuple] if v is not None] 

if values: 

new_kwds[name] = getattr(builtins, name[1:])(values) 

return new_kwds 

def __getitem__(self, i): 

""" 

Get a frame from an animation or 

slice this animation returning a subanimation. 

EXAMPLES:: 

sage: a = animate([circle((i,-i), 1-1/(i+1), hue=i/10) for i in srange(0,2,0.2)], 

....: xmin=0,ymin=-2,xmax=2,ymax=0,figsize=[2,2]) 

sage: a # optional -- ImageMagick 

Animation with 10 frames 

sage: frame2 = a[2] # indirect doctest 

sage: frame2.show() 

sage: a.show() # optional -- ImageMagick 

sage: a[3:7] # optional -- ImageMagick # indirect doctest 

Animation with 4 frames 

sage: a[3:7].show() # optional -- ImageMagick 

""" 

if isinstance(i, slice): 

return Animation(self._frames[i], **self._kwds) 

else: 

return self._frames[i] 

def _repr_(self): 

""" 

Print representation for an animation. 

EXAMPLES:: 

sage: a = animate([circle((i,-i), 1-1/(i+1), hue=i/10) for i in srange(0,2,0.2)], 

....: xmin=0,ymin=-2,xmax=2,ymax=0,figsize=[2,2]) 

sage: a # optional -- ImageMagick 

Animation with 10 frames 

sage: a._repr_() 

'Animation with 10 frames' 

""" 

try: 

num = len(self) 

except TypeError: 

num = "unknown number of" 

return "Animation with %s frames"%num 

def __add__(self, other): 

""" 

Add two animations. This has the effect of superimposing the two 

animations frame-by-frame. 

EXAMPLES:: 

sage: a = animate([circle((i,0),1) for i in srange(0,2,0.4)], 

....: xmin=0, ymin=-1, xmax=3, ymax=1, 

....: figsize=[3,1], ticks=[1,1]) 

sage: a.show() # optional -- ImageMagick 

sage: b = animate([circle((0,i),1,hue=0) for i in srange(0,2,0.4)], 

....: xmin=0, ymin=-1, xmax=2, ymax=3, 

....: figsize=[1,2], ticks=[1,1]) 

sage: b.show() # optional -- ImageMagick 

sage: s = a+b # indirect doctest 

sage: len(a), len(b) 

(5, 5) 

sage: len(s) 

5 

sage: s.show() # optional -- ImageMagick 

""" 

if not isinstance(other, Animation): 

other = Animation(other) 

kwds = self._combine_kwds(self._kwds, other._kwds) 

#Combine the frames 

m = max(len(self), len(other)) 

frames = [a+b for a,b in zip(self._frames, other._frames)] 

frames += self._frames[m:] + other._frames[m:] 

return Animation(frames, **kwds) 

def __mul__(self, other): 

""" 

Multiply two animations. This has the effect of appending the two 

animations (the second comes after the first). 

EXAMPLES:: 

sage: a = animate([circle((i,0),1,thickness=20*i) for i in srange(0,2,0.4)], 

....: xmin=0, ymin=-1, xmax=3, ymax=1, figsize=[2,1], axes=False) 

sage: a.show() # optional -- ImageMagick 

sage: b = animate([circle((0,i),1,hue=0,thickness=20*i) for i in srange(0,2,0.4)], 

....: xmin=0, ymin=-1, xmax=1, ymax=3, figsize=[1,2], axes=False) 

sage: b.show() # optional -- ImageMagick 

sage: p = a*b # indirect doctest 

sage: len(a), len(b) 

(5, 5) 

sage: len(p) 

10 

sage: (a*b).show() # optional -- ImageMagick 

""" 

if not isinstance(other, Animation): 

other = Animation(other) 

kwds = self._combine_kwds(self._kwds, other._kwds) 

return Animation(self._frames + other._frames, **kwds) 

def __len__(self): 

""" 

Length of self 

EXAMPLES:: 

sage: a = animate([circle((i,0),1,thickness=20*i) for i in srange(0,2,0.4)], 

....: xmin=0, ymin=-1, xmax=3, ymax=1, figsize=[2,1], axes=False) 

sage: len(a) 

5 

""" 

try: 

return self._num_frames 

except AttributeError: 

return len(self._frames) 

def make_image(self, frame, filename, **kwds): 

r""" 

Given a frame which has no ``save_image()`` method, make a graphics 

object and save it as an image with the given filename. By default, this is 

:meth:`sage.plot.plot.plot`. To make animations of other objects, 

override this method in a subclass. 

EXAMPLES:: 

sage: from sage.plot.animate import Animation 

sage: class MyAnimation(Animation): 

....: def make_image(self, frame, filename, **kwds): 

....: P = parametric_plot(frame[0], frame[1], **frame[2]) 

....: P.save_image(filename,**kwds) 

sage: t = var('t') 

sage: x = lambda t: cos(t) 

sage: y = lambda n,t: sin(t)/n 

sage: B = MyAnimation([([x(t), y(i+1,t)],(t,0,1), {'color':Color((1,0,i/4)), 'aspect_ratio':1, 'ymax':1}) for i in range(4)]) 

sage: d = B.png(); v = os.listdir(d); v.sort(); v # long time 

['00000000.png', '00000001.png', '00000002.png', '00000003.png'] 

sage: B.show() # not tested 

sage: class MyAnimation(Animation): 

....: def make_image(self, frame, filename, **kwds): 

....: G = frame.plot() 

....: G.set_axes_range(floor(G.xmin()),ceil(G.xmax()),floor(G.ymin()),ceil(G.ymax())) 

....: G.save_image(filename, **kwds) 

sage: B = MyAnimation([graphs.CompleteGraph(n) for n in range(7,11)], figsize=5) 

sage: d = B.png() 

sage: v = os.listdir(d); v.sort(); v 

['00000000.png', '00000001.png', '00000002.png', '00000003.png'] 

sage: B.show() # not tested 

""" 

p = plot.plot(frame, **kwds) 

p.save_image(filename) 

def png(self, dir=None): 

r""" 

Render PNG images of the frames in this animation, saving them 

in ``dir``. Return the absolute path to that directory. If 

the frames have been previously rendered and ``dir`` is 

``None``, just return the directory in which they are stored. 

When ``dir`` is other than ``None``, force re-rendering of 

frames. 

INPUT: 

- ``dir`` -- Directory in which to store frames. Default 

``None``; in this case, a temporary directory will be 

created for storing the frames. 

EXAMPLES:: 

sage: a = animate([plot(x^2 + n) for n in range(4)], ymin=0, ymax=4) 

sage: d = a.png(); v = os.listdir(d); v.sort(); v # long time 

['00000000.png', '00000001.png', '00000002.png', '00000003.png'] 

""" 

if dir is None: 

try: 

return self._png_dir 

except AttributeError: 

pass 

dir = tmp_dir() 

i = 0 

for frame in self._frames: 

filename = '%s/%08d.png'%(dir,i) 

try: 

save_image = frame.save_image 

except AttributeError: 

self.make_image(frame, filename, **self._kwds) 

else: 

save_image(filename, **self._kwds) 

i += 1 

self._num_frames = i 

self._png_dir = dir 

return dir 

def graphics_array(self, ncols=3): 

r""" 

Return a :class:`sage.plot.graphics.GraphicsArray` with plots of the 

frames of this animation, using the given number of columns. 

The frames must be acceptable inputs for 

:class:`sage.plot.graphics.GraphicsArray`. 

EXAMPLES:: 

sage: E = EllipticCurve('37a') 

sage: v = [E.change_ring(GF(p)).plot(pointsize=30) for p in [97, 101, 103, 107]] 

sage: a = animate(v, xmin=0, ymin=0, axes=False) 

sage: a # optional -- ImageMagick 

Animation with 4 frames 

sage: a.show() # optional -- ImageMagick 

Modify the default arrangement of array:: 

sage: g = a.graphics_array(); print(g) 

Graphics Array of size 2 x 3 

sage: g.show(figsize=[6,3]) # not tested 

Specify different arrangement of array and save it with a given file name:: 

sage: g = a.graphics_array(ncols=2); print(g) 

Graphics Array of size 2 x 2 

sage: f = tmp_filename(ext='.png') 

sage: g.save(f) 

Frames can be specified as a generator too; it is internally converted to a list:: 

sage: t = var('t') 

sage: b = animate((plot(sin(c*pi*t)) for c in sxrange(1,2,.2))) 

sage: g = b.graphics_array() 

sage: g 

Graphics Array of size 2 x 3 

""" 

ncols = int(ncols) 

frame_list = list(self._frames) 

n = len(frame_list) 

nrows, rem = divmod(n,ncols) 

if rem > 0: 

nrows += 1 

return plot.graphics_array(frame_list, nrows, ncols) 

def gif(self, delay=20, savefile=None, iterations=0, show_path=False, 

use_ffmpeg=False): 

r""" 

Returns an animated gif composed from rendering the graphics 

objects in self. 

This method will only work if either (a) the ImageMagick 

software suite is installed, i.e., you have the ``convert`` 

command or (b) ``ffmpeg`` is installed. See the web sites of 

ImageMagick_ and FFmpeg_ for more details. By default, this 

produces the gif using ``convert`` if it is present. If this 

can't find ``convert`` or if ``use_ffmpeg`` is True, then it 

uses ``ffmpeg`` instead. 

INPUT: 

- ``delay`` - (default: 20) delay in hundredths of a 

second between frames 

- ``savefile`` - file that the animated gif gets saved 

to 

- ``iterations`` - integer (default: 0); number of 

iterations of animation. If 0, loop forever. 

- ``show_path`` - boolean (default: False); if True, 

print the path to the saved file 

- ``use_ffmpeg`` - boolean (default: False); if True, use 

'ffmpeg' by default instead of 'convert'. 

If ``savefile`` is not specified: in notebook mode, display the 

animation; otherwise, save it to a default file name. 

EXAMPLES:: 

sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)], 

....: xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1]) 

sage: td = tmp_dir() 

sage: a.gif() # not tested 

sage: a.gif(savefile=td + 'my_animation.gif', delay=35, iterations=3) # optional -- ImageMagick 

sage: with open(td + 'my_animation.gif', 'rb') as f: print('\x21\xf9\x04\x08\x23\x00') in f.read() # optional -- ImageMagick 

True 

sage: a.gif(savefile=td + 'my_animation.gif', show_path=True) # optional -- ImageMagick 

Animation saved to .../my_animation.gif. 

sage: a.gif(savefile=td + 'my_animation_2.gif', show_path=True, use_ffmpeg=True) # optional -- ffmpeg 

Animation saved to .../my_animation_2.gif. 

.. note:: 

If neither ffmpeg nor ImageMagick is installed, you will 

get an error message like this:: 

Error: Neither ImageMagick nor ffmpeg appears to be installed. Saving an 

animation to a GIF file or displaying an animation requires one of these 

packages, so please install one of them and try again. 

See www.imagemagick.org and www.ffmpeg.org for more information. 

REFERENCES: 

- `ImageMagick <http://www.imagemagick.org>`_ 

- `FFmpeg <http://www.ffmpeg.org>`_ 

""" 

from sage.misc.sage_ostools import have_program 

have_convert = have_program('convert') 

have_ffmpeg = self._have_ffmpeg() 

if use_ffmpeg or not have_convert: 

if have_ffmpeg: 

self.ffmpeg(savefile=savefile, show_path=show_path, 

output_format='.gif', delay=delay, 

iterations=iterations) 

else: 

if not have_convert: 

msg = """ 

Error: Neither ImageMagick nor ffmpeg appears to be installed. Saving an 

animation to a GIF file or displaying an animation requires one of these 

packages, so please install one of them and try again. 

See www.imagemagick.org and www.ffmpeg.org for more information.""" 

else: 

msg = """ 

Error: ffmpeg does not appear to be installed. Download it from 

www.ffmpeg.org, or use 'convert' to produce gifs instead.""" 

raise OSError(msg) 

else: 

if not savefile: 

savefile = graphics_filename(ext='.gif') 

if not savefile.endswith('.gif'): 

savefile += '.gif' 

savefile = os.path.abspath(savefile) 

d = self.png() 

cmd = ( 'cd "%s"; sage-native-execute convert -dispose Background ' 

'-delay %s -loop %s *.png "%s"' ) % ( d, int(delay), 

int(iterations), savefile ) 

from subprocess import check_call, CalledProcessError 

try: 

check_call(cmd, shell=True) 

if show_path: 

print("Animation saved to file %s." % savefile) 

except (CalledProcessError, OSError): 

msg = """ 

Error: Cannot generate GIF animation. Verify that convert 

(ImageMagick) or ffmpeg is installed, and that the objects passed to 

the animate command can be saved in PNG image format. 

See www.imagemagick.org and www.ffmpeg.org for more information.""" 

raise OSError(msg) 

def _rich_repr_(self, display_manager, **kwds): 

""" 

Rich Output Magic Method 

See :mod:`sage.repl.rich_output` for details. 

EXAMPLES:: 

sage: a = animate([plot(x^2 + n) for n in range(4)], ymin=0, ymax=4) 

sage: from sage.repl.rich_output import get_display_manager 

sage: dm = get_display_manager() 

sage: a._rich_repr_(dm) # optional -- ImageMagick 

OutputImageGif container 

""" 

iterations = kwds.get('iterations', 0) 

loop = (iterations == 0) 

t = display_manager.types 

supported = display_manager.supported_output() 

format = kwds.pop("format", None) 

if format is None: 

if t.OutputImageGif in supported: 

format = "gif" 

else: 

return # No supported format could be guessed 

suffix = None 

outputType = None 

if format == "gif": 

outputType = t.OutputImageGif 

suffix = ".gif" 

if format == "ogg": 

outputType = t.OutputVideoOgg 

if format == "webm": 

outputType = t.OutputVideoWebM 

if format == "mp4": 

outputType = t.OutputVideoMp4 

if format == "flash": 

outputType = t.OutputVideoFlash 

if format == "matroska": 

outputType = t.OutputVideoMatroska 

if format == "avi": 

outputType = t.OutputVideoAvi 

if format == "wmv": 

outputType = t.OutputVideoWmv 

if format == "quicktime": 

outputType = t.OutputVideoQuicktime 

if format is None: 

raise ValueError("Unknown video format") 

if outputType not in supported: 

return # Sorry, requested format is not supported 

if suffix is not None: 

return display_manager.graphics_from_save( 

self.save, kwds, suffix, outputType) 

# Now we save for OutputVideoBase 

filename = tmp_filename(ext=outputType.ext) 

self.save(filename, **kwds) 

from sage.repl.rich_output.buffer import OutputBuffer 

buf = OutputBuffer.from_file(filename) 

return outputType(buf, loop=loop) 

def show(self, delay=None, iterations=None, **kwds): 

r""" 

Show this animation immediately. 

This method attempts to display the graphics immediately, 

without waiting for the currently running code (if any) to 

return to the command line. Be careful, calling it from within 

a loop will potentially launch a large number of external 

viewer programs. 

INPUT: 

- ``delay`` -- (default: 20) delay in hundredths of a 

second between frames. 

- ``iterations`` -- integer (default: 0); number of 

iterations of animation. If 0, loop forever. 

- ``format`` - (default: gif) format to use for output. 

Currently supported formats are: gif, 

ogg, webm, mp4, flash, matroska, avi, wmv, quicktime. 

OUTPUT: 

This method does not return anything. Use :meth:`save` if you 

want to save the figure as an image. 

.. note:: 

Currently this is done using an animated gif, though this 

could change in the future. This requires that either 

ffmpeg or the ImageMagick suite (in particular, the 

``convert`` command) is installed. 

See also the :meth:`ffmpeg` method. 

EXAMPLES:: 

sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)], 

....: xmin=0, xmax=2*pi, figsize=[2,1]) 

sage: a.show() # optional -- ImageMagick 

The preceding will loop the animation forever. If you want to show 

only three iterations instead:: 

sage: a.show(iterations=3) # optional -- ImageMagick 

To put a half-second delay between frames:: 

sage: a.show(delay=50) # optional -- ImageMagick 

You can also make use of the HTML5 video element in the Sage Notebook:: 

sage: a.show(format="ogg") # optional -- ffmpeg 

sage: a.show(format="webm") # optional -- ffmpeg 

sage: a.show(format="mp4") # optional -- ffmpeg 

sage: a.show(format="webm", iterations=1) # optional -- ffmpeg 

Other backends may support other file formats as well:: 

sage: a.show(format="flash") # optional -- ffmpeg 

sage: a.show(format="matroska") # optional -- ffmpeg 

sage: a.show(format="avi") # optional -- ffmpeg 

sage: a.show(format="wmv") # optional -- ffmpeg 

sage: a.show(format="quicktime") # optional -- ffmpeg 

TESTS: 

Use of positional parameters is discouraged, will likely get 

deprecated, but should still work for the time being:: 

sage: a.show(50, 3) # optional -- ImageMagick 

.. note:: 

If you don't have ffmpeg or ImageMagick installed, you will 

get an error message like this:: 

Error: Neither ImageMagick nor ffmpeg appears to be installed. Saving an 

animation to a GIF file or displaying an animation requires one of these 

packages, so please install one of them and try again. 

See www.imagemagick.org and www.ffmpeg.org for more information. 

""" 

# Positional parameters for the sake of backwards compatibility 

if delay is not None: 

kwds.setdefault("delay", delay) 

if iterations is not None: 

kwds.setdefault("iterations", iterations) 

from sage.repl.rich_output import get_display_manager 

dm = get_display_manager() 

dm.display_immediately(self, **kwds) 

def _have_ffmpeg(self): 

""" 

Return True if the program 'ffmpeg' is installed. See 

www.ffmpeg.org to download ffmpeg. 

EXAMPLES:: 

sage: a = animate([plot(sin, -1,1)], xmin=0, ymin=0) 

sage: a._have_ffmpeg() # random: depends on whether ffmpeg is installed 

False 

""" 

from sage.misc.sage_ostools import have_program 

return have_program('ffmpeg') 

def ffmpeg(self, savefile=None, show_path=False, output_format=None, 

ffmpeg_options='', delay=None, iterations=0, pix_fmt='rgb24'): 

r""" 

Returns a movie showing an animation composed from rendering 

the frames in self. 

This method will only work if ffmpeg is installed. See 

http://www.ffmpeg.org for information about ffmpeg. 

INPUT: 

- ``savefile`` - file that the mpeg gets saved to. 

.. warning: 

This will overwrite ``savefile`` if it already exists. 

- ``show_path`` - boolean (default: False); if True, print the 

path to the saved file 

- ``output_format`` - string (default: None); format and 

suffix to use for the video. This may be 'mpg', 'mpeg', 

'avi', 'gif', or any other format that ffmpeg can handle. 

If this is None and the user specifies ``savefile`` with a 

suffix, say ``savefile='animation.avi'``, try to determine the 

format ('avi' in this case) from that file name. If no file 

is specified or if the suffix cannot be determined, 'mpg' is 

used. 

- ``ffmpeg_options`` - string (default: ''); this string is 

passed directly to ffmpeg. 

- ``delay`` - integer (default: None); delay in hundredths of a 

second between frames. The framerate is 100/delay. 

This is not supported for mpeg files: for mpegs, the frame 

rate is always 25 fps. 

- ``iterations`` - integer (default: 0); number of iterations 

of animation. If 0, loop forever. This is only supported 

for animated gif output and requires ffmpeg version 0.9 or 

later. For older versions, set ``iterations=None``. 

- ``pix_fmt`` - string (default: 'rgb24'); used only for gif 

output. Different values such as 'rgb8' or 'pal8' may be 

necessary depending on how ffmpeg was installed. Set 

``pix_fmt=None`` to disable this option. 

If ``savefile`` is not specified: in notebook mode, display 

the animation; otherwise, save it to a default file name. Use 

:func:`sage.misc.misc.set_verbose` with ``level=1`` to see 

additional output. 

EXAMPLES:: 

sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)], 

....: xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1]) 

sage: td = tmp_dir() 

sage: a.ffmpeg(savefile=td + 'new.mpg') # optional -- ffmpeg 

sage: a.ffmpeg(savefile=td + 'new.avi') # optional -- ffmpeg 

sage: a.ffmpeg(savefile=td + 'new.gif') # optional -- ffmpeg 

sage: a.ffmpeg(savefile=td + 'new.mpg', show_path=True) # optional -- ffmpeg 

Animation saved to .../new.mpg. 

.. note:: 

If ffmpeg is not installed, you will get an error message 

like this:: 

Error: ffmpeg does not appear to be installed. Saving an animation to 

a movie file in any format other than GIF requires this software, so 

please install it and try again. 

See www.ffmpeg.org for more information. 

TESTS:: 

sage: a.ffmpeg(output_format='gif',delay=30,iterations=5) # optional -- ffmpeg 

doctest:...: DeprecationWarning: use tmp_filename instead 

See http://trac.sagemath.org/17234 for details. 

""" 

if not self._have_ffmpeg(): 

msg = """Error: ffmpeg does not appear to be installed. Saving an animation to 

a movie file in any format other than GIF requires this software, so 

please install it and try again.""" 

raise OSError(msg) 

else: 

if savefile is None: 

if output_format is None: 

output_format = '.mpg' 

else: 

if output_format[0] != '.': 

output_format = '.'+output_format 

savefile = graphics_filename(ext=output_format) 

else: 

if output_format is None: 

suffix = os.path.splitext(savefile)[1] 

if len(suffix) > 0: 

output_format = suffix 

else: 

output_format = '.mpg' 

if not savefile.endswith(output_format): 

savefile += output_format 

early_options = '' 

if output_format == '.gif': 

# We try to set reasonable options for gif output. 

# 

# Older versions of ffmpeg (before 0.9, summer 2011) 

# use the option -loop_output instead of -loop. 

# Setting iterations=None is a way of preventing sage 

# from adding the -loop option. A separate 

# -loop_output option can be added with the 

# ffmpeg_options argument. 

if iterations is not None: 

loop_cmd = '-loop {0} '.format(iterations) 

else: 

loop_cmd = '' 

# A pix_fmt value is required for some but not all 

# ffmpeg installations. Setting pix_fmt=None will 

# prevent sage from adding this option, and it may be 

# controlled separately through ffmpeg_options. 

if pix_fmt is not None: 

pix_fmt_cmd = '-pix_fmt {0} '.format(pix_fmt) 

else: 

pix_fmt_cmd = '' 

ffmpeg_options += ' {0}{1}'.format(pix_fmt_cmd,loop_cmd) 

if delay is not None and output_format != '.mpeg' and output_format != '.mpg': 

early_options += ' -r %s ' % int(100/delay) 

savefile = os.path.abspath(savefile) 

pngdir = self.png() 

pngs = os.path.join(pngdir, "%08d.png") 

# For ffmpeg, it seems that some options, like '-g ... -r 

# ...', need to come before the input file names, while 

# some options, like '-pix_fmt rgb24', need to come 

# afterwards. Hence 'early_options' and 'ffmpeg_options' 

cmd = 'cd "%s"; sage-native-execute ffmpeg -y -f image2 %s -i %s %s %s' % (pngdir, early_options, pngs, ffmpeg_options, savefile) 

from subprocess import check_call, CalledProcessError, PIPE 

try: 

if sage.misc.misc.get_verbose() > 0: 

set_stderr = None 

else: 

set_stderr = PIPE 

sage.misc.misc.verbose("Executing '%s'" % cmd,level=1) 

sage.misc.misc.verbose("\n---- ffmpeg output below ----\n") 

check_call(cmd, shell=True, stderr=set_stderr) 

if show_path: 

print("Animation saved to file %s." % savefile) 

except (CalledProcessError, OSError): 

print("Error running ffmpeg.") 

raise 

def apng(self, savefile=None, show_path=False, delay=20, iterations=0): 

r""" 

Creates an animated PNG composed from rendering the graphics 

objects in self. Return the absolute path to that file. 

Notice that not all web browsers are capable of displaying APNG 

files, though they should still present the first frame of the 

animation as a fallback. 

The generated file is not optimized, so it may be quite large. 

Input: 

- ``delay`` - (default: 20) delay in hundredths of a 

second between frames 

- ``savefile`` - file that the animated gif gets saved 

to 

- ``iterations`` - integer (default: 0); number of 

iterations of animation. If 0, loop forever. 

- ``show_path`` - boolean (default: False); if True, 

print the path to the saved file 

EXAMPLES:: 

sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)], 

....: xmin=0, xmax=2*pi, figsize=[2,1]) 

sage: dir = tmp_dir() 

sage: a.apng() # long time 

sage: a.apng(savefile=dir + 'my_animation.png', delay=35, iterations=3) # long time 

sage: a.apng(savefile=dir + 'my_animation.png', show_path=True) # long time 

Animation saved to .../my_animation.png. 

If the individual frames have different sizes, an error will be raised:: 

sage: a = animate([plot(sin(x), (x, 0, k)) for k in range(1,4)], 

....: ymin=-1, ymax=1, aspect_ratio=1, figsize=[2,1]) 

sage: a.apng() # long time 

Traceback (most recent call last): 

... 

ValueError: Chunk IHDR mismatch 

""" 

pngdir = self.png() 

if savefile is None: 

savefile = graphics_filename('.png') 

with open(savefile, "wb") as out: 

apng = APngAssembler( 

out, len(self), 

delay=delay, num_plays=iterations) 

for i in range(len(self)): 

png = os.path.join(pngdir, "%08d.png" % i) 

apng.add_frame(png) 

if show_path: 

print("Animation saved to file %s." % savefile) 

def save(self, filename=None, show_path=False, use_ffmpeg=False, **kwds): 

r""" 

Save this animation. 

INPUT: 

- ``filename`` - (default: None) name of save file 

- ``show_path`` - boolean (default: False); if True, 

print the path to the saved file 

- ``use_ffmpeg`` - boolean (default: False); if True, use 

'ffmpeg' by default instead of 'convert' when creating GIF 

files. 

If filename is None, then in notebook mode, display the 

animation; otherwise, save the animation to a GIF file. If 

filename ends in '.sobj', save to an sobj file. Otherwise, 

try to determine the format from the filename extension 

('.mpg', '.gif', '.avi', etc.). If the format cannot be 

determined, default to GIF. 

For GIF files, either ffmpeg or the ImageMagick suite must be 

installed. For other movie formats, ffmpeg must be installed. 

An sobj file can be saved with no extra software installed. 

EXAMPLES:: 

sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)], 

....: xmin=0, xmax=2*pi, ymin=-1, ymax=1, figsize=[2,1]) 

sage: td = tmp_dir() 

sage: a.save() # not tested 

sage: a.save(td + 'wave.gif') # optional -- ImageMagick 

sage: a.save(td + 'wave.gif', show_path=True) # optional -- ImageMagick 

Animation saved to file .../wave.gif. 

sage: a.save(td + 'wave.avi', show_path=True) # optional -- ffmpeg 

Animation saved to file .../wave.avi. 

sage: a.save(td + 'wave0.sobj') 

sage: a.save(td + 'wave1.sobj', show_path=True) 

Animation saved to file .../wave1.sobj. 

TESTS: 

Ensure that we can pass delay and iteration count to the saved 

GIF image (see :trac:`18176`):: 

sage: a.save(td + 'wave.gif') # optional -- ImageMagick 

sage: with open(td + 'wave.gif', 'rb') as f: print('!\xf9\x04\x08\x14\x00') in f.read() # optional -- ImageMagick 

True 

sage: with open(td + 'wave.gif', 'rb') as f: print('!\xff\x0bNETSCAPE2.0\x03\x01\x00\x00\x00') in f.read() # optional -- ImageMagick 

True 

sage: a.save(td + 'wave.gif', delay=35) # optional -- ImageMagick 

sage: with open(td + 'wave.gif', 'rb') as f: print('!\xf9\x04\x08\x14\x00') in f.read() # optional -- ImageMagick 

False 

sage: with open(td + 'wave.gif', 'rb') as f: print('!\xf9\x04\x08\x23\x00') in f.read() # optional -- ImageMagick 

True 

sage: a.save(td + 'wave.gif', iterations=3) # optional -- ImageMagick 

sage: with open(td + 'wave.gif', 'rb') as f: print('!\xff\x0bNETSCAPE2.0\x03\x01\x00\x00\x00') in f.read() # optional -- ImageMagick 

False 

sage: with open(td + 'wave.gif', 'rb') as f: print('!\xff\x0bNETSCAPE2.0\x03\x01\x03\x00\x00') in f.read() # optional -- ImageMagick 

True 

""" 

if filename is None: 

suffix = '.gif' 

else: 

suffix = os.path.splitext(filename)[1] 

if len(suffix) == 0: 

suffix = '.gif' 

if filename is None or suffix == '.gif': 

self.gif(savefile=filename, show_path=show_path, 

use_ffmpeg=use_ffmpeg, **kwds) 

elif suffix == '.sobj': 

SageObject.save(self, filename) 

if show_path: 

print("Animation saved to file %s." % filename) 

else: 

self.ffmpeg(savefile=filename, show_path=show_path, **kwds) 

class APngAssembler(object): 

r""" 

Builds an APNG_ (Animated PNG) from a sequence of PNG files. 

This is used by the :meth:`sage.plot.animate.Animation.apng` method. 

This code is quite simple; it does little more than copying chunks 

from input PNG files to the output file. There is no optimization 

involved. This does not depend on external programs or libraries. 

INPUT: 

- ``out`` -- a file opened for binary writing to which the data 

will be written 

- ``num_frames`` -- the number of frames in the animation 

- ``num_plays`` -- how often to iterate, 0 means infinitely 

- ``delay`` -- numerator of the delay fraction in seconds 

- ``delay_denominator`` -- denominator of the delay in seconds 

EXAMPLES:: 

sage: from sage.plot.animate import APngAssembler 

sage: def assembleAPNG(): 

....: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.7)], 

....: xmin=0, xmax=2*pi, figsize=[2,1]) 

....: pngdir = a.png() 

....: outfile = sage.misc.temporary_file.tmp_filename(ext='.png') 

....: with open(outfile, "wb") as f: 

....: apng = APngAssembler(f, len(a)) 

....: for i in range(len(a)): 

....: png = os.path.join(pngdir, "{:08d}.png".format(i)) 

....: apng.add_frame(png, delay=10*i + 10) 

....: return outfile 

....: 

sage: assembleAPNG() # long time 

'...png' 

REFERENCES: 

- `APNG <https://wiki.mozilla.org/APNG_Specification>`_ 

""" 

magic = b"\x89PNG\x0d\x0a\x1a\x0a" 

mustmatch = frozenset([b"IHDR", b"PLTE", b"bKGD", b"cHRM", b"gAMA", 

b"pHYs", b"sBIT", b"tRNS"])