#######################################################################
#
#         Copyright 2009-2011 by Ullrich Koethe
#
#    This file is part of the VIGRA computer vision library.
#    The VIGRA Website is
#        http://hci.iwr.uni-heidelberg.de/vigra/
#    Please direct questions, bug reports, and contributions to
#        ullrich.koethe@iwr.uni-heidelberg.de    or
#        vigra@informatik.uni-hamburg.de
#
#    Permission is hereby granted, free of charge, to any person
#    obtaining a copy of this software and associated documentation
#    files (the "Software"), to deal in the Software without
#    restriction, including without limitation the rights to use,
#    copy, modify, merge, publish, distribute, sublicense, and/or
#    sell copies of the Software, and to permit persons to whom the
#    Software is furnished to do so, subject to the following
#    conditions:
#
#    The above copyright notice and this permission notice shall be
#    included in all copies or substantial portions of the
#    Software.
#
#    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND
#    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
#    OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
#    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
#    HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
#    WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
#    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
#    OTHER DEALINGS IN THE SOFTWARE.
#
#######################################################################
from functools import reduce

import sys
import copy
import numpy

from . import ufunc
import vigra.vigranumpycore as vigranumpycore

from vigra.vigranumpycore import AxisType, AxisInfo, AxisTags

from collections.abc import Iterable

numpyHasPtp = numpy.__version__.startswith(("1.", "2.0.", "2.1.", "2.2.", "2.3."))

def _preserve_doc(f):
    npy_doc = eval('numpy.ndarray.%s.__doc__' % f.__name__)
    f.__doc__ =  ("" if npy_doc is None else npy_doc) + \
                 ("" if f.__doc__ is None else "\n" + f.__doc__)
    return f

# a decorator to finalize the return value of a
# dimension-reducing function (e.g. array.max())
def _finalize_reduce_result(f):
    def new_f(self, axis=None, out=None):
        if type(axis) == str:
            axis = self.axistags.index(axis)
        res = f(self, axis, out)
        if out is None:
            if axis is not None:
                res.axistags = self._copy_axistags()
                del res.axistags[axis]
            else:
                # this 'else' is necessary because numpy 1.6.0 gives
                #     type(res) == type(self)
                # instead of the desired
                #     type(res) == self.dtype
                # when res is scalar and self is a subclass of ndarray
                # (this is probably a bug in numpy, since it works correctly
                #  when self is a plain ndarray)
                res = res.dtype.type(res)
        return res
    new_f.__doc__ = f.__doc__
    return new_f

def _numpyarray_overloaded_function(f, self, axis=None, dtype=None, out=None):
    if type(axis) == str:
        axis = self.axistags.index(axis)
    if axis is None:
        return f(self.transposeToOrder('C').view(numpy.ndarray), dtype=dtype, out=out)
    else:
        res = f(self.view(numpy.ndarray), axis, dtype, out)
        if out is None:
            res = res.view(VigraArray)
            res.axistags = self._copy_axistags()
            del res.axistags[axis]
        return res

class classproperty:
    def __get__(self, instance, cls):
            if self.__instance_method is not None and instance is not None:
                return self.__instance_method(instance)
            else:
                return self.__class_method(cls)
    def __init__(self, class_method, instance_method=None):
            self.__class_method = class_method
            self.__instance_method = instance_method

def newaxis(axisinfo=AxisInfo()):
    '''
    Create a new singleton axis via the indexing operator. This works similar to
    `numpy.newaxis`, but allows to provide an AxisInfo object for the new axis.
    For example::

        >>> s = vigra.ScalarImage((width, height))
        >>> s.axistags  # no channel axis
        x y
        >>> t = s[..., numpy.newaxis]
        >>> t.axistags  # with unknown axis type
        x y ?
        >>> t = s[..., vigra.newaxis(vigra.AxisInfo.c)]
        >>> t.axistags  # with channel axis
        x y c
    '''
    if isinstance(axisinfo, str):
        return eval('AxisInfo.'+axisinfo)
    else:
        return axisinfo

def makeAxistags(spec, order=None, noChannels=None):
    '''
    Create a new :class:`~vigra.AxisTags` object from the specification ``spec``.
    ``spec`` can be one of the following:

    * an instance of the ``AxisTags`` class. In this case, the function creates
      a copy of ``spec``. If ``order`` is given, the resulting axistags are
      transposed to the desired order ('C', 'F', or 'V'). If ``noChannels=True``,
      the channel axis (if any) is dropped from the specification.

    * a string or tuple of axis keys (e.g. ``'xyc'`` or ``('x', 'y', 'c')`` respectively)
      or a tuple of :class:`~vigra.AxisInfo` objects (e.g.
      ``(AxisInfo.x, AxisInfo.y, AxisInfo.c)``). The function then constructs a
      new ``AxisTags`` object from this specification. If ``order`` is given,
      the resulting axistags are transposed to the desired order ('C', 'F', or 'V').
      If ``noChannels=True``, the channel axis (if any) is dropped from the specification.

    * an integer signifying the desired number of axes. In this case, the call (including
      optional arguments ``order`` and ``noChannels``) is forwarded to the function
      :meth:`~vigra.VigraArray.defaultAxistags`, whose output is returned.
    '''
    if isinstance(spec, int):
        return VigraArray.defaultAxistags(spec, order=order, noChannels=noChannels)

    if isinstance(spec, AxisTags):
        res = copy.copy(spec)
    else:
        tags = [k if isinstance(k, AxisInfo) else eval('AxisInfo.'+k) for k in spec]
        res = AxisTags(*tuple(tags))
    if order:
        res.transpose(res.permutationToOrder(order))
    if noChannels:
        res.dropChannelAxis()
    return res

def taggedView(array, axistags='', force=False, order=None, noChannels=False):
    '''
    Create a view to the given array with type :class:`~vigra.VigraArray` and
    desired axistags.

    You can either explicitly provide axistags to be imposed on the array
    (parameter ``axistags``), or a general description for the desired axis
    ordering (parameters ``order`` and ``noChannels``). It is an error to
    specify axistags and order simultaneously. In addition, the effect of
    ``taggedView()`` depends on whether ``array`` already has axistags or not.

    1. If ``array`` has no axistags or ``force=True`` (i.e. existing axistags
       shall be ignored) and neither the ``axistags`` nor the ``order`` parameters
       are given, the function acts as if ``order="C"`` was specified (case 2 below).

    2. If ``array`` has no axistags or ``force=True`` (i.e. existing axistags
       shall be ignored) and the ``order`` parameter is given, the function
       constructs appropriate axistags via :meth:`~vigra.VigraArray.defaultAxistags`::

       >>> view = array.view(VigraArray)
       >>> view.axistags = VigraArray.defaultAxistags(view.ndim, order, noChannels)

    3. If ``array`` has no axistags (or ``force=True``) and the ``axistags`` parameter
       is given, the function transforms this specification into an object of type
       :class:`~vigra.AxisTags` and attaches the result to the view::

       >>> view = array.view(VigraArray)
       >>> view.axistags = makeAxistags(axistags)

    4. If ``array`` has axistags (and ``force=False``) and the ``order`` parameter is
       given, the function transposes the array into the desired order::

       >>> view = array.transposeToOrder(order)
       >>> if noChannels:
       ...     view = view.dropChannelAxis()

    5. If ``array`` has axistags (and ``force=False``) and the ``axistags`` parameter
       is given, the function calls :meth:`~vigra.VigraArray.withAxes` to transforms
       the present axistags into the desired ones::

       >>> view = array.withAxes(axistags)

    The function raises a RuntimeError when the axistag specification is incompatible
    with the array.
    '''
    if axistags and order:
        raise RuntimeError("vigra.taggedView(): you cannot specify 'axistags' and 'order' at the same time.")
    if hasattr(array, 'axistags') and not force:
        if not axistags:
            array = array.transposeToOrder(order)
            if noChannels:
                array = array.dropChannelAxis()
        else:
            array = array.withAxes(axistags)
    else:
        if not axistags:
            if not order:
                order = 'C'
            axistags = VigraArray.defaultAxistags(array.ndim, order, noChannels)
        else:
            axistags = makeAxistags(axistags)
        if array.ndim != len(axistags):
            raise RuntimeError('vigra.taggedView(): array.ndim must match len(axistags).')
        array = array.view(VigraArray)
        array.axistags = axistags
    return array

def dropChannelAxis(array):
    '''
    Return the view created by ``array.``:meth:`~vigra.VigraArray.dropChannelAxis` if
    the given array supports that function, or return ``array`` unchanged otherwise.
    '''
    try:
        return array.dropChannelAxis()
    except:
        return array

# FIXME: This is a workaround for the disabled C++ function for the same purpose.
#        Enable the C++ version when boost 1.41 is available on all relevant platforms.
def _AxisTags_fromJSON(json_rep):
    '''
        Construct a new AxisTags object from the given JSON representation.
        This is mainly used to reconstruct arrays from HDF5 datasets with
        a suitable axistags attribute (see :func:`~vigra.impex.readHDF5`).
    '''
    tag_dict = eval(json_rep)
    tag_list = []
    for tags in tag_dict['axes']:
        tags['typeFlags'] = AxisType(tags['typeFlags'])
        tag_list.append(AxisInfo(**tags))
    return AxisTags(tag_list)

def _AxisTags__reduce__(self):
    '''
        enable pickling of AxisTags
    '''
    return _AxisTags_fromJSON, (self.toJSON(),)

AxisTags.__reduce__ = _AxisTags__reduce__
AxisTags.fromJSON = staticmethod(_AxisTags_fromJSON)
AxisTags.fromJSON.__doc__ = _AxisTags_fromJSON.__doc__

# How to construct a VigraArray
#
# case 1: from shape and order or axistags
# conventions: - shape has explicit channel axis
#              - 'A' order defaults to 'V' order
#              - order implies axistags and vice versa, you cannot provide both
# * look up the array type. If it is a plain ndarray, skip axistags
# * construct array according to order, optionally init with a constant
# * create and assign normalized axistags, if not explicitly given
# * optionally remove a singleton channel dimension (while we know where it is)
# * permute the array by the inverse normalization
# * assign axistags, if explicitly given (check compatibility)
#
# case 2: from another array
# * if taget order is 'A' or source and target order are equal, copy as is (including axistags)
# * otherwise, normalize the shape according to target order and
#   remember the normalizing permutation
# * construct array in normalized order
# * permute the array by the inverse normalization
# * copy original data and axistags

_constructArrayFromAxistags = vigranumpycore.constructArrayFromAxistags

def _constructArrayFromOrder(cls, shape, dtype, order, init):
    axistags = VigraArray.defaultAxistags(len(shape), order)
    if hasattr(dtype, "type"):
        dtype = dtype.type
    return _constructArrayFromAxistags(cls, shape, dtype, axistags, init)

def _constructArrayFromArray(cls, obj, dtype, order, init, axistags):
    if order is None:
        order = 'A'
    if order == 'A':
        # we cannot use ndarray.copy('A') here, because this only preserves 'C' and 'F'
        # order, whereas any other order is silently transformed into 'C'

        # we must also make sure that a singleton channel index has the smallest stride
        # (otherwise, strides in the copy may not exactly match those in obj)
        strides = list(obj.strides)
        try:
            channelIndex = obj.channelIndex
            if channelIndex < obj.ndim and obj.shape[channelIndex] == 1:
                strides[channelIndex] = 0
        except:
            pass
        permutation = list(numpy.array(strides).argsort())
        norm_shape = tuple(numpy.array(obj.shape)[permutation])
        inverse_permutation = list(numpy.array(permutation).argsort())
        array = numpy.ndarray.__new__(cls, norm_shape, dtype, order='F')
        array = array.transpose(inverse_permutation)
    else:
        array = _constructArrayFromOrder(cls, obj.shape, dtype, order, False)

    if init:
        array[...] = obj
    if cls is not numpy.ndarray:
        if axistags is not None:
            array.axistags = axistags
        elif hasattr(array, 'axistags'):
            del array.axistags
    return array

def _constructArrayFromPickle(_arraypickle, _permutation, _axistags):
    reconstructionFunction = _arraypickle[0]
    reconstructionArgs = _arraypickle[1]
    array = reconstructionFunction(*reconstructionArgs)
    array.__setstate__(_arraypickle[2])
    array = array.transpose(_permutation)
    array.axistags = AxisTags.fromJSON(_axistags)
    return array

def _constructArrayFromZMQSocket(socket, flags=0, copy=True, track=False):
    metadata = socket.recv_json(flags=flags)
    axistags = AxisTags.fromJSON(socket.recv(flags=flags))
    data = memoryview(socket.recv(flags=flags, copy=copy, track=track))
    array = numpy.frombuffer(data, dtype=metadata['dtype']).reshape(metadata['shape'])
    array = taggedView(array.transpose(metadata['permutation']), axistags)
    return array

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

class VigraArray(numpy.ndarray):
    '''
    This class extends numpy.ndarray with the concept of **axistags**
    which encode the semantics of the array's axes. VigraArray overrides all
    numpy.ndarray methods in order to handle axistags in a sensible way.
    In particular, operations acting on two arrays simultaneously (e.g.
    addition) will first transpose the arguments such that their axis
    ordering matches.

    Constructor:

    .. method:: VigraArray(obj, dtype=numpy.float32, order=None, init=True, value=None, axistags=None)

        :param obj: an array or shape object (see below)
        :param dtype: desired element type
        :param order: desired memory layout (see below)
        :param init: True: initialize the image with zeros; False: do not
                     initialize the image
        :type init: boolean
        :param value: initialize the image with this value (overrides init)
        :type value: convertible to dtype
        :param axistags: the AxisTags object of the new array. The length of
                         axistags must match the array's shape. It axistags=None,
                         obj.axistags is used if it exists. Otherwise, a new
                         axistags object is created by a call to
                         :meth:`~vigra.VigraArray.defaultAxistags`.

        **obj** may be one of the following

        * If obj is a numpy.ndarray or a subtype, a copy of obj with the given
          dtype, order and resulting class VigraArray is created. If obj.axistags
          exists, the new array will have these axistags as well, unless new
          axistags are explicitly passed to the constructor.
        * If obj is a sequence, it is interpreted as a shape.
        * Otherwise, or if shape and axistags are incompatible, an exception
          is raised.

        **order** can be 'C' (C order), 'F' (Fortran order), 'V' (VIGRA
        order), 'A' (any), or None. This parameter controls the order of strides
        and axistags (unless axistags are explicit passed into the constructor).
        See the :ref:`order definitions <array-order-parameter>` for details. If
        'order=None', the order is determined by :attr:`VigraArray.defaultOrder`.
    '''

    ###############################################################
    #                                                             #
    #       a number of helper functions related to axistags      #
    #                                                             #
    ###############################################################

    # a number of helper functions related to axistags

    # IMPORTANT: do not remove or rename this function, it is called from C++
    @classproperty
    def defaultOrder(cls):
        '''
        Get the default axis ordering, currently 'V' (VIGRA order)
        '''
        return 'V'

    # IMPORTANT: do not remove or rename this function, it is called from C++
    @staticmethod
    def defaultAxistags(tagSpec, order=None, noChannels=False):
        '''
        Get default axistags for the given specification 'tagSpec'. TagSpec can be the
        number of dimensions of the array (``array.ndim``, must be <= 5) or a string
        containing a sequence of axis keys (only the default keys 'x', 'y', 'z', 't',
        and 'c' are currently supported). The 'order' parameter determines the axis
        ordering, see the :ref:`order definitions <array-order-parameter>` for details.
        If 'noChannels' is True, there will be no channel axis. Examples::

            >>> vigra.VigraArray.defaultAxistags(3)
            x y c
            >>> vigra.VigraArray.defaultAxistags(4)
            x y z c
            >>> vigra.VigraArray.defaultAxistags(5)
            x y z t c
            >>> vigra.VigraArray.defaultAxistags(3, order='C')
            y x c
            >>> vigra.VigraArray.defaultAxistags(2, noChannels=True)
            x y
            >>> vigra.VigraArray.defaultAxistags(3, noChannels=True)
            x y z
            >>> vigra.VigraArray.defaultAxistags(4, noChannels=True)
            x y z t
            >>> vigra.VigraArray.defaultAxistags('xty')
            x t y
            >>> vigra.VigraArray.defaultAxistags('xty', order='V')
            x y t
        '''
        if type(tagSpec) == str:
            taglist = [eval('AxisInfo.' + k) for k in tagSpec]
        else:
            start = 1 if noChannels else 0
            end = start + tagSpec
            taglist = [AxisInfo.c, AxisInfo.x, AxisInfo.y, AxisInfo.z, AxisInfo.t][start:end]
            if order is None or order == 'A':
                order = VigraArray.defaultOrder
        tags = AxisTags(taglist)
        if order is not None:
            tags.transpose(tags.permutationToOrder(order))
        return tags

    # IMPORTANT: do not remove or rename this function, it is called from C++
    @staticmethod
    def _copyValuesImpl(target, source):
        try:
            target = target.squeeze()
            target = target.transposeToNumpyOrder()
        except:
            pass

        try:
            source = source.squeeze()
            source = source.transposeToNumpyOrder()
        except:
            pass

        try:
            compatible = source.axistags.compatible(target.axistags)
        except:
            compatible = True

        if not compatible:
            raise RuntimeError("VigraArray._copyValuesImpl(): incompatible axistags")

        target[...] = source

    # IMPORTANT: do not remove or rename this function, it is called from C++
    @staticmethod
    def _empty_axistags(ndim):
        '''Create an axistags object with non-informative entries.
           That is, all axisinfo objects are '?'.
        '''
        return AxisTags(ndim)

    def _copy_axistags(self):
        '''Create a copy of 'self.axistags'. If the array doesn't have axistags, _empty_axistags()
           will be returned.
        '''
        return copy.copy(getattr(self, 'axistags', self._empty_axistags(self.ndim)))

    def _transform_axistags(self, index):
        if hasattr(self, 'axistags'):
            return self.axistags.transform(index, self.ndim)
        else:
            return self._empty_axistags(self.ndim)

    def _transpose_axistags(self, *permutation):
        '''Create a copy of self.axistags with transposed entries.
        '''
        if hasattr(self, 'axistags'):
            res = copy.copy(self.axistags)
            try:
                len(permutation[0])
                res.transpose(permutation[0])
            except:
                res.transpose(permutation)
            return res
        else:
            return self._empty_axistags(self.ndim)

    ###############################################################
    #                                                             #
    #                   standard array functions                  #
    #                                                             #
    ###############################################################

    def __new__(cls, obj, dtype=numpy.float32, order=None, init=True, value=None, axistags=None):
        if value is not None:
            init = False
        if isinstance(obj, numpy.ndarray):
            if axistags is None:
                if hasattr(obj, 'axistags'):
                    axistags = copy.copy(obj.axistags)
                else:
                    raise RuntimeError("VigraArray(): axistags must be given when constructing from plain array.")
            elif obj.ndim != len(axistags):
                raise RuntimeError("VigraArray(): axistags have wrong length.")
            if order is None:
                res = _constructArrayFromAxistags(cls, obj.shape, dtype, axistags, init)
                if init:
                    res[...] = obj
            else:
                res = _constructArrayFromArray(cls, obj, dtype, order, init, axistags)
        else:
            if axistags is None:
                if order is None:
                    order = VigraArray.defaultOrder
            elif len(axistags) != len(obj):
                raise RuntimeError("VigraArray(): axistags have wrong length.")
            if order is None:
                res = _constructArrayFromAxistags(cls, obj, dtype, axistags, init)
            else:
                res = _constructArrayFromOrder(cls, obj, dtype, order, init)
                if cls is not numpy.ndarray and axistags is not None:
                    res.axistags = axistags
        if value is not None:
            res.fill(value)
        return res

    __array_priority__ = 15.0

    def __array_finalize__(self, obj):
        if hasattr(obj, 'axistags'):
            self.axistags = obj.axistags

    def __copy__(self, order='A'):
        result = numpy.ndarray.__copy__(self, order)
        result.axistags = result._copy_axistags()
        return result

    @_preserve_doc
    def __deepcopy__(self, memo):
        # numpy.ndarray.__deepcopy__ always creates C-order arrays =>
        #   transpose self accordingly, and transpose back after the copy
        result = numpy.ndarray.__deepcopy__(self.transposeToNumpyOrder(), memo)
        result = result.transpose(self.permutationFromNumpyOrder())
        memo[id(self)] = result
        result.__dict__ = copy.deepcopy(self.__dict__, memo)
        return result

    def __repr__(self):
        return "%s(shape=%s, axistags=%s, dtype=%s, data=\n%s)" % \
          (self.__class__.__name__, str(self.shape), repr(self.axistags), str(self.dtype), str(self))

    def __str__(self):
        try:
            self = self.transposeToVigraOrder().transpose()
        except:
            pass
        return str(self.view(numpy.ndarray))

    def __reduce__(self):
        '''
            Enable pickling of a VigraArray, including axistags. The stride ordering
            will be preserved in the unpickled array. Note that user-defined attributes
            will not be saved and restored.
        '''
        # since the stride ordering is not necessarily preserved by ndarray's pickling
        # functions, we need to normalize stride ordering, and permute to the original
        # ordering upon reconstruction
        pickled = numpy.ndarray.__reduce__(self.transposeToNumpyOrder())
        return _constructArrayFromPickle, (pickled, self.permutationFromNumpyOrder(), self.axistags.toJSON())

    @staticmethod
    def receiveSocket(socket, flags=0, copy=True, track=False):
        '''
        Reconstruct an array that has been transferred via a ZMQ socket by a call to
        VigraArray.sendSocket(). This only works when the 'zmq' module is available.
        The meaning of the arguments is described in zmq.Socket.recv().
        '''
        return _constructArrayFromZMQSocket(socket, flags, copy, track)


    ###############################################################
    #                                                             #
    #                     array I/O and display                   #
    #                                                             #
    ###############################################################

    def writeImage(self, filename, dtype = '', compression = '', mode='w'):
        '''Write an image to a file.
        Consult :func:`vigra.impex.writeImage` for detailed documentation'''
        import vigra.impex

        ndim = self.ndim
        if self.channelIndex < ndim:
            ndim -= 1
        if ndim != 2:
            raise RuntimeError("VigraArray.writeImage(): array must have 2 non-channel axes.")

        vigra.impex.writeImage(self, filename, dtype, compression, mode)

    def writeSlices(self, filename_base, filename_ext, dtype = '', compression = ''):
        '''Write a volume to a sequence of files.
        Consult :func:`vigra.impex.writeVolume` for detailed documentation.
        '''
        import vigra.impex

        ndim = self.ndim
        if self.channelIndex < ndim:
            ndim -= 1
        if ndim != 3:
            raise RuntimeError("VigraArray.writeSlices(): array must have 3 non-channel axes.")

        vigra.impex.writeVolume(self, filename_base, filename_ext, dtype, compression)

    def writeHDF5(self, filenameOurGroup, pathInFile):
        '''Write the array to a HDF5 file.
           This is just a shortcut for :func:`vigra.impex.writeHDF5`
        '''
        import vigra.impex

        vigra.impex.writeHDF5(self, filenameOurGroup, pathInFile)

    def sendSocket(self, socket, flags=0, copy=True, track=False):
        '''
        Send array and metadata over a ZMQ socket. Only works if the 'zmq' module is available.
        The meaning of the arguments is described in zmq.Socket.send().
        '''
        import zmq

        transposed = self.transposeToNumpyOrder().view(numpy.ndarray)
        metadata = dict(
            dtype = str(transposed.dtype),
            shape = transposed.shape,
            permutation = self.permutationFromNumpyOrder()
        )
        socket.send_json(metadata, flags|zmq.SNDMORE)
        socket.send(self.axistags.toJSON().encode('ascii'), flags|zmq.SNDMORE)
        return socket.send(transposed, flags, copy=copy, track=track)

    def imshow(self):
        '''
        Shorthand for 'vigra.imshow(self)'.
        '''
        import vigra
        return vigra.imshow(self)

    def show(self, normalize=True):
        '''
        Display this image in a vigra.pyqt.ImageWindow.

        The channels are intepreted as follows: 1 channel = gray image,
        2 channels = gray + alpha, 3 channels = RGB, 4 channels = RGB + alpha.

        The parameter `normalize` can be used to normalize an image's
        value range to 0..255:

        `normalize` = (nmin, nmax):
          scale & clip image values from nmin..nmax to 0..255

        `normalize` = nmax:
          lets nmin default to zero, i.e. scale & clip the range 0..nmax
          to 0..255

        `normalize` = True: (default)
          scale the image's actual range min()..max() to 0..255

        `normalize` = False:
          don't scale the image's values

        '''
        from pyqt.imagewindow import showImage

        ndim = self.ndim
        channelIndex = self.channelIndex
        if channelIndex < ndim:
            if self.channels > 4:
                raise RuntimeError("VigraArray.show(): array can have at most 4 channels.")
            ndim -= 1
        if ndim != 2:
            raise RuntimeError("VigraArray.show(): array must have 2 non-channel axes.")

        return showImage(self.transposeToVigraOrder(), normalize)

    def qimage(self, normalize=True):
        '''
        Convert this image to a Qt QImage (mainly for display purposes).
        The present image must have 1, 2, 3, or 4 channels, and the resulting
        QImage will have QImage.Format_Indexed8 iff there was only one
        channel and QImage.Format_[A]RGB32 otherwise (with the last of
        2/4 channels being used as alpha channel).

        The parameter `normalize` can be used to normalize an image's
        value range to 0..255:

        `normalize` = (nmin, nmax):
          scale & clip image values from nmin..nmax to 0..255

        `normalize` = nmax:
          lets nmin default to zero, i.e. scale & clip the range 0..nmax
          to 0..255

        `normalize` = True: (default)
          scale the image's actual range min()..max() to 0..255

        `normalize` = False:
          don't scale the image's values

        '''
        try:
            import qimage2ndarray
        except Exception as e:
            from vigra import _fallbackModule
            _fallbackModule('qimage2ndarray',
            '''
            %s

            If qimage2ndarray is missing on your system, download it from
            http://pypi.python.org/pypi/qimage2ndarray/.''' % str(e))
            import qimage2ndarray

        ndim = self.ndim
        if self.channelIndex < ndim:
            ndim -= 1
        if ndim != 2:
            raise RuntimeError("VigraArray.qimage(): array must have 2 non-channel axes.")

        yxImage = self.transposeToNumpyOrder()

        if self.channels == 1:
            q = qimage2ndarray.gray2qimage(yxImage.dropChannelAxis(), normalize)
        else:
            q = qimage2ndarray.array2qimage(yxImage, normalize)

        return q

    def asRGB(self, normalize=True):
        '''
        Expand a scalar array (i.e. an array with a single channel) into an RGB array with
        three identical color channels. This is useful when you want to paste color
        annotations (e.g. user labels) into the array.

        The parameter `normalize` can be used to normalize the array's
        value range to 0..255:

        `normalize` = (nmin, nmax):
          scale & clip array values from nmin..nmax to 0..255

        `normalize` = True: (default)
          scale the array's actual range min()..max() to 0..255

        `normalize` = False:
          don't scale the array's values

        '''
        if self.channels != 1:
            raise RuntimeError("VigraArray.asRGB(): array must have a single channel.")
        img = self.dropChannelAxis()
        shape = img.shape + (3,)
        axistags = copy.copy(img.axistags)
        axistags.append(AxisInfo.c)
        res = VigraArray(shape, axistags=axistags)
        if normalize:
            try:
                m, M = normalize
                clip = True
            except:
                m, M = img.min(), img.max()
                clip = False
            if m == M:
                return res
            f = 255.0 / (M - m)
            img = f * (img - m)
            if clip:
                img = numpy.minimum(255.0, numpy.maximum(0.0, img))
        res[...,0] = img
        res[...,1] = img
        res[...,2] = img
        return res

    ###############################################################
    #                                                             #
    #           new functionality enabled by axistags             #
    #                                                             #
    ###############################################################

    def copyValues(self, other):
        '''
        Copy the values of an array to another one. This is similar to::

            self[...] = other

        but will first transpose both arrays so that axistags are aligned. If
        there is no valid alignment, RuntimeError will be raised.
        '''
        self._copyValuesImpl(self, other)

    # IMPORTANT: do not remove or rename this property, it is called from C++
    @property
    def channelIndex(self):
        '''
        The index of the channel axis according to the axistags.
        For example, when axistags are 'x y c', the channel index is 2.
        If the axistags contain no channel axis, self.ndim is returned.
        '''
        return self.axistags.channelIndex

    # IMPORTANT: do not remove or rename this property, it is called from C++
    @property
    def innerNonchannelIndex(self):
        '''
        The index of the innermost non-channel axis according to the axistags.
        The innermost axis is determined by the AxisInfo sorting rules (see
        the :ref:`order definitions <array-order-parameter>` for details).
        For example, when axistags are 'x y c', the innerNonchannelIndex is 0.
        '''
        return self.axistags.innerNonchannelIndex

    @property
    def channels(self):
        '''
        The number of channels in this array (shape of the 'c' axis).
        If the axistags contain no channel axis, the number of channels is implicitly 1.
        '''
        i = self.channelIndex
        if i < self.ndim:
            return self.shape[i]
        else:
            return 1

    @property
    def width(self):
        '''
        The width of the array (shape of the 'x' axis).
        If the axistags contain no 'x' axis, RuntimeError will be raised.
        '''
        i = self.axistags.index('x')
        if i < self.ndim:
            return self.shape[i]
        else:
            raise RuntimeError("VigraArray.width(): axistag 'x' does not exist.")

    @property
    def height(self):
        '''
        The height of the array (shape of the 'y' axis).
        If the axistags contain no 'y' axis, RuntimeError will be raised.
        '''
        i = self.axistags.index('y')
        if i < self.ndim:
            return self.shape[i]
        else:
            raise RuntimeError("VigraArray.height(): axistag 'y' does not exist.")

    @property
    def depth(self):
        '''
        The depth of the array (shape of the 'z' axis).
        If the axistags contain no 'z' axis, RuntimeError will be raised.
        '''
        i = self.axistags.index('z')
        if i < self.ndim:
            return self.shape[i]
        else:
            raise RuntimeError("VigraArray.depth(): axistag 'z' does not exist.")

    @property
    def duration(self):
        '''
        The number of time steps in the array (shape of the 't' axis).
        If the axistags contain no 't' axis, RuntimeError will be raised.
        '''
        i = self.axistags.index('t')
        if i < self.ndim:
            return self.shape[i]
        else:
            raise RuntimeError("VigraArray.duration(): axistag 't' does not exist.")

    @property
    def spatialDimensions(self):
        '''
        The number of spatial axes in the array.
        That is, the number of entries in the axistags where the flag 'AxisType.Space'
        is set.
        '''
        return self.axistags.axisTypeCount(AxisType.Space)

    def iterImpl(self, type):
        axes = [k for k in range(self.ndim) if self.axistags[k].isType(type)]
        if axes:
            axes.sort(key=lambda x: self.axistags[x], reverse=True)
            slices = [slice(None)]*self.ndim
            for point in numpy.ndindex(*(self.shape[k] for k in axes)):
                for j in range(len(point)):
                    slices[axes[j]] = point[j]
                yield self[tuple(slices)]
        else:
            yield self

    def channelIter(self):
        '''
        Create an iterator over the channels of the array.
        In each iteration, you get the array corresponding to a single channel.
        If the axistags contain no channel axis, there is only one iteration
        which yields the entire array. Example::

            >>> rgb = vigra.RGBImage((200, 100))
            >>> rgb.axistags
            x y c
            >>> red, green, blue = rgb.channelIter()
            >>> red.axistags
            x y
            >>> red.shape
            (200, 100)
        '''
        return self.iterImpl(AxisType.Channels)

    def spaceIter(self):
        '''
        Create an iterator over all the spatial coordinates in the array.
        In each iteration, you get the value corresponding to a single
        coordinate location. If the axistags contain no spatial axes,
        there is only one iteration which yields the entire array. Example::

            >>> s = vigra.ScalarImage((2,2))
            >>> s.ravel()[...] = range(4)
            >>> for p in s.spaceIter():
            ....    print(p)
            0.0
            1.0
            2.0
            3.0
        '''
        return self.iterImpl(AxisType.Space)

    def timeIter(self):
        '''
        Create an iterator over the time points of the array.
        In each iteration, you get the array corresponding to a single time point.
        If the axistags contain no time axis, there is only one iteration
        which yields the entire array. Example::

            >>> from vigra import *
            >>> axistags = AxisTags(AxisInfo.t, AxisInfo.x, AxisInfo.y)
            >>> timesteps, width, height = 2, 200, 100
            >>> image_sequence = Image((timesteps, width, height), axistags=axistags)
            >>> step1, step2 = image_sequence.timeIter()
        '''
        return self.iterImpl(AxisType.Time)

    def sliceIter(self, key='z'):
        '''
        Create an iterator over a single spatial axis of the array.
        In each iteration, you get the array corresponding to one coordinate
        along the axis given by 'key'. For example, to iterate along the z-axis
        to get all x-y-slices in turn, you write::

            >>> volume = vigra.Volume((width, height, depth))
            >>> for slice in volume.sliceIter('z'):
            ...     processSlice(slice)
        '''
        i = self.axistags.index(key)
        if i < self.ndim:
            if not self.axistags[i].isSpatial():
                raise RuntimeError("VigraArray.sliceIter(): %s is not a spatial axis." % key)
            for k in range(self.shape[i]):
                yield self.bindAxis(i, k)
        else:
            yield self

    def bindAxis(self, which, index=0):
        '''
        Bind the axis identified by 'which' to the given 'index'.
        This is similar to::

            array[:, index, ...]

        but you do not need to know the position of the axis when you use the
        axis key (according to axistags). For example, to get the green channel
        of an RGBImage, you write::

            >>> rgb = vigra.RGBImage((200, 100))
            >>> green = rgb.bindAxis('c', 1)

        This gives the correct result irrespective of the axis ordering.
        '''
        if type(which) == str:
            which = self.axistags.index(which)
        return self[(slice(None),)*which + (index,) + (slice(None),)*(self.ndim-which-1)]

    def dropChannelAxis(self, ignoreMultiChannel=False):
        '''
        Drop the channel axis when it is a singleton.
        This function is for easy transformation of an array shaped
        (width, height, 1) into (width, height). A RuntimeError
        is raised when there is more than one channel, unless ignoreMultiChannel=True,
        in which case 'self' is returned.
        '''
        ci = self.channelIndex
        if ci == self.ndim:
            return self

        if self.shape[ci] != 1:
            if ignoreMultiChannel:
                return self
            raise RuntimeError("dropChannelAxis(): only allowed when there is a single channel.")
        return self.bindAxis(ci, 0)

    def insertChannelAxis(self, order=None):
        '''
        Insert a singleton channel axis.
        This function is for easy transformation of an array shaped
        (width, height) into (width, height, 1). The 'order' parameter
        determines the position of the new axis: when order is 'F', it
        will become the first axis, otherwise it will become the last
        one. A RuntimeError is raised when the array already contains a
        channel axis.
        '''
        ci = self.channelIndex
        if ci != self.ndim:
            return self

        if order == 'F':
            res = self[numpy.newaxis,...]
            res.axistags[0] = AxisInfo.c
        else:
            res = self[..., numpy.newaxis]
            res.axistags[-1] = AxisInfo.c
        return res

    def noTags(self):
        '''
        Drop the axistags. This is a shorthand for ``array.view(numpy.ndarray)``.
        '''
        return self.view(numpy.ndarray)

    def withAxes(self, *axistags, **kw):
        '''
        This function creates a view whose axistags are standardized in a
        desired way. The standardization can be specified in two forms:

        1. Provide ``axistags`` explicitly in any format understood by
           :func:`vigra.makeAxistags`. The original axistags are then
           transposed into the given order. When the original array contains
           axes not listed in the new specification, these axes are dropped
           if they are singletons (otherwise, an exception is raised).
           If requested axes is not present in the original array,
           singleton axes are inserted at the appropriate positions, provided
           the axis keys are among the predefined standard keys ('x', 'y', 'z',
           't', 'c', 'n', 'e', 'fx', 'fy', 'fz', 'ft'). The function fails if
           the original array contains axes of unknown type (key '?')::

                >>> array.axistags
                x y c
                >>> array.shape
                (100, 50, 1)
                >>> view = array.withAxes('tzyx')
                >>> view.axistags
                t z y x
                >>> view.shape
                (1, 1, 50, 100)

        2. Provide keyword arguments ``order`` and (optionally) ``noChannels``.
           The array is then transposed into the desired order ('C', 'F', or 'V').
           If ``noChannels=True``, the channel axis is dropped if it is a
           singleton, otherwise an exception is raised::

                >>> array.axistags
                x y c
                >>> array.shape
                (100, 50, 1)
                >>> view = array.withAxes(order='F')
                >>> view.axistags
                c x y
                >>> view.shape
                (1, 100, 50)
                >>> view = array.withAxes(order='C', noChannels=True)
                >>> view.axistags
                y x
                >>> view.shape
                (50, 100)

        The parameters ``axistags`` and ``order`` cannot be specified simultaneously.
        '''
        if len(axistags) == 1:
            axistags = axistags[0]
        if axistags and kw.get('order'):
            raise RuntimeError("vigra.withAxes(): you cannot specify 'axistags' and 'order' at the same time.")
        if axistags:
            axistags = makeAxistags(axistags)
            if self.axistags.compatible(axistags):
                return self
            axisinfo = []
            slicing = [0]*self.ndim
            for tag in axistags:
                index = self.axistags.index(tag.key)
                if index < self.ndim:
                    axisinfo.append(self.axistags[index])
                    slicing[index] = slice(None)
                else:
                    axisinfo.append(tag)
                    slicing.append(axisinfo[-1])
            for k in range(self.ndim):
                if self.axistags[k].isType(AxisType.UnknownAxisType):
                    raise RuntimeError("VigraArray.withAxes(): array must not contain axes of unknown type (key '?').")
                if slicing[k] == 0 and self.shape[k] != 1:
                    raise RuntimeError("VigraArray.withAxes(): cannot drop non-singleton axis '%s'." % self.axistags[k].key)
            permutation = AxisTags(axisinfo).permutationFromNumpyOrder()
            res = self[tuple(slicing)].transposeToNumpyOrder().transpose(permutation)
        else:
            res = self.transposeToOrder(kw.get('order'))
            if kw.get('noChannels'):
                res = res.dropChannelAxis()
        return res

    def view5D(self, order='C'):
        '''
            Create a 5-dimensional view containing the standard tags
            'x', 'y', 'z', 't', 'c' in the desired 'order' (which can be
            'C', 'F', and 'V' with the usual meaning). If 'self' has an
            axis key that is not among the five admissible keys, an
            exception is raised. Axes missing in 'self' are added as
            singleton axes with the appropriate tags.
        '''
        stdTags = ['x', 'y', 'z', 't', 'c']
        for tag in self.axistags:
            try:
                del stdTags[stdTags.index(tag.key)]
            except:
                raise RuntimeError("VigraArray.view5D(): array contains unsuitable axis key '%s'." % tag.key)
        index = [Ellipsis] + [newaxis(eval('AxisInfo.' + k)) for k in stdTags]
        return self[tuple(index)].transposeToOrder(order)

    def permutationToOrder(self, order):
        '''Create the permutation that would transpose this array into
           an array view with the given order (where order can be 'A',
           'C', 'F', 'V' with the usual meaning).
        '''
        return list(self.axistags.permutationToOrder(order))

    def permutationToNormalOrder(self, types=AxisType.AllAxes):
        '''Create the permutation that would transpose this array to
           normal order (that is, from the current axis order into
           ascending order, e.g. 'x y c' into 'c x y').
           If 'types' is not 'AxisType.AllAxes', only the axes with the
           desired types are considered.
        '''
        return list(self.axistags.permutationToNormalOrder(types))

    def permutationFromNormalOrder(self):
        '''Create the permutation that would transpose an array that is
           in normal (ascending) order into the axis order of this array.
           (e.g. 'c x y' into 'x y c').
        '''
        return list(self.axistags.permutationFromNormalOrder())

    def permutationToNumpyOrder(self):
        '''Create the permutation that would transpose this array to
           numpy order (that is, from the current axis order into
           descending order, e.g. 'x y c' into 'y x c').
        '''
        return list(self.axistags.permutationToNumpyOrder())

    def permutationFromNumpyOrder(self):
        '''Create the permutation that would transpose an array that is
           in numpy (descending) order into the axis order of this array.
           (e.g.  'y x c' into 'x y c').
        '''
        return list(self.axistags.permutationFromNumpyOrder())

    def permutationToVigraOrder(self):
        '''Create the permutation that would transpose this array to
           VIGRA order (that is, from the current axis order into
           ascending spatial order, but with the channel axis at the
           last position, e.g. 'c x y' into 'x y c').
        '''
        return list(self.axistags.permutationToVigraOrder())

    def permutationFromVigraOrder(self):
        '''Create the permutation that would transpose an array that is
           in VIGRA order (ascending spatial order, but with the channel
           axis at the last position) into the axis order of this array.
           (e.g.  'x y c' into 'c x y').
        '''
        return list(self.axistags.permutationFromVigraOrder())

    def transposeToOrder(self, order):
        '''
        Get a transposed view onto this array according to the given 'order'.
        Possible orders are:

        'A' or '' or None:
            return the array unchanged
        'C':
            transpose to descending axis order (e.g. 'z y x c')
        'F':
            transpose to ascending axis order (e.g. 'c x y z')
        'V':
            transpose to VIGRA order, i.e. ascending spatial axes, but
            the channel axis is last (e.g. 'x y z c')
        '''
        if not order or order == 'A':
            return self
        permutation = self.permutationToOrder(order)
        return self.transpose(permutation)

    def transposeToDefaultOrder(self):
        '''Equivalent to self.transposeToOrder(VigraArray.defaultOrder).
        '''
        return self.transposeToOrder(VigraArray.defaultOrder)

    def transposeToNormalOrder(self):
        '''Equivalent to self.transposeToOrder('F').
        '''
        return self.transposeToOrder('F')

    def transposeToVigraOrder(self):
        '''Equivalent to self.transposeToOrder('V').
        '''
        return self.transposeToOrder('V')

    def transposeToNumpyOrder(self):
        '''Equivalent to self.transposeToOrder('C').
        '''
        return self.transposeToOrder('C')

    @property
    def T(self):
        '''
        Equivalent to self.transpose()
        '''
        return self.transpose()

    def __getitem__(self, index):
        '''
        ``array.__getitem__(index)`` implements the indexing operator ``array[index]``.
        In addition to the usual numpy.ndarray indexing functionality, this function
        also updates the axistags of the result array. There are three cases:

            * getitem creates a scalar value => no axistags are required
            * getitem creates an array view => axistags are transferred from the
              corresponding axes of the base array
            * getitem creates a copy of an array (fancy indexing) => all axistags are '?'

        If the index contains 'numpy.newaxis', a new singleton axis is inserted at the
        appropriate position, whose axisinfo is set to '?' (unknown). If the index contains
        'vigra.newaxis(axisinfo)', the singleton axis will get the given axisinfo.
        '''
        try:
            res = numpy.ndarray.__getitem__(self, index)
        except:
            if not isinstance(index, Iterable):
                raise
            #create temporary index without AxisInfor in order to use np.ndarray.__getitem__
            tmpindex = tuple(None if isinstance(x, AxisInfo) else x for x in index)
            res = numpy.ndarray.__getitem__(self, tmpindex)
        if res is not self and hasattr(res, 'axistags'):
            if res.base is self or res.base is self.base:
                res.axistags = res._transform_axistags(index)
            else:
                res.axistags = res._empty_axistags(res.ndim)
        return res

    def subarray(self, p1, p2=None):
        '''
        Construct a subarray view from a pair of points. The first point denotes the start
        of the subarray (inclusive), the second its end (exclusive). For example,

            a.subarray((1,2,3), (4,5,6))  # equivalent to a[1:4, 2:5, 3:6]

        The given points must have the same dimension, otherwise an IndexError is raised.
        If only one point is given, it refers to the subarray's end, and the start is set
        to the point (0, 0, ...) with appropriate dimension, for example

            a.subarray((4,5,6))           # equivalent to a[:4, :5, :6]

        The function transforms the given point pair into a tuple of slices and calls
        self.__getitem__() in it. If the points have lower dimension than the array, an
        Ellipsis ('...') is implicitly appended to the slicing, so that missing axes
        are left unaltered.
        '''
        if p2 is not None:
            if len(p1) != len(p2):
                raise IndexError('VigraArray.subarray(): points must have the same dimension.')
            return self.__getitem__(tuple(map(lambda x,y: slice(x.__int__(), y.__int__()), p1, p2)))
        else:
            return self.__getitem__(tuple(map(lambda x: slice(x.__int__()), p1)))

    ###############################################################
    #                                                             #
    #      re-implement ndarray methods to handle axistags        #
    #                                                             #
    ###############################################################

    @_finalize_reduce_result
    @_preserve_doc
    def all(self, axis=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        if type(axis) == str:
            axis = self.axistags.index(axis)
        return numpy.ndarray.all(self, axis, out)

    @_finalize_reduce_result
    @_preserve_doc
    def any(self, axis=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        if type(axis) == str:
            axis = self.axistags.index(axis)
        return numpy.ndarray.any(self, axis, out)

    @_finalize_reduce_result
    @_preserve_doc
    def argmax(self, axis=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        if type(axis) == str:
            axis = self.axistags.index(axis)
        return numpy.ndarray.argmax(self, axis, out)

    @_finalize_reduce_result
    @_preserve_doc
    def argmin(self, axis=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        if type(axis) == str:
            axis = self.axistags.index(axis)
        return numpy.ndarray.argmin(self, axis, out)

    @_preserve_doc
    def copy(self, order='A'):
        return self.__class__(self, dtype=self.dtype, order=order)

    @_preserve_doc
    def cumprod(self, axis=None, dtype=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        if type(axis) == str:
            axis = self.axistags.index(axis)
        res = numpy.ndarray.cumprod(self, axis, dtype, out)
        if axis is None and out is None:
            res.axistags = res._empty_axistags(res.ndim)
        return res

    @_preserve_doc
    def cumsum(self, axis=None, dtype=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        if type(axis) == str:
            axis = self.axistags.index(axis)
        res = numpy.ndarray.cumsum(self, axis, dtype, out)
        if axis is None and out is None:
            res.axistags = res._empty_axistags(res.ndim)
        return res

    @property
    def flat(self):
        '''
        The array is always transposed to 'C' order before flattening.
        '''
        return self.transposeToNumpyOrder().view(numpy.ndarray).flat

    @_preserve_doc
    def flatten(self, order='C'):
        '''
        The array is always transposed to 'C' order before flattening.
        '''
        res = self.transposeToNumpyOrder().view(numpy.ndarray).flatten(order)
        return taggedView(res, self._empty_axistags(1))

    @_finalize_reduce_result
    @_preserve_doc
    def max(self, axis=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        return numpy.ndarray.max(self, axis, out)

    @_preserve_doc
    def mean(self, axis=None, dtype=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        return _numpyarray_overloaded_function(numpy.ndarray.mean, self, axis, dtype, out)

    @_finalize_reduce_result
    @_preserve_doc
    def min(self, axis=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        return numpy.ndarray.min(self, axis, out)

    @_preserve_doc
    def nonzero(self):
        res = tuple(k.view(type(self)) for k in numpy.ndarray.nonzero(self))
        for k in range(len(res)):
            res[k].axistags = AxisTags(AxisInfo(self.axistags[k]))
        return res

    @property
    def order(self):
        if self.flags.c_contiguous:
            return 'C'
        elif self.flags.f_contiguous:
            return 'F'
        elif self.channelIndex == self.ndim-1 and self.itemsize == self.strides[-1] and \
             reduce(lambda x, y: y if y >= x and x >= 0 else -1, self.strides[:-1], 0) >= 0:
            return 'V'
        return 'A'

    @_preserve_doc
    def prod(self, axis=None, dtype=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        return _numpyarray_overloaded_function(numpy.ndarray.prod, self, axis, dtype, out)

    if numpyHasPtp:
        @_preserve_doc
        def ptp(self, axis=None, out=None):
            '''
            The 'axis' parameter can be an int (axis position) or string (axis key).
            '''
            if type(axis) == str:
                axis = self.axistags.index(axis)
            if axis is None:
                return numpy.ptp(self.transposeToOrder('C').view(numpy.ndarray), out=out)
            else:
                res = numpy.ptp(self.view(numpy.ndarray), axis=axis, out=out)
                if out is None:
                    res = res.view(VigraArray)
                    res.axistags = self._copy_axistags()
                    del res.axistags[axis]
                return res

    @_preserve_doc
    def ravel(self, order='C'):
        '''
        The array is always transposed to 'C' order before flattening.
        '''
        res = self.transposeToNumpyOrder().view(numpy.ndarray).ravel(order)
        return taggedView(res, self._empty_axistags(1))

    @_preserve_doc
    def repeat(self, repeats, axis=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        if type(axis) == str:
            axis = self.axistags.index(axis)
        if axis is None:
            return numpy.ndarray.repeat(self.ravel(), repeats)
        else:
            return numpy.ndarray.repeat(self, repeats, axis)

    @_preserve_doc
    def reshape(self, shape, order='C', axistags=None):
        '''
        An additional keyword argument 'axistags' can be used to determine
        the result's axistags. If not given, all axes of the result will
        have type 'unknown'.
        '''
        if axistags is not None and len(shape) != len(axistags):
            raise RuntimeError("VigraArray.reshape(): size mismatch between shape and axistags.")
        res = numpy.ndarray.reshape(self, shape, order=order)
        if axistags is not None:
            res.axistags = copy.copy(axistags)
        else:
            res.axistags = res._empty_axistags(res.ndim)
        return res

    @_preserve_doc
    def resize(self, new_shape, refcheck=True, order=False, axistags=None):
        '''
        An additional keyword argument 'axistags' can be used to determine
        the self's axistags after the resize. If not given, all axes will have
        type 'unknown'.
        '''
        # ndarray.resize() internally checks for refcount <= 2
        # We need to increase the threshold because we have two
        # additional references ('self' and the argument to 'sys.getrefcount')
        if sys.getrefcount(self) <= 4:
            refcheck = False
        if axistags is not None and len(new_shape) != len(axistags):
            raise RuntimeError("VigraArray.resize(): size mismatch between shape and axistags.")
        numpy.ndarray.resize(self, new_shape, refcheck=refcheck)
        if axistags is not None:
            self.axistags = copy.copy(axistags)
        else:
            self.axistags = self._empty_axistags(self.ndim)

    @_preserve_doc
    def squeeze(self):
        res = numpy.ndarray.squeeze(self)
        if self.ndim != res.ndim:
            res.axistags = res._copy_axistags()
            for k in range(self.ndim-1, -1, -1):
                if self.shape[k] == 1:
                    del res.axistags[k]
        return res

    @_preserve_doc
    def std(self, axis=None, dtype=None, out=None, ddof=0):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        return _numpyarray_overloaded_function(numpy.ndarray.std, self, axis, dtype, out)

    @_preserve_doc
    def sum(self, axis=None, dtype=None, out=None):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        return _numpyarray_overloaded_function(numpy.ndarray.sum, self, axis, dtype, out)

    @_preserve_doc
    def swapaxes(self, i, j, keepTags=False):
        '''
        Parameters 'i' and 'j' can also be ints (axis positions) or strings (axis keys).

        If 'keepsTags' is False, axistags are swapped like the axes, otherwise they remain
        unchanged such that the swapped axes aquire a new meaning.
        '''
        if type(i) == str:
            i = self.axistags.index(i)
        if type(j) == str:
            j = self.axistags.index(j)
        res = numpy.ndarray.swapaxes(self, i, j)
        res.axistags = res._copy_axistags()
        if not keepTags:
            try:
                res.axistags.swapaxes(i, j)
            except:
                res.axistags[i], res.axistags[j] = res.axistags[j], res.axistags[i]
        return res

    @_preserve_doc
    def take(self, indices, axis=None, out=None, mode='raise'):
        '''
        The array is always transposed to 'C' order before flattening.
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        if type(axis) == str:
            axis = self.axistags.index(axis)
        if axis is None:
            return numpy.ndarray.take(self.ravel(), indices, axis, out, mode)
        else:
            return numpy.ndarray.take(self, indices, axis, out, mode)

    @_preserve_doc
    def transpose(self, *axes, **keepTags):
        '''
        An additional keyword parameter 'keepTags' can be provided (it has to be passed as an explicit
        keyword parameter). If it is True, the axistags will remain unchanged such that the transposed
        axes aquire a new meaning.
        '''
        keepTags = keepTags.get('keepTags', False)
        res = numpy.ndarray.transpose(self, *axes)
        if not keepTags:
            res.axistags = res._transpose_axistags(*axes)
        return res

    @_preserve_doc
    def var(self, axis=None, dtype=None, out=None, ddof=0):
        '''
        The 'axis' parameter can be an int (axis position) or string (axis key).
        '''
        return _numpyarray_overloaded_function(numpy.ndarray.var, self, axis, dtype, out)

    ###############################################################
    #                                                             #
    #        reimplement the numerical operators to make          #
    #             sure that array order is preserved              #
    #                                                             #
    ###############################################################

    def __abs__(self):
        return ufunc.absolute(self)

    def __add__(self, other):
        return ufunc.add(self, other)

    def __and__(self, other):
        return ufunc.bitwise_and(self, other)

    def __div__(self, other):
        return ufunc.divide(self, other)

    def __divmod__(self, other):
        return ufunc.floor_divide(self, other), ufunc.remainder(self, other)

    def __eq__(self, other):
        return ufunc.equal(self, other)

    def __floordiv__(self, other):
        return ufunc.floor_divide(self, other)

    def __ge__(self, other):
        return ufunc.greater_equal(self, other)

    def __gt__(self, other):
        return ufunc.greater(self, other)

    def __invert__(self):
        return ufunc.invert(self)

    def __le__(self, other):
        return ufunc.less_equal(self, other)

    def __lshift__(self, other):
        return ufunc.left_shift(self, other)

    def __lt__(self, other):
        return ufunc.less(self, other)

    def __mod__(self, other):
        return ufunc.remainder(self, other)

    def __mul__(self, other):
        return ufunc.multiply(self, other)

    def __ne__(self, other):
        return ufunc.not_equal(self, other)

    def __neg__(self):
        return ufunc.negative(self)

    def __or__(self, other):
        return ufunc.bitwise_or(self, other)

    def __pos__(self):
        return self

    def __pow__(self, other):
        return ufunc.power(self, other)

    def __radd__(self, other):
        return ufunc.add(other, self)

    def __radd__(self, other):
        return ufunc.add(other, self)

    def __rand__(self, other):
        return ufunc.bitwise_and(other, self)

    def __rdiv__(self, other):
        return ufunc.divide(other, self)

    def __rdivmod__(self, other):
        return ufunc.floor_divide(other, self), ufunc.remainder(other, self)

    def __rfloordiv__(self, other):
        return ufunc.floor_divide(other, self)

    def __rlshift__(self, other):
        return ufunc.left_shoft(other, self)

    def __rmod__(self, other):
        return ufunc.remainder(other, self)

    def __rmul__(self, other):
        return ufunc.multiply(other, self)

    def __ror__(self, other):
        return ufunc.bitwise_or(other, self)

    def __rpow__(self, other):
        return ufunc.power(other, self)

    def __rrshift__(self, other):
        return ufunc.right_shift(other, self)

    def __rshift__(self, other):
        return ufunc.right_shift(self, other)

    def __rsub__(self, other):
        return ufunc.subtract(other, self)

    def __rtruediv__(self, other):
        return ufunc.true_divide(other, self)

    def __rxor__(self, other):
        return ufunc.bitwise_xor(other, self)

    def __sub__(self, other):
        return ufunc.subtract(self, other)

    def __truediv__(self, other):
        return ufunc.true_divide(self, other)

    def __xor__(self, other):
        return ufunc.bitwise_xor(self, other)


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

# channelCount == None: array must not have channels
# channelCount == 0:    array can have arbitrary number of channels (including None)
def _adjustShape(shape, order, spatialDimensions, channelCount, axistags, name):
    if order is None:
        order = VigraArray.defaultOrder
    if len(shape) == spatialDimensions:
        if channelCount is not None and channelCount == 0:
            channelCount = 1
        if channelCount:
            if order == 'F':
                shape = (channelCount,) + shape
            else:
                shape = shape + (channelCount,)
    else:
        if channelCount is None or len(shape) != spatialDimensions + 1:
            raise RuntimeError("%s: input shape has wrong length." % name)
        if channelCount > 0:
            if order == 'F':
                if shape[0] != channelCount:
                    raise RuntimeError("%s: input shape has wrong number of channels." % name)
            else:
                if shape[-1] != channelCount:
                    raise RuntimeError("%s: input shape has wrong number of channels." % name)
    if axistags is None:
        axistags = VigraArray.defaultAxistags(spatialDimensions+1, order)
    if len(shape) == spatialDimensions:
        axistags.dropChannelAxis()
    if len(shape) != len(axistags):
        raise RuntimeError("%s: size mismatch between shape and axistags." % name)
    return shape, axistags

def _adjustArray(array, order, spatialDimensions, channelCount, axistags, name):
    if order is None:
        order = VigraArray.defaultOrder
    if array.ndim == spatialDimensions:
        if channelCount is not None and channelCount > 1:
            raise RuntimeError("%s: input array has too few dimensions." % name)
        if hasattr(array, 'axistags'):
            if array.channelIndex != array.ndim:
                raise RuntimeError("%s: input array has too few non-channel axes." % name)
        if channelCount:
            if hasattr(array, 'axistags'):
                array = array.insertChannelAxis(order)
            elif order == 'F':
                array = array[numpy.newaxis,...]
            else:
                array = array[...,numpy.newaxis]
    else:
        if channelCount is None or array.ndim != spatialDimensions+1:
            raise RuntimeError("%s: input array has wrong number of dimensions." % name)
        if hasattr(array, 'axistags'):
            channelIndex = array.channelIndex
            if channelIndex == array.ndim:
                raise RuntimeError("%s: input array has no channel axis." % name)
            if channelCount > 0 and array.shape[channelIndex] != channelCount:
                raise RuntimeError("%s: input array has wrong number of channels." % name)
    if axistags is None:
        if hasattr(array, 'axistags'):
            axistags = copy.copy(array.axistags)
        else:
            axistags = VigraArray.defaultAxistags(spatialDimensions+1, order)
    if array.ndim == spatialDimensions:
        axistags.dropChannelAxis()
    if array.ndim != len(axistags):
        raise RuntimeError("%s: axistags have wrong number of axes." % name)
    return array, axistags

def _adjustInput(obj, order, spatialDimensions, channelCount, axistags, name):
    if isinstance(obj, numpy.ndarray):
        return _adjustArray(obj, order, spatialDimensions, channelCount, axistags, name)
    else:
        return _adjustShape(obj, order, spatialDimensions, channelCount, axistags, name)

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

def Image(obj, dtype=numpy.float32, order=None,
          init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing an image (i.e. an array with
    two spatial axes 'x' and 'y' and optionally a channel axis 'c').
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are not image-like.
    '''
    obj, axistags = _adjustInput(obj, order, 2, 0, axistags, "vigra.Image()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def ScalarImage(obj, dtype=numpy.float32, order=None,
                init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a single-band image (i.e. an
    array with two spatial axes 'x' and 'y' and no channel axis).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a single-band image.
    '''
    obj, axistags = _adjustInput(obj, order, 2, None, axistags, "vigra.ScalarImage()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def Vector2Image(obj, dtype=numpy.float32, order=None,
                 init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a 2-band image (i.e. an
    array with two spatial axes 'x' and 'y' and channel axis 'c' with 2 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a 2-band image.
    '''
    obj, axistags = _adjustInput(obj, order, 2, 2, axistags, "vigra.Vector2Image()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def Vector3Image(obj, dtype=numpy.float32, order=None,
                 init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a 3-band image (i.e. an
    array with two spatial axes 'x' and 'y' and channel axis 'c' with 3 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a 3-band image.
    '''
    obj, axistags = _adjustInput(obj, order, 2, 3, axistags, "vigra.Vector3Image()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def Vector4Image(obj, dtype=numpy.float32, order=None,
                 init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a 4-band image (i.e. an
    array with two spatial axes 'x' and 'y' and channel axis 'c' with 4 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a 4-band image.
    '''
    obj, axistags = _adjustInput(obj, order, 2, 4, axistags, "vigra.Vector4Image()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def RGBImage(obj, dtype=numpy.float32, order=None,
             init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a RGB image (i.e. an
    array with two spatial axes 'x' and 'y' and channel axis 'c' with 3 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for an RGB image.
    '''
    obj, axistags = _adjustInput(obj, order, 2, 3, axistags, "vigra.RGBImage()")
    res = VigraArray(obj, dtype, None, init, value, axistags)
    res.axistags['c'].description = 'RGB'
    return res

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

def Volume(obj, dtype=numpy.float32, order=None,
           init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a volume (i.e. an array with
    three spatial axes 'x', 'y' and 'z' and optionally a channel axis 'c').
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are not volume-like.
    '''
    obj, axistags = _adjustInput(obj, order, 3, 0, axistags, "vigra.Volume()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def ScalarVolume(obj, dtype=numpy.float32, order=None,
                 init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a single-band volume (i.e. an
    array with three spatial axes 'x', 'y' and 'z' and no channel axis).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a single-band volume.
    '''
    obj, axistags = _adjustInput(obj, order, 3, None, axistags, "vigra.ScalarVolume()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def Vector2Volume(obj, dtype=numpy.float32, order=None,
                  init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a 2-band volume (i.e. an
    array with three spatial axes 'x', 'y' and 'z' and channel axis 'c' with 2 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a 2-band volume.
    '''
    obj, axistags = _adjustInput(obj, order, 3, 2, axistags, "vigra.Vector2Volume()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def Vector3Volume(obj, dtype=numpy.float32, order=None,
                  init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a 3-band volume (i.e. an
    array with three spatial axes 'x', 'y' and 'z' and channel axis 'c' with 3 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a 3-band volume.
    '''
    obj, axistags = _adjustInput(obj, order, 3, 3, axistags, "vigra.Vector3Volume()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def Vector4Volume(obj, dtype=numpy.float32, order=None,
                  init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a 4-band volume (i.e. an
    array with three spatial axes 'x', 'y' and 'z' and channel axis 'c' with 4 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a 4-band volume.
    '''
    obj, axistags = _adjustInput(obj, order, 3, 4, axistags, "vigra.Vector4Volume()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def Vector6Volume(obj, dtype=numpy.float32, order=None,
                  init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing a 6-band volume (i.e. an
    array with three spatial axes 'x', 'y' and 'z' and channel axis 'c' with 6 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for a 6-band volume.
    '''
    obj, axistags = _adjustInput(obj, order, 3, 6, axistags, "vigra.Vector6Volume()")
    return VigraArray(obj, dtype, None, init, value, axistags)

def RGBVolume(obj, dtype=numpy.float32, order=None,
              init=True, value=None, axistags=None):
    '''
    Factory function for a :class:`~vigra.VigraArray` representing an RGB volume (i.e. an
    array with three spatial axes 'x', 'y' and 'z' and channel axis 'c' with 3 channels).
    Paramters are interpreted as in the VigraArray constructor, but an exception
    will be raised if the shape or axistags are unsuitable for an RGB volume.
    '''
    obj, axistags = _adjustInput(obj, order, 3, 3, axistags, "vigra.RGBVolume()")
    res = VigraArray(obj, dtype, None, init, value, axistags)
    res.axistags['c'].description = 'RGB'
    return res

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

class ImagePyramid(list):
    def __init__(self, image, copyImageToLevel = 0, lowestLevel = 0, highestLevel = 0):
        ''' Create a new pyramid.
            The new pyramid levels range from 'lowestLevel' to 'highestLevel' (inclusive),
            and the given 'image' is copied to 'copyImageToLevel'. The images at other
            levels are filled with zeros and sized so that the shape is reduced by half
            when going up (to higher levels), and doubled when going down.

            This class can handle multi-channel images, but only when image.channelIndex
            exists and returns image.ndim-1 (i.e. the image must have axistags, and the
            channel axis must correspond to the last index, as in C- or V-order).
        '''
        if lowestLevel > copyImageToLevel or highestLevel < copyImageToLevel:
            raise ValueError('ImagePyramid(): copyImageToLevel must be between lowestLevel and highestLevel (inclusive)')

        import copy
        list.__init__(self, [copy.deepcopy(image)])
        self._lowestLevel = copyImageToLevel
        self._highestLevel = copyImageToLevel
        self.createLevel(lowestLevel)
        self.createLevel(highestLevel)

    @property
    def lowestLevel(self):
        '''The pyramids lowest level.
        '''
        return self._lowestLevel

    @property
    def highestLevel(self):
        '''The pyramids highest level (inclusive).
        '''
        return self._highestLevel

    @property
    def ndim(self):
        '''The dimension of the images in this pyramid.
        '''
        return self[self._highestLevel].ndim

    @property
    def dtype(self):
        '''The pixel type of the images in this pyramid.
        '''
        return self[self._highestLevel].dtype

    @property
    def channelIndex(self):
        '''The channel dimension of the images in this pyramid.
           If the images have no axistags, or no channel axis is
           specified, this defaults to 'ndim'.
        '''
        return getattr(self[self._highestLevel], 'channelIndex', self.ndim)

    @property
    def axistags(self):
        '''The axistags of the images in this pyramid.
        '''
        return getattr(self[self._highestLevel], 'axistags', None)

    def __getitem__(self, level):
        '''Get the image at 'level'.
           Raises IndexError when the level does not exist.
        '''
        if level < self.lowestLevel or level > self.highestLevel:
            raise IndexError("ImagePyramid[level]: level out of range.")
        return list.__getitem__(self, level - self.lowestLevel)

    def __setitem__(self, level, image):
        '''Copy the data of the given 'image' to the image at 'level'.
           Raises IndexError when the level does not exist.
        '''
        self[level][...] = image[...]

    def expandImpl(self, src, dest, centerValue):
        import vigra.filters as filters

        ss, ds = src.shape, dest.shape
        s = [ss[k] if 2*ss[k] == ds[k] else -1 for k in range(len(ss))]

        smooth1 = filters.explictKernel(-1, 1, numpy.array([0.5 - centerValue, 2.0*centerValue, 0.5 - centerValue]))
        smooth2 = filters.explictKernel(-1, 0, numpy.array([0.5, 0.5]));

        filters.convolve(src, (smooth1, smooth1), out=dest[::2,::2])
        filters.convolve(src[:,:s[1]], (smooth1, smooth2), out=dest[::2,1::2])
        filters.convolve(src[:s[0],:], (smooth2, smooth1), out=dest[1::2,::2])
        filters.convolve(src[:s[0],:s[1]], (smooth2, smooth2), out=dest[1::2,1::2])

    def reduce(self, srcLevel, destLevel, centerValue = 0.42):
        '''Reduce the image at 'srcLevel' to 'destLevel', using the Burt smoothing filter
           with the given 'centerValue'. srcLevel must be smaller than destLevel.

           For more details, see pyramidReduceBurtFilter_ in the C++ documentation.
        '''
        # FIXME: This should be implemented in C++
        # FIXME: This should be implemented for arbitrary dimensions
        import vigra.filters as filters

        if srcLevel > destLevel:
            raise RuntimeError("ImagePyramid::reduce(): srcLevel <= destLevel required.")
        if srcLevel < self.lowestLevel or srcLevel > self.highestLevel:
            raise RuntimeError("ImagePyramid::reduce(): srcLevel does not exist.")
        self.createLevel(destLevel)

        smooth = filters.burtFilterKernel(0.25 - 0.5*centerValue)
        for k in range(srcLevel, destLevel):
            i = filters.convolve(self[k], smooth)
            self[k+1] = i[::2,::2]

    def expand(self, srcLevel, destLevel, centerValue = 0.42):
        '''Expand the image at 'srcLevel' to 'destLevel', using the Burt smoothing filter
           with the given 'centerValue'. srcLevel must be larger than destLevel.

           For more details, see pyramidExpandBurtFilter_ in the C++ documentation.
        '''
        # FIXME: This should be implemented in C++
        # FIXME: This should be implemented for arbitrary dimensions
        if srcLevel < destLevel:
            raise RuntimeError("ImagePyramid::expand(): srcLevel >= destLevel required.")
        if srcLevel < self.lowestLevel or srcLevel > self.highestLevel:
            raise RuntimeError("ImagePyramid::expand(): srcLevel does not exist.")
        self.createLevel(destLevel)

        for k in range(srcLevel, destLevel, -1):
            self.expandImpl(self[k], self[k-1], centerValue)

    def reduceLaplacian(self, srcLevel, destLevel, centerValue = 0.42):
        '''Reduce the image at 'srcLevel' to 'destLevel', using the Burt smoothing filter
           with the given 'centerValue', and compute Laplacian images for the levels
           srcLevel ... destLevel-1. srcLevel must be smaller than destLevel.

           For more details, see pyramidReduceBurtLaplacian_ in the C++ documentation.
        '''
        # FIXME: This should be implemented in C++
        # FIXME: This should be implemented for arbitrary dimensions
        import vigra.filters as filters

        if srcLevel > destLevel:
            raise RuntimeError("ImagePyramid::reduceLaplacian(): srcLevel <= destLevel required.")
        if srcLevel < self.lowestLevel or srcLevel > self.highestLevel:
            raise RuntimeError("ImagePyramid::reduceLaplacian(): srcLevel does not exist.")
        self.createLevel(destLevel)

        smooth = filters.burtFilterKernel(0.25 - 0.5*centerValue)
        for k in range(srcLevel, destLevel):
            i = filters.convolve(self[k], smooth)
            self[k+1] = i[::2,::2]
            self.expandImpl(self[k+1], i, centerValue)
            self[k] = i - self[k]

    def expandLaplacian(self, srcLevel, destLevel, centerValue = 0.42):
        '''Expand the image at 'srcLevel' to 'destLevel', using the Burt smoothing filter
           with the given 'centerValue', and reconstruct the images for the levels
           srcLevel-1 ... destLevel from their Laplacian images. srcLevel must be larger than destLevel.

           For more details, see pyramidExpandBurtLaplacian_ in the C++ documentation.
        '''
        # FIXME: This should be implemented in C++
        # FIXME: This should be implemented for arbitrary dimensions
        import vigra.filters as filters

        if srcLevel < destLevel:
            raise RuntimeError("ImagePyramid::expandLaplacian(): srcLevel >= destLevel required.")
        if srcLevel < self.lowestLevel or srcLevel > self.highestLevel:
            raise RuntimeError("ImagePyramid::expandLaplacian(): srcLevel does not exist.")
        self.createLevel(destLevel)

        smooth1 = filters.explictKernel(-1, 1, numpy.array([0.5 - centerValue, 2.0*centerValue, 0.5 - centerValue]))
        smooth2 = filters.explictKernel(-1, 0, numpy.array([0.5, 0.5]));
        for k in range(srcLevel, destLevel, -1):
            i = self[k-1].__class__(self[k-1].shape, dtype = self[k-1].dtype)
            self.expandImpl(self[k], i, centerValue)
            self[k-1] = i - self[k-1]

    def createLevel(self, level):
        ''' Make sure that 'level' exists. If 'level' is outside the current range of levels,
            empty images of the appropriate shape are inserted into the pyramid.
        '''
        channelIndex = self.channelIndex
        hasChannels = channelIndex < self.ndim
        axistags = self.axistags
        if level > self.highestLevel:
            image = list.__getitem__(self, -1)
            for i in range(self.highestLevel, level):
                newShape = [int((k + 1) // 2) for k in image.shape]
                if hasChannels:
                    newShape[channelIndex] = image.shape[channelIndex]
                if axistags:
                    image = image.__class__(newShape, dtype=image.dtype, axistags=axistags)
                else:
                    image = image.__class__(newShape, dtype=image.dtype)
                    image[...] = 0
                self.append(image)
            self._highestLevel = level
        elif level < self.lowestLevel:
            image = list.__getitem__(self, 0)
            for i in range(self.lowestLevel, level, -1):
                newShape = [2*k-1 for k in image.shape]
                if hasChannels:
                    newShape[channelIndex] = image.shape[channelIndex]
                if axistags:
                    image = image.__class__(newShape, dtype=image.dtype, axistags=axistags)
                else:
                    image = image.__class__(newShape, dtype=image.dtype)
                    image[...] = 0
                self.insert(0, image)
            self._lowestLevel = level

