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trigonometric.py
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trigonometric.py
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import numpy
from chainer import backend
from chainer.backends import cuda
from chainer import function_node
import chainer.functions
from chainer import utils
from chainer.utils import type_check
class Sin(function_node.FunctionNode):
@property
def label(self):
return 'sin'
def check_type_forward(self, in_types):
type_check._argname(in_types, ('x',))
type_check.expect(in_types[0].dtype.kind == 'f')
def forward(self, x):
self.retain_inputs((0,))
xp = backend.get_array_module(*x)
return utils.force_array(xp.sin(x[0])),
def backward(self, indexes, grad_outputs):
x, = self.get_retained_inputs()
return SinGrad().apply((x, grad_outputs[0]))
class SinGrad(function_node.FunctionNode):
def forward_cpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = utils.force_array(numpy.cos(x))
gx *= gy
return gx,
def forward_gpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = cuda.elementwise(
'T x, T gy', 'T gx', 'gx = cos(x) * gy', 'sin_bwd'
)(x, gy)
return gx,
def backward(self, indexes, grad_outputs):
x, gy = self.get_retained_inputs()
ret = []
if 0 in indexes:
ret.append(- sin(x) * gy * grad_outputs[0])
if 1 in indexes:
ret.append(cos(x) * grad_outputs[0])
return ret
def sin(x):
"""Elementwise sin function.
Args:
x (:class:`~chainer.Variable` or :ref:`ndarray`): Input variable.
Returns:
~chainer.Variable: Output variable.
"""
return Sin().apply((x,))[0]
class Cos(function_node.FunctionNode):
@property
def label(self):
return 'cos'
def check_type_forward(self, in_types):
type_check._argname(in_types, ('x',))
type_check.expect(in_types[0].dtype.kind == 'f')
def forward(self, x):
self.retain_inputs((0,))
xp = backend.get_array_module(*x)
return utils.force_array(xp.cos(x[0])),
def backward(self, indexes, grad_outputs):
x, = self.get_retained_inputs()
return CosGrad().apply((x, grad_outputs[0]))
class CosGrad(function_node.FunctionNode):
def forward_cpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = utils.force_array(numpy.sin(x))
numpy.negative(gx, out=gx)
gx *= gy
return gx,
def forward_gpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = cuda.elementwise(
'T x, T gy', 'T gx', 'gx = -sin(x) * gy', 'cos_bwd'
)(x, gy)
return gx,
def backward(self, indexes, grad_outputs):
x, gy = self.get_retained_inputs()
ret = []
if 0 in indexes:
ret.append(- cos(x) * gy * grad_outputs[0])
if 1 in indexes:
ret.append(- sin(x) * grad_outputs[0])
return ret
def cos(x):
"""Elementwise cos function.
Args:
x (:class:`~chainer.Variable` or :ref:`ndarray`): Input variable.
Returns:
~chainer.Variable: Output variable.
"""
return Cos().apply((x,))[0]
class Tan(function_node.FunctionNode):
@property
def label(self):
return 'tan'
def check_type_forward(self, in_types):
type_check._argname(in_types, ('x',))
type_check.expect(in_types[0].dtype.kind == 'f')
def forward(self, x):
self.retain_inputs((0,))
xp = backend.get_array_module(*x)
return utils.force_array(xp.tan(x[0])),
def backward(self, indexes, grad_outputs):
x, = self.get_retained_inputs()
return grad_outputs[0] / chainer.functions.square(cos(x)),
def tan(x):
"""Elementwise tan function.
Args:
x (:class:`~chainer.Variable` or :ref:`ndarray`): Input variable.
Returns:
~chainer.Variable: Output variable.
"""
return Tan().apply((x,))[0]
class Arcsin(function_node.FunctionNode):
@property
def label(self):
return 'arcsin'
def check_type_forward(self, in_types):
type_check._argname(in_types, ('x',))
type_check.expect(in_types[0].dtype.kind == 'f')
def forward(self, x):
self.retain_inputs((0,))
xp = backend.get_array_module(*x)
return utils.force_array(xp.arcsin(x[0])),
def backward(self, indexes, grad_outputs):
x = self.get_retained_inputs()
return ArcsinGrad().apply((x[0], grad_outputs[0]))
class ArcsinGrad(function_node.FunctionNode):
def forward_cpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = utils.force_array(numpy.square(x))
numpy.negative(gx, out=gx)
gx += 1
numpy.sqrt(gx, out=gx)
numpy.reciprocal(gx, out=gx)
gx *= gy
return gx,
def forward_gpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = cuda.elementwise(
'T x, T gy', 'T gx',
'gx = rsqrt((T)1.0 - x * x) * gy',
'arcsin_bwd'
)(x, gy)
return gx,
def backward(self, indexes, grad_outputs):
x, gy = self.get_retained_inputs()
ret = []
if 0 in indexes:
ret.append(grad_outputs[0] * gy * x / ((1 - x ** 2) ** 1.5))
if 1 in indexes:
ret.append(ArcsinGrad().apply((x, grad_outputs[0]))[0])
return ret
def arcsin(x):
"""Elementwise arcsine function.
.. math::
y_i = \\arcsin x_i.
Args:
x (:class:`~chainer.Variable` or :ref:`ndarray`): Input variable.
Returns:
~chainer.Variable: Output variable.
"""
return Arcsin().apply((x,))[0]
class Arccos(function_node.FunctionNode):
@property
def label(self):
return 'arccos'
def check_type_forward(self, in_types):
type_check._argname(in_types, ('x',))
type_check.expect(in_types[0].dtype.kind == 'f')
def forward(self, x):
self.retain_inputs((0,))
xp = backend.get_array_module(*x)
return utils.force_array(xp.arccos(x[0])),
def backward(self, indexes, grad_outputs):
x = self.get_retained_inputs()
return ArccosGrad().apply((x[0], grad_outputs[0]))
class ArccosGrad(function_node.FunctionNode):
def forward_cpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = utils.force_array(numpy.square(x))
numpy.negative(gx, out=gx)
gx += 1
numpy.sqrt(gx, out=gx)
numpy.reciprocal(gx, out=gx)
numpy.negative(gx, out=gx)
gx *= gy
return gx,
def forward_gpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = cuda.elementwise(
'T x, T gy', 'T gx',
'gx = -rsqrt((T)1.0 - x * x) * gy',
'arccos_bwd'
)(x, gy)
return gx,
def backward(self, indexes, grad_outputs):
x, gy = self.get_retained_inputs()
ret = []
if 0 in indexes:
ret.append(- grad_outputs[0] * (gy * x) / ((1 - x ** 2) ** 1.5))
if 1 in indexes:
ret.append(ArccosGrad().apply((x, grad_outputs[0]))[0])
return ret
def arccos(x):
"""Elementwise arccosine function.
.. math::
y_i = \\arccos x_i.
Args:
x (:class:`~chainer.Variable` or :ref:`ndarray`): Input variable.
Returns:
~chainer.Variable: Output variable.
"""
return Arccos().apply((x,))[0]
class Arctan(function_node.FunctionNode):
@property
def label(self):
return 'arctan'
def check_type_forward(self, in_types):
type_check._argname(in_types, ('x',))
type_check.expect(in_types[0].dtype.kind == 'f')
def forward(self, x):
self.retain_inputs((0,))
xp = backend.get_array_module(*x)
return utils.force_array(xp.arctan(x[0])),
def backward(self, indexes, grad_outputs):
x = self.get_retained_inputs()
return ArctanGrad().apply((x[0], grad_outputs[0]))
class ArctanGrad(function_node.FunctionNode):
def forward_cpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = utils.force_array(numpy.square(x))
gx += 1
numpy.reciprocal(gx, out=gx)
gx *= gy
return gx,
def forward_gpu(self, inputs):
self.retain_inputs((0, 1))
x, gy = inputs
gx = cuda.elementwise(
'T x, T gy', 'T gx',
'gx = (T)1.0 / ((T)1.0 + x * x) * gy',
'arctan_bwd'
)(x, gy)
return gx,
def backward(self, indexes, grad_outputs):
x, gy = self.get_retained_inputs()
ret = []
x_sq = chainer.functions.square(x)
if 0 in indexes:
ret.append(
-2 * gy * x * grad_outputs[0] /
(chainer.functions.square(x_sq) + 2 * x_sq + 1))
if 1 in indexes:
ret.append(grad_outputs[0] / (x_sq + 1))
return ret
def arctan(x):
"""Elementwise arctangent function.
.. math::
y_i = \\arctan x_i.
Args:
x (:class:`~chainer.Variable` or :ref:`ndarray`): Input variable.
Returns:
~chainer.Variable: Output variable.
"""
return Arctan().apply((x,))[0]
class Arctan2(function_node.FunctionNode):
@property
def label(self):
return 'arctan2'
def check_type_forward(self, in_types):
type_check._argname(in_types, ('x1', 'x2'))
type_check.expect(in_types[0].dtype.kind == 'f')
type_check.expect(in_types[1].dtype.kind == 'f')
def forward(self, inputs):
self.retain_inputs((0, 1))
xp = backend.get_array_module(*inputs)
x1, x2 = inputs
return utils.force_array(xp.arctan2(x1, x2)),
def backward(self, indexes, grad_outputs):
x1, x2 = self.get_retained_inputs()
return Arctan2Grad().apply((x1, x2, grad_outputs[0]))
class Arctan2Grad(function_node.FunctionNode):
def forward_cpu(self, inputs):
self.retain_inputs((0, 1, 2))
x1, x2, gy = inputs
sqnorm = x1 ** 2 + x2 ** 2
gx1 = utils.force_array(x2 / sqnorm * gy)
gx2 = utils.force_array(-x1 / sqnorm * gy)
return gx1, gx2
def forward_gpu(self, inputs):
self.retain_inputs((0, 1, 2))
x1, x2, gy = inputs
gx1, gx2 = cuda.elementwise(
'T x1, T x2, T gy',
'T gx1, T gx2',
('T sqnorm = x1 * x1 + x2 * x2;'
'gx1 = x2 / sqnorm * gy;'
'gx2 = -x1 / sqnorm * gy;'),
'arctan2_bwd'
)(x1, x2, gy)
return gx1, gx2
def backward(self, indexes, grad_outputs):
x1, x2, gy = self.get_retained_inputs()
ggx1, ggx2 = grad_outputs
x1_sq = x1 ** 2
x2_sq = x2 ** 2
sqnorm = x1_sq + x2_sq
ret = []
if 0 in indexes:
ret.append(
(- ggx1 * 2 * x1 * x2 + ggx2 * (x1_sq - x2_sq)) * gy /
sqnorm ** 2)
if 1 in indexes:
ret.append(
(ggx1 * (x1_sq - x2_sq) + ggx2 * (2 * x1 * x2)) * gy /
sqnorm ** 2)
if 2 in indexes:
ret.append((ggx1 * x2 - ggx2 * x1) / sqnorm)
return ret
def arctan2(x1, x2):
"""Elementwise arctangent function with two arguments.
Args:
x1 (:class:`~chainer.Variable` or :ref:`ndarray`):
Y-coordinates.
x2 (:class:`~chainer.Variable` or :ref:`ndarray`):
X-coordinates.
Returns:
~chainer.Variable: Angles in radians, in the range [-pi, pi].
"""
return Arctan2().apply((x1, x2))[0]