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convolution_nd.py
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convolution_nd.py
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import numpy
from six import moves
import chainer
from chainer.backends import cuda
from chainer import configuration
from chainer import function_node
from chainer.utils import conv
from chainer.utils import conv_nd
from chainer.utils import type_check
class ConvolutionND(function_node.FunctionNode):
def __init__(self, ndim, stride=1, pad=0, cover_all=False):
self.ndim = ndim
self.stride = conv_nd.as_tuple(stride, ndim)
self.pad = conv_nd.as_tuple(pad, ndim)
self.cover_all = cover_all
def check_type_forward(self, in_types):
n_in = in_types.size()
type_check.expect(2 <= n_in, n_in <= 3)
x_type = in_types[0]
w_type = in_types[1]
type_check.expect(
x_type.dtype.kind == 'f',
w_type.dtype.kind == 'f',
x_type.ndim == self.ndim + 2,
w_type.ndim == self.ndim + 2,
x_type.shape[1] == w_type.shape[1],
)
if type_check.eval(n_in) == 3:
b_type = in_types[2]
type_check.expect(
b_type.dtype == x_type.dtype,
b_type.ndim == 1,
b_type.shape[0] == w_type.shape[0],
)
def _use_cudnn(self, x, W):
return (not self.cover_all and
chainer.should_use_cudnn('>=auto') and
self.ndim > 1 and x.dtype == W.dtype)
def _forward_xp(self, x, W, b, xp):
ndim = self.ndim
ksize = W.shape[2:]
stride = self.stride
pad = self.pad
# Make patch array.
if xp is numpy:
col = conv_nd.im2col_nd_cpu(
x, ksize, stride, pad, cover_all=self.cover_all)
else:
col = conv_nd.im2col_nd_gpu(
x, ksize, stride, pad, cover_all=self.cover_all)
# Compute correlation.
axes = tuple(moves.range(1, ndim + 2)) # (1, 2, ..., N+1)
y = xp.tensordot(col, W, (axes, axes)).astype(x.dtype, copy=False)
# Apply bias if given.
if b is not None:
y += b
# Roll c_O before the second in (n, y_1, y_2, ..., y_N, c_O).
return xp.rollaxis(y, ndim + 1, 1),
def _forward_cudnn(self, x, W, b):
out_c = W.shape[0] # (c_O, _, k_1, k_2, ..., k_N)
ksize = W.shape[2:]
n, c = x.shape[:2] # (n, c_I, d_1, d_2, ..., d_N)
dims = x.shape[2:]
stride = self.stride
pad = self.pad
# Make empty array for result.
outs = tuple(
conv.get_conv_outsize(d, k, s, p, cover_all=self.cover_all)
for (d, k, s, p) in zip(dims, ksize, stride, pad))
assert all(out > 0 for out in outs), 'Output sizes should be positive.'
y_shape = (n, out_c) + outs # (n, c_O, out_1, out_2, ..., out_N)
y = cuda.cupy.empty(y_shape, dtype=x.dtype)
dilation = (1,) * self.ndim
groups = 1
auto_tune = configuration.config.autotune
tensor_core = configuration.config.use_cudnn_tensor_core
cuda.cudnn.convolution_forward(
x, W, b, y, pad, stride, dilation, groups,
auto_tune=auto_tune, tensor_core=tensor_core)
return y,
def forward(self, inputs):
self.retain_inputs((0, 1)) # retain only x and W
x, W = inputs[:2]
b = inputs[2] if len(inputs) == 3 else None
xp = cuda.get_array_module(*inputs)
if xp is numpy:
return self._forward_xp(x, W, b, numpy)
elif not self._use_cudnn(x, W):
return self._forward_xp(x, W, b, cuda.cupy)
else:
return self._forward_cudnn(x, W, b)
def backward(self, indexes, grad_outputs):
x, W = self.get_retained_inputs()
gy, = grad_outputs
ret = []
if 0 in indexes:
x_shape = x.shape[2:]
gx = chainer.functions.deconvolution_nd(
gy, W, stride=self.stride, pad=self.pad, outsize=x_shape)
ret.append(gx)
if 1 in indexes:
gW, = ConvolutionNDGradW(self).apply((x, gy))
ret.append(gW)
if 2 in indexes:
axis = (0,) + tuple(moves.range(2, gy.ndim))
gb = chainer.functions.sum(gy, axis=axis)
ret.append(gb)
return ret
class ConvolutionNDGradW(function_node.FunctionNode):
def __init__(self, convnd):
W_node = convnd.inputs[1]
self.ndim = convnd.ndim
self.ksize = W_node.shape[2:]
self.stride = convnd.stride
self.pad = convnd.pad
self.cover_all = convnd.cover_all
self.W_dtype = W_node.dtype
def _use_cudnn(self, x, gy):
return (
chainer.should_use_cudnn('>=auto')
and not self.cover_all
and x.dtype == self.W_dtype
and gy.dtype == self.W_dtype
and self.ndim > 1)
def forward(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
xp = cuda.get_array_module(*inputs)
if xp is numpy:
return self._forward_xp(x, gy, numpy)
elif not self._use_cudnn(x, gy):
return self._forward_xp(x, gy, cuda.cupy)
else:
return self._forward_cudnn(x, gy)
def _forward_xp(self, x, gy, xp):
# Compute filter weight gradient.
# (n, _, out_1, out_2, ..., out_N)
out_axes = (0,) + tuple(moves.range(2, self.ndim + 2))
# (n, _, _, ..., _, out_1, out_2, ..., out_N)
col_axes = (0,) + tuple(moves.range(self.ndim + 2, self.ndim * 2 + 2))
# NumPy raises an error when the array is not contiguous.
# See: https://github.com/chainer/chainer/issues/2744
# TODO(niboshi): Remove this code when NumPy is fixed.
if (xp is numpy and
not (gy.flags.c_contiguous or gy.flags.f_contiguous) and
1 in gy.shape):
gy = numpy.ascontiguousarray(gy)
if xp is numpy:
col = conv_nd.im2col_nd_cpu(
x, self.ksize, self.stride, self.pad, cover_all=self.cover_all)
else:
col = conv_nd.im2col_nd_gpu(
x, self.ksize, self.stride, self.pad, cover_all=self.cover_all)
gW = xp.tensordot(gy, col, (out_axes, col_axes)).astype(
self.W_dtype, copy=False)
return gW,
def _forward_cudnn(self, x, gy):
# Make empty arrays for result.
out_c = gy.shape[1]
in_c = x.shape[1]
gW = cuda.cupy.empty(
(out_c, in_c) + self.ksize, dtype=self.W_dtype)
# Compute
pad = self.pad
stride = self.stride
dilation = (1,) * self.ndim
groups = 1
deterministic = configuration.config.cudnn_deterministic
auto_tune = configuration.config.autotune
tensor_core = configuration.config.use_cudnn_tensor_core
cuda.cudnn.convolution_backward_filter(
x, gy, gW, pad, stride, dilation, groups,
deterministic=deterministic, auto_tune=auto_tune,
tensor_core=tensor_core)
return gW,
def backward(self, indexes, grad_outputs):
x, gy = self.get_retained_inputs()
ggW, = grad_outputs
ret = []
if 0 in indexes:
x_shape = x.shape[2:]
gx = chainer.functions.deconvolution_nd(
gy, ggW, stride=self.stride, pad=self.pad, outsize=x_shape)
ret.append(gx)
if 1 in indexes:
ggy = convolution_nd(
x, ggW, stride=self.stride, pad=self.pad,
cover_all=self.cover_all)
ret.append(ggy)
return ret
def convolution_nd(x, W, b=None, stride=1, pad=0, cover_all=False):
"""N-dimensional convolution function.
This is an implementation of N-dimensional convolution which is generalized
two-dimensional convolution in ConvNets. It takes three variables: the
input ``x``, the filter weight ``W`` and the bias vector ``b``.
Notation: here is a notation for dimensionalities.
- :math:`N` is the number of spatial dimensions.
- :math:`n` is the batch size.
- :math:`c_I` and :math:`c_O` are the number of the input and output
channels, respectively.
- :math:`d_1, d_2, ..., d_N` are the size of each axis of the input's
spatial dimensions, respectively.
- :math:`k_1, k_2, ..., k_N` are the size of each axis of the filters,
respectively.
- :math:`l_1, l_2, ..., l_N` are the size of each axis of the output's
spatial dimensions, respectively.
- :math:`p_1, p_2, ..., p_N` are the size of each axis of the spatial
padding size, respectively.
Then the ``convolution_nd`` function computes correlations between filters
and patches of size :math:`(k_1, k_2, ..., k_N)` in ``x``.
Note that correlation here is equivalent to the inner product between
expanded tensors.
Patches are extracted at positions shifted by multiples of ``stride`` from
the first position ``(-p_1, -p_2, ..., -p_N)`` for each spatial axis.
Let :math:`(s_1, s_2, ..., s_N)` be the stride of filter application.
Then, the output size :math:`(l_1, l_2, ..., l_N)` is determined by the
following equations:
.. math::
l_n = (d_n + 2p_n - k_n) / s_n + 1 \\ \\ (n = 1, ..., N)
If ``cover_all`` option is ``True``, the filter will cover the all
spatial locations. So, if the last stride of filter does not cover the
end of spatial locations, an addtional stride will be applied to the end
part of spatial locations. In this case, the output size is determined by
the following equations:
.. math::
l_n = (d_n + 2p_n - k_n + s_n - 1) / s_n + 1 \\ \\ (n = 1, ..., N)
The N-dimensional convolution function is defined as follows.
Args:
x (:class:`~chainer.Variable` or :class:`numpy.ndarray` or \
:class:`cupy.ndarray`):
Input variable of shape :math:`(n, c_I, d_1, d_2, ..., d_N)`.
W (:class:`~chainer.Variable` or :class:`numpy.ndarray` or \
:class:`cupy.ndarray`):
Weight variable of shape :math:`(c_O, c_I, k_1, k_2, ..., k_N)`.
b (:class:`~chainer.Variable` or :class:`numpy.ndarray` or \
:class:`cupy.ndarray`):
One-dimensional bias variable with length :math:`c_O` (optional).
stride (:class:`int` or :class:`tuple` of :class:`int` s):
Stride of filter applications :math:`(s_1, s_2, ..., s_N)`.
``stride=s`` is equivalent to ``(s, s, ..., s)``.
pad (:class:`int` or :class:`tuple` of :class:`int` s):
Spatial padding width for input arrays
:math:`(p_1, p_2, ..., p_N)`. ``pad=p`` is equivalent to
``(p, p, ..., p)``.
cover_all (bool): If ``True``, all spatial locations are convoluted
into some output pixels. It may make the output size larger.
`cover_all` needs to be ``False`` if you want to use cuDNN.
Returns:
~chainer.Variable:
Output variable of shape :math:`(n, c_O, l_1, l_2, ..., l_N)`.
.. note::
This function uses cuDNN implementation for its forward and backward
computation if ALL of the following conditions are satisfied:
- ``cuda.cudnn_enabled`` is ``True``
- ``chainer.config.use_cudnn`` is ``'always'`` or ``'auto'``
- The number of spatial dimensions is more than one.
- ``cover_all`` is ``False``
- The input's ``dtype`` is equal to the filter weight's.
- The ``dtype`` is FP16, FP32 or FP64. (FP16 is only available when
cuDNN version :math:`\\geq` v3.)
Convolution links can use a feature of cuDNN called autotuning, which
selects the most efficient CNN algorithm for images of fixed-size,
can provide a significant performance boost for fixed neural nets.
To enable, set `chainer.using_config('autotune', True)`
.. seealso:: :class:`~chainer.links.ConvolutionND`, :func:`convolution_2d`
.. admonition:: Example
>>> n = 10
>>> c_i, c_o = 3, 1
>>> d1, d2, d3 = 30, 40, 50
>>> k1, k2, k3 = 10, 10, 10
>>> p1, p2, p3 = 5, 5, 5
>>> x = np.random.uniform(0, 1, (n, c_i, d1, d2, d3)).\
astype(np.float32)
>>> x.shape
(10, 3, 30, 40, 50)
>>> W = np.random.uniform(0, 1, (c_o, c_i, k1, k2, k3)).\
astype(np.float32)
>>> W.shape
(1, 3, 10, 10, 10)
>>> b = np.random.uniform(0, 1, (c_o)).astype(np.float32)
>>> b.shape
(1,)
>>> s1, s2, s3 = 2, 4, 6
>>> y = F.convolution_nd(x, W, b, stride=(s1, s2, s3),\
pad=(p1, p2, p3))
>>> y.shape
(10, 1, 16, 11, 9)
>>> l1 = int((d1 + 2 * p1 - k1) / s1 + 1)
>>> l2 = int((d2 + 2 * p2 - k2) / s2 + 1)
>>> l3 = int((d3 + 2 * p3 - k3) / s3 + 1)
>>> y.shape == (n, c_o, l1, l2, l3)
True
>>> y = F.convolution_nd(x, W, b, stride=(s1, s2, s3),\
pad=(p1, p2, p3), cover_all=True)
>>> y.shape == (n, c_o, l1, l2, l3 + 1)
True
"""
ndim = len(x.shape[2:])
fnode = ConvolutionND(ndim, stride, pad, cover_all)
args = (x, W) if b is None else (x, W, b)
y, = fnode.apply(args)
return y