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Paddle/python/paddle/tensor/stat.py

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# Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# TODO: define statistical functions of a tensor
__all__ = ['mean', 'std', 'var', 'numel', 'median']
import numpy as np
from ..fluid.framework import Variable
from ..fluid.layer_helper import LayerHelper
from ..fluid.framework import core, in_dygraph_mode
from ..fluid import layers
from .search import where
from ..fluid.data_feeder import convert_dtype, check_variable_and_dtype, check_type, check_dtype
import paddle
def mean(x, axis=None, keepdim=False, name=None):
"""
Computes the mean of the input tensor's elements along ``axis``.
Args:
x (Tensor): The input Tensor with data type float32, float64.
axis (int|list|tuple, optional): The axis along which to perform mean
calculations. ``axis`` should be int, list(int) or tuple(int). If
``axis`` is a list/tuple of dimension(s), mean is calculated along
all element(s) of ``axis`` . ``axis`` or element(s) of ``axis``
should be in range [-D, D), where D is the dimensions of ``x`` . If
``axis`` or element(s) of ``axis`` is less than 0, it works the
same way as :math:`axis + D` . If ``axis`` is None, mean is
calculated over all elements of ``x``. Default is None.
keepdim (bool, optional): Whether to reserve the reduced dimension(s)
in the output Tensor. If ``keepdim`` is True, the dimensions of
the output Tensor is the same as ``x`` except in the reduced
dimensions(it is of size 1 in this case). Otherwise, the shape of
the output Tensor is squeezed in ``axis`` . Default is False.
name (str, optional): Name for the operation (optional, default is None).
For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor, results of average along ``axis`` of ``x``, with the same data
type as ``x``.
Examples:
.. code-block:: python
import paddle
import numpy as np
paddle.disable_static()
x = np.array([[[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12]],
[[13, 14, 15, 16],
[17, 18, 19, 20],
[21, 22, 23, 24]]], 'float32')
x = paddle.to_tensor(x)
out1 = paddle.mean(x)
# [12.5]
out2 = paddle.mean(x, axis=-1)
# [[ 2.5 6.5 10.5]
# [14.5 18.5 22.5]]
out3 = paddle.mean(x, axis=-1, keepdim=True)
# [[[ 2.5]
# [ 6.5]
# [10.5]]
# [[14.5]
# [18.5]
# [22.5]]]
out4 = paddle.mean(x, axis=[0, 2])
# [ 8.5 12.5 16.5]
"""
if isinstance(axis, int):
axis = [axis]
reduce_all = True if axis is None \
or len(axis)==0 \
or len(axis) == len(x.shape) else False
if axis is None or len(axis) == 0:
axis = [0]
if in_dygraph_mode():
return core.ops.reduce_mean(x, 'dim', axis, 'keep_dim', keepdim,
'reduce_all', reduce_all)
check_variable_and_dtype(x, 'x/input', ['float32', 'float64'],
'mean/reduce_mean')
check_type(axis, 'axis/dim', (int, list, tuple), 'mean/reduce_mean')
if isinstance(axis, (list, tuple)):
for item in axis:
check_type(item, 'elements of axis/dim', (int), 'mean/reduce_mean')
helper = LayerHelper('mean', **locals())
attrs = {'dim': axis, 'keep_dim': keepdim, 'reduce_all': reduce_all}
out = helper.create_variable_for_type_inference(x.dtype)
helper.append_op(
type='reduce_mean', inputs={'X': x}, outputs={'Out': out}, attrs=attrs)
return out
def var(x, axis=None, unbiased=True, keepdim=False, name=None):
"""
Computes the variance of ``x`` along ``axis`` .
Args:
x (Tensor): The input Tensor with data type float32, float64.
axis (int|list|tuple, optional): The axis along which to perform
variance calculations. ``axis`` should be int, list(int) or
tuple(int). If ``axis`` is a list/tuple of dimension(s), variance
is calculated along all element(s) of ``axis`` . ``axis`` or
element(s) of ``axis`` should be in range [-D, D), where D is the
dimensions of ``x`` . If ``axis`` or element(s) of ``axis`` is less
than 0, it works the same way as :math:`axis + D` . If ``axis`` is
None, variance is calculated over all elements of ``x``. Default
is None.
unbiased (bool, optional): Whether to use the unbiased estimation. If
``unbiased`` is True, the divisor used in the computation is
:math:`N - 1`, where :math:`N` represents the number of elements
along ``axis`` , otherwise the divisor is :math:`N`. Default is True.
keepdim (bool, optional): Whether to reserve the reduced dimension(s)
in the output Tensor. If ``keepdim`` is True, the dimensions of
the output Tensor is the same as ``x`` except in the reduced
dimensions(it is of size 1 in this case). Otherwise, the shape of
the output Tensor is squeezed in ``axis`` . Default is False.
name (str, optional): Name for the operation (optional, default is None).
For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor, results of variance along ``axis`` of ``x``, with the same data
type as ``x``.
Examples:
.. code-block:: python
import paddle
import numpy as np
paddle.disable_static()
x = np.array([[1.0, 2.0, 3.0], [1.0, 4.0, 5.0]])
x = paddle.to_tensor(x)
out1 = paddle.var(x)
# [2.66666667]
out2 = paddle.var(x, axis=1)
# [1. 4.33333333]
"""
if not in_dygraph_mode():
check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'var')
u = mean(x, axis, True, name)
out = paddle.sum((x - u)**2, axis, keepdim=keepdim, name=name)
n = paddle.cast(paddle.numel(x), x.dtype) \
/ paddle.cast(paddle.numel(out), x.dtype)
if unbiased:
one_const = paddle.ones([1], x.dtype)
n = where(n > one_const, n - 1., one_const)
out /= n
return out
def std(x, axis=None, unbiased=True, keepdim=False, name=None):
"""
Computes the standard-deviation of ``x`` along ``axis`` .
Args:
x (Tensor): The input Tensor with data type float32, float64.
axis (int|list|tuple, optional): The axis along which to perform
standard-deviation calculations. ``axis`` should be int, list(int)
or tuple(int). If ``axis`` is a list/tuple of dimension(s),
standard-deviation is calculated along all element(s) of ``axis`` .
``axis`` or element(s) of ``axis`` should be in range [-D, D),
where D is the dimensions of ``x`` . If ``axis`` or element(s) of
``axis`` is less than 0, it works the same way as :math:`axis + D` .
If ``axis`` is None, standard-deviation is calculated over all
elements of ``x``. Default is None.
unbiased (bool, optional): Whether to use the unbiased estimation. If
``unbiased`` is True, the standard-deviation is calculated via the
unbiased estimator. If ``unbiased`` is True, the divisor used in
the computation is :math:`N - 1`, where :math:`N` represents the
number of elements along ``axis`` , otherwise the divisor is
:math:`N`. Default is True.
keepdim (bool, optional): Whether to reserve the reduced dimension(s)
in the output Tensor. If ``keepdim`` is True, the dimensions of
the output Tensor is the same as ``x`` except in the reduced
dimensions(it is of size 1 in this case). Otherwise, the shape of
the output Tensor is squeezed in ``axis`` . Default is False.
name (str, optional): Name for the operation (optional, default is None).
For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor, results of standard-deviation along ``axis`` of ``x``, with the
same data type as ``x``.
Examples:
.. code-block:: python
import paddle
import numpy as np
paddle.disable_static()
x = np.array([[1.0, 2.0, 3.0], [1.0, 4.0, 5.0]])
x = paddle.to_tensor(x)
out1 = paddle.std(x)
# [1.63299316]
out2 = paddle.std(x, axis=1)
# [1. 2.081666]
"""
if not in_dygraph_mode():
check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'std')
out = var(**locals())
return paddle.sqrt(out)
def numel(x, name=None):
"""
Returns the number of elements for a tensor, which is a int64 Tensor with shape [1] in static mode
or a scalar value in imperative mode
Args:
x (Tensor): The input Tensor, it's data type can be bool, float16, float32, float64, int32, int64.
Returns:
Tensor: The number of elements for the input Tensor.
Examples:
.. code-block:: python
import paddle
paddle.disable_static()
x = paddle.full(shape=[4, 5, 7], fill_value=0, dtype='int32')
numel = paddle.numel(x) # 140
"""
if in_dygraph_mode():
return core.ops.size(x)
if not isinstance(x, Variable):
raise TypeError("x must be a Tensor in numel")
helper = LayerHelper('numel', **locals())
out = helper.create_variable_for_type_inference(
dtype=core.VarDesc.VarType.INT64)
helper.append_op(type='size', inputs={'Input': x}, outputs={'Out': out})
return out
def median(x, axis=None, keepdim=False, name=None):
"""
Compute the median along the specified axis.
Args:
x (Tensor): The input Tensor, it's data type can be bool, float16, float32, float64, int32, int64.
axis (int, optional): The axis along which to perform median calculations ``axis`` should be int.
``axis`` should be in range [-D, D), where D is the dimensions of ``x`` .
If ``axis`` is less than 0, it works the same way as :math:`axis + D`.
If ``axis`` is None, median is calculated over all elements of ``x``. Default is None.
keepdim (bool, optional): Whether to reserve the reduced dimension(s)
in the output Tensor. If ``keepdim`` is True, the dimensions of
the output Tensor is the same as ``x`` except in the reduced
dimensions(it is of size 1 in this case). Otherwise, the shape of
the output Tensor is squeezed in ``axis`` . Default is False.
name (str, optional): Name for the operation (optional, default is None).
For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor, results of median along ``axis`` of ``x``. If data type of ``x`` is float64, data type of results will be float64, otherwise data type will be float32.
Examples:
.. code-block:: python
import paddle
x = paddle.arange(12).reshape([3, 4])
# x is [[0 , 1 , 2 , 3 ],
# [4 , 5 , 6 , 7 ],
# [8 , 9 , 10, 11]]
y1 = paddle.median(x)
# y1 is [5.5]
y2 = paddle.median(x, axis=0)
# y2 is [4., 5., 6., 7.]
y3 = paddle.median(x, axis=1)
# y3 is [1.5, 5.5, 9.5]
y4 = paddle.median(x, axis=0, keepdim=True)
# y4 is [[4., 5., 6., 7.]]
"""
if not isinstance(x, Variable):
raise TypeError("In median, the input x should be a Tensor.")
is_flatten = axis is None
dims = len(x.shape)
if is_flatten:
x = paddle.flatten(x)
axis = 0
else:
if not isinstance(axis, int) or not (axis < dims and axis >= -dims):
raise ValueError(
"In median, axis should be none or an integer in range [-rank(x), rank(x))."
)
if axis < 0:
axis += dims
sz = x.shape[axis]
kth = sz >> 1
tensor_topk, idx = paddle.topk(x, kth + 1, axis=axis, largest=False)
dtype = 'float64' if x.dtype == core.VarDesc.VarType.FP64 else 'float32'
if sz & 1 == 0:
out_tensor = paddle.slice(
tensor_topk, axes=[axis], starts=[kth - 1],
ends=[kth]) + paddle.slice(
tensor_topk, axes=[axis], starts=[kth], ends=[kth + 1])
out_tensor = paddle.cast(out_tensor, dtype=dtype) / 2
else:
out_tensor = paddle.cast(
paddle.slice(
tensor_topk, axes=[axis], starts=[kth], ends=[kth + 1]),
dtype=dtype)
if not keepdim or is_flatten:
if not is_flatten:
newshape = x.shape[:axis] + x.shape[axis + 1:]
elif not keepdim:
newshape = [1]
else:
newshape = [1] * dims
else:
newshape = out_tensor.shape
out_tensor = out_tensor.reshape(newshape, name=name)
return out_tensor
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