imaging.images2gif — GRASS Python Library documentation

# Source code for imaging.images2gif

    #   Copyright (C) 2012, Almar Klein, Ant1, Marius van Voorden
    #
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    """ Module images2gif

    Provides functionality for reading and writing animated GIF images.
    Use writeGif to write a series of numpy arrays or PIL images as an
    animated GIF. Use readGif to read an animated gif as a series of numpy
    arrays.

    Note that since July 2004, all patents on the LZW compression patent have
    expired. Therefore the GIF format may now be used freely.

    Acknowledgements:

    Many thanks to Ant1 for:

    * noting the use of "palette=PIL.Image.ADAPTIVE", which significantly
      improves the results.
    * the modifications to save each image with its own palette, or optionally
      the global palette (if its the same).

    Many thanks to Marius van Voorden for porting the NeuQuant quantization
    algorithm of Anthony Dekker to Python (See the NeuQuant class for its
    license).

    Many thanks to Alex Robinson for implementing the concept of subrectangles,
    which (depending on image content) can give a very significant reduction in
    file size.

    This code is based on gifmaker (in the scripts folder of the source
    distribution of PIL)

    Useful links:

      * http://tronche.com/computer-graphics/gif/
      * https://en.wikipedia.org/wiki/Graphics_Interchange_Format
      * http://www.w3.org/Graphics/GIF/spec-gif89a.txt

    """
    # todo: This module should be part of imageio (or at least based on)

    import os

    try:
        import PIL
        from PIL import Image

        pillow = True
        try:
            PIL.__version__  # test if user has Pillow or PIL
        except AttributeError:
            pillow = False
        from PIL.GifImagePlugin import getheader, getdata
    except ImportError:
        PIL = None

    try:
        import numpy as np
    except ImportError:
        np = None

    def get_cKDTree():
        try:
            from scipy.spatial import cKDTree
        except ImportError:
            cKDTree = None
        return cKDTree

    # getheader gives a 87a header and a color palette (two elements in a list)
    # getdata()[0] gives the Image Descriptor up to (including) "LZW min code size"
    # getdatas()[1:] is the image data itself in chunks of 256 bytes (well
    # technically the first byte says how many bytes follow, after which that
    # amount (max 255) follows)

    def checkImages(images):
        """checkImages(images)
        Check numpy images and correct intensity range etc.
        The same for all movie formats.

        :param images:
        """
        # Init results
        images2 = []

        for im in images:
            if PIL and isinstance(im, PIL.Image.Image):
                # We assume PIL images are alright
                images2.append(im)

            elif np and isinstance(im, np.ndarray):
                # Check and convert dtype
                if im.dtype == np.uint8:
                    images2.append(im)  # Ok
                elif im.dtype in [np.float32, np.float64]:
                    im = im.copy()
                    im[im < 0] = 0
                    im[im > 1] = 1
                    im *= 255
                    images2.append(im.astype(np.uint8))
                else:
                    im = im.astype(np.uint8)
                    images2.append(im)
                # Check size
                if im.ndim == 2:
                    pass  # ok
                elif im.ndim == 3:
                    if im.shape[2] not in [3, 4]:
                        raise ValueError("This array can not represent an image.")
                else:
                    raise ValueError("This array can not represent an image.")
            else:
                raise ValueError("Invalid image type: " + str(type(im)))

        # Done
        return images2

    def intToBin(i):
        """Integer to two bytes"""
        # divide in two parts (bytes)
        i1 = i % 256
        i2 = int(i / 256)
        # make string (little endian)
        return chr(i1) + chr(i2)

    class GifWriter:
        """Class that contains methods for helping write the animated GIF file."""

        def getheaderAnim(self, im):
            """Get animation header. To replace PILs getheader()[0]

            :param im:
            """
            bb = "GIF89a"
            bb += intToBin(im.size[0])
            bb += intToBin(im.size[1])
            bb += "\x87\x00\x00"
            return bb

        def getImageDescriptor(self, im, xy=None):
            """Used for the local color table properties per image.
            Otherwise global color table applies to all frames irrespective of
            whether additional colors comes in play that require a redefined
            palette. Still a maximum of 256 color per frame, obviously.

            Written by Ant1 on 2010-08-22
            Modified by Alex Robinson in Janurari 2011 to implement subrectangles.

            :param im:
            :param xy:
            """

            # Default use full image and place at upper left
            if xy is None:
                xy = (0, 0)

            # Image separator,
            bb = "\x2C"

            # Image position and size
            bb += intToBin(xy[0])  # Left position
            bb += intToBin(xy[1])  # Top position
            bb += intToBin(im.size[0])  # image width
            bb += intToBin(im.size[1])  # image height

            # packed field: local color table flag1, interlace0, sorted table0,
            # reserved00, lct size111=7=2^(7 + 1)=256.
            bb += "\x87"

            # LZW min size code now comes later, beginning of [image data] blocks
            return bb

        def getAppExt(self, loops=float("inf")):
            """Application extension. This part specifies the amount of loops.
            If loops is 0 or inf, it goes on infinitely.

            :param float loops:
            """

            if loops == 0 or loops == float("inf"):
                loops = 2**16 - 1
                # bb = ""
                # application extension should not be used
                # (the extension interprets zero loops
                # to mean an infinite number of loops)
                # Mmm, does not seem to work
            if True:
                bb = "\x21\xFF\x0B"  # application extension
                bb += "NETSCAPE2.0"
                bb += "\x03\x01"
                bb += intToBin(loops)
                bb += "\x00"  # end
            return bb

        def getGraphicsControlExt(self, duration=0.1, dispose=2):
            """Graphics Control Extension. A sort of header at the start of
            each image. Specifies duration and transparency.

            Dispose:

              * 0 - No disposal specified.
              * 1 - Do not dispose. The graphic is to be left in place.
              * 2 -	Restore to background color. The area used by the graphic
                must be restored to the background color.
              * 3 -	Restore to previous. The decoder is required to restore the
                area overwritten by the graphic with what was there prior to
                rendering the graphic.
              * 4-7 -To be defined.

            :param double duration:
            :param dispose:
            """

            bb = "\x21\xF9\x04"
            bb += chr((dispose & 3) << 2)  # low bit 1 == transparency,
            # 2nd bit 1 == user input , next 3 bits, the low two of which are used,
            # are dispose.
            bb += intToBin(int(duration * 100))  # in 100th of seconds
            bb += "\x00"  # no transparent color
            bb += "\x00"  # end
            return bb

        def handleSubRectangles(self, images, subRectangles):
            """Handle the sub-rectangle stuff. If the rectangles are given by the
            user, the values are checked. Otherwise the subrectangles are
            calculated automatically.

            """

            if isinstance(subRectangles, (tuple, list)):
                # xy given directly

                # Check xy
                xy = subRectangles
                if xy is None:
                    xy = (0, 0)
                if hasattr(xy, "__len__"):
                    if len(xy) == len(images):
                        xy = [xxyy for xxyy in xy]
                    else:
                        raise ValueError("len(xy) doesn't match amount of images.")
                else:
                    xy = [xy for im in images]
                xy[0] = (0, 0)

            else:
                # Calculate xy using some basic image processing

                # Check Numpy
                if np is None:
                    raise RuntimeError("Need Numpy to use auto-subRectangles.")

                # First make numpy arrays if required
                for i in range(len(images)):
                    im = images[i]
                    if isinstance(im, Image.Image):
                        tmp = im.convert()  # Make without palette
                        a = np.asarray(tmp)
                        if len(a.shape) == 0:
                            raise MemoryError(
                                "Too little memory to convert PIL image to array"
                            )
                        images[i] = a

                # Determine the sub rectangles
                images, xy = self.getSubRectangles(images)

            # Done
            return images, xy

        def getSubRectangles(self, ims):
            """getSubRectangles(ims)

            Calculate the minimal rectangles that need updating each frame.
            Returns a two-element tuple containing the cropped images and a
            list of x-y positions.

            Calculating the subrectangles takes extra time, obviously. However,
            if the image sizes were reduced, the actual writing of the GIF
            goes faster. In some cases applying this method produces a GIF faster.

            """

            # Check image count
            if len(ims) < 2:
                return ims, [(0, 0) for i in ims]

            # We need numpy
            if np is None:
                raise RuntimeError("Need Numpy to calculate sub-rectangles. ")

            # Prepare
            ims2 = [ims[0]]
            xy = [(0, 0)]

            # Iterate over images
            prev = ims[0]
            for im in ims[1:]:
                # Get difference, sum over colors
                diff = np.abs(im - prev)
                if diff.ndim == 3:
                    diff = diff.sum(2)
                # Get begin and end for both dimensions
                X = np.argwhere(diff.sum(0))
                Y = np.argwhere(diff.sum(1))
                # Get rect coordinates
                if X.size and Y.size:
                    x0, x1 = int(X[0]), int(X[-1] + 1)
                    y0, y1 = int(Y[0]), int(Y[-1] + 1)
                else:  # No change ... make it minimal
                    x0, x1 = 0, 2
                    y0, y1 = 0, 2

                # Cut out and store
                im2 = im[y0:y1, x0:x1]
                prev = im
                ims2.append(im2)
                xy.append((x0, y0))

            # Done
            # print('%1.2f seconds to determine subrectangles of  %i images' %
            #    (time.time()-t0, len(ims2)))
            return ims2, xy

        def convertImagesToPIL(self, images, dither, nq=0):
            """convertImagesToPIL(images, nq=0)

            Convert images to Paletted PIL images, which can then be
            written to a single animaged GIF.

            """

            # Convert to PIL images
            images2 = []
            for im in images:
                if isinstance(im, Image.Image):
                    images2.append(im)
                elif np and isinstance(im, np.ndarray):
                    if im.ndim == 3 and im.shape[2] == 3:
                        im = Image.fromarray(im, "RGB")
                    elif im.ndim == 3 and im.shape[2] == 4:
                        im = Image.fromarray(im[:, :, :3], "RGB")
                    elif im.ndim == 2:
                        im = Image.fromarray(im, "L")
                    images2.append(im)

            # Convert to paletted PIL images
            images, images2 = images2, []
            if nq >= 1:
                # NeuQuant algorithm
                for im in images:
                    im = im.convert("RGBA")  # NQ assumes RGBA
                    nqInstance = NeuQuant(im, int(nq))  # Learn colors from image
                    if dither:
                        im = im.convert("RGB").quantize(palette=nqInstance.paletteImage())
                    else:
                        # Use to quantize the image itself
                        im = nqInstance.quantize(im)
                    images2.append(im)
            else:
                # Adaptive PIL algorithm
                AD = Image.ADAPTIVE
                for im in images:
                    im = im.convert("P", palette=AD, dither=dither)
                    images2.append(im)

            # Done
            return images2

        def writeGifToFile(self, fp, images, durations, loops, xys, disposes):
            """writeGifToFile(fp, images, durations, loops, xys, disposes)

            Given a set of images writes the bytes to the specified stream.
            Requires different handling of palette for PIL and Pillow:
            based on https://github.com/rec/echomesh/blob/master/
            code/python/external/images2gif.py

            """

            # Obtain palette for all images and count each occurrence
            palettes, occur = [], []
            for im in images:
                if not pillow:
                    palette = getheader(im)[1]
                else:
                    palette = getheader(im)[0][-1]
                    if not palette:
                        palette = im.palette.tobytes()
                palettes.append(palette)
            for palette in palettes:
                occur.append(palettes.count(palette))

            # Select most-used palette as the global one (or first in case no max)
            globalPalette = palettes[occur.index(max(occur))]

            # Init
            frames = 0
            firstFrame = True

            for im, palette in zip(images, palettes):
                if firstFrame:
                    # Write header

                    # Gather info
                    header = self.getheaderAnim(im)
                    appext = self.getAppExt(loops)

                    # Write
                    fp.write(header)
                    fp.write(globalPalette)
                    fp.write(appext)

                    # Next frame is not the first
                    firstFrame = False

                if True:
                    # Write palette and image data

                    # Gather info
                    data = getdata(im)
                    imdes, data = data[0], data[1:]
                    graphext = self.getGraphicsControlExt(
                        durations[frames], disposes[frames]
                    )
                    # Make image descriptor suitable for using 256 local color palette
                    lid = self.getImageDescriptor(im, xys[frames])

                    # Write local header
                    if (palette != globalPalette) or (disposes[frames] != 2):
                        # Use local color palette
                        fp.write(graphext)
                        fp.write(lid)  # write suitable image descriptor
                        fp.write(palette)  # write local color table
                        fp.write("\x08")  # LZW minimum size code
                    else:
                        # Use global color palette
                        fp.write(graphext)
                        fp.write(imdes)  # write suitable image descriptor

                    # Write image data
                    for d in data:
                        fp.write(d)

                # Prepare for next round
                frames = frames + 1

            fp.write(";")  # end gif
            return frames

    def writeGif(filename, images, duration=0.1, repeat=True, **kwargs):
        """Write an animated gif from the specified images.
        Depending on which PIL library is used, either writeGifVisvis or writeGifPillow
        is used here.

        :param str filename: the name of the file to write the image to.
        :param list images: should be a list consisting of PIL images or numpy
                            arrays. The latter should be between 0 and 255 for
                            integer types, and between 0 and 1 for float types.
        :param duration: scalar or list of scalars The duration for all frames, or
                         (if a list) for each frame.
        :param repeat: bool or integer The amount of loops. If True, loops infinitetel
        :param kwargs: additional parameters for writeGifVisvis

        """
        if pillow:
            # Pillow >= 3.4.0 has animated GIF writing
            version = [int(i) for i in PIL.__version__.split(".")]
            if version[0] > 3 or (version[0] == 3 and version[1] >= 4):
                writeGifPillow(filename, images, duration, repeat)
                return
        # otherwise use the old one
        writeGifVisvis(filename, images, duration, repeat, **kwargs)

    def writeGifPillow(filename, images, duration=0.1, repeat=True):
        """Write an animated gif from the specified images.
        Uses native Pillow implementation, which is available since Pillow 3.4.0.

        :param str filename: the name of the file to write the image to.
        :param list images: should be a list consisting of PIL images or numpy
                            arrays. The latter should be between 0 and 255 for
                            integer types, and between 0 and 1 for float types.
        :param duration: scalar or list of scalars The duration for all frames, or
                         (if a list) for each frame.
        :param repeat: bool or integer The amount of loops. If True, loops infinitetel

        """
        loop = 0 if repeat else 1
        quantized = []
        for im in images:
            quantized.append(im.quantize())
        quantized[0].save(
            filename,
            save_all=True,
            append_images=quantized[1:],
            loop=loop,
            duration=duration * 1000,
        )

    def writeGifVisvis(
        filename,
        images,
        duration=0.1,
        repeat=True,
        dither=False,
        nq=0,
        subRectangles=True,
        dispose=None,
    ):
        """Write an animated gif from the specified images.
        Uses VisVis implementation. Unfortunately it produces corrupted GIF
        with Pillow >= 3.4.0.

        :param str filename: the name of the file to write the image to.
        :param list images: should be a list consisting of PIL images or numpy
                            arrays. The latter should be between 0 and 255 for
                            integer types, and between 0 and 1 for float types.
        :param duration: scalar or list of scalars The duration for all frames, or
                         (if a list) for each frame.
        :param repeat: bool or integer The amount of loops. If True, loops infinitetely.
        :param bool dither: whether to apply dithering
        :param int nq: If nonzero, applies the NeuQuant quantization algorithm to
                       create the color palette. This algorithm is superior, but
                       slower than the standard PIL algorithm. The value of nq is
                       the quality parameter. 1 represents the best quality. 10 is
                       in general a good tradeoff between quality and speed. When
                       using this option, better results are usually obtained when
                       subRectangles is False.
        :param subRectangles: False, True, or a list of 2-element tuples
                              Whether to use sub-rectangles. If True, the minimal
                              rectangle that is required to update each frame is
                              automatically detected. This can give significant
                              reductions in file size, particularly if only a part
                              of the image changes. One can also give a list of x-y
                              coordinates if you want to do the cropping yourself.
                              The default is True.
        :param int dispose: how to dispose each frame. 1 means that each frame is
                            to be left in place. 2 means the background color
                            should be restored after each frame. 3 means the
                            decoder should restore the previous frame. If
                            subRectangles==False, the default is 2, otherwise it is 1.

        """

        # Check PIL
        if PIL is None:
            raise RuntimeError("Need PIL to write animated gif files.")

        # Check images
        images = checkImages(images)

        # Instantiate writer object
        gifWriter = GifWriter()

        # Check loops
        if repeat is False:
            loops = 1
        elif repeat is True:
            loops = 0  # zero means infinite
        else:
            loops = int(repeat)

        # Check duration
        if hasattr(duration, "__len__"):
            if len(duration) == len(images):
                duration = [d for d in duration]
            else:
                raise ValueError("len(duration) doesn't match amount of images.")
        else:
            duration = [duration for im in images]

        # Check subrectangles
        if subRectangles:
            images, xy = gifWriter.handleSubRectangles(images, subRectangles)
            defaultDispose = 1  # Leave image in place
        else:
            # Normal mode
            xy = [(0, 0) for im in images]
            defaultDispose = 2  # Restore to background color.

        # Check dispose
        if dispose is None:
            dispose = defaultDispose
        if hasattr(dispose, "__len__"):
            if len(dispose) != len(images):
                raise ValueError("len(xy) doesn't match amount of images.")
        else:
            dispose = [dispose for im in images]

        # Make images in a format that we can write easy
        images = gifWriter.convertImagesToPIL(images, dither, nq)

        # Write
        fp = open(filename, "wb")
        try:
            gifWriter.writeGifToFile(fp, images, duration, loops, xy, dispose)
        finally:
            fp.close()

    def readGif(filename, asNumpy=True):
        """Read images from an animated GIF file.  Returns a list of numpy
        arrays, or, if asNumpy is false, a list if PIL images.

        """

        # Check PIL
        if PIL is None:
            raise RuntimeError("Need PIL to read animated gif files.")

        # Check Numpy
        if np is None:
            raise RuntimeError("Need Numpy to read animated gif files.")

        # Check whether it exists
        if not os.path.isfile(filename):
            raise OSError("File not found: " + str(filename))

        # Load file using PIL
        pilIm = PIL.Image.open(filename)
        pilIm.seek(0)

        # Read all images inside
        images = []
        try:
            while True:
                # Get image as numpy array
                tmp = pilIm.convert()  # Make without palette
                a = np.asarray(tmp)
                if len(a.shape) == 0:
                    raise MemoryError("Too little memory to convert PIL image to array")
                # Store, and next
                images.append(a)
                pilIm.seek(pilIm.tell() + 1)
        except EOFError:
            pass

        # Convert to normal PIL images if needed
        if not asNumpy:
            images2 = images
            images = []
            for im in images2:
                images.append(PIL.Image.fromarray(im))

        # Done
        return images

    class NeuQuant:
        """NeuQuant(image, samplefac=10, colors=256)

        samplefac should be an integer number of 1 or higher, 1
        being the highest quality, but the slowest performance.
        With avalue of 10, one tenth of all pixels are used during
        training. This value seems a nice tradeof between speed
        and quality.

        colors is the amount of colors to reduce the image to. This
        should best be a power of two.

        See also:
        http://members.ozemail.com.au/~dekker/NEUQUANT.HTML

        **License of the NeuQuant Neural-Net Quantization Algorithm**

        Copyright (c) 1994 Anthony Dekker
        Ported to python by Marius van Voorden in 2010

        NEUQUANT Neural-Net quantization algorithm by Anthony Dekker, 1994.
        See "Kohonen neural networks for optimal colour quantization"
        in "network: Computation in Neural Systems" Vol. 5 (1994) pp 351-367.
        for a discussion of the algorithm.
        See also  http://members.ozemail.com.au/~dekker/NEUQUANT.HTML

        Any party obtaining a copy of these files from the author, directly or
        indirectly, is granted, free of charge, a full and unrestricted
        irrevocable, world-wide, paid up, royalty-free, nonexclusive right and
        license to deal in this software and documentation files (the "Software"),
        including without limitation the rights to use, copy, modify, merge,
        publish, distribute, sublicense, and/or sell copies of the Software, and
        to permit persons who receive copies from any such party to do so, with
        the only requirement being that this copyright notice remain intact.

        """

        NCYCLES = None  # Number of learning cycles
        NETSIZE = None  # Number of colours used
        SPECIALS = None  # Number of reserved colours used
        BGCOLOR = None  # Reserved background colour
        CUTNETSIZE = None
        MAXNETPOS = None

        INITRAD = None  # For 256 colours, radius starts at 32
        RADIUSBIASSHIFT = None
        RADIUSBIAS = None
        INITBIASRADIUS = None
        RADIUSDEC = None  # Factor of 1/30 each cycle

        ALPHABIASSHIFT = None
        INITALPHA = None  # biased by 10 bits

        GAMMA = None
        BETA = None
        BETAGAMMA = None

        network = None  # The network itself
        colormap = None  # The network itself

        netindex = None  # For network lookup - really 256

        bias = None  # Bias and freq arrays for learning
        freq = None

        pimage = None

        # Four primes near 500 - assume no image has a length so large
        # that it is divisible by all four primes
        PRIME1 = 499
        PRIME2 = 491
        PRIME3 = 487
        PRIME4 = 503
        MAXPRIME = PRIME4

        pixels = None
        samplefac = None

        a_s = None

        def setconstants(self, samplefac, colors):
            self.NCYCLES = 100  # Number of learning cycles
            self.NETSIZE = colors  # Number of colours used
            self.SPECIALS = 3  # Number of reserved colours used
            self.BGCOLOR = self.SPECIALS - 1  # Reserved background colour
            self.CUTNETSIZE = self.NETSIZE - self.SPECIALS
            self.MAXNETPOS = self.NETSIZE - 1

            self.INITRAD = self.NETSIZE / 8  # For 256 colours, radius starts at 32
            self.RADIUSBIASSHIFT = 6
            self.RADIUSBIAS = 1 << self.RADIUSBIASSHIFT
            self.INITBIASRADIUS = self.INITRAD * self.RADIUSBIAS
            self.RADIUSDEC = 30  # Factor of 1/30 each cycle

            self.ALPHABIASSHIFT = 10  # Alpha starts at 1
            self.INITALPHA = 1 << self.ALPHABIASSHIFT  # biased by 10 bits

            self.GAMMA = 1024.0
            self.BETA = 1.0 / 1024.0
            self.BETAGAMMA = self.BETA * self.GAMMA

            # The network itself
            self.network = np.empty((self.NETSIZE, 3), dtype="float64")
            # The network itself
            self.colormap = np.empty((self.NETSIZE, 4), dtype="int32")

            self.netindex = np.empty(256, dtype="int32")  # For network lookup - really 256

            # Bias and freq arrays for learning
            self.bias = np.empty(self.NETSIZE, dtype="float64")
            self.freq = np.empty(self.NETSIZE, dtype="float64")

            self.pixels = None
            self.samplefac = samplefac

            self.a_s = {}

        def __init__(self, image, samplefac=10, colors=256):
            # Check Numpy
            if np is None:
                raise RuntimeError("Need Numpy for the NeuQuant algorithm.")

            # Check image
            if image.size[0] * image.size[1] < NeuQuant.MAXPRIME:
                raise OSError("Image is too small")
            if image.mode != "RGBA":
                raise OSError("Image mode should be RGBA.")

            # Initialize
            self.setconstants(samplefac, colors)
            self.pixels = np.fromstring(image.tobytes(), np.uint32)
            self.setUpArrays()

            self.learn()
            self.fix()
            self.inxbuild()

        def writeColourMap(self, rgb, outstream):
            for i in range(self.NETSIZE):
                bb = self.colormap[i, 0]
                gg = self.colormap[i, 1]
                rr = self.colormap[i, 2]
                outstream.write(rr if rgb else bb)
                outstream.write(gg)
                outstream.write(bb if rgb else rr)
            return self.NETSIZE

        def setUpArrays(self):
            self.network[0, 0] = 0.0  # Black
            self.network[0, 1] = 0.0
            self.network[0, 2] = 0.0

            self.network[1, 0] = 255.0  # White
            self.network[1, 1] = 255.0
            self.network[1, 2] = 255.0

            # RESERVED self.BGCOLOR # Background

            for i in range(self.SPECIALS):
                self.freq[i] = 1.0 / self.NETSIZE
                self.bias[i] = 0.0

            for i in range(self.SPECIALS, self.NETSIZE):
                p = self.network[i]
                p[:] = (255.0 * (i - self.SPECIALS)) / self.CUTNETSIZE

                self.freq[i] = 1.0 / self.NETSIZE
                self.bias[i] = 0.0

        # Omitted: setPixels

        def altersingle(self, alpha, i, b, g, r):
            """Move neuron i towards biased (b, g, r) by factor alpha"""
            n = self.network[i]  # Alter hit neuron
            n[0] -= alpha * (n[0] - b)
            n[1] -= alpha * (n[1] - g)
            n[2] -= alpha * (n[2] - r)

        def geta(self, alpha, rad):
            try:
                return self.a_s[(alpha, rad)]
            except KeyError:
                length = rad * 2 - 1
                mid = length / 2
                q = np.array(list(range(mid - 1, -1, -1)) + list(range(-1, mid)))
                a = alpha * (rad * rad - q * q) / (rad * rad)
                a[mid] = 0
                self.a_s[(alpha, rad)] = a
                return a

        def alterneigh(self, alpha, rad, i, b, g, r):
            if i - rad >= self.SPECIALS - 1:
                lo = i - rad
                start = 0
            else:
                lo = self.SPECIALS - 1
                start = self.SPECIALS - 1 - (i - rad)

            if i + rad <= self.NETSIZE:
                hi = i + rad
                end = rad * 2 - 1
            else:
                hi = self.NETSIZE
                end = self.NETSIZE - (i + rad)

            a = self.geta(alpha, rad)[start:end]

            p = self.network[lo + 1 : hi]
            p -= np.transpose(np.transpose(p - np.array([b, g, r])) * a)

        # def contest(self, b, g, r):
        #    """ Search for biased BGR values
        #            Finds closest neuron (min dist) and updates self.freq
        #            finds best neuron (min dist-self.bias) and returns position
        #            for frequently chosen neurons, self.freq[i] is high and self.bias[i]
        #            is negative
        #            self.bias[i] = self.GAMMA * ((1/self.NETSIZE)-self.freq[i])"""
        #
        #    i, j = self.SPECIALS, self.NETSIZE
        #    dists = abs(self.network[i:j] - np.array([b, g, r])).sum(1)
        #    bestpos = i + np.argmin(dists)
        #    biasdists = dists - self.bias[i:j]
        #    bestbiaspos = i + np.argmin(biasdists)
        #    self.freq[i:j] -= self.BETA * self.freq[i:j]
        #    self.bias[i:j] += self.BETAGAMMA * self.freq[i:j]
        #    self.freq[bestpos] += self.BETA
        #    self.bias[bestpos] -= self.BETAGAMMA
        #    return bestbiaspos

        def contest(self, b, g, r):
            """Search for biased BGR values
            Finds closest neuron (min dist) and updates self.freq
            finds best neuron (min dist-self.bias) and returns position
            for frequently chosen neurons, self.freq[i] is high and self.bias[i]
            is negative self.bias[i] = self.GAMMA * ((1/self.NETSIZE)-self.freq[i])
            """
            i, j = self.SPECIALS, self.NETSIZE
            dists = abs(self.network[i:j] - np.array([b, g, r])).sum(1)
            bestpos = i + np.argmin(dists)
            biasdists = dists - self.bias[i:j]
            bestbiaspos = i + np.argmin(biasdists)
            self.freq[i:j] *= 1 - self.BETA
            self.bias[i:j] += self.BETAGAMMA * self.freq[i:j]
            self.freq[bestpos] += self.BETA
            self.bias[bestpos] -= self.BETAGAMMA
            return bestbiaspos

        def specialFind(self, b, g, r):
            for i in range(self.SPECIALS):
                n = self.network[i]
                if n[0] == b and n[1] == g and n[2] == r:
                    return i
            return -1

        def learn(self):
            biasRadius = self.INITBIASRADIUS
            alphadec = 30 + ((self.samplefac - 1) / 3)
            lengthcount = self.pixels.size
            samplepixels = lengthcount / self.samplefac
            delta = samplepixels / self.NCYCLES
            alpha = self.INITALPHA

            i = 0
            rad = biasRadius >> self.RADIUSBIASSHIFT
            if rad <= 1:
                rad = 0

            print(
                "Beginning 1D learning: samplepixels = %1.2f  rad = %i"
                % (samplepixels, rad)
            )
            step = 0
            pos = 0
            if lengthcount % NeuQuant.PRIME1 != 0:
                step = NeuQuant.PRIME1
            elif lengthcount % NeuQuant.PRIME2 != 0:
                step = NeuQuant.PRIME2
            elif lengthcount % NeuQuant.PRIME3 != 0:
                step = NeuQuant.PRIME3
            else:
                step = NeuQuant.PRIME4

            i = 0
            printed_string = ""
            while i < samplepixels:
                if i % 100 == 99:
                    tmp = "\b" * len(printed_string)
                    printed_string = str((i + 1) * 100 / samplepixels) + "%\n"
                    print(tmp + printed_string)
                p = self.pixels[pos]
                r = (p >> 16) & 0xFF
                g = (p >> 8) & 0xFF
                b = (p) & 0xFF

                if i == 0:  # Remember background colour
                    self.network[self.BGCOLOR] = [b, g, r]

                j = self.specialFind(b, g, r)
                if j < 0:
                    j = self.contest(b, g, r)

                if j >= self.SPECIALS:  # Don't learn for specials
                    a = (1.0 * alpha) / self.INITALPHA
                    self.altersingle(a, j, b, g, r)
                    if rad > 0:
                        self.alterneigh(a, rad, j, b, g, r)

                pos = (pos + step) % lengthcount

                i += 1
                if i % delta == 0:
                    alpha -= alpha / alphadec
                    biasRadius -= biasRadius / self.RADIUSDEC
                    rad = biasRadius >> self.RADIUSBIASSHIFT
                    if rad <= 1:
                        rad = 0

            finalAlpha = (1.0 * alpha) / self.INITALPHA
            print("Finished 1D learning: final alpha = %1.2f!" % finalAlpha)

        def fix(self):
            for i in range(self.NETSIZE):
                for j in range(3):
                    x = int(0.5 + self.network[i, j])
                    x = max(0, x)
                    x = min(255, x)
                    self.colormap[i, j] = x
                self.colormap[i, 3] = i

        def inxbuild(self):
            previouscol = 0
            startpos = 0
            for i in range(self.NETSIZE):
                p = self.colormap[i]
                q = None
                smallpos = i
                smallval = p[1]  # Index on g
                # Find smallest in i..self.NETSIZE-1
                for j in range(i + 1, self.NETSIZE):
                    q = self.colormap[j]
                    if q[1] < smallval:  # Index on g
                        smallpos = j
                        smallval = q[1]  # Index on g

                q = self.colormap[smallpos]
                # Swap p (i) and q (smallpos) entries
                if i != smallpos:
                    p[:], q[:] = q, p.copy()

                # smallval entry is now in position i
                if smallval != previouscol:
                    self.netindex[previouscol] = (startpos + i) >> 1
                    for j in range(previouscol + 1, smallval):
                        self.netindex[j] = i
                    previouscol = smallval
                    startpos = i
            self.netindex[previouscol] = (startpos + self.MAXNETPOS) >> 1
            for j in range(previouscol + 1, 256):  # Really 256
                self.netindex[j] = self.MAXNETPOS

        def paletteImage(self):
            """PIL weird interface for making a paletted image: create an image
            which already has the palette, and use that in Image.quantize. This
            function returns this palette image."""
            if self.pimage is None:
                palette = []
                for i in range(self.NETSIZE):
                    palette.extend(self.colormap[i][:3])

                palette.extend([0] * (256 - self.NETSIZE) * 3)

                # a palette image to use for quant
                self.pimage = Image.new("P", (1, 1), 0)
                self.pimage.putpalette(palette)
            return self.pimage

        def quantize(self, image):
            """Use a kdtree to quickly find the closest palette colors for the
            pixels

            :param image:
            """
            if get_cKDTree():
                return self.quantize_with_scipy(image)
            else:
                print("Scipy not available, falling back to slower version.")
                return self.quantize_without_scipy(image)

        def quantize_with_scipy(self, image):
            w, h = image.size
            px = np.asarray(image).copy()
            px2 = px[:, :, :3].reshape((w * h, 3))

            cKDTree = get_cKDTree()
            kdtree = cKDTree(self.colormap[:, :3], leafsize=10)
            result = kdtree.query(px2)
            colorindex = result[1]
            print("Distance: %1.2f" % (result[0].sum() / (w * h)))
            px2[:] = self.colormap[colorindex, :3]

            return Image.fromarray(px).convert("RGB").quantize(palette=self.paletteImage())

        def quantize_without_scipy(self, image):
            """ " This function can be used if no scipy is available.
            It's 7 times slower though.

            :param image:
            """
            w, h = image.size
            px = np.asarray(image).copy()
            memo = {}
            for j in range(w):
                for i in range(h):
                    key = (px[i, j, 0], px[i, j, 1], px[i, j, 2])
                    try:
                        val = memo[key]
                    except KeyError:
                        val = self.convert(*key)
                        memo[key] = val
                    px[i, j, 0], px[i, j, 1], px[i, j, 2] = val
            return Image.fromarray(px).convert("RGB").quantize(palette=self.paletteImage())

        def convert(self, *color):
            i = self.inxsearch(*color)
            return self.colormap[i, :3]

        def inxsearch(self, r, g, b):
            """Search for BGR values 0..255 and return colour index"""
            dists = self.colormap[:, :3] - np.array([r, g, b])
            a = np.argmin((dists * dists).sum(1))
            return a

    if __name__ == "__main__":
        im = np.zeros((200, 200), dtype=np.uint8)
        im[10:30, :] = 100
        im[:, 80:120] = 255
        im[-50:-40, :] = 50

        images = [im * 1.0, im * 0.8, im * 0.6, im * 0.4, im * 0]
        writeGif("lala3.gif", images, duration=0.5, dither=0)

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