"""
Abstract conv interface
"""
from __future__ import absolute_import, print_function, division

import logging
from six import reraise, integer_types
import sys

import theano

from theano.tensor import as_tensor_variable, patternbroadcast
from theano.tensor import get_scalar_constant_value, NotScalarConstantError
from theano.gof import Apply, Op

from six.moves import xrange

import warnings
import numpy
import numpy as np

try:
    from scipy.signal.signaltools import _valfrommode, _bvalfromboundary, convolve
    from scipy.signal.sigtools import _convolve2d
    imported_scipy_signal = True
except ImportError:
    imported_scipy_signal = False


__docformat__ = "restructuredtext en"
_logger = logging.getLogger("theano.tensor.nnet.abstract_conv")


def get_conv_output_shape(image_shape, kernel_shape,
                          border_mode, subsample,
                          filter_dilation=None):
    """
    This function compute the output shape of convolution operation.

    Parameters
    ----------
    image_shape: tuple of int (symbolic or numeric) corresponding to the input
        image shape. Its four (or five) element must correspond respectively
        to: batch size, number of input channels, height and width (and
        possibly depth) of the image. None where undefined.
    kernel_shape: tuple of int (symbolic or numeric) corresponding to the
        kernel shape. Its four (or five) elements must correspond respectively
        to: number of output channels, number of input channels, height and
        width (and possibly depth) of the kernel. None where undefined.
    border_mode: string, int (symbolic or numeric) or tuple of int (symbolic
        or numeric). If it is a string, it must be 'valid', 'half' or 'full'.
        If it is a tuple, its two (or three) elements respectively correspond
        to the padding on height and width (and possibly depth) axis.
    subsample: tuple of int (symbolic or numeric). Its or three elements
        espectively correspond to the subsampling on height and width (and
        possibly depth) axis.
    filter_dilation: tuple of int (symbolic or numeric). Its two elements
        correspond respectively to the dilation on height and width axis.

    Returns
    -------
    output_shape: tuple of int corresponding to the output image shape. Its
        four element must correspond respectively to: batch size, number of
        output channels, height and width of the image. None where undefined.

    """
    bsize, imshp = image_shape[0], image_shape[2:]
    nkern, kshp = kernel_shape[0], kernel_shape[2:]

    if filter_dilation is None:
        filter_dilation = numpy.ones(len(subsample), dtype='int')

    if isinstance(border_mode, tuple):
        out_shp = tuple(get_conv_shape_1axis(
            imshp[i], kshp[i], border_mode[i],
            subsample[i], filter_dilation[i]) for i in range(len(subsample)))
    else:
        out_shp = tuple(get_conv_shape_1axis(
            imshp[i], kshp[i], border_mode,
            subsample[i], filter_dilation[i]) for i in range(len(subsample)))
    return (bsize, nkern) + out_shp


# filter dilation set by default to 1
# for compatibility with other tests.
def get_conv_shape_1axis(image_shape, kernel_shape, border_mode,
                         subsample, dilation=1):
    """
    This function compute the output shape of convolution operation.

    Parameters
    ----------
    image_shape: int or None. Corresponds to the input image shape on a
        given axis. None if undefined.
    kernel_shape: int or None. Corresponds to the kernel shape on a given
        axis. None if undefined.
    border_mode: string or int. If it is a string, it must be
        'valid', 'half' or 'full'. If it is an integer, it must correspond to
        the padding on the considered axis.
    subsample: int. It must correspond to the subsampling on the
        considered axis.
    dilation: int. It must correspond to the dilation on the
        considered axis.

    Returns
    -------
    out_shp: int corresponding to the output image shape on the
        considered axis. None if undefined.

    """
    if None in [image_shape, kernel_shape, border_mode,
                subsample, dilation]:
        return None
    # Implicit dilated kernel shape
    dil_kernel_shape = (kernel_shape - 1) * dilation + 1
    if border_mode == "half":
        pad = dil_kernel_shape // 2
    elif border_mode == "full":
        pad = dil_kernel_shape - 1
    elif border_mode == "valid":
        pad = 0
    else:
        pad = border_mode
        if pad < 0:
            raise ValueError("border_mode must be >= 0")

    # In case of symbolic shape, we want to build the smallest graph
    # (image_shape + 2 * pad - dil_kernel_shape) // subsample + 1
    if pad == 0:
        out_shp = (image_shape - dil_kernel_shape)
    else:
        out_shp = (image_shape + 2 * pad - dil_kernel_shape)
    if subsample != 1:
        out_shp = out_shp // subsample
    out_shp = out_shp + 1

    return out_shp


def conv2d(input,
           filters,
           input_shape=None,
           filter_shape=None,
           border_mode='valid',
           subsample=(1, 1),
           filter_flip=True,
           filter_dilation=(1, 1)):
    """This function will build the symbolic graph for convolving a mini-batch of a
    stack of 2D inputs with a set of 2D filters. The implementation is modelled
    after Convolutional Neural Networks (CNN).

    Refer to :func:`nnet.conv2d <theano.tensor.nnet.conv2d>` for a more detailed documentation.
    """

    input = as_tensor_variable(input)
    filters = as_tensor_variable(filters)
    conv_op = AbstractConv2d(imshp=input_shape,
                             kshp=filter_shape,
                             border_mode=border_mode,
                             subsample=subsample,
                             filter_flip=filter_flip,
                             filter_dilation=filter_dilation)
    return conv_op(input, filters)


def conv3d(input,
           filters,
           input_shape=None,
           filter_shape=None,
           border_mode='valid',
           subsample=(1, 1, 1),
           filter_flip=True,
           filter_dilation=(1, 1, 1)):
    """
    This function will build the symbolic graph for convolving a mini-batch of a
    stack of 3D inputs with a set of 3D filters. The implementation is modelled
    after Convolutional Neural Networks (CNN).


    Parameters
    ----------
    input: symbolic 5D tensor
        Mini-batch of feature map stacks, of shape
        (batch size, input channels, input depth, input rows, input columns).
        See the optional parameter ``input_shape``.

    filters: symbolic 5D tensor
        Set of filters used in CNN layer of shape
        (output channels, input channels, filter depth, filter rows, filter columns).
        See the optional parameter ``filter_shape``.

    input_shape: None, tuple/list of len 5 of int or Constant variable
        The shape of the input parameter.
        Optional, possibly used to choose an optimal implementation.
        You can give ``None`` for any element of the list to specify that this
        element is not known at compile time.

    filter_shape: None, tuple/list of len 5 of int or Constant variable
        The shape of the filters parameter.
        Optional, possibly used to choose an optimal implementation.
        You can give ``None`` for any element of the list to specify that this
        element is not known at compile time.

    border_mode: str, int or tuple of three int
        Either of the following:

        ``'valid'``: apply filter wherever it completely overlaps with the
            input. Generates output of shape: input shape - filter shape + 1
        ``'full'``: apply filter wherever it partly overlaps with the input.
            Generates output of shape: input shape + filter shape - 1
        ``'half'``: pad input with a symmetric border of ``filter // 2``,
            then perform a valid convolution. For filters with an odd
            number of slices, rows and columns, this leads to the output
            shape being equal to the input shape.
        ``int``: pad input with a symmetric border of zeros of the given
            width, then perform a valid convolution.
        ``(int1, int2, int3)``
            pad input with a symmetric border of ``int1``, ``int2`` and
            ``int3`` columns, then perform a valid convolution.

    subsample: tuple of len 3
        Factor by which to subsample the output.
        Also called strides elsewhere.

    filter_flip: bool
        If ``True``, will flip the filter x, y and z dimensions before
        sliding them over the input. This operation is normally
        referred to as a convolution, and this is the default. If
        ``False``, the filters are not flipped and the operation is
        referred to as a cross-correlation.

    filter_dilation: tuple of len 3
        Factor by which to subsample (stride) the input.
        Also called dilation elsewhere.

    Returns
    -------
    Symbolic 5D tensor
        Set of feature maps generated by convolutional layer. Tensor is
        is of shape (batch size, output channels, output depth,
        output rows, output columns)

    Notes
    -----
        If cuDNN is available, it will be used on the
        GPU. Otherwise, it is the *Corr3dMM* convolution that will be used
        "caffe style convolution".

        This is only supported in Theano 0.8 or the development
        version until it is released.

    """

    input = as_tensor_variable(input)
    filters = as_tensor_variable(filters)
    conv_op = AbstractConv3d(imshp=input_shape,
                             kshp=filter_shape,
                             border_mode=border_mode,
                             subsample=subsample,
                             filter_flip=filter_flip,
                             filter_dilation=filter_dilation)
    return conv_op(input, filters)


def conv2d_grad_wrt_inputs(output_grad,
                           filters,
                           input_shape,
                           filter_shape=None,
                           border_mode='valid',
                           subsample=(1, 1),
                           filter_flip=True,
                           filter_dilation=(1, 1)):
    """Compute conv output gradient w.r.t its inputs

    This function builds the symbolic graph for getting the
    gradient of the output of a convolution (namely output_grad)
    w.r.t the input of the convolution, given a set of 2D filters
    used by the convolution, such that the output_grad is upsampled
    to the input_shape.

    Parameters
    ----------
    output_grad : symbolic 4D tensor
        mini-batch of feature map stacks, of shape (batch size, input
        channels, input rows, input columns).  This is the tensor that
        will be upsampled or the output gradient of the convolution
        whose gradient will be taken with respect to the input of the
        convolution.
    filters : symbolic 4D tensor
        set of filters used in CNN layer of shape (output channels,
        input channels, filter rows, filter columns).  See the
        optional parameter ``filter_shape``.
    input_shape : [None/int/Constant] * 2 + [Tensor/int/Constant] * 2
        The shape of the input (upsampled) parameter.
        A tuple/list of len 4, with the first two dimensions
        being None or int or Constant and the last two dimensions being
        Tensor or int or Constant.
        Not Optional, since given the output_grad shape
        and the subsample values, multiple input_shape may be
        plausible.
    filter_shape : None or [None/int/Constant] * 4
        The shape of the filters parameter. None or a tuple/list of len 4.
        Optional, possibly used  to choose an optimal implementation.
        You can give ``None`` for any element of the list to specify that
        this element is not known at compile time.
    border_mode : str, int or tuple of two int
        Either of the following:

          ``'valid'``
            apply filter wherever it completely overlaps with the
            input. Generates output of shape: input shape - filter
            shape + 1

          ``'full'``
            apply filter wherever it partly overlaps with the input.
            Generates output of shape: input shape + filter shape - 1

          ``'half'``
            pad input with a symmetric border of ``filter rows // 2``
            rows and ``filter columns // 2`` columns, then perform a
            valid convolution. For filters with an odd number of rows
            and columns, this leads to the output shape being equal to
            the input shape. It is known as 'same' elsewhere.

          ``int``
            pad input with a symmetric border of zeros of the given
            width, then perform a valid convolution.

          ``(int1, int2)``
            pad input with a symmetric border of ``int1`` rows and
            ``int2`` columns, then perform a valid convolution.

    subsample : tuple of len 2
        The subsampling used in the forward pass.  Also called strides
        elsewhere.
    filter_flip : bool
        If ``True``, will flip the filter rows and columns before
        sliding them over the input. This operation is normally
        referred to as a convolution, and this is the default. If
        ``False``, the filters are not flipped and the operation is
        referred to as a cross-correlation.
    filter_dilation : tuple of len 2
        The filter dilation used in the forward pass.
        Also known as input striding.

    Returns
    -------
    symbolic 4D tensor
        set of feature maps generated by convolutional layer. Tensor
        is of shape (batch size, output channels, output rows, output
        columns)

    Notes
    -----

    :note: If cuDNN is available, it will be used on the
        GPU. Otherwise, it is the *CorrMM* convolution that will be used
        "caffe style convolution".

    :note: This is only supported in Theano 0.8 or the development
        version until it is released.

    """

    filters = as_tensor_variable(filters)
    output_grad = as_tensor_variable(output_grad)

    # checking the type of input_shape
    for dim in [0, 1]:
        assert isinstance(input_shape[dim], (theano.tensor.TensorConstant,
                                             integer_types, type(None)))
    for dim in [2, 3]:
        assert isinstance(input_shape[dim], (theano.tensor.TensorVariable,
                                             theano.tensor.TensorConstant,
                                             integer_types))

    # checking the type of filter_shape
    if filter_shape is not None:
        for dim in [0, 1, 2, 3]:
            assert isinstance(filter_shape[dim], (theano.tensor.TensorConstant,
                                                  integer_types, type(None)))

    # setting the last two dimensions of input_shape to None, if
    # the type of these dimensions is TensorVariable.
    numerical_input_shape = list(input_shape)
    for dim in [2, 3]:
        if isinstance(input_shape[dim], theano.tensor.TensorVariable):
            numerical_input_shape[dim] = None

    grad_input_op = AbstractConv2d_gradInputs(imshp=numerical_input_shape,
                                              kshp=filter_shape,
                                              border_mode=border_mode,
                                              subsample=subsample,
                                              filter_flip=filter_flip,
                                              filter_dilation=filter_dilation)

    return grad_input_op(filters, output_grad, input_shape[-2:])


def conv3d_grad_wrt_inputs(output_grad,
                           filters,
                           input_shape,
                           filter_shape=None,
                           border_mode='valid',
                           subsample=(1, 1, 1),
                           filter_flip=True,
                           filter_dilation=(1, 1, 1)):
    """Compute conv output gradient w.r.t its inputs

    This function builds the symbolic graph for getting the
    gradient of the output of a convolution (namely output_grad)
    w.r.t the input of the convolution, given a set of 3D filters
    used by the convolution, such that the output_grad is upsampled
    to the input_shape.

    Parameters
    ----------
    output_grad : symbolic 5D tensor
        mini-batch of feature map stacks, of shape (batch size, input
        channels, input depth, input rows, input columns).  This is the
        tensor that will be upsampled or the output gradient of the
        convolution whose gradient will be taken with respect to the
        input of the convolution.
    filters : symbolic 5D tensor
        set of filters used in CNN layer of shape (output channels,
        input channels, filter depth, filter rows, filter columns).
        See the optional parameter ``filter_shape``.
    input_shape : [None/int/Constant] * 2 + [Tensor/int/Constant] * 2
        The shape of the input (upsampled) parameter.
        A tuple/list of len 5, with the first two dimensions
        being None or int or Constant and the last three dimensions being
        Tensor or int or Constant.
        Not Optional, since given the output_grad shape
        and the subsample values, multiple input_shape may be
        plausible.
    filter_shape : None or [None/int/Constant] * 5
        The shape of the filters parameter. None or a tuple/list of len 5.
        Optional, possibly used  to choose an optimal implementation.
        You can give ``None`` for any element of the list to specify that
        this element is not known at compile time.
    border_mode : str, int or tuple of three int
        Either of the following:

          ``'valid'``
            apply filter wherever it completely overlaps with the
            input. Generates output of shape: input shape - filter
            shape + 1

          ``'full'``
            apply filter wherever it partly overlaps with the input.
            Generates output of shape: input shape + filter shape - 1

          ``'half'``
            pad input with a symmetric border of ``filter // 2``,
            then perform a valid convolution. For filters with an odd
            number of slices, rows and columns, this leads to the output
            shape being equal to the input shape. It is known as 'same'
            elsewhere.

          ``int``
            pad input with a symmetric border of zeros of the given
            width, then perform a valid convolution.

          ``(int1, int2, int3)``
            pad input with a symmetric border of ``int1``, ``int2`` and
            ``int3`` columns, then perform a valid convolution.

    subsample : tuple of len 3
        The subsampling used in the forward pass.  Also called strides
        elsewhere.
    filter_flip : bool
        If ``True``, will flip the filter x, y and z dimensions before
        sliding them over the input. This operation is normally
        referred to as a convolution, and this is the default. If
        ``False``, the filters are not flipped and the operation is
        referred to as a cross-correlation.
    filter_dilation : tuple of len 3
        The filter dilation used in the forward pass.
        Also known as input striding.

    Returns
    -------
    symbolic 5D tensor
        set of feature maps generated by convolutional layer. Tensor
        is of shape (batch size, output channels, output depth,
        output rows, output columns)

    Notes
    -----

    :note: If cuDNN is available, it will be used on the
        GPU. Otherwise, it is the *Corr3dMM* convolution that will be used
        "caffe style convolution".

    :note: This is only supported in Theano 0.8 or the development
        version until it is released.

    """

    filters = as_tensor_variable(filters)
    output_grad = as_tensor_variable(output_grad)

    # checking the type of input_shape
    for dim in [0, 1]:
        assert isinstance(input_shape[dim], (theano.tensor.TensorConstant,
                                             integer_types, type(None)))
    for dim in [2, 3, 4]:
        assert isinstance(input_shape[dim], (theano.tensor.TensorVariable,
                                             theano.tensor.TensorConstant,
                                             integer_types))

    # checking the type of filter_shape
    if filter_shape is not None:
        for dim in [0, 1, 2, 3, 4]:
            assert isinstance(filter_shape[dim], (theano.tensor.TensorConstant,
                                                  integer_types, type(None)))

    # setting the last three dimensions of input_shape to None, if
    # the type of these dimensions is TensorVariable.
    numerical_input_shape = list(input_shape)
    for dim in [2, 3, 4]:
        if isinstance(input_shape[dim], theano.tensor.TensorVariable):
            numerical_input_shape[dim] = None

    grad_input_op = AbstractConv3d_gradInputs(imshp=numerical_input_shape,
                                              kshp=filter_shape,
                                              border_mode=border_mode,
                                              subsample=subsample,
                                              filter_flip=filter_flip,
                                              filter_dilation=filter_dilation)

    return grad_input_op(filters, output_grad, input_shape[-3:])


def conv2d_grad_wrt_weights(input,
                            output_grad,
                            filter_shape,
                            input_shape=None,
                            border_mode='valid',
                            subsample=(1, 1),
                            filter_flip=True,
                            filter_dilation=(1, 1)):
    """Compute conv output gradient w.r.t its weights

    This function will build the symbolic graph for getting the
    gradient of the output of a convolution (output_grad) w.r.t its wights.

    Parameters
    ----------
    input : symbolic 4D tensor
        mini-batch of feature map stacks, of shape (batch size, input
        channels, input rows, input columns).  This is the input of
        the convolution in the forward pass.
    output_grad : symbolic 4D tensor
        mini-batch of feature map stacks, of shape (batch size, input
        channels, input rows, input columns).  This is the gradient of
        the output of convolution.
    filter_shape : [None/int/Constant] * 2 + [Tensor/int/Constant] * 2
        The shape of the filter parameter.  A tuple/list of len 4, with the
        first two dimensions being None or int or Constant and the last two
        dimensions being Tensor or int or Constant.
        Not Optional, since given the output_grad shape and
        the input_shape, multiple filter_shape may be plausible.
    input_shape : None or [None/int/Constant] * 4
        The shape of the input parameter. None or a tuple/list of len 4.
        Optional, possibly used to choose an optimal implementation.
        You can give ``None`` for any element of the list to specify
        that this element is not known at compile time.
    border_mode : str, int or tuple of two ints
        Either of the following:

          ``'valid'``
            apply filter wherever it completely overlaps with the
            input. Generates output of shape: input shape - filter
            shape + 1

          ``'full'``
            apply filter wherever it partly overlaps with the input.
            Generates output of shape: input shape + filter shape - 1

          ``'half'``
            pad input with a symmetric border of ``filter rows // 2``
            rows and ``filter columns // 2`` columns, then perform a
            valid convolution. For filters with an odd number of rows
            and columns, this leads to the output shape being equal to
            the input shape. It is known as 'same' elsewhere.

          ``int``
            pad input with a symmetric border of zeros of the given
            width, then perform a valid convolution.

          ``(int1, int2)``
            pad input with a symmetric border of ``int1`` rows and
            ``int2`` columns, then perform a valid convolution.
    subsample : tuple of len 2
        The subsampling used in the forward pass of the convolutional
        operation.  Also called strides elsewhere.
    filter_flip : bool
        If ``True``, will flip the filter rows and columns before
        sliding them over the input. This operation is normally
        referred to as a convolution, and this is the default. If
        ``False``, the filters are not flipped and the operation is
        referred to as a cross-correlation.
    filter_dilation : tuple of len 2
        The filter dilation used in the forward pass.
        Also known as input striding.

    Returns
    -------
    symbolic 4D tensor
        set of feature maps generated by convolutional layer. Tensor
        is of shape (batch size, output channels, output rows, output
        columns)

    Notes
    -----

    :note: If cuDNN is available, it will be used on the
        GPU. Otherwise, it is the *CorrMM* convolution that will be used
        "caffe style convolution".

    :note: This is only supported in Theano 0.8 or the development
        version until it is released.

    """

    input = as_tensor_variable(input)
    output_grad = as_tensor_variable(output_grad)

    # checking the type of filter_shape
    for dim in [0, 1]:
        assert isinstance(filter_shape[dim], (theano.tensor.TensorConstant,
                                              integer_types, type(None)))
    for dim in [2, 3]:
        assert isinstance(filter_shape[dim], (theano.tensor.TensorVariable,
                                              theano.tensor.TensorConstant,
                                              integer_types))

    # checking the type of input_shape
    if input_shape is not None:
        for dim in [0, 1, 2, 3]:
            assert isinstance(input_shape[dim], (theano.tensor.TensorConstant,
                                                 integer_types, type(None)))

    # setting the last two dimensions of filter_shape to None, if
    # the type of these dimensions is TensorVariable.
    numerical_filter_shape = list(filter_shape)
    for dim in [2, 3]:
        if isinstance(filter_shape[dim], theano.tensor.TensorVariable):
            numerical_filter_shape[dim] = None

    gradWeight_op = AbstractConv2d_gradWeights(imshp=input_shape,
                                               kshp=numerical_filter_shape,
                                               border_mode=border_mode,
                                               subsample=subsample,
                                               filter_flip=filter_flip,
                                               filter_dilation=filter_dilation)

    return gradWeight_op(input, output_grad, filter_shape[-2:])


def conv3d_grad_wrt_weights(input,
                            output_grad,
                            filter_shape,
                            input_shape=None,
                            border_mode='valid',
                            subsample=(1, 1, 1),
                            filter_flip=True,
                            filter_dilation=(1, 1, 1)):
    """Compute conv output gradient w.r.t its weights

    This function will build the symbolic graph for getting the
    gradient of the output of a convolution (output_grad) w.r.t its weights.

    Parameters
    ----------
    input : symbolic 5D tensor
        mini-batch of feature map stacks, of shape (batch size, input
        channels, input depth, input rows, input columns).  This is the input
        of the convolution in the forward pass.
    output_grad : symbolic 5D tensor
        mini-batch of feature map stacks, of shape (batch size, input
        channels, input depth, input rows, input columns).  This is the
        gradient of the output of convolution.
    filter_shape : [None/int/Constant] * 2 + [Tensor/int/Constant] * 2
        The shape of the filter parameter.  A tuple/list of len 5, with the
        first two dimensions being None or int or Constant and the last three
        dimensions being Tensor or int or Constant.
        Not Optional, since given the output_grad shape and
        the input_shape, multiple filter_shape may be plausible.
    input_shape : None or [None/int/Constant] * 5
        The shape of the input parameter. None or a tuple/list of len 5.
        Optional, possibly used to choose an optimal implementation.
        You can give ``None`` for any element of the list to specify
        that this element is not known at compile time.
    border_mode : str, int or tuple of two ints
        Either of the following:

          ``'valid'``
            apply filter wherever it completely overlaps with the
            input. Generates output of shape: input shape - filter
            shape + 1

          ``'full'``
            apply filter wherever it partly overlaps with the input.
            Generates output of shape: input shape + filter shape - 1

          ``'half'``
            pad input with a symmetric border of ``filter rows // 2``
            rows and ``filter columns // 2`` columns, then perform a
            valid convolution. For filters with an odd number of rows
            and columns, this leads to the output shape being equal to
            the input shape. It is known as 'same' elsewhere.

          ``int``
            pad input with a symmetric border of zeros of the given
            width, then perform a valid convolution.

          ``(int1, int2, int3)``
            pad input with a symmetric border of ``int1``, ``int2`` and
            ``int3``, then perform a valid convolution.
    subsample : tuple of len 3
        The subsampling used in the forward pass of the convolutional
        operation.  Also called strides elsewhere.
    filter_flip : bool
        If ``True``, will flip the filters before sliding them over the
        input. This operation is normally referred to as a convolution,
        and this is the default. If ``False``, the filters are not
        flipped and the operation is referred to as a cross-correlation.
    filter_dilation : tuple of len 3
        The filter dilation used in the forward pass.
        Also known as input striding.

    Returns
    -------
    symbolic 5D tensor
        set of feature maps generated by convolutional layer. Tensor
        is of shape (batch size, output channels, output time, output
        rows, output columns)

    Notes
    -----

    :note: If cuDNN is available, it will be used on the
        GPU. Otherwise, it is the *Corr3dMM* convolution that will be used
        "caffe style convolution".

    :note: This is only supported in Theano 0.8 or the development
        version until it is released.

    """

    input = as_tensor_variable(input)
    output_grad = as_tensor_variable(output_grad)

    # checking the type of filter_shape
    for dim in [0, 1]:
        assert isinstance(filter_shape[dim], (theano.tensor.TensorConstant,
                                              integer_types, type(None)))
    for dim in [2, 3, 4]:
        assert isinstance(filter_shape[dim], (theano.tensor.TensorVariable,
                                              theano.tensor.TensorConstant,
                                              integer_types))

    # checking the type of input_shape
    if input_shape is not None:
        for dim in [0, 1, 2, 3, 4]:
            assert isinstance(input_shape[dim], (theano.tensor.TensorConstant,
                                                 integer_types, type(None)))

    # setting the last three dimensions of filter_shape to None, if
    # the type of these dimensions is TensorVariable.
    numerical_filter_shape = list(filter_shape)
    for dim in [2, 3, 4]:
        if isinstance(filter_shape[dim], theano.tensor.TensorVariable):
            numerical_filter_shape[dim] = None

    gradWeight_op = AbstractConv3d_gradWeights(imshp=input_shape,
                                               kshp=numerical_filter_shape,
                                               border_mode=border_mode,
                                               subsample=subsample,
                                               filter_flip=filter_flip,
                                               filter_dilation=filter_dilation)

    return gradWeight_op(input, output_grad, filter_shape[:-3])


def bilinear_kernel_2D(ratio, normalize=True):
    """Compute 2D kernel for bilinear upsampling

    This function builds the 2D kernel that can be used to upsample
    a tensor by the given ratio using bilinear interpolation.

    Parameters
    ----------
    ratio: int or Constant/Scalar Theano tensor of int* dtype
        the ratio by which an image will be upsampled by the returned filter
        in the 2D space.

    normalize: bool
        param normalize: indicates whether to normalize the kernel or not.
        Default is True.

    Returns
    -------
    symbolic 2D tensor
        the 2D kernels that can be applied to any given image to upsample it
        by the indicated ratio using bilinear interpolation in two dimensions.

    """

    hkern = bilinear_kernel_1D(ratio=ratio, normalize=normalize).dimshuffle('x', 0)
    vkern = bilinear_kernel_1D(ratio=ratio, normalize=normalize).dimshuffle(0, 'x')
    kern = hkern * vkern
    return kern


def bilinear_kernel_1D(ratio, normalize=True):
    """Compute 1D kernel for bilinear upsampling

    This function builds the 1D kernel that can be used to upsample
    a tensor by the given ratio using bilinear interpolation.

    Parameters
    ----------
    ratio: int or Constant/Scalar Theano tensor of int* dtype
        the ratio by which an image will be upsampled by the returned filter
        in the 2D space.

    normalize: bool
        param normalize: indicates whether to normalize the kernel or not.
        Default is True.

    Returns
    -------
    symbolic 1D tensor
        the 1D kernels that can be applied to any given image to upsample it
        by the indicated ratio using bilinear interpolation in one dimension.

    """

    T = theano.tensor
    half_kern = T.arange(1, ratio + 1, dtype=theano.config.floatX)
    kern = T.concatenate([half_kern, half_kern[-2::-1]])

    if normalize:
        kern /= ratio
    return kern


def bilinear_upsampling(input,
                        ratio,
                        batch_size=None,
                        num_input_channels=None,
                        use_1D_kernel=True):
    """Compute bilinear upsampling

    This function will build the symbolic graph for upsampling
    a tensor by the given ratio using bilinear interpolation.

    Parameters
    ----------
    input: symbolic 4D tensor
        mini-batch of feature map stacks, of shape (batch size,
        input channels, input rows, input columns) that will be upsampled.

    ratio: `int or Constant or Scalar Tensor of int* dtype`
        the ratio by which the input is upsampled in the 2D space (row and
        col size).

    batch_size: None, int or Constant variable
        The size of the first dimension of the input variable.
        Optional, possibly used to choose an optimal implementation.
        batch_size will be used only if num_input_channels is not None.

    num_input_channels: None, int or Constant variable
        The size of the second dimension of the input variable.
        Optional, possibly used to choose an optimal implementation.
        num_input_channels will be used only if batch_size is not None.

    use_1D_kernel: bool
        if set to true, row and column will be upsampled seperately by 1D
        kernels, otherwise they are upsampled together using a 2D kernel. The
        final result is the same, only the speed can differ, given factors such
        as upsampling ratio.

    Returns
    -------
    symbolic 4D tensor
        set of feature maps generated by bilinear upsampling. Tensor
        is of shape (batch size, num_input_channels, input row size * ratio,
        input column size * ratio)

    Notes
    -----

    :note: The kernel used for bilinear interpolation is fixed (not learned).

    :note: When the upsampling ratio is even, the last row and column is
        repeated one extra time compared to the first row and column which makes
        the upsampled tensor asymmetrical on both sides. This does not happen when
        the upsampling ratio is odd.

    """

    T = theano.tensor
    try:
        up_bs = batch_size * num_input_channels
    except TypeError:
        up_bs = None
    row, col = input.shape[2:]
    up_input = input.reshape((-1, 1, row, col))

    # concatenating the first and last row and column
    # first and last row
    concat_mat = T.concatenate((up_input[:, :, :1, :], up_input,
                                up_input[:, :, -1:, :]), axis=2)
    # first and last col
    concat_mat = T.concatenate((concat_mat[:, :, :, :1], concat_mat,
                                concat_mat[:, :, :, -1:]), axis=3)
    concat_col = col + 2

    pad = 2 * ratio - (ratio - 1) // 2 - 1

    if use_1D_kernel:
        kern = bilinear_kernel_1D(ratio=ratio, normalize=True)
        # upsampling rows
        upsampled_row = conv2d_grad_wrt_inputs(output_grad=concat_mat,
                                               filters=kern[np.newaxis,
                                                            np.newaxis, :,
                                                            np.newaxis],
                                               input_shape=(up_bs, 1,
                                                            row * ratio,
                                                            concat_col),
                                               filter_shape=(1, 1, None, 1),
                                               border_mode=(pad, 0),
                                               subsample=(ratio, 1),
                                               filter_flip=True,
                                               filter_dilation=(1, 1))
        # upsampling cols
        upsampled_mat = conv2d_grad_wrt_inputs(output_grad=upsampled_row,
                                               filters=kern[np.newaxis,
                                                            np.newaxis,
                                                            np.newaxis, :],
                                               input_shape=(up_bs, 1,
                                                            row * ratio,
                                                            col * ratio),
                                               filter_shape=(1, 1, 1, None),
                                               border_mode=(0, pad),
                                               subsample=(1, ratio),
                                               filter_flip=True,
                                               filter_dilation=(1, 1))
    else:
        kern = bilinear_kernel_2D(ratio=ratio, normalize=True)
        upsampled_mat = conv2d_grad_wrt_inputs(output_grad=concat_mat,
                                               filters=kern[np.newaxis,
                                                            np.newaxis, :, :],
                                               input_shape=(up_bs, 1,
                                                            row * ratio,
                                                            col * ratio),
                                               filter_shape=(1, 1, None, None),
                                               border_mode=(pad, pad),
                                               subsample=(ratio, ratio),
                                               filter_flip=True,
                                               filter_dilation=(1, 1))

    return upsampled_mat.reshape((input.shape[0], input.shape[1],
                                  row * ratio, col * ratio))


class BaseAbstractConv(Op):
    """Base class for AbstractConv

    Parameters
    ----------
     convdim: The number of convolution dimensions (2 or 3).

     imshp: None, tuple/list of len ``(2 + convdim)`` of int or Constant variable
        The shape of the input parameter.
        Optional, possibly used to choose an optimal implementation.
        You can give ``None`` for any element of the list to specify that this
        element is not known at compile time.
        imshp is defined w.r.t the forward conv.

     kshp: None, tuple/list of len ``(2 + convdim)`` of int or Constant variable
        The shape of the filters parameter.
        Optional, possibly used to choose an optimal implementation.
        You can give ``None`` for any element of the list to specify that this
        element is not known at compile time.
        kshp is defined w.r.t the forward conv.

     border_mode: str, int or tuple of ``convdim`` ints
        Either of the following:

        ``'valid'``: apply filter wherever it completely overlaps with the
            input. Generates output of shape: input shape - filter shape + 1
        ``'full'``: apply filter wherever it partly overlaps with the input.
            Generates output of shape: input shape + filter shape - 1
        ``'half'``: pad input with a symmetric border of ``filter size // 2``
            in each convolution dimension, then perform a valid convolution.
            For filters with an odd filter size, this leads to the output
            shape being equal to the input shape.
        ``int``: pad input with a symmetric border of zeros of the given
            width, then perform a valid convolution.
        ``(int1, int2)``: (for 2D) pad input with a symmetric border of ``int1``,
            ``int2``, then perform a valid convolution.
        ``(int1, int2, int3)``: (for 3D) pad input with a symmetric border of
            ``int1``, ``int2`` and ``int3``, then perform a valid convolution.

    subsample: tuple of len ``convdim``
        Factor by which to subsample the output.
        Also called strides elsewhere.

    filter_flip: bool
        If ``True``, will flip the filter rows and columns
        before sliding them over the input. This operation is normally referred
        to as a convolution, and this is the default. If ``False``, the filters
        are not flipped and the operation is referred to as a
        cross-correlation.

    filter_dilation: tuple of len ``convdim``
        Factor by which to subsample (stride) the input.
        Also called dilation factor.
    """
    check_broadcast = False
    __props__ = ('convdim', 'border_mode', 'subsample', 'filter_flip',
                 'imshp', 'kshp', 'filter_dilation')

    def __init__(self, convdim,
                 imshp=None, kshp=None, border_mode="valid",
                 subsample=None, filter_flip=True, filter_dilation=None):

        self.convdim = convdim
        if convdim not in (2, 3):
            raise ValueError(
                'convolution dimension {} is not supported', convdim)

        if subsample is None:
            subsample = (1,) * convdim
        if filter_dilation is None:
            filter_dilation = (1,) * convdim

        if isinstance(border_mode, integer_types):
            border_mode = (border_mode,) * convdim
        if isinstance(border_mode, tuple):
            if len(border_mode) != convdim:
                raise ValueError(
                    'border mode must have exactly {} values, '
                    'but was {}'.format(convdim, border_mode))
            border_mode = tuple(map(int, border_mode))
        if border_mode == (0,) * convdim:
            border_mode = 'valid'
        if not ((isinstance(border_mode, tuple) and min(border_mode) >= 0) or
                border_mode in ('valid', 'full', 'half')):
            raise ValueError(
                'invalid border_mode {}, which must be either '
                '"valid", "full", "half", an integer or a tuple of {}'
                ' integers'.format(border_mode, convdim))

        self.imshp = tuple(imshp) if imshp else (None,) * (2 + convdim)
        for imshp_i in self.imshp:
            if imshp_i is not None:
                # Components of imshp should be constant or ints
                try:
                    get_scalar_constant_value(imshp_i,
                                              only_process_constants=True)
                except NotScalarConstantError:
                    reraise(ValueError,
                            ValueError("imshp should be None or a tuple of "
                                       "constant int values"),
                            sys.exc_info()[2])
        self.kshp = tuple(kshp) if kshp else (None,) * (2 + convdim)
        for kshp_i in self.kshp:
            if kshp_i is not None:
                # Components of kshp should be constant or ints
                try:
                    get_scalar_constant_value(kshp_i,
                                              only_process_constants=True)
                except NotScalarConstantError:
                    reraise(ValueError,
                            ValueError("kshp should be None or a tuple of "
                                       "constant int values"),
                            sys.exc_info()[2])
        self.border_mode = border_mode
        self.filter_flip = filter_flip

        if len(subsample) != convdim:
            raise ValueError("subsample must have {} elements".format(convdim))
        self.subsample = tuple(subsample)
        if len(filter_dilation) != convdim:
            raise ValueError("filter_dilation must have {} elements".format(convdim))
        self.filter_dilation = tuple(filter_dilation)

    def do_constant_folding(self, node):
        # Disable constant folding since there is no implementation.
        # This may change in the future.
        return False

    def flops(self, inp, outp):
        """ Useful with the hack in profiling to print the MFlops"""
        if self.convdim == 2:
            # if the output shape is correct, then this gives the correct
            # flops for any direction, sampling, padding, and border mode
            inputs, filters = inp
            outputs, = outp
            assert inputs[1] == filters[1]
            # nb mul and add by output pixel
            flops = filters[2] * filters[3] * 2
            # nb flops by output image
            flops *= outputs[2] * outputs[3]
            # nb patch multiplied
            flops *= inputs[1] * filters[0] * inputs[0]
            return flops
        else:
            # TODO implement for convdim == 3
            raise NotImplementedError(
                'flops not implemented for convdim={}', self.convdim)

    def conv(self, img, kern, mode="valid", dilation=1):
        """
        Basic slow Python 2D or 3D convolution for DebugMode
        """

        if not imported_scipy_signal:
            raise NotImplementedError(
                "AbstractConv perform requires the python package"
                " for scipy.signal to be installed.")
        if not (mode in ('valid', 'full')):
            raise ValueError(
                'invalid mode {}, which must be either '
                '"valid" or "full"'.format(mode))
        if isinstance(dilation, integer_types):
            dilation = (dilation,) * self.convdim
        if len(dilation) != self.convdim:
            raise ValueError(
                'invalid dilation {}, expected {} values'.format(dilation,
                                                                 self.convdim))

        out_shape = get_conv_output_shape(img.shape, kern.shape,
                                          mode, [1] * self.convdim, dilation)

        out = numpy.zeros(out_shape, dtype=img.dtype)
        dil_kern_shp = kern.shape[:-self.convdim] + tuple(
            (kern.shape[-self.convdim + i] - 1) * dilation[i] + 1
            for i in range(self.convdim))
        dilated_kern = numpy.zeros(dil_kern_shp, dtype=kern.dtype)
        dilated_kern[(slice(None), slice(None)) +
                     tuple(slice(None, None, dilation[i]) for i in range(self.convdim))
                     ] = kern

        if self.convdim == 2:
            val = _valfrommode(mode)
            bval = _bvalfromboundary('fill')

            with warnings.catch_warnings():
                warnings.simplefilter('ignore', numpy.ComplexWarning)
                for b in xrange(img.shape[0]):
                    for n in xrange(kern.shape[0]):
                        for im0 in xrange(img.shape[1]):
                            # some cast generates a warning here
                            out[b, n, ...] += _convolve2d(img[b, im0, ...],
                                                          dilated_kern[n, im0, ...],
                                                          1, val, bval, 0)
        elif self.convdim == 3:
            for b in xrange(img.shape[0]):
                for n in xrange(kern.shape[0]):
                    for im0 in xrange(img.shape[1]):
                        out[b, n, ...] += convolve(img[b, im0, ...],
                                                   dilated_kern[n, im0, ...],
                                                   mode)
        else:
            raise NotImplementedError('only 2D and 3D convolution are implemented')
        return out


class AbstractConv(BaseAbstractConv):
    """ Abstract Op for the forward convolution.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.
    """

    def __init__(self,
                 convdim,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=None,
                 filter_flip=True,
                 filter_dilation=None):
        super(AbstractConv, self).__init__(convdim=convdim,
                                           imshp=imshp, kshp=kshp,
                                           border_mode=border_mode,
                                           subsample=subsample,
                                           filter_flip=filter_flip,
                                           filter_dilation=filter_dilation)

    def make_node(self, img, kern):
        # Make sure both inputs are Variables with the same Type
        if not isinstance(img, theano.Variable):
            img = as_tensor_variable(img)
        if not isinstance(kern, theano.Variable):
            kern = as_tensor_variable(kern)
        ktype = img.type.clone(dtype=kern.dtype,
                               broadcastable=kern.broadcastable)
        kern = ktype.filter_variable(kern)

        if img.type.ndim != 2 + self.convdim:
            raise TypeError('img must be %dD tensor' % (2 + self.convdim))
        if kern.type.ndim != 2 + self.convdim:
            raise TypeError('kern must be %dD tensor' % (2 + self.convdim))

        broadcastable = [img.broadcastable[0],
                         kern.broadcastable[0]] + ([False] * self.convdim)
        output = img.type.clone(broadcastable=broadcastable)()
        return Apply(self, [img, kern], [output])

    def perform(self, node, inp, out_):
        img, kern = inp
        img = numpy.asarray(img)
        kern = numpy.asarray(kern)
        dil_kernshp = tuple((kern.shape[2 + i] - 1) * self.filter_dilation[i] + 1
                            for i in range(self.convdim))
        o, = out_
        mode = self.border_mode

        if not ((isinstance(mode, tuple) and min(mode) >= 0) or
                mode in ('valid', 'full', 'half')):
            raise ValueError(
                'invalid border_mode {}, which must be either '
                '"valid", "full", "half", an integer or a tuple of'
                ' integers'.format(mode))

        if mode == "full":
            mode = tuple(dil_kernshp[i] - 1 for i in range(self.convdim))
        elif mode == "half":
            mode = tuple(dil_kernshp[i] // 2 for i in range(self.convdim))
        if isinstance(mode, tuple):
            pad = tuple(int(mode[i]) for i in range(self.convdim))
            mode = "valid"
            new_img = numpy.zeros((img.shape[0], img.shape[1]) +
                                  tuple(img.shape[i + 2] + 2 * pad[i]
                                        for i in range(self.convdim)),
                                  dtype=img.dtype)
            new_img[(slice(None), slice(None)) +
                    tuple(slice(pad[i], img.shape[i + 2] + pad[i])
                          for i in range(self.convdim))] = img
            img = new_img
        if not self.filter_flip:
            kern = kern[(slice(None), slice(None)) + (slice(None, None, -1),) * self.convdim]
        conv_out = self.conv(img, kern, mode="valid", dilation=self.filter_dilation)
        conv_out = conv_out[(slice(None), slice(None)) +
                            tuple(slice(None, None, self.subsample[i])
                                  for i in range(self.convdim))]

        o[0] = node.outputs[0].type.filter(conv_out)

    def R_op(self, inputs, eval_points):
        rval = None
        if eval_points[0] is not None:
            rval = self.make_node(eval_points[0], inputs[1]).outputs[0]
        if eval_points[1] is not None:
            if rval is None:
                rval = self.make_node(inputs[0], eval_points[1]).outputs[0]
            else:
                rval += self.make_node(inputs[0], eval_points[1]).outputs[0]
        return [rval]

    def infer_shape(self, node, input_shapes):
        imshp = input_shapes[0]
        kshp = input_shapes[1]

        # replace symbolic shapes with known constant shapes
        if self.imshp is not None:
            imshp = [imshp[i] if self.imshp[i] is None else self.imshp[i]
                     for i in range(2 + self.convdim)]
        if self.kshp is not None:
            kshp = [kshp[i] if self.kshp[i] is None else self.kshp[i]
                    for i in range(2 + self.convdim)]
        res = get_conv_output_shape(imshp, kshp, self.border_mode,
                                    self.subsample, self.filter_dilation)
        return [res]


class AbstractConv2d(AbstractConv):
    """ Abstract Op for the forward convolution.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.
    """

    def __init__(self,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=(1, 1),
                 filter_flip=True,
                 filter_dilation=(1, 1)):
        super(AbstractConv2d, self).__init__(convdim=2,
                                             imshp=imshp, kshp=kshp,
                                             border_mode=border_mode,
                                             subsample=subsample,
                                             filter_flip=filter_flip,
                                             filter_dilation=filter_dilation)

    def grad(self, inp, grads):
        bottom, weights = inp
        top, = grads
        d_bottom = AbstractConv2d_gradInputs(self.imshp, self.kshp,
                                             self.border_mode,
                                             self.subsample,
                                             self.filter_flip,
                                             self.filter_dilation)(
            weights, top, bottom.shape[-2:])
        d_weights = AbstractConv2d_gradWeights(self.imshp, self.kshp,
                                               self.border_mode,
                                               self.subsample,
                                               self.filter_flip,
                                               self.filter_dilation)(

            bottom, top, weights.shape[-2:])

        # Make sure that the broadcastable pattern of the inputs is used
        # for the gradients, even if the grad opts are not able to infer
        # that the dimensions are broadcastable.
        # Also make sure that the gradient lives on the same device than
        # the corresponding input.
        d_bottom = patternbroadcast(d_bottom, bottom.broadcastable)
        d_bottom = bottom.type.filter_variable(d_bottom)
        d_weights = patternbroadcast(d_weights, weights.broadcastable)
        d_weights = weights.type.filter_variable(d_weights)
        return d_bottom, d_weights


class AbstractConv3d(AbstractConv):
    """ Abstract Op for the forward convolution.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.
    """

    def __init__(self,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=(1, 1, 1),
                 filter_flip=True,
                 filter_dilation=(1, 1, 1)):
        super(AbstractConv3d, self).__init__(convdim=3,
                                             imshp=imshp, kshp=kshp,
                                             border_mode=border_mode,
                                             subsample=subsample,
                                             filter_flip=filter_flip,
                                             filter_dilation=filter_dilation)

    def grad(self, inp, grads):
        bottom, weights = inp
        top, = grads
        d_bottom = AbstractConv3d_gradInputs(self.imshp, self.kshp,
                                             self.border_mode,
                                             self.subsample,
                                             self.filter_flip,
                                             self.filter_dilation)(
            weights, top, bottom.shape[-3:])
        d_weights = AbstractConv3d_gradWeights(self.imshp, self.kshp,
                                               self.border_mode,
                                               self.subsample,
                                               self.filter_flip,
                                               self.filter_dilation)(

            bottom, top, weights.shape[-3:])

        # Make sure that the broadcastable pattern of the inputs is used
        # for the gradients, even if the grad opts are not able to infer
        # that the dimensions are broadcastable.
        # Also make sure that the gradient lives on the same device than
        # the corresponding input.
        d_bottom = patternbroadcast(d_bottom, bottom.broadcastable)
        d_bottom = bottom.type.filter_variable(d_bottom)
        d_weights = patternbroadcast(d_weights, weights.broadcastable)
        d_weights = weights.type.filter_variable(d_weights)
        return d_bottom, d_weights


class AbstractConv_gradWeights(BaseAbstractConv):
    """Gradient wrt. filters for `AbstractConv`.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.

    :note: You will not want to use this directly, but rely on
           Theano's automatic differentiation or graph optimization to
           use it as needed.

    """
    def __init__(self,
                 convdim,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=None,
                 filter_flip=True,
                 filter_dilation=None):
        super(AbstractConv_gradWeights, self).__init__(convdim=convdim,
                                                       imshp=imshp, kshp=kshp,
                                                       border_mode=border_mode,
                                                       subsample=subsample,
                                                       filter_flip=filter_flip,
                                                       filter_dilation=filter_dilation)

    # Update shape/height_width
    def make_node(self, img, topgrad, shape):
        # Make sure both inputs are Variables with the same Type
        if not isinstance(img, theano.Variable):
            img = as_tensor_variable(img)
        if not isinstance(topgrad, theano.Variable):
            topgrad = as_tensor_variable(topgrad)
        gtype = img.type.clone(dtype=topgrad.dtype,
                               broadcastable=topgrad.broadcastable)
        topgrad = gtype.filter_variable(topgrad)

        if img.type.ndim != 2 + self.convdim:
            raise TypeError('img must be %dD tensor' % (2 + self.convdim))
        if topgrad.type.ndim != 2 + self.convdim:
            raise TypeError('topgrad must be %dD tensor' % (2 + self.convdim))

        shape = as_tensor_variable(shape)
        broadcastable = [topgrad.broadcastable[1],
                         img.broadcastable[1]] + ([False] * self.convdim)
        output = img.type.clone(broadcastable=broadcastable)()
        return Apply(self, [img, topgrad, shape], [output])

    def perform(self, node, inp, out_):
        img, topgrad, shape = inp
        img = numpy.asarray(img)
        topgrad = numpy.asarray(topgrad)

        o, = out_

        mode = self.border_mode
        if not ((isinstance(mode, tuple) and min(mode) >= 0) or
                mode in ('valid', 'full', 'half')):
            raise ValueError(
                'invalid border_mode {}, which must be either '
                '"valid", "full", "half", an integer or a tuple of'
                ' integers'.format(mode))

        dil_shape = tuple((shape[i] - 1) * self.filter_dilation[i] + 1
                          for i in range(self.convdim))

        if mode == "full":
            mode = tuple(dil_shape[i] - 1 for i in range(self.convdim))
        elif mode == "half":
            mode = tuple(dil_shape[i] // 2 for i in range(self.convdim))
        if isinstance(mode, tuple):
            pad = tuple(int(mode[i]) for i in range(self.convdim))

            mode = "valid"
            new_img = numpy.zeros((img.shape[0], img.shape[1]) +
                                  tuple(img.shape[i + 2] + 2 * pad[i]
                                        for i in range(self.convdim)),
                                  dtype=img.dtype)
            new_img[(slice(None), slice(None)) +
                    tuple(slice(pad[i], img.shape[i + 2] + pad[i])
                          for i in range(self.convdim))] = img
            img = new_img

        if any(self.subsample[i] > 1 for i in range(self.convdim)):
            new_shape = ((topgrad.shape[0], topgrad.shape[1]) +
                         tuple(img.shape[i + 2] - dil_shape[i] + 1
                               for i in range(self.convdim)))
            new_topgrad = numpy.zeros((new_shape), dtype=topgrad.dtype)
            new_topgrad[(slice(None), slice(None)) +
                        tuple(slice(None, None, self.subsample[i])
                              for i in range(self.convdim))] = topgrad
            topgrad = new_topgrad

        axes_order = (1, 0) + tuple(range(2, self.convdim + 2))
        flip_filters = ((slice(None), slice(None)) +
                        (slice(None, None, -1),) * self.convdim)
        topgrad = topgrad.transpose(axes_order)[flip_filters]
        img = img.transpose(axes_order)
        kern = self.conv(img, topgrad, mode="valid")
        if any(self.filter_dilation[i] > 1 for i in range(self.convdim)):
            kern = kern[(slice(None), slice(None)) +
                        tuple(slice(None, None, self.filter_dilation[i])
                              for i in range(self.convdim))]
        if self.filter_flip:
            kern = kern.transpose(axes_order)[flip_filters]
        else:
            kern = kern.transpose(axes_order)
        o[0] = node.outputs[0].type.filter(kern)

    def connection_pattern(self, node):
        return [[1], [1], [0]]  # no connection to height, width

    def infer_shape(self, node, input_shapes):
        # We use self.kshp (that was passed when creating the Op) if possible,
        # or fall back to the `shape` input of the node.
        # TODO: when there is no subsampling, try to infer the kernel shape
        # from the shapes of inputs.
        imshp = input_shapes[0]
        topshp = input_shapes[1]
        kshp = self.kshp[:] if self.kshp is not None else [None] * (2 + self.convdim)
        fallback_kshp = ([topshp[1], imshp[1]] +
                         [node.inputs[2][i] for i in range(self.convdim)])
        kshp = [fallback_kshp[i] if kshp[i] is None else kshp[i]
                for i in range(2 + self.convdim)]
        return [kshp]


class AbstractConv2d_gradWeights(AbstractConv_gradWeights):
    """Gradient wrt. filters for `AbstractConv2d`.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.

    :note: You will not want to use this directly, but rely on
           Theano's automatic differentiation or graph optimization to
           use it as needed.

    """
    def __init__(self,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=(1, 1),
                 filter_flip=True,
                 filter_dilation=(1, 1)):
        super(AbstractConv2d_gradWeights, self).__init__(convdim=2,
                                                         imshp=imshp, kshp=kshp,
                                                         border_mode=border_mode,
                                                         subsample=subsample,
                                                         filter_flip=filter_flip,
                                                         filter_dilation=filter_dilation)

    def grad(self, inp, grads):
        bottom, top = inp[:2]
        weights, = grads
        d_bottom = AbstractConv2d_gradInputs(self.imshp, self.kshp,
                                             self.border_mode,
                                             self.subsample,
                                             self.filter_flip,
                                             self.filter_dilation)(weights,
                                                                   top,
                                                                   bottom.shape[-2:])
        d_top = AbstractConv2d(self.imshp,
                               self.kshp,
                               self.border_mode,
                               self.subsample,
                               self.filter_flip,
                               self.filter_dilation)(bottom, weights)
        # Make sure that the broadcastable pattern of the inputs is used
        # for the gradients, even if the grad opts are not able to infer
        # that the dimensions are broadcastable.
        # Also make sure that the gradient lives on the same device than
        # the corresponding input.
        d_bottom = patternbroadcast(d_bottom, bottom.broadcastable)
        d_bottom = bottom.type.filter_variable(d_bottom)
        d_top = patternbroadcast(d_top, top.broadcastable)
        d_top = top.type.filter_variable(d_top)

        d_height_width = (theano.gradient.DisconnectedType()(),)
        return (d_bottom, d_top) + d_height_width


class AbstractConv3d_gradWeights(AbstractConv_gradWeights):
    """Gradient wrt. filters for `AbstractConv3d`.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.

    :note: You will not want to use this directly, but rely on
           Theano's automatic differentiation or graph optimization to
           use it as needed.

    """
    def __init__(self,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=(1, 1, 1),
                 filter_flip=True,
                 filter_dilation=(1, 1, 1)):
        super(AbstractConv3d_gradWeights, self).__init__(convdim=3,
                                                         imshp=imshp, kshp=kshp,
                                                         border_mode=border_mode,
                                                         subsample=subsample,
                                                         filter_flip=filter_flip,
                                                         filter_dilation=filter_dilation)

    def grad(self, inp, grads):
        bottom, top = inp[:2]
        weights, = grads
        d_bottom = AbstractConv3d_gradInputs(self.imshp, self.kshp,
                                             self.border_mode,
                                             self.subsample,
                                             self.filter_flip,
                                             self.filter_dilation)(weights,
                                                                   top,
                                                                   bottom.shape[-3:])
        d_top = AbstractConv3d(self.imshp,
                               self.kshp,
                               self.border_mode,
                               self.subsample,
                               self.filter_flip,
                               self.filter_dilation)(bottom, weights)
        # Make sure that the broadcastable pattern of the inputs is used
        # for the gradients, even if the grad opts are not able to infer
        # that the dimensions are broadcastable.
        # Also make sure that the gradient lives on the same device than
        # the corresponding input.
        d_bottom = patternbroadcast(d_bottom, bottom.broadcastable)
        d_bottom = bottom.type.filter_variable(d_bottom)
        d_top = patternbroadcast(d_top, top.broadcastable)
        d_top = top.type.filter_variable(d_top)

        d_depth_height_width = (theano.gradient.DisconnectedType()(),)
        return (d_bottom, d_top) + d_depth_height_width


class AbstractConv_gradInputs(BaseAbstractConv):
    """Gradient wrt. inputs for `AbstractConv`.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.

    :note: You will not want to use this directly, but rely on
           Theano's automatic differentiation or graph optimization to
           use it as needed.

    """

    def __init__(self,
                 convdim,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=None,
                 filter_flip=True,
                 filter_dilation=None):
        super(AbstractConv_gradInputs, self).__init__(convdim=convdim,
                                                      imshp=imshp, kshp=kshp,
                                                      border_mode=border_mode,
                                                      subsample=subsample,
                                                      filter_flip=filter_flip,
                                                      filter_dilation=filter_dilation)

    # Update shape/height_width
    def make_node(self, kern, topgrad, shape):
        # Make sure both inputs are Variables with the same Type
        if not isinstance(kern, theano.Variable):
            kern = as_tensor_variable(kern)
        if not isinstance(topgrad, theano.Variable):
            topgrad = as_tensor_variable(topgrad)
        gtype = kern.type.clone(dtype=topgrad.dtype,
                                broadcastable=topgrad.broadcastable)
        topgrad = gtype.filter_variable(topgrad)

        if kern.type.ndim != 2 + self.convdim:
            raise TypeError('kern must be %dD tensor' % (2 + self.convdim))
        if topgrad.type.ndim != 2 + self.convdim:
            raise TypeError('topgrad must be %dD tensor' % (2 + self.convdim))

        shape = as_tensor_variable(shape)
        broadcastable = [topgrad.type.broadcastable[0],
                         kern.type.broadcastable[1]] + ([False] * self.convdim)
        output = kern.type.clone(broadcastable=broadcastable)()
        return Apply(self, [kern, topgrad, shape], [output])

    def perform(self, node, inp, out_):
        kern, topgrad, shape = inp
        kern = numpy.asarray(kern)
        topgrad = numpy.asarray(topgrad)
        o, = out_

        mode = self.border_mode
        if not ((isinstance(mode, tuple) and min(mode) >= 0) or
                mode in ('valid', 'full', 'half')):
            raise ValueError(
                'invalid border_mode {}, which must be either '
                '"valid", "full", "half", an integer or a tuple of'
                ' integers'.format(mode))

        dil_kernshp = tuple((kern.shape[i + 2] - 1) * self.filter_dilation[i] + 1
                            for i in range(self.convdim))
        pad = (0,) * self.convdim
        if mode == "full":
            pad = tuple(dil_kernshp[i] - 1 for i in range(self.convdim))
        elif mode == "half":
            pad = tuple(dil_kernshp[i] // 2 for i in range(self.convdim))
        elif isinstance(mode, tuple):
            pad = tuple(mode[i] for i in range(self.convdim))
        if any(self.subsample[i] > 1 for i in range(self.convdim)):
            new_shape = ((topgrad.shape[0], topgrad.shape[1]) +
                         tuple(shape[i] + 2 * pad[i] - dil_kernshp[i] + 1
                               for i in range(self.convdim)))
            new_topgrad = numpy.zeros((new_shape), dtype=topgrad.dtype)
            new_topgrad[(slice(None), slice(None)) +
                        tuple(slice(None, None, self.subsample[i])
                              for i in range(self.convdim))] = topgrad
            topgrad = new_topgrad

        axes_order = (1, 0) + tuple(range(2, self.convdim + 2))
        flip_filters = ((slice(None), slice(None)) +
                        (slice(None, None, -1),) * self.convdim)
        kern = kern.transpose(axes_order)
        if self.filter_flip:
            topgrad = topgrad[flip_filters]
        img = self.conv(topgrad, kern, mode="full", dilation=self.filter_dilation)
        if self.filter_flip:
            img = img[flip_filters]
        if any(p > 0 for p in pad):
            img = img[(slice(None), slice(None)) +
                      tuple(slice(pad[i], img.shape[i + 2] - pad[i])
                            for i in range(self.convdim))]
        o[0] = node.outputs[0].type.filter(img)

    def connection_pattern(self, node):
        return [[1], [1], [0]]  # no connection to height, width

    def infer_shape(self, node, input_shapes):
        # We use self.imshp (that was passed when creating the Op) if possible,
        # or fall back to the `shape` input of the node.
        # TODO: when there is no subsampling, try to infer the image shape
        # from the shapes of inputs.
        kshp = input_shapes[0]
        topshp = input_shapes[1]
        imshp = self.imshp[:] if self.imshp is not None else [None] * (2 + self.convdim)
        fallback_imshp = ([topshp[0], kshp[1]] +
                          [node.inputs[2][i] for i in range(self.convdim)])
        imshp = [fallback_imshp[i] if imshp[i] is None else imshp[i]
                 for i in range(2 + self.convdim)]
        return [imshp]


class AbstractConv2d_gradInputs(AbstractConv_gradInputs):
    """Gradient wrt. inputs for `AbstractConv2d`.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.

    :note: You will not want to use this directly, but rely on
           Theano's automatic differentiation or graph optimization to
           use it as needed.

    """

    def __init__(self,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=(1, 1),
                 filter_flip=True,
                 filter_dilation=(1, 1)):
        super(AbstractConv2d_gradInputs, self).__init__(convdim=2,
                                                        imshp=imshp, kshp=kshp,
                                                        border_mode=border_mode,
                                                        subsample=subsample,
                                                        filter_flip=filter_flip,
                                                        filter_dilation=filter_dilation)

    def grad(self, inp, grads):
        weights, top = inp[:2]
        bottom, = grads
        d_weights = AbstractConv2d_gradWeights(self.imshp, self.kshp,
                                               self.border_mode,
                                               self.subsample,
                                               self.filter_flip,
                                               self.filter_dilation)(bottom, top,
                                                                     weights.shape[-2:])
        d_top = AbstractConv2d(self.imshp, self.kshp,
                               self.border_mode,
                               self.subsample,
                               self.filter_flip,
                               self.filter_dilation)(bottom, weights)
        # Make sure that the broadcastable pattern of the inputs is used
        # for the gradients, even if the grad opts are not able to infer
        # that the dimensions are broadcastable.
        # Also make sure that the gradient lives on the same device than
        # the corresponding input.
        d_weights = patternbroadcast(d_weights, weights.broadcastable)
        d_weights = weights.type.filter_variable(d_weights)
        d_top = patternbroadcast(d_top, top.broadcastable)
        d_top = top.type.filter_variable(d_top)

        d_height_width = (theano.gradient.DisconnectedType()(),)
        return (d_weights, d_top) + d_height_width


class AbstractConv3d_gradInputs(AbstractConv_gradInputs):
    """Gradient wrt. inputs for `AbstractConv3d`.
    Refer to :func:`BaseAbstractConv <theano.tensor.nnet.abstract_conv.BaseAbstractConv>`
    for a more detailed documentation.

    :note: You will not want to use this directly, but rely on
           Theano's automatic differentiation or graph optimization to
           use it as needed.

    """

    def __init__(self,
                 imshp=None,
                 kshp=None,
                 border_mode="valid",
                 subsample=(1, 1, 1),
                 filter_flip=True,
                 filter_dilation=(1, 1, 1)):
        super(AbstractConv3d_gradInputs, self).__init__(convdim=3,
                                                        imshp=imshp, kshp=kshp,
                                                        border_mode=border_mode,
                                                        subsample=subsample,
                                                        filter_flip=filter_flip,
                                                        filter_dilation=filter_dilation)

    def grad(self, inp, grads):
        weights, top = inp[:2]
        bottom, = grads
        d_weights = AbstractConv3d_gradWeights(self.imshp, self.kshp,
                                               self.border_mode,
                                               self.subsample,
                                               self.filter_flip,
                                               self.filter_dilation)(bottom, top,
                                                                     weights.shape[-3:])
        d_top = AbstractConv3d(self.imshp, self.kshp,
                               self.border_mode,
                               self.subsample,
                               self.filter_flip,
                               self.filter_dilation)(bottom, weights)
        # Make sure that the broadcastable pattern of the inputs is used
        # for the gradients, even if the grad opts are not able to infer
        # that the dimensions are broadcastable.
        # Also make sure that the gradient lives on the same device than
        # the corresponding input.
        d_weights = patternbroadcast(d_weights, weights.broadcastable)
        d_weights = weights.type.filter_variable(d_weights)
        d_top = patternbroadcast(d_top, top.broadcastable)
        d_top = top.type.filter_variable(d_top)

        d_depth_height_width = (theano.gradient.DisconnectedType()(),)
        return (d_weights, d_top) + d_depth_height_width
