""" Ops for downsampling images.

Planned:
DownsampleFactorMax, DownsampleAvg, DownsampleSoftmax.

"""
from __future__ import print_function
# This file should move along with conv.py
from six.moves import xrange
import six.moves.builtins as builtins

import numpy

import theano
from theano import gof, Op, tensor, Variable, Apply

from theano.tensor.opt import register_canonicalize

def max_pool2D(*args, **kwargs):
    import sys
    print("DEPRECATION: max_pool2D renamed to max_pool_2d", file=sys.stderr)
    return max_pool_2d(*args, **kwargs)


def max_pool_2d_same_size(input, patch_size):
    """
    Takes as input a 4-D tensor. It sets all non maximum values
    of non-overlapping patches of size (patch_size[0],patch_size[1]) to zero,
    keeping only the maximum values. The output has the same dimensions as
    the input.

    :type input: 4-D theano tensor of input images.
    :param input: input images. Max pooling will be done over the 2 last
        dimensions.
    :type patch_size: tuple of length 2
    :param patch_size: size of the patch (patch height, patch width).
        (2,2) will retain only one non-zero value per patch of 4 values.
    """
    output = DownsampleFactorMax(patch_size, True)(input)
    outs = MaxPoolGrad(patch_size, True)(input, output, output)
    return outs


def max_pool_2d(input, ds, ignore_border=False, st=None, padding=(0, 0),
                mode='max'):
    """
    Takes as input a N-D tensor, where N >= 2. It downscales the input image by
    the specified factor, by keeping only the maximum value of non-overlapping
    patches of size (ds[0],ds[1])

    :type input: N-D theano tensor of input images.
    :param input: input images. Max pooling will be done over the 2 last
        dimensions.
    :type ds: tuple of length 2
    :param ds: factor by which to downscale (vertical ds, horizontal ds).
        (2,2) will halve the image in each dimension.
    :type ignore_border: bool
    :param ignore_border: When True, (5,5) input with ds=(2,2)
        will generate a (2,2) output. (3,3) otherwise.
    :type st: tuple of lenght 2
    :param st: stride size, which is the number of shifts
        over rows/cols to get the the next pool region.
        if st is None, it is considered equal to ds
        (no overlap on pooling regions)
    :param padding: (pad_h, pad_w), pad zeros to extend beyond four borders
            of the images, pad_h is the size of the top and bottom margins,
            and pad_w is the size of the left and right margins.
    :type padding: tuple of two ints
    :param mode: 'max', 'sum', 'average_inc_pad' or 'average_exc_pad'.
        Operation executed on each window.  `max` and `sum` always exclude
        the padding in the computation. `average` gives you the choice to
        include or exclude it.
    :type mode: string
    """
    if input.ndim < 2:
        raise NotImplementedError('max_pool_2d requires a dimension >= 2')
    if input.ndim == 4:
        op = DownsampleFactorMax(ds, ignore_border, st=st, padding=padding,
                                 mode=mode)
        output = op(input)
        return output

    # extract image dimensions
    img_shape = input.shape[-2:]

    # count the number of "leading" dimensions, store as dmatrix
    batch_size = tensor.prod(input.shape[:-2])
    batch_size = tensor.shape_padright(batch_size, 1)

    # store as 4D tensor with shape: (batch_size,1,height,width)
    new_shape = tensor.cast(tensor.join(0, batch_size,
                                        tensor.as_tensor([1]),
                                        img_shape), 'int64')
    input_4D = tensor.reshape(input, new_shape, ndim=4)

    # downsample mini-batch of images
    op = DownsampleFactorMax(ds, ignore_border, st=st, padding=padding,
                             mode=mode)
    output = op(input_4D)

    # restore to original shape
    outshp = tensor.join(0, input.shape[:-2], output.shape[-2:])
    return tensor.reshape(output, outshp, ndim=input.ndim)


class DownsampleFactorMax(Op):
    """For N-dimensional tensors, consider that the last two
    dimensions span images.  This Op downsamples these images by
    taking the max, sum or average over different patch.

    """
    __props__ = ('ds', 'ignore_border', 'st', 'padding', 'mode')

    @staticmethod
    def out_shape(imgshape, ds, ignore_border=False, st=None, padding=(0, 0)):
        """Return the shape of the output from this op, for input of given
        shape and flags.

        :param imgshape: the shape of a tensor of images. The last two elements
            are interpreted as the number of rows, and the number of cols.
        :type imgshape: tuple, list, or similar of integer or
            scalar Theano variable.

        :param ds: downsample factor over rows and columns
                   this parameter indicates the size of the pooling region
        :type ds: list or tuple of two ints

        :param st: the stride size. This is the distance between the pooling
                   regions. If it's set to None, in which case it equlas ds.
        :type st: list or tuple of two ints

        :param ignore_border: if ds doesn't divide imgshape, do we include an
            extra row/col of partial downsampling (False) or ignore it (True).
        :type ignore_border: bool

        :param padding: (pad_h, pad_w), pad zeros to extend beyond four borders
            of the images, pad_h is the size of the top and bottom margins,
            and pad_w is the size of the left and right margins.
        :type padding: tuple of two ints

        :rtype: list
        :returns: the shape of the output from this op, for input of given
            shape.  This will have the same length as imgshape, but with last
            two elements reduced as per the downsampling & ignore_border flags.
        """
        if len(imgshape) < 2:
            raise TypeError('imgshape must have at least two elements '
                            '(rows, cols)')

        if st is None:
            st = ds
        r, c = imgshape[-2:]
        r += padding[0] * 2
        c += padding[1] * 2

        if ignore_border:
            out_r = (r - ds[0]) // st[0] + 1
            out_c = (c - ds[1]) // st[1] + 1
            if isinstance(r, theano.Variable):
                nr = tensor.maximum(out_r, 0)
            else:
                nr = numpy.maximum(out_r, 0)
            if isinstance(c, theano.Variable):
                nc = tensor.maximum(out_c, 0)
            else:
                nc = numpy.maximum(out_c, 0)
        else:
            if isinstance(r, theano.Variable):
                nr = tensor.switch(tensor.ge(st[0], ds[0]),
                                   (r - 1) // st[0] + 1,
                                   tensor.maximum(0, (r - 1 - ds[0])
                                                  // st[0] + 1) + 1)
            elif st[0] >= ds[0]:
                nr = (r - 1) // st[0] + 1
            else:
                nr = max(0, (r - 1 - ds[0]) // st[0] + 1) + 1

            if isinstance(c, theano.Variable):
                nc = tensor.switch(tensor.ge(st[1], ds[1]),
                                   (c - 1) // st[1] + 1,
                                   tensor.maximum(0, (c - 1 - ds[1])
                                                  // st[1] + 1) + 1)
            elif st[1] >= ds[1]:
                nc = (c - 1) // st[1] + 1
            else:
                nc = max(0, (c - 1 - ds[1]) // st[1] + 1) + 1

        rval = list(imgshape[:-2]) + [nr, nc]
        return rval

    def __init__(self, ds, ignore_border=False, st=None, padding=(0, 0),
                 mode='max'):
        """ Take the max, sum or average or different input patches.

        :param ds: downsample factor over rows and column.
                   ds indicates the pool region size.
        :type ds: list or tuple of two ints

        :param ignore_border: if ds doesn't divide imgshape, do we include
            an extra row/col of partial downsampling (False) or
            ignore it (True).
        :type ignore_border: bool

        : param st: stride size, which is the number of shifts
            over rows/cols to get the the next pool region.
            if st is None, it is considered equal to ds
            (no overlap on pooling regions)
        : type st: list or tuple of two ints or None

        :param padding: (pad_h, pad_w), pad zeros to extend beyond four borders
            of the images, pad_h is the size of the top and bottom margins,
            and pad_w is the size of the left and right margins.
        :type padding: tuple of two ints

        :param mode: 'max', 'sum', 'average_inc_pad', 'average_exc_pad'.
            ('average_inc_pad' excludes the padding from the count,
            'average_exc_pad' include it)

        """
        self.ds = tuple(ds)
        if not all([isinstance(d, int) for d in ds]):
            raise ValueError(
                "DownsampleFactorMax downsample parameters must be ints."
                " Got %s" % str(ds))
        if st is None:
            st = ds
        assert isinstance(st, (tuple, list))
        self.st = tuple(st)
        self.ignore_border = ignore_border
        self.padding = tuple(padding)
        if self.padding != (0, 0) and not ignore_border:
            raise NotImplementedError(
                'padding works only with ignore_border=True')
        if self.padding[0] >= self.ds[0] or self.padding[1] >= self.ds[1]:
            raise NotImplementedError(
                'padding_h and padding_w must be smaller than strides')
        if mode not in ['max', 'average_inc_pad', 'average_exc_pad', 'sum']:
            raise ValueError(
                "DownsampleFactorMax mode parameter only support 'max', 'sum',"
                " 'average_inc_pad' and 'average_exc_pad'. Got %s" % mode)
        self.mode = mode

    def make_node(self, x):
        if x.type.ndim != 4:
            raise TypeError()
        # TODO: consider restricting the dtype?
        x = tensor.as_tensor_variable(x)
        return gof.Apply(self, [x], [x.type()])

    def perform(self, node, inp, out):
        x, = inp
        z, = out
        if len(x.shape) != 4:
            raise NotImplementedError(
                'DownsampleFactorMax requires 4D input for now')
        z_shape = self.out_shape(x.shape, self.ds, self.ignore_border, self.st,
                                 self.padding)
        if (z[0] is None) or (z[0].shape != z_shape):
            z[0] = numpy.empty(z_shape, dtype=x.dtype)
        zz = z[0]
        # number of pooling output rows
        pr = zz.shape[-2]
        # number of pooling output cols
        pc = zz.shape[-1]
        ds0, ds1 = self.ds
        st0, st1 = self.st
        pad_h = self.padding[0]
        pad_w = self.padding[1]
        img_rows = x.shape[-2] + 2 * pad_h
        img_cols = x.shape[-1] + 2 * pad_w
        inc_pad = self.mode == 'average_inc_pad'

        # pad the image
        if self.padding != (0, 0):
            y = numpy.zeros(
                (x.shape[0], x.shape[1], img_rows, img_cols),
                dtype=x.dtype)
            y[:, :, pad_h:(img_rows-pad_h), pad_w:(img_cols-pad_w)] = x
        else:
            y = x
        func = numpy.max
        if self.mode == 'sum':
            func = numpy.sum
        elif self.mode != 'max':
            func = numpy.average

        for n in xrange(x.shape[0]):
            for k in xrange(x.shape[1]):
                for r in xrange(pr):
                    row_st = r * st0
                    row_end = builtins.min(row_st + ds0, img_rows)
                    if not inc_pad:
                        row_st = builtins.max(row_st, self.padding[0])
                        row_end = builtins.min(row_end, x.shape[-2] + pad_h)
                    for c in xrange(pc):
                        col_st = c * st1
                        col_end = builtins.min(col_st + ds1, img_cols)
                        if not inc_pad:
                            col_st = builtins.max(col_st, self.padding[1])
                            col_end = builtins.min(col_end,
                                                      x.shape[-1] + pad_w)
                        zz[n, k, r, c] = func(y[
                            n, k, row_st:row_end, col_st:col_end])

    def infer_shape(self, node, in_shapes):
        shp = self.out_shape(in_shapes[0], self.ds,
                             self.ignore_border, self.st, self.padding)
        return [shp]

    def grad(self, inp, grads):
        x, = inp
        gz, = grads
        if self.mode == 'max':
            maxout = self(x)
            return [MaxPoolGrad(self.ds,
                                ignore_border=self.ignore_border,
                                st=self.st, padding=self.padding)(
                                    x, maxout, gz)]
        else:
            return [AveragePoolGrad(self.ds,
                                    ignore_border=self.ignore_border,
                                    st=self.st, padding=self.padding,
                                    mode=self.mode)(
                                        x, gz)]
    def c_headers(self):
        return ['<algorithm>']

    def c_code(self, node, name, inp, out, sub):
        if self.mode not in ('max', 'sum', 'average_exc_pad', 'average_inc_pad'):
            raise theano.gof.utils.MethodNotDefined()
        x, = inp
        z, = out
        fail = sub['fail']
        ignore_border = int(self.ignore_border)
        ds0, ds1 = self.ds
        st0, st1 = self.st
        pd0, pd1 = self.padding
        ccode = """
        int typenum = PyArray_ObjectType((PyObject*)%(x)s, 0);
        int z_r, z_c; // shape of the output
        int r, c; // shape of the padded_input
        if(PyArray_NDIM(%(x)s)!=4)
        {
            PyErr_SetString(PyExc_ValueError, "x must be a 4d ndarray");
            %(fail)s;
        }
        r = PyArray_DIMS(%(x)s)[2];
        c = PyArray_DIMS(%(x)s)[3];
        r += %(pd0)s * 2;
        c += %(pd1)s * 2;

        if (%(pd0)s != 0 && %(pd1)s != 0 && !%(ignore_border)s)
            {
              PyErr_SetString(PyExc_ValueError,
                "padding must be (0,0) when ignore border is False");
              %(fail)s;
            }
        if (%(ignore_border)s)
        {

            // '/' in C is different from '/' in python
            if (r - %(ds0)s < 0)
            {
              z_r = 0;
            }
            else
            {
              z_r = (r - %(ds0)s) / %(st0)s + 1;
            }
            if (c - %(ds1)s < 0)
            {
              z_c = 0;
            }
            else
            {
              z_c = (c - %(ds1)s) / %(st1)s + 1;
            }
        }
        else
        {
            // decide how many rows the output has
            if (%(st0)s >= %(ds0)s)
            {
                z_r = (r - 1) / %(st0)s + 1;
            }
            else
            {
                z_r = std::max(0, (r - 1 - %(ds0)s) / %(st0)s + 1) + 1;
            }
            // decide how many columns the output has
            if (%(st1)s >= %(ds1)s)
            {
                z_c = (c - 1) / %(st1)s + 1;
            }
            else
            {
                z_c = std::max(0, (c - 1 - %(ds1)s) / %(st1)s + 1) + 1;
            }
        }
        // memory allocation of z if necessary
        if ((!%(z)s)
          || *PyArray_DIMS(%(z)s)!=4
          ||(PyArray_DIMS(%(z)s)[0] != PyArray_DIMS(%(x)s)[0])
          ||(PyArray_DIMS(%(z)s)[1] != PyArray_DIMS(%(x)s)[1])
          ||(PyArray_DIMS(%(z)s)[2] != z_r)
          ||(PyArray_DIMS(%(z)s)[3] != z_c)
          )
        {
          if (%(z)s) Py_XDECREF(%(z)s);
          npy_intp dims[4] = {0,0,0,0};
          dims[0]=PyArray_DIMS(%(x)s)[0];
          dims[1]=PyArray_DIMS(%(x)s)[1];
          dims[2]=z_r;
          dims[3]=z_c;
          //TODO: zeros not necessary
          %(z)s = (PyArrayObject*) PyArray_ZEROS(4, dims, typenum,0);
        }

        // used for indexing a pool region inside the input
        int r_st, r_end, c_st, c_end;
        dtype_%(x)s collector; // temp var for the value in a region
        if (z_r && z_c)
        {
            for(int b=0; b<PyArray_DIMS(%(x)s)[0]; b++){
              for(int k=0; k<PyArray_DIMS(%(x)s)[1]; k++){
                for(int i=0; i< z_r; i++){
                  r_st = i * %(st0)s;
                  r_end = r_st + %(ds0)s;
                  // skip the padding
                  r_st = r_st < %(pd0)s ? %(pd0)s : r_st;
                  r_end = r_end > (r - %(pd0)s) ? r - %(pd0)s : r_end;
                  // from padded_img space to img space
                  r_st -= %(pd0)s;
                  r_end -= %(pd0)s;

                  // handle the case where no padding, ignore border is True
                  if (%(ignore_border)s)
                  {
                    r_end = r_end > r ? r : r_end;
                  }
                  for(int j=0; j<z_c; j++){
                    c_st = j * %(st1)s;
                    c_end = c_st + %(ds1)s;
                    // skip the padding
                    c_st = c_st < %(pd1)s ? %(pd1)s : c_st;
                    c_end = c_end > (c - %(pd1)s) ? c - %(pd1)s : c_end;
                    dtype_%(z)s * z = (
                          (dtype_%(z)s*)(PyArray_GETPTR4(%(z)s, b, k, i, j)));
                    // change coordinates from padding_img space into img space
                    c_st -= %(pd1)s;
                    c_end -= %(pd1)s;
                    // handle the case where no padding, ignore border is True
                    if (%(ignore_border)s)
                    {
                      c_end = c_end > c ? c : c_end;
                    }
        """
        if self.mode == 'max':
            ccode += """
                    // use the first element as the initial value of collector
                    collector = ((dtype_%(x)s*)(PyArray_GETPTR4(%(x)s,b,k,r_st,c_st)))[0];
                    // go through the pooled region in the unpadded input
                    for(int m=r_st; m<r_end; m++)
                    {
                      for(int n=c_st; n<c_end; n++)
                      {
                        dtype_%(x)s a = ((dtype_%(x)s*)(PyArray_GETPTR4(%(x)s,b,k,m,n)))[0];
                        collector = (a > collector) ? a : collector;
                      }
                    }
                    z[0] = collector;
            """
        elif self.mode in ('sum', 'average_exc_pad', 'average_inc_pad'):
            ccode += """
                    // initialize the sum at zero
                    collector = ((dtype_%(x)s)(0));
                    // go through the pooled region in the unpadded input
                    for(int m=r_st; m<r_end; m++)
                    {
                      for(int n=c_st; n<c_end; n++)
                      {
                        dtype_%(x)s a = ((dtype_%(x)s*)(PyArray_GETPTR4(%(x)s,b,k,m,n)))[0];
                        collector += a;
                      }
                    }
            """
            if self.mode == "sum":
                ccode += """
                    z[0] = collector;
                """
            elif self.mode == 'average_inc_pad' and self.ignore_border:
                ccode += """
                    z[0] = collector / (%(ds0)s * %(ds1)s);
                """
            else:
                ccode += """
                    z[0] = collector / ((r_end-r_st)*(c_end-c_st));
                """
        ccode += """
                  }
                }
              }
            }
        }
        """
        return ccode % locals()

    def c_code_cache_version(self):
        return (0, 6, 8, 3)

class PoolGrad(Op):
    __props__ = ('ds', 'ignore_border', 'st', 'padding', 'mode')

    @staticmethod
    def out_shape(imgshape, ds, ignore_border=False, st=None, padding=(0, 0)):
        """Return the shape of the output from this op, for input of given
        shape and flags.

        :param imgshape: the shape of a tensor of images. The last two elements
            are interpreted as the number of rows, and the number of cols.
        :type imgshape: tuple, list, or similar of integer or
            scalar Theano variable.

        :param ds: downsample factor over rows and columns
                   this parameter indicates the size of the pooling region
        :type ds: list or tuple of two ints

        :param st: the stride size. This is the distance between the pooling
                   regions. If it's set to None, in which case it equlas ds.
        :type st: list or tuple of two ints

        :param ignore_border: if ds doesn't divide imgshape, do we include an
            extra row/col of partial downsampling (False) or ignore it (True).
        :type ignore_border: bool

        :param padding: (pad_h, pad_w), pad zeros to extend beyond four borders
            of the images, pad_h is the size of the top and bottom margins,
            and pad_w is the size of the left and right margins.
        :type padding: tuple of two ints

        :rtype: list
        :returns: the shape of the output from this op, for input of given
            shape.  This will have the same length as imgshape, but with last
            two elements reduced as per the downsampling & ignore_border flags.
        """
        if len(imgshape) < 2:
            raise TypeError('imgshape must have at least two elements '
                            '(rows, cols)')

        if st is None:
            st = ds
        r, c = imgshape[-2:]
        r += padding[0] * 2
        c += padding[1] * 2

        if ignore_border:
            out_r = (r - ds[0]) // st[0] + 1
            out_c = (c - ds[1]) // st[1] + 1
            if isinstance(r, theano.Variable):
                nr = tensor.maximum(out_r, 0)
            else:
                nr = numpy.maximum(out_r, 0)
            if isinstance(c, theano.Variable):
                nc = tensor.maximum(out_c, 0)
            else:
                nc = numpy.maximum(out_c, 0)
        else:
            if isinstance(r, theano.Variable):
                nr = tensor.switch(tensor.ge(st[0], ds[0]),
                                   (r - 1) // st[0] + 1,
                                   tensor.maximum(0, (r - 1 - ds[0])
                                                  // st[0] + 1) + 1)
            elif st[0] >= ds[0]:
                nr = (r - 1) // st[0] + 1
            else:
                nr = max(0, (r - 1 - ds[0]) // st[0] + 1) + 1

            if isinstance(c, theano.Variable):
                nc = tensor.switch(tensor.ge(st[1], ds[1]),
                                   (c - 1) // st[1] + 1,
                                   tensor.maximum(0, (c - 1 - ds[1])
                                                  // st[1] + 1) + 1)
            elif st[1] >= ds[1]:
                nc = (c - 1) // st[1] + 1
            else:
                nc = max(0, (c - 1 - ds[1]) // st[1] + 1) + 1

        rval = list(imgshape[:-2]) + [nr, nc]
        return rval

    def __init__(self, ds, ignore_border, st=None, padding=(0, 0), mode='max'):
        self.ds = tuple(ds)
        self.ignore_border = ignore_border
        if st is None:
            st = ds
        self.st = tuple(st)
        self.padding = tuple(padding)
        if mode not in ['max', 'sum', 'average_inc_pad', 'average_exc_pad']:
            raise ValueError(
                "DownsampleFactorMax mode parameter only support 'max', 'sum',"
                " 'average_inc_pad' and 'average_exc_pad'. Got %s" % mode)
        self.mode = mode

    def infer_shape(self, node, in_shapes):
        return [in_shapes[0]]


class MaxPoolGrad(PoolGrad):

    def __init__(self, ds, ignore_border, st=None, padding=(0, 0), mode='max'):
        PoolGrad.__init__(self, ds, ignore_border, st, padding, mode)

    def make_node(self, x, maxout, gz):
        # make_node should only be called by the grad function of
        # DownsampleFactorMax, so these asserts should not fail.
        assert isinstance(x, Variable) and x.ndim == 4
        assert isinstance(maxout, Variable) and maxout.ndim == 4
        assert isinstance(gz, Variable) and gz.ndim == 4
        x = tensor.as_tensor_variable(x)
        maxout = tensor.as_tensor_variable(maxout)
        gz = tensor.as_tensor_variable(gz)

        return Apply(self, [x, maxout, gz], [x.type()])

    def perform(self, node, inp, out):
        assert self.mode == 'max'
        x, maxout, gz = inp
        gx_stg, = out
        # number of pooling output rows
        pr = maxout.shape[-2]
        # number of pooling output cols
        pc = maxout.shape[-1]
        ds0, ds1 = self.ds
        st0, st1 = self.st
        pad_h = self.padding[0]
        pad_w = self.padding[1]
        img_rows = x.shape[-2] + 2 * pad_h
        img_cols = x.shape[-1] + 2 * pad_w

        # pad the image
        if self.padding != (0, 0):
            y = numpy.zeros(
                (x.shape[0], x.shape[1], img_rows, img_cols),
                dtype=x.dtype)
            y[:, :, pad_h:(img_rows-pad_h), pad_w:(img_cols-pad_w)] = x
        else:
            y = x
        gx = numpy.zeros_like(y)
        for n in xrange(x.shape[0]):
            for k in xrange(x.shape[1]):
                for r in xrange(pr):
                    row_st = builtins.max(r * st0, self.padding[0])
                    row_end = builtins.min(row_st + ds0, img_rows)
                    for c in xrange(pc):
                        col_st = builtins.max(c * st1, self.padding[1])
                        col_end = builtins.min(col_st + ds1, img_cols)
                        for row_ind in xrange(row_st, row_end):
                            for col_ind in xrange(col_st, col_end):
                                if (maxout[n, k, r, c] == y[n, k, row_ind, col_ind]):
                                    gx[n, k, row_ind, col_ind] += gz[n, k, r, c]
        # unpad the image
        gx = gx[:, :, pad_h:(img_rows-pad_h), pad_w:(img_cols-pad_w)]
        gx_stg[0] = gx

    def grad(self, inp, grads):
        x, maxout, gz = inp
        ggx, = grads
        return [theano.tensor.zeros_like(x),
                theano.tensor.zeros_like(maxout),
                DownsampleFactorMaxGradGrad(
                    self.ds, ignore_border=self.ignore_border,
                    st=self.st, padding=self.padding)(x, maxout, ggx)]

    def c_code(self, node, name, inp, out, sub):
        assert self.mode == 'max'
        x, z, gz = inp
        gx, = out
        fail = sub['fail']
        ignore_border = int(self.ignore_border)
        ds0, ds1 = self.ds
        st0, st1 = self.st
        pd0, pd1 = self.padding
        return """
        // sanity checks
        int x_typenum = PyArray_ObjectType((PyObject*)%(x)s, 0);
        int z_typenum = PyArray_ObjectType((PyObject*)%(z)s, 0);
        int gz_typenum = PyArray_ObjectType((PyObject*)%(gz)s, 0);

        if ((x_typenum != z_typenum) || (x_typenum != gz_typenum))
        {
            PyErr_SetString(PyExc_ValueError, "input types must all match");
            %(fail)s;
        }
        if(PyArray_NDIM(%(x)s)!=4)
        {
            PyErr_SetString(PyExc_ValueError, "x must be a 4d ndarray");
            %(fail)s;
        }
        if(PyArray_NDIM(%(z)s)!=4)
        {
            PyErr_SetString(PyExc_ValueError, "z must be a 4d ndarray");
            %(fail)s;
        }
        if(PyArray_NDIM(%(gz)s)!=4)
        {
            PyErr_SetString(PyExc_ValueError, "gz must be a 4d ndarray");
            %(fail)s;
        }

        int z_r, z_c;
        z_r = PyArray_DIMS(%(z)s)[2];
        z_c = PyArray_DIMS(%(z)s)[3];

        int r, c; // shape of the padded_input
        r = PyArray_DIMS(%(x)s)[2];
        c = PyArray_DIMS(%(x)s)[3];
        r += %(pd0)s * 2;
        c += %(pd1)s * 2;

        // allocating memory for gx
        if ((!%(gx)s)
          || !PyArray_ISCONTIGUOUS(%(gx)s)
          || *PyArray_DIMS(%(gx)s)!=4
          ||(PyArray_DIMS(%(gx)s)[0] != PyArray_DIMS(%(x)s)[0])
          ||(PyArray_DIMS(%(gx)s)[1] != PyArray_DIMS(%(x)s)[1])
          ||(PyArray_DIMS(%(gx)s)[2] != PyArray_DIMS(%(x)s)[2])
          ||(PyArray_DIMS(%(gx)s)[3] != PyArray_DIMS(%(x)s)[3])
          )
        {
          Py_XDECREF(%(gx)s);
          %(gx)s = (PyArrayObject*) PyArray_ZEROS(4, PyArray_DIMS(%(x)s), x_typenum,0);
        }
        else {
          PyArray_FILLWBYTE(%(gx)s, 0);
        }
        int r_st, r_end, c_st, c_end; // used to index into the input img x
        dtype_%(z)s maximum; // temp var for maximum value in a region
        if (z_r && z_c)
        {
            for(int b=0; b<PyArray_DIMS(%(x)s)[0]; b++){
              for(int k=0; k<PyArray_DIMS(%(x)s)[1]; k++){
                for(int i=0; i< z_r; i++){
                  r_st = i * %(st0)s;
                  r_end = r_st + %(ds0)s;
                  // skip the padding
                  r_st = r_st < %(pd0)s ? %(pd0)s : r_st;
                  r_end = r_end > (r - %(pd0)s) ? r - %(pd0)s : r_end;
                  // from padded_img space to img space
                  r_st -= %(pd0)s;
                  r_end -= %(pd0)s;

                  for(int j=0; j<z_c; j++){
                    c_st = j * %(st1)s;
                    c_end = c_st + %(ds1)s;
                    // skip the padding
                    c_st = c_st < %(pd1)s ? %(pd1)s : c_st;
                    c_end = c_end > (c - %(pd1)s) ? c - %(pd1)s : c_end;

                    // change coordinates from padding_img space into img space
                    c_st -= %(pd1)s;
                    c_end -= %(pd1)s;
                    // the maximum value
                    maximum = ((dtype_%(z)s*)(PyArray_GETPTR4(%(z)s,b,k,i,j)))[0];
                    // the gradient corresponding to this maximum value in z
                    dtype_%(gz)s * gz = (
                          (dtype_%(gz)s*)(PyArray_GETPTR4(%(gz)s, b, k, i, j)));
                    // go through the pooled region in the unpadded input
                    for(int m=r_st; m<r_end; m++)
                    {
                      for(int n=c_st; n<c_end; n++)
                      {
                        dtype_%(x)s a = ((dtype_%(x)s*)(PyArray_GETPTR4(%(x)s,b,k,m,n)))[0];
                        dtype_%(gx)s * gx = (
                          (dtype_%(gx)s*)(PyArray_GETPTR4(%(gx)s, b, k, m, n)));
                        if (a == maximum){
                          gx[0] = gx[0] + gz[0];
                        }
                      }
                    }
                  }
                }
              }
            }

        }
        """ % locals()

    def c_code_cache_version(self):
        return (0, 7)

DownsampleFactorMaxGrad = MaxPoolGrad

class AveragePoolGrad(PoolGrad):

    def __init__(self, ds, ignore_border, st=None, padding=(0, 0), mode='average_inc_pad'):
        assert mode in ['sum', 'average_inc_pad', 'average_exc_pad']
        PoolGrad.__init__(self, ds, ignore_border, st, padding, mode)

    def make_node(self, x, gz):
        # make_node should only be called by the grad function of
        # DownsampleFactorMax, so these asserts should not fail.
        assert isinstance(x, Variable) and x.ndim == 4
        assert isinstance(gz, Variable) and gz.ndim == 4
        x = tensor.as_tensor_variable(x)
        gz = tensor.as_tensor_variable(gz)

        return Apply(self, [x, gz], [x.type()])

    def perform(self, node, inp, out):
        if self.mode == 'average_exc_pad' and self.padding != (0, 0):
            raise NotImplementedError()
        x, gz = inp
        gx_stg, = out
        z_shape = self.out_shape(x.shape, self.ds, self.ignore_border, self.st,
                                 self.padding)
        if (gx_stg[0] is None) or (gx_stg[0].shape != z_shape):
            gx_stg[0] = numpy.empty(z_shape, dtype=x.dtype)
        zz = gx_stg[0]
        # number of pooling output rows
        pr = zz.shape[-2]
        # number of pooling output cols
        pc = zz.shape[-1]
        ds0, ds1 = self.ds
        st0, st1 = self.st
        pad_h = self.padding[0]
        pad_w = self.padding[1]
        img_rows = x.shape[-2] + 2 * pad_h
        img_cols = x.shape[-1] + 2 * pad_w
        inc_pad = self.mode == 'average_inc_pad'
        sum_mode = self.mode == 'sum'

        # pad the image
        if self.padding != (0, 0):
            y = numpy.zeros(
                (x.shape[0], x.shape[1], img_rows, img_cols),
                dtype=x.dtype)
            y[:, :, pad_h:(img_rows-pad_h), pad_w:(img_cols-pad_w)] = x
        else:
            y = x
        gx = numpy.zeros_like(y)
        for n in xrange(x.shape[0]):
            for k in xrange(x.shape[1]):
                for r in xrange(pr):
                    if sum_mode or inc_pad:
                        row_st = r * st0
                    else:
                        row_st = builtins.max(r * st0, self.padding[0])
                    row_end = builtins.min(row_st + ds0, img_rows)
                    for c in xrange(pc):
                        if sum_mode or inc_pad:
                            col_st = c * st1
                        else:
                            col_st = builtins.max(c * st1,
                                                     self.padding[1])
                        col_end = builtins.min(col_st + ds1, img_cols)
                        if sum_mode:
                          val = gz[n, k, r, c]
                        else:
                          val = gz[n, k, r, c] / ((row_end - row_st) *
                                                  (col_end - col_st))
                        gx[n, k, row_st:row_end, col_st:col_end] += val
        # unpad the image
        gx = gx[:, :, pad_h:(img_rows-pad_h), pad_w:(img_cols-pad_w)]
        gx_stg[0] = gx

    def grad(self, inp, grads):
        x, gz = inp
        ggx, = grads
        return [theano.tensor.zeros_like(x),
                DownsampleFactorMax(
                    self.ds, ignore_border=self.ignore_border,
                    st=self.st, padding=self.padding, mode=self.mode)(ggx)]

class DownsampleFactorMaxGradGrad(Op):
    __props__ = ('ds', 'ignore_border', 'st', 'padding', 'mode')

    @staticmethod
    def out_shape(imgshape, ds, ignore_border=False, st=None, padding=(0, 0)):
        """Return the shape of the output from this op, for input of given
        shape and flags.

        :param imgshape: the shape of a tensor of images. The last two elements
            are interpreted as the number of rows, and the number of cols.
        :type imgshape: tuple, list, or similar of integer or
            scalar Theano variable.

        :param ds: downsample factor over rows and columns
                   this parameter indicates the size of the pooling region
        :type ds: list or tuple of two ints

        :param st: the stride size. This is the distance between the pooling
                   regions. If it's set to None, in which case it equlas ds.
        :type st: list or tuple of two ints

        :param ignore_border: if ds doesn't divide imgshape, do we include an
            extra row/col of partial downsampling (False) or ignore it (True).
        :type ignore_border: bool

        :param padding: (pad_h, pad_w), pad zeros to extend beyond four borders
            of the images, pad_h is the size of the top and bottom margins,
            and pad_w is the size of the left and right margins.
        :type padding: tuple of two ints

        :rtype: list
        :returns: the shape of the output from this op, for input of given
            shape.  This will have the same length as imgshape, but with last
            two elements reduced as per the downsampling & ignore_border flags.
        """
        if len(imgshape) < 2:
            raise TypeError('imgshape must have at least two elements '
                            '(rows, cols)')

        if st is None:
            st = ds
        r, c = imgshape[-2:]
        r += padding[0] * 2
        c += padding[1] * 2

        if ignore_border:
            out_r = (r - ds[0]) // st[0] + 1
            out_c = (c - ds[1]) // st[1] + 1
            if isinstance(r, theano.Variable):
                nr = tensor.maximum(out_r, 0)
            else:
                nr = numpy.maximum(out_r, 0)
            if isinstance(c, theano.Variable):
                nc = tensor.maximum(out_c, 0)
            else:
                nc = numpy.maximum(out_c, 0)
        else:
            if isinstance(r, theano.Variable):
                nr = tensor.switch(tensor.ge(st[0], ds[0]),
                                   (r - 1) // st[0] + 1,
                                   tensor.maximum(0, (r - 1 - ds[0])
                                                  // st[0] + 1) + 1)
            elif st[0] >= ds[0]:
                nr = (r - 1) // st[0] + 1
            else:
                nr = max(0, (r - 1 - ds[0]) // st[0] + 1) + 1

            if isinstance(c, theano.Variable):
                nc = tensor.switch(tensor.ge(st[1], ds[1]),
                                   (c - 1) // st[1] + 1,
                                   tensor.maximum(0, (c - 1 - ds[1])
                                                  // st[1] + 1) + 1)
            elif st[1] >= ds[1]:
                nc = (c - 1) // st[1] + 1
            else:
                nc = max(0, (c - 1 - ds[1]) // st[1] + 1) + 1

        rval = list(imgshape[:-2]) + [nr, nc]
        return rval

    def __init__(self, ds, ignore_border, st=None, padding=(0,0), mode='max'):
        self.ds = tuple(ds)
        if not all([isinstance(d, int) for d in ds]):
            raise ValueError(
                "DownsampleFactorMax downsample parameters must be ints."
                " Got %s" % str(ds))
        if st is None:
            st = ds
        assert isinstance(st, (tuple, list))
        self.st = tuple(st)
        self.ignore_border = ignore_border
        self.padding = tuple(padding)
        if self.padding != (0, 0) and not ignore_border:
            raise NotImplementedError(
                'padding works only with ignore_border=True')
        if self.padding[0] >= self.ds[0] or self.padding[1] >= self.ds[1]:
            raise NotImplementedError(
                'padding_h and padding_w must be smaller than strides')
        self.mode = mode
        assert self.mode == 'max'

    def make_node(self, x, maxout, gz):
        # make_node should only be called by the grad function of
        # MaxPoolGrad, so these asserts should not fail.
        x = tensor.as_tensor_variable(x)
        maxout = tensor.as_tensor_variable(maxout)
        gz = tensor.as_tensor_variable(gz)
        assert x.ndim == 4
        assert maxout.ndim == 4
        assert gz.ndim == 4

        return Apply(self, [x, maxout, gz], [x.type()])

    def perform(self, node, inp, out):
        x, maxout, ggx = inp
        z, = out
        if len(x.shape) != 4:
            raise NotImplementedError(
                'DownsampleFactorMaxGradGrad requires 4D input for now')
        z_shape = self.out_shape(x.shape, self.ds, self.ignore_border,
                                 self.st, self.padding)
        if (z[0] is None) or (z[0].shape != z_shape):
            z[0] = numpy.zeros(z_shape, dtype=x.dtype)
        ggz = z[0] # grad wrt maxout_grad has the same shape as maxout
        # number of pooling output rows
        pr = ggz.shape[-2]
        # number of pooling output cols
        pc = ggz.shape[-1]
        ds0, ds1 = self.ds
        st0, st1 = self.st
        pd0, pd1 = self.padding
        img_rows = x.shape[-2] + 2 * pd0
        img_cols = x.shape[-1] + 2 * pd1

        # pad the image and its gradients
        if self.padding != (0, 0):
            y_padded = numpy.zeros(
                (x.shape[0], x.shape[1], img_rows, img_cols),
                dtype=x.dtype) + x.min() - 1
            y_padded[:, :, pd0:(img_rows-pd0), pd1:(img_cols-pd1)] = x
            ggx_padded = numpy.zeros(
                (x.shape[0], x.shape[1], img_rows, img_cols),
                dtype=x.dtype)
            ggx_padded[:, :, pd0:(img_rows-pd0), pd1:(img_cols-pd1)] = ggx

        else:
            y_padded = x
            ggx_padded = ggx
        for n in xrange(x.shape[0]):
            for k in xrange(x.shape[1]):
                for r in xrange(pr):
                    row_st = r * st0
                    row_end = builtins.min(row_st + ds0, img_rows)
                    for c in xrange(pc):
                        col_st = c * st1
                        col_end = builtins.min(col_st + ds1, img_cols)
                        for row_ind in xrange(row_st, row_end):
                            for col_ind in xrange(col_st, col_end):
                                if (maxout[n, k, r, c] == y_padded[n, k, row_ind, col_ind]):
                                    ggz[n, k, r, c] = ggx_padded[n, k, row_ind, col_ind]

    def infer_shape(self, node, in_shapes):
        return [in_shapes[0]]

    def c_code(self, node, name, inp, out, sub):
        if self.mode != 'max':
            raise theano.gof.utils.MethodNotDefined()
        x, maxout, ggx = inp
        z, = out # the grad of grad
        fail = sub['fail']
        ignore_border = int(self.ignore_border)
        ds0, ds1 = self.ds
        st0, st1 = self.st
        pd0, pd1 = self.padding
        return """
        int z_typenum = PyArray_ObjectType((PyObject*)%(maxout)s, 0);
        int z_r, z_c;
        z_r = PyArray_DIMS(%(maxout)s)[2];
        z_c = PyArray_DIMS(%(maxout)s)[3];
        int r, c; // shape of the padded_input
        r = PyArray_DIMS(%(x)s)[2];
        c = PyArray_DIMS(%(x)s)[3];
        r += %(pd0)s * 2;
        c += %(pd1)s * 2;
        // allocating memory for output
        if ((!%(z)s)
          || !PyArray_ISCONTIGUOUS(%(z)s)
          || *PyArray_DIMS(%(z)s)!=4
          ||(PyArray_DIMS(%(z)s)[0] != PyArray_DIMS(%(maxout)s)[0])
          ||(PyArray_DIMS(%(z)s)[1] != PyArray_DIMS(%(maxout)s)[1])
          ||(PyArray_DIMS(%(z)s)[2] != PyArray_DIMS(%(maxout)s)[2])
          ||(PyArray_DIMS(%(z)s)[3] != PyArray_DIMS(%(maxout)s)[3])
          )
        {
          Py_XDECREF(%(z)s);
          %(z)s = (PyArrayObject*) PyArray_ZEROS(4, PyArray_DIMS(%(maxout)s), z_typenum,0);
        }
        else {
          PyArray_FILLWBYTE(%(z)s, 0);
        }
        dtype_%(maxout)s maximum; // temp var for maximum value in a region
        int r_st, r_end, c_st, c_end; // used to index into the input img x
        for(int b=0; b<PyArray_DIMS(%(x)s)[0]; b++){
              for(int k=0; k<PyArray_DIMS(%(x)s)[1]; k++){
                for(int i=0; i< z_r; i++){
                  r_st = i * %(st0)s;
                  r_end = r_st + %(ds0)s;
                  // skip the padding
                  r_st = r_st < %(pd0)s ? %(pd0)s : r_st;
                  r_end = r_end > (r - %(pd0)s) ? r - %(pd0)s : r_end;
                  // from padded_img space to img space
                  r_st -= %(pd0)s;
                  r_end -= %(pd0)s;
                  for(int j=0; j<z_c; j++){
                    c_st = j * %(st1)s;
                    c_end = c_st + %(ds1)s;
                    // skip the padding
                    c_st = c_st < %(pd1)s ? %(pd1)s : c_st;
                    c_end = c_end > (c - %(pd1)s) ? c - %(pd1)s : c_end;
                    // from padding_img space into img space
                    c_st -= %(pd1)s;
                    c_end -= %(pd1)s;

                    // the maximum value
                    maximum = ((dtype_%(maxout)s*)(PyArray_GETPTR4(%(maxout)s,b,k,i,j)))[0];
                    // z at this position
                    dtype_%(z)s * z = ((dtype_%(z)s*)(PyArray_GETPTR4(%(z)s, b, k, i, j)));
                    // go through the pooled region in the unpadded input
                    for(int m=r_st; m<r_end; m++)
                    {
                      for(int n=c_st; n<c_end; n++)
                      {
                        dtype_%(x)s a = ((dtype_%(x)s*)(PyArray_GETPTR4(%(x)s,b,k,m,n)))[0];
                        dtype_%(ggx)s * ggx = (
                          (dtype_%(ggx)s*)(PyArray_GETPTR4(%(ggx)s, b, k, m, n)));
                        if (a == maximum){
                          z[0] += ggx[0];
                        }
                      }
                    }
                  }
                }
              }
         }
        """%locals()

    def c_code_cache_version(self):
        return (0,1)

@register_canonicalize('fast_compile')
@gof.local_optimizer([MaxPoolGrad])
def local_average_pool_grad(node):
    # To assure backward compatibility with
    # DownsampleFactorMaxGrad
    if (not isinstance(node.op, MaxPoolGrad) or node.op.mode not in
            ['sum','average_exc_pad', 'average_inc_pad']):
        return False
    return [AveragePoolGrad(ds=node.op.ds,
                            ignore_border=node.op.ignore_border,
                            st=node.op.st,
                            padding=node.op.padding,
                            mode=node.op.mode)(node.inputs[0],
                                               node.inputs[2])]
