# Copyright 2022-2023 XProbe Inc.
# derived from copyright 1999-2021 Alibaba Group Holding Ltd.
#
# 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.
import numpy as np
from ... import opcodes as OperandDef
from ...serialization.serializables import Int32Field
from ..array_utils import as_same_device, device, get_array_module
from ..datasource import tensor as astensor
from .core import TensorReduction, TensorReductionMixin, nannumel
from .var import reduce_var_square
class TensorNanMoment(TensorReduction, TensorReductionMixin):
_op_type_ = OperandDef.NANMOMENT
_moment = Int32Field("moment", default=2)
_ddof = Int32Field("ddof")
def __init__(
self,
axis=None,
keepdims=None,
moment=None,
ddof=None,
combine_size=None,
stage=None,
**kw
):
stage = self._rewrite_stage(stage)
if moment is not None:
kw["_moment"] = moment
super().__init__(
_axis=axis,
_keepdims=keepdims,
_ddof=ddof,
_combine_size=combine_size,
stage=stage,
**kw
)
@property
def moment(self):
return getattr(self, "_moment", 2)
@property
def ddof(self):
return self._ddof
@classmethod
def execute_agg(cls, ctx, op):
axis = cls.get_axis(op.axis)
dtype = op.dtype
(_data, _count, _var_square), device_id, xp = as_same_device(
ctx[op.inputs[0].key], device=op.device, ret_extra=True
)
with device(device_id):
chunk_count = xp.nansum(_count, axis=axis, dtype=np.int64, keepdims=True)
chunk_sum = xp.nansum(_data, axis=axis, dtype=dtype, keepdims=True)
avg = xp.true_divide(chunk_sum, chunk_count, dtype=dtype)
avg_diff = xp.true_divide(_data, _count, dtype=dtype) - avg
var_square = reduce_var_square(
_var_square, avg_diff, _count, op, axis, xp.nansum
)
ctx[op.outputs[0].key] = xp.true_divide(
var_square,
xp.nansum(
chunk_count, axis=axis, dtype=dtype, keepdims=bool(op.keepdims)
)
- op.ddof,
dtype=dtype,
)
@classmethod
def execute_map(cls, ctx, op):
(in_chunk,), device_id, xp = as_same_device(
[ctx[c.key] for c in op.inputs], device=op.device, ret_extra=True
)
axis = cls.get_axis(op.axis)
moment = op.moment
dtype = op.dtype
empty = get_array_module(in_chunk, nosparse=True).empty
with device(device_id):
chunk_count = nannumel(
in_chunk, axis=axis, dtype=np.int64, keepdims=bool(op.keepdims)
)
chunk_sum = xp.nansum(
in_chunk, axis=axis, dtype=dtype, keepdims=bool(op.keepdims)
)
avg = xp.true_divide(chunk_sum, chunk_count)
var_square = empty(chunk_count.shape + (moment - 1,), dtype=dtype)
for i in range(2, moment + 1):
var_square[..., i - 2] = xp.nansum(
(in_chunk - avg) ** i,
axis=axis,
dtype=dtype,
keepdims=bool(op.keepdims),
)
ctx[op.outputs[0].key] = (chunk_sum, chunk_count, var_square)
@classmethod
def execute_combine(cls, ctx, op):
axis = cls.get_axis(op.axis)
moment = op.moment
dtype = op.dtype
(_data, _count, _var_square), device_id, xp = as_same_device(
ctx[op.inputs[0].key], device=op.device, ret_extra=True
)
empty = get_array_module(_data, nosparse=True).empty
with device(device_id):
chunk_count = xp.nansum(
_count, axis=axis, dtype=np.int64, keepdims=bool(op.keepdims)
)
chunk_sum = xp.nansum(
_data, axis=axis, dtype=dtype, keepdims=bool(op.keepdims)
)
avg = xp.true_divide(chunk_sum, chunk_count, dtype=dtype)
avg_diff = xp.true_divide(_data, _count, dtype=dtype) - avg
var_square = empty(chunk_count.shape + (moment - 1,), dtype=dtype)
for m in range(2, moment + 1):
var_square[..., m - 2] = reduce_var_square(
_var_square, avg_diff, _count, op, axis, xp.nansum
)
ctx[op.outputs[0].key] = (chunk_sum, chunk_count, var_square)
class TensorNanVar(TensorReduction, TensorReductionMixin):
_op_type_ = OperandDef.NANVAR
_ddof = Int32Field("ddof")
def __new__(cls, *args, **kwargs):
if kwargs.get("stage") is not None:
return TensorNanMoment(*args, **kwargs)
return super().__new__(cls)
def __init__(
self, axis=None, dtype=None, keepdims=None, ddof=0, combine_size=None, **kw
):
super().__init__(
_axis=axis,
dtype=dtype,
_keepdims=keepdims,
_ddof=ddof,
_combine_size=combine_size,
**kw
)
@property
def ddof(self):
return self._ddof
def _get_op_kw(self):
kw = dict()
kw["ddof"] = self.ddof
return kw
@classmethod
def execute(cls, ctx, op):
axis = cls.get_axis(op.axis)
(in_chunk,), device_id, xp = as_same_device(
[ctx[c.key] for c in op.inputs], device=op.device, ret_extra=True
)
with device(device_id):
ctx[op.outputs[0].key] = xp.nanvar(
in_chunk,
axis=axis,
dtype=op.dtype,
ddof=op.ddof,
keepdims=bool(op.keepdims),
)
[docs]def nanvar(
a, axis=None, dtype=None, out=None, ddof=0, keepdims=None, combine_size=None
):
"""
Compute the variance along the specified axis, while ignoring NaNs.
Returns the variance of the tensor elements, a measure of the spread of
a distribution. The variance is computed for the flattened tensor by
default, otherwise over the specified axis.
For all-NaN slices or slices with zero degrees of freedom, NaN is
returned and a `RuntimeWarning` is raised.
Parameters
----------
a : array_like
Tensor containing numbers whose variance is desired. If `a` is not a
tensor, a conversion is attempted.
axis : int, optional
Axis along which the variance is computed. The default is to compute
the variance of the flattened array.
dtype : data-type, optional
Type to use in computing the variance. For tensors of integer type
the default is `float32`; for tensors of float types it is the same as
the tensor type.
out : Tensor, optional
Alternate output tensor in which to place the result. It must have
the same shape as the expected output, but the type is cast if
necessary.
ddof : int, optional
"Delta Degrees of Freedom": the divisor used in the calculation is
``N - ddof``, where ``N`` represents the number of non-NaN
elements. By default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `a`.
combine_size: int, optional
The number of chunks to combine.
Returns
-------
variance : Tensor, see dtype parameter above
If `out` is None, return a new tensor containing the variance,
otherwise return a reference to the output tensor. If ddof is >= the
number of non-NaN elements in a slice or the slice contains only
NaNs, then the result for that slice is NaN.
See Also
--------
std : Standard deviation
mean : Average
var : Variance while not ignoring NaNs
nanstd, nanmean
Notes
-----
The variance is the average of the squared deviations from the mean,
i.e., ``var = mean(abs(x - x.mean())**2)``.
The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
If, however, `ddof` is specified, the divisor ``N - ddof`` is used
instead. In standard statistical practice, ``ddof=1`` provides an
unbiased estimator of the variance of a hypothetical infinite
population. ``ddof=0`` provides a maximum likelihood estimate of the
variance for normally distributed variables.
Note that for complex numbers, the absolute value is taken before
squaring, so that the result is always real and nonnegative.
For floating-point input, the variance is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for `float32` (see example
below). Specifying a higher-accuracy accumulator using the ``dtype``
keyword can alleviate this issue.
For this function to work on sub-classes of Tensor, they must define
`sum` with the kwarg `keepdims`
Examples
--------
>>> import mars.tensor as mt
>>> a = mt.array([[1, mt.nan], [3, 4]])
>>> mt.nanvar(a).execute()
1.5555555555555554
>>> mt.nanvar(a, axis=0).execute()
array([ 1., 0.])
>>> mt.nanvar(a, axis=1).execute()
array([ 0., 0.25])
"""
a = astensor(a)
if dtype is None:
dtype = np.nanvar(np.ones((1,), dtype=a.dtype)).dtype
op = TensorNanVar(
axis=axis, dtype=dtype, keepdims=keepdims, ddof=ddof, combine_size=combine_size
)
return op(a, out=out)