text: # -*- coding: utf-8 -*-
  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
  
  import six
  
  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"])
  
      def __init__(self, out, num_frames,
                   num_plays=0, delay=200, delay_denominator=100):
          r"""
          Initialize for creation of an APNG file.
          """
          self._last_seqno = -1
          self._idx = 0
          self._first = True
          self.out = out
          self.num_frames = num_frames
          self.num_plays = num_plays
          self.default_delay_numerator = delay
          self.default_delay_denominator = delay_denominator
          self._matchref = dict()
          self.out.write(self.magic)
  
      def add_frame(self, pngfile, delay=None, delay_denominator=None):
          r"""
          Adds a single frame to the APNG file.
  
          INPUT:
  
          - ``pngfile`` -- file name of the PNG file with data for this frame
  
          - ``delay`` -- numerator of the delay fraction in seconds
  
          - ``delay_denominator`` -- denominator of the delay in seconds
  
          If the delay is not specified, the default from the constructor
          applies.
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: from io import BytesIO
              sage: buf = BytesIO()
              sage: apng = APngAssembler(buf, 2)
              sage: fn = APngAssembler._testData("input1", True)
              sage: apng.add_frame(fn, delay=0x567, delay_denominator=0x1234)
              sage: fn = APngAssembler._testData("input2", True)
              sage: apng.add_frame(fn)
              sage: len(buf.getvalue())
              217
              sage: buf.getvalue() == APngAssembler._testData("anim12", False)
              True
              sage: apng.add_frame(fn)
              Traceback (most recent call last):
              ...
              RuntimeError: Already reached the declared number of frames
  
          """
          if self._idx == self.num_frames:
              raise RuntimeError("Already reached the declared number of frames")
          self.delay_numerator = self.default_delay_numerator
          self.delay_denominator = self.default_delay_denominator
          self._actl_written = False
          self._fctl_written = False
          if delay is not None:
              self.delay_numerator = delay
          if delay_denominator is not None:
              self.delay_denominator = delay_denominator
          self._add_png(pngfile)
          self._idx += 1
          if self._idx == self.num_frames:
              self._chunk(b"IEND", b"")
  
      def set_default(self, pngfile):
          r"""
          Adds a default image for the APNG file.
  
          This image is used as a fallback in case some application does
          not understand the APNG format.  This method must be called
          prior to any calls to the ``add_frame`` method, if it is called
          at all.  If it is not called, then the first frame of the
          animation will be the default.
  
          INPUT:
  
          - ``pngfile`` -- file name of the PNG file with data
            for the default image
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: from io import BytesIO
              sage: buf = BytesIO()
              sage: apng = APngAssembler(buf, 1)
              sage: fn = APngAssembler._testData("input1", True)
              sage: apng.set_default(fn)
              sage: fn = APngAssembler._testData("input2", True)
              sage: apng.add_frame(fn, delay=0x567, delay_denominator=0x1234)
              sage: len(buf.getvalue())
              179
              sage: buf.getvalue() == APngAssembler._testData("still1anim2", False)
              True
              sage: apng.add_frame(fn)
              Traceback (most recent call last):
              ...
              RuntimeError: Already reached the declared number of frames
  
          """
          if self._idx != 0:
              raise RuntimeError("Default image must precede all animation frames")
          self._actl_written = False
          self._fctl_written = True
          self._add_png(pngfile)
  
      def _add_png(self, pngfile):
          r"""
          Add data from one PNG still image.
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testCase1("_add_png", reads=False)
              enter _add_png('...png')
                write _current_chunk = (...'\x00\x00\x00\r', ...'IHDR', ...'\x00\x00\x00\x03\x00\x00\x00\x02\x08\x00\x00\x00\x00', ...'\xb8\x1f9\xc6')
                call _copy() -> None
                call _first_IHDR(...'\x00\x00\x00\x03\x00\x00\x00\x02\x08\x00\x00\x00\x00') -> None
                write _current_chunk = (...'\x00\x00\x00\x04', ...'gAMA', ...'\x00\x01\x86\xa0', ...'1\xe8\x96_')
                call _copy() -> None
                write _current_chunk = (...'\x00\x00\x00\x07', ...'tIME', ...'\x07\xde\x06\x1b\x0b&$', ...'\x1f0z\xd5')
                write _current_chunk = (...'\x00\x00\x00\x08', ...'IDAT', ...'img1data', ...'\xce\x8aI\x99')
                call _first_IDAT(...'img1data') -> None
                write _current_chunk = (...'\x00\x00\x00\x00', ...'IEND', ...'', ...'\xaeB`\x82')
                write _first = False
              exit _add_png -> None
              enter _add_png('...png')
                write _current_chunk = (...'\x00\x00\x00\r', ...'IHDR', ...'\x00\x00\x00\x03\x00\x00\x00\x02\x08\x00\x00\x00\x00', ...'\xb8\x1f9\xc6')
                write _current_chunk = (...'\x00\x00\x00\x04', ...'gAMA', ...'\x00\x01\x86\xa0', ...'1\xe8\x96_')
                write _current_chunk = (...'\x00\x00\x00\x04', ...'IDAT', ...'img2', ...'\x0ei\xab\x1d')
                call _next_IDAT(...'img2') -> None
                write _current_chunk = (...'\x00\x00\x00\x04', ...'IDAT', ...'data', ...'f\x94\xcbx')
                call _next_IDAT(...'data') -> None
                write _current_chunk = (...'\x00\x00\x00\x00', ...'IEND', ...'', ...'\xaeB`\x82')
                write _first = False
              exit _add_png -> None
          """
          with open(pngfile, 'rb') as png:
              if png.read(8) != self.magic:
                  raise ValueError("{} is not a PNG file".format(pngfile))
              while True:
                  chead = png.read(8)
                  if len(chead) == 0:
                      break
                  clen, ctype = struct.unpack(">L4s", chead)
                  cdata = png.read(clen)
                  ccrc = png.read(4)
                  utype = ctype.decode("ascii")
                  self._current_chunk = (chead[:4], ctype, cdata, ccrc)
                  if ctype in self.mustmatch:
                      ref = self._matchref.get(ctype)
                      if ref is None:
                          self._matchref[ctype] = cdata
                          self._copy()
                      else:
                          if cdata != ref:
                              raise ValueError("Chunk {} mismatch".format(utype))
                  met = ("_first_" if self._first else "_next_") + utype
                  try:
                      met = getattr(self, met)
                  except AttributeError:
                      pass
                  else:
                      met(cdata)
          self._first = False
  
      def _seqno(self):
          r"""
          Generate next sequence number.
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: from io import BytesIO
              sage: buf = BytesIO()
              sage: apng = APngAssembler(buf, 1)
              sage: apng._seqno() == b'\x00\x00\x00\x00'
              True
              sage: apng._seqno() == b'\x00\x00\x00\x01'
              True
              sage: apng._seqno() == b'\x00\x00\x00\x02'
              True
          """
          self._last_seqno += 1
          return struct.pack(">L", self._last_seqno)
  
      def _first_IHDR(self, data):
          r"""
          Remember image size.
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testCase1("_first_IHDR")
              enter _first_IHDR(...'\x00\x00\x00\x03\x00\x00\x00\x02\x08\x00\x00\x00\x00')
                write width = 3
                write height = 2
              exit _first_IHDR -> None
          """
          w, h, d, ctype, comp, filt, ilace = struct.unpack(">2L5B", data)
          self.width = w
          self.height = h
  
      def _first_IDAT(self, data):
          r"""
          Write acTL and fcTL, then copy as IDAT.
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testCase1("_first_IDAT")
              enter _first_IDAT(...'img1data')
                call _actl() -> None
                call _fctl() -> None
                call _copy() -> None
              exit _first_IDAT -> None
          """
          self._actl()
          self._fctl()
          self._copy()
  
      def _next_IDAT(self, data):
          r"""
          Write fcTL, then convert to fdAT.
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testCase1("_next_IDAT")
              enter _next_IDAT(...'img2')
                call _fctl() -> None
                call _seqno() -> ...'\x00\x00\x00\x02'
                call _chunk(...'fdAT', ...'\x00\x00\x00\x02img2') -> None
              exit _next_IDAT -> None
              enter _next_IDAT(...'data')
                call _fctl() -> None
                call _seqno() -> ...'\x00\x00\x00\x03'
                call _chunk(...'fdAT', ...'\x00\x00\x00\x03data') -> None
              exit _next_IDAT -> None
          """
          self._fctl()
          maxlen = 0x7ffffffb
          while len(data) > maxlen:
              self._chunk(b"fdAT", self._seqno() + data[:maxlen])
              data = data[maxlen:]
          self._chunk(b"fdAT", self._seqno() + data)
  
      def _copy(self):
          r"""
          Copy an existing chunk without modification.
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testCase1("_copy")
              enter _copy()
                read _current_chunk = (...'\x00\x00\x00\r', ...'IHDR', ...'\x00\x00\x00\x03\x00\x00\x00\x02\x08\x00\x00\x00\x00', ...'\xb8\x1f9\xc6')
                read out = <_io.BytesIO object at ...
                read out = <_io.BytesIO object at ...
                read out = <_io.BytesIO object at ...
                read out = <_io.BytesIO object at ...
              exit _copy -> None
              enter _copy()
                read _current_chunk = (...'\x00\x00\x00\x04', ...'gAMA', ...'\x00\x01\x86\xa0', ...'1\xe8\x96_')
              ...
                read _current_chunk = (...'\x00\x00\x00\x08', ...'IDAT', ...'img1data', ...'\xce\x8aI\x99')
              ...
              exit _copy -> None
          """
          for d in self._current_chunk:
              self.out.write(d)
  
      def _actl(self):
          r"""
          Write animation control data (acTL).
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testCase1("_actl")
              enter _actl()
                read _actl_written = False
                read num_frames = 2
                read num_plays = 0
                call _chunk(...'acTL', ...'\x00\x00\x00\x02\x00\x00\x00\x00') -> None
                write _actl_written = True
              exit _actl -> None
          """
          if self._actl_written:
              return
          data = struct.pack(">2L", self.num_frames, self.num_plays)
          self._chunk(b"acTL", data)
          self._actl_written = True
  
      def _fctl(self):
          r"""
          Write frame control data (fcTL).
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testCase1("_fctl")
              enter _fctl()
                read _fctl_written = False
                read width = 3
                read height = 2
                read delay_numerator = 1383
                read delay_denominator = 4660
                call _seqno() -> ...'\x00\x00\x00\x00'
                call _chunk(...'fcTL', ...'\x00\x00\x00\x00\x00\x00\x00\x03\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x00\x05g\x124\x01\x00') -> None
                write _fctl_written = True
              exit _fctl -> None
              enter _fctl()
                read _fctl_written = False
                read width = 3
                read height = 2
                read delay_numerator = 200
                read delay_denominator = 100
                call _seqno() -> ...'\x00\x00\x00\x01'
                call _chunk(...'fcTL', ...'\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x00\x00\xc8\x00d\x01\x00') -> None
                write _fctl_written = True
              exit _fctl -> None
              enter _fctl()
                read _fctl_written = True
              exit _fctl -> None
          """
          if self._fctl_written:
              return
          data = struct.pack(
              ">4L2H2B",
              self.width, self.height, 0, 0,
              self.delay_numerator, self.delay_denominator,
              1, 0)
          self._chunk(b"fcTL", self._seqno() + data)
          self._fctl_written = True
  
      def _chunk(self, ctype, cdata):
          r"""
          Write a new (or modified) chunk of data
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: from io import BytesIO
              sage: buf = BytesIO()
              sage: apng = APngAssembler(buf, 1)
              sage: buf.getvalue() == b'\x89PNG\r\n\x1a\n'
              True
              sage: apng._chunk(b"abcd", b"efgh")
              sage: buf.getvalue() == b'\x89PNG\r\n\x1a\n\x00\x00\x00\x04abcdefgh\xae\xef*P'
              True
          """
          ccrc = struct.pack(">L", zlib.crc32(ctype + cdata) & 0xffffffff)
          clen = struct.pack(">L", len(cdata))
          for d in [clen, ctype, cdata, ccrc]:
              self.out.write(d)
  
      @classmethod
      def _hex2bin(cls, h):
          r"""
          Convert hex data to binary.
  
          This is a helper method used for testing.
          Most data is given as lower-case hex digits,
          possibly intermixed with whitespace.
          A dot causes the next four bytes to be copied verbatim
          even if they look like hex digits. This is used for chunk types.
          Other characters which are not hex digits are passed verbatim.
  
          EXAMPLES::
  
              sage: from sage.plot.animate import APngAssembler
              sage: h2b = APngAssembler._hex2bin
              sage: h2b("0123") == b"\x01\x23"
              True
              sage: h2b(" 01 \n 23 ") == b"\x01\x23"
              True
              sage: h2b(".abcdef") == b"abcd\xef"
              True
              sage: h2b("PNG") == b"PNG"
              True
          """
          b = []
          while h:
              if h[0] in ' \n': # ignore whitespace
                  h = h[1:]
              elif h[0] in '0123456789abcdef': # hex byte
                  b.append(int(h[:2], 16))
                  h = h[2:]
              elif h[0] == '.': # for chunk type
                  b.extend(ord(h[i]) for i in range(1, 5))
                  h = h[5:]
              else: # for PNG magic
                  b.append(ord(h[0]))
                  h = h[1:]
          if six.PY2:
              return ''.join(map(chr, b))
          else:
              return bytes(b)
  
      @classmethod
      def _testData(cls, name, asFile):
          r"""
          Retrieve data for test cases.
  
          INPUT:
  
          - ``name``: The name of the file content.
  
          - ``asFile``: Whether to return a binary string of the named data
                        or the path of a file containing that data.
  
          EXAMPLES::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testData("input1", False).startswith(b'\x89PNG')
              True
              sage: APngAssembler._testData("input2", True)
              '...png'
          """
          data = {
  
              # Input 1: one PNG image, except the data makes no real sense
              "input1": """89 PNG 0d0a1a0a
              0000000d.IHDR 00000003000000020800000000 b81f39c6
              00000004.gAMA 000186a0 31e8965f
              00000007.tIME 07de061b0b2624 1f307ad5
              00000008.IDAT 696d673164617461 ce8a4999
              00000000.IEND ae426082""",
  
              # Input 2: slightly different, data in two chunks
              "input2": """89 PNG 0d0a1a0a
              0000000d.IHDR 00000003000000020800000000 b81f39c6
              00000004.gAMA 000186a0 31e8965f
              00000004.IDAT 696d6732 0e69ab1d
              00000004.IDAT 64617461 6694cb78
              00000000.IEND ae426082""",
  
              # Expected output 1: both images as frames of an animation
              "anim12": """89 PNG 0d0a1a0a
              0000000d.IHDR 00000003000000020800000000 b81f39c6
              00000004.gAMA 000186a0 31e8965f
              00000008.acTL 0000000200000000 f38d9370
              0000001a.fcTL 000000000000000300000002
                            0000000000000000056712340100 b4f729c9
              00000008.IDAT 696d673164617461 ce8a4999
              0000001a.fcTL 000000010000000300000002
                            000000000000000000c800640100 1b92eb4d
              00000008.fdAT 00000002696d6732 9cfb89a3
              00000008.fdAT 0000000364617461 c966c076
              00000000.IEND ae426082""",
  
              # Expected output 2: first image as fallback, second as animation
              "still1anim2": """89 PNG 0d0a1a0a
              0000000d.IHDR 00000003000000020800000000 b81f39c6
              00000004.gAMA 000186a0 31e8965f
              00000008.acTL 0000000100000000 b42de9a0
              00000008.IDAT 696d673164617461 ce8a4999
              0000001a.fcTL 000000000000000300000002
                            0000000000000000056712340100 b4f729c9
              00000008.fdAT 00000001696d6732 db5bf373
              00000008.fdAT 0000000264617461 f406e9c6
              00000000.IEND ae426082""",
  
          }
          d = cls._hex2bin(data[name])
          if asFile:
              from sage.misc.temporary_file import tmp_filename
              fn = tmp_filename(ext=".png")
              with open(fn, 'wb') as f:
                  f.write(d)
              return fn
          return d
  
      @classmethod
      def _testCase1(cls, methodToTrace=None, **kwds):
          r"""
          Run common test case.
  
          This test case is one animation of two frames.
          The named method (if not None) will be traced during execution.
          This will demonstrate the role of each method in the doctests.
  
          TESTS::
  
              sage: from sage.plot.animate import APngAssembler
              sage: APngAssembler._testCase1()
          """
          from sage.doctest.fixtures import trace_method
          from io import BytesIO
          buf = BytesIO()
          apng = cls(buf, 2)
          if methodToTrace is not None:
              trace_method(apng, methodToTrace, **kwds)
          apng.add_frame(cls._testData("input1", True),
                         delay=0x567, delay_denominator=0x1234)
          apng.add_frame(cls._testData("input2", True))
          out = buf.getvalue()
          assert len(out) == 217
          assert out == cls._testData("anim12", False)
  