MegEngine/imperative/python/megengine/functional/math.py

# -*- coding: utf-8 -*-
# MegEngine is Licensed under the Apache License, Version 2.0 (the "License")
#
# Copyright (c) 2014-2020 Megvii Inc. All rights reserved.
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT ARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
import collections
import functools
import math
import numbers
from typing import Optional, Sequence, Tuple, Union

from ..core.ops import builtin
from ..core.ops._internal import param_defs as P
from ..core.ops.special import Const
from ..core.tensor import utils
from ..core.tensor.core import TensorBase, TensorWrapperBase, apply
from ..tensor import Tensor
from .elemwise import clip, exp, log, log1p
from .tensor import reshape, squeeze

__all__ = [
    "argmax",
    "argmin",
    "argsort",
    "isinf",
    "isnan",
    "max",
    "mean",
    "min",
    "norm",
    "normalize",
    "prod",
    "sign",
    "sort",
    "std",
    "sum",
    "topk",
    "var",
]


def isnan(inp: Tensor) -> Tensor:
    r"""
    Returns a new tensor representing if each element is ``NaN`` or not.

    :param inp: input tensor.
    :return: result tensor.

    Examples:

    .. testcode::

        from megengine import tensor
        import megengine.functional as F

        x = tensor([1, float("nan"), 0])
        print(F.isnan(x).numpy())

    Outputs:

    .. testoutput::

        [False  True False]

    """
    return inp != inp


def isinf(inp: Tensor) -> Tensor:
    r"""
    Returns a new tensor representing if each element is ``Inf`` or not.

    :param inp: input tensor.
    :return: result tensor.

    Examples:

    .. testcode::

        from megengine import tensor
        import megengine.functional as F

        x = tensor([1, float("inf"), 0])
        print(F.isinf(x).numpy())

    Outputs:

    .. testoutput::

        [False  True False]

    """
    return abs(inp).astype("float32") == float("inf")


def sign(inp: Tensor):
    r"""
    Returns a new tensor representing the sign of each element in input tensor.

    :param: input tensor.
    :return: the sign of input tensor.

    Examples:

    .. testcode::

        from megengine import tensor
        import megengine.functional as F

        x = tensor([1, -1, 0])
        print(F.sign(x).numpy())

    Outputs:

    .. testoutput::

        [ 1 -1  0]

    """
    return (inp > 0).astype(inp.dtype) - (inp < 0).astype(inp.dtype)


def sum(
    inp: Tensor,
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdims: bool = False,
) -> Tensor:
    r"""
    Returns the sum of input tensor along given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced.
        Default: None
    :param keepdims: whether the output tensor has axis retained or not.
        Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.arange(1, 7, dtype=np.int32).reshape(2, 3))
        out = F.sum(x)
        print(out.numpy())

    Outputs:

    .. testoutput::

        [21]

    """
    return inp.sum(axis=axis, keepdims=keepdims)


def prod(
    inp: Tensor, axis: Optional[Union[int, Sequence[int]]] = None, keepdims=False
) -> Tensor:
    r"""
    Returns the product of input tensor along given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.arange(1, 7, dtype=np.int32).reshape(2, 3))
        out = F.prod(x)
        print(out.numpy())

    Outputs:

    .. testoutput::

        [720]

    """
    return inp.prod(axis=axis, keepdims=keepdims)


def mean(
    inp: Tensor,
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdims: bool = False,
) -> Tensor:
    """
    Returns the mean value of input tensor along
    given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.arange(1, 7, dtype=np.int32).reshape(2, 3))
        out = F.mean(x)
        print(out.numpy())

    Outputs:

    .. testoutput::

        [3.5]

    """
    return inp.mean(axis=axis, keepdims=keepdims)


def var(
    inp: Tensor,
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdims: bool = False,
) -> Tensor:
    """
    Returns the variance value of input tensor along
    given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        data = tensor(np.arange(1, 7, dtype=np.float32).reshape(2, 3))
        out = F.var(data)
        print(out.numpy().round(decimals=4))

    Outputs:

    .. testoutput::

        [2.9167]
    """
    if axis is None:
        m = mean(inp, axis=axis, keepdims=False)
    else:
        m = mean(inp, axis=axis, keepdims=True)
    v = inp - m
    return mean(v ** 2, axis=axis, keepdims=keepdims)


def std(
    inp: Tensor,
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdims: bool = False,
) -> Tensor:
    """
    Returns the standard deviation of input tensor along
    given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        data = tensor(np.arange(1, 7, dtype=np.float32).reshape(2, 3))
        out = F.std(data, axis=1)
        print(out.numpy().round(decimals=4))

    Outputs:

    .. testoutput::

        [0.8165 0.8165]
    """
    return var(inp, axis=axis, keepdims=keepdims) ** 0.5


def min(
    inp: Tensor,
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdims: bool = False,
) -> Tensor:
    r"""
    Returns the min value of input tensor along
    given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.arange(1, 7, dtype=np.int32).reshape(2,3))
        out = F.min(x)
        print(out.numpy())

    Outputs:

    .. testoutput::

        [1]

    """
    return inp.min(axis=axis, keepdims=keepdims)


def max(
    inp: Tensor,
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdims: bool = False,
) -> Tensor:
    r"""
    Returns the max value of the input tensor along
    given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.arange(1, 7, dtype=np.int32).reshape(2,3))
        out = F.max(x)
        print(out.numpy())

    Outputs:

    .. testoutput::

        [6]

    """
    return inp.max(axis=axis, keepdims=keepdims)


def norm(
    inp: Tensor, ord: float = None, axis: int = None, keepdims=False,
):
    """
    Calculates ``p``-norm of input tensor along
    given axis.

    :param inp: input tensor.
    :param ord: power of value applied to inp. Default: 2
    :param axis: dimension to reduce. If None, input must be a vector. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.arange(-3, 3, dtype=np.float32))
        out = F.norm(x)
        print(out.numpy().round(decimals=4))

    Outputs:

    .. testoutput::

        [4.3589]

    """
    if axis is None:
        if inp.ndim != 1:
            raise TypeError("axis is required unless input is a vector")
    if ord is None:
        ord = 2
    if ord == 0:
        return sum(inp != 0, axis=axis, keepdims=keepdims)
    if ord == math.inf:
        return max(abs(inp))
    if ord == -math.inf:
        return min(abs(inp))
    return sum(abs(inp) ** ord, axis=axis, keepdims=keepdims) ** (1.0 / ord)


def argmin(
    inp: Tensor,
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdims: bool = False,
) -> Tensor:
    r"""
    Returns the indices of the minimum values along
    given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.arange(1, 7, dtype=np.int32).reshape(2,3))
        out = F.argmin(x)
        print(out.numpy())

    Outputs:

    .. testoutput::

        [0]

    """
    if isinstance(axis, collections.abc.Iterable):
        axis = list(axis)
        axis.sort(reverse=True)

        for ai in axis:
            op = builtin.Argmin(axis=ai)
            (inp,) = apply(op, inp)

            if not keepdims:
                inp = squeeze(inp, ai)

        return inp

    if axis is None:
        assert not keepdims, "can not set axis=None and keepdims=True"
        inp = inp.flatten()
        axis = 0

    op = builtin.Argmin(axis=axis)
    (result,) = apply(op, inp)
    if not keepdims:
        result = squeeze(result, axis)
    return result


def argmax(
    inp: Tensor,
    axis: Optional[Union[int, Sequence[int]]] = None,
    keepdims: bool = False,
) -> Tensor:
    r"""
    Returns the indices of the maximum values along
    given axis. If axis is a list of dimensions,
    reduce over all of them.

    :param inp: input tensor.
    :param axis: dimension to reduce. If None, all dimensions will be reduced. Default: None
    :param keepdims: whether the output tensor has axis retained or not. Default: False
    :return: output tensor.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.arange(1, 7, dtype=np.int32).reshape(2,3))
        out = F.argmax(x)
        print(out.numpy())

    Outputs:

    .. testoutput::

        [5]

    """
    if isinstance(axis, collections.abc.Iterable):
        axis = list(axis)
        axis.sort(reverse=True)

        for ai in axis:
            op = builtin.Argmax(axis=ai)
            (inp,) = apply(op, inp)

            if not keepdims:
                inp = squeeze(inp, ai)

        return inp

    if axis is None:
        assert not keepdims, "can not set axis=None and keepdims=True"
        inp = inp.flatten()
        axis = 0

    op = builtin.Argmax(axis=axis)
    (result,) = apply(op, inp)
    if not keepdims:
        result = squeeze(result, axis)
    return result


def normalize(
    inp: Tensor, ord: float = None, axis: int = None, eps: float = 1e-12,
) -> Tensor:
    r"""
    Performs :math:`L_p` normalization of input tensor along
    given axis.

    For a tensor of shape :math:`(n_0, ..., n_{dim}, ..., n_k)`, each
    :math:`n_{dim}` -element vector :math:`v` along dimension :attr:`axis` is transformed as:

    .. math::
        v = \frac{v}{\max(\lVert v \rVert_p, \epsilon)}.

    :param inp: input tensor.
    :param ord: power of value applied to input tensor. Default: 2
    :param axis: dimension to reduce.If None, input must be a vector. Default: None
    :param eps: a small value to avoid division by zero. Default: 1e-12
    :return: normalized output tensor.
    """
    if axis is None:
        return inp / clip(norm(inp, ord, axis), lower=eps)
    else:
        return inp / clip(norm(inp, ord, axis, keepdims=True), lower=eps)


def argsort(inp: Tensor, descending: bool = False) -> Tensor:
    r"""
    Returns the indices that would sort the input tensor.

    :param inp: input tensor. If it's 2d, the result would be array of indices show how to sort each row in the input tensor.
    :param descending: sort in descending order, where the largest comes first. Default: False
    :return: indices of int32 indicates how to sort the input.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.array([1,2], dtype=np.float32))
        indices = F.argsort(x)
        print(indices.numpy())

    Outputs:

    .. testoutput::

        [0 1]

    """
    assert len(inp.shape) <= 2, "Input should be 1d or 2d"
    if descending:
        order = P.Argsort.Order.DESCENDING
    else:
        order = P.Argsort.Order.ASCENDING

    op = builtin.Argsort(order=order)
    if len(inp.shape) == 1:
        inp = inp.reshape(1, -1)
        _, result = apply(op, inp)
        return result[0]
    _, result = apply(op, inp)
    return result


def sort(inp: Tensor, descending: bool = False) -> Tuple[Tensor, Tensor]:
    r"""
    Returns sorted tensor and the indices would sort the input tensor.

    :param inp: input tensor. If it's 2d, the result would be sorted by row.
    :param descending: sort in descending order, where the largest comes first. Default: False
    :return: tuple of two tensors `(sorted_tensor, indices_of_int32)`.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import megengine.functional as F

        x = tensor(np.array([1,2], dtype=np.float32))
        out, indices = F.sort(x)
        print(out.numpy())

    Outputs:

    .. testoutput::

        [1. 2.]

    """
    assert len(inp.shape) <= 2, "Input should be 1d or 2d"
    if descending:
        order = P.Argsort.Order.DESCENDING
    else:
        order = P.Argsort.Order.ASCENDING

    op = builtin.Argsort(order=order)
    if len(inp.shape) == 1:
        inp = inp.reshape(1, -1)
        tns, ind = apply(op, inp)
        return tns[0], ind[0]
    tns, ind = apply(op, inp)
    return tns, ind


def topk(
    inp: Tensor,
    k: int,
    descending: bool = False,
    kth_only: bool = False,
    no_sort: bool = False,
) -> Tuple[Tensor, Tensor]:
    r"""
    Selects the ``Top-K``(by default) smallest elements of 2d matrix by row.

    :param inp: input tensor. If input tensor is 2d, each row will be sorted.
    :param k: number of elements needed.
    :param descending: if True, return the largest elements instead. Default: False
    :param kth_only: if True, only the k-th element will be returned. Default: False
    :param no_sort: if True, the returned elements can be unordered. Default: False
    :return: tuple of two tensors `(topk_tensor, indices_of_int32)`.

    Examples:

    .. testcode::

        import numpy as np
        from megengine import tensor
        import  megengine.functional as F

        x = tensor(np.array([2, 4, 6, 8, 7, 5, 3, 1], dtype=np.float32))
        top, indices = F.topk(x, 5)
        print(top.numpy(), indices.numpy())

    Outputs:

    .. testoutput::

        [1. 2. 3. 4. 5.] [7 0 6 1 5]

    """
    if descending:
        inp = -inp

    Mode = P.TopK.Mode
    if kth_only:
        mode = Mode.KTH_ONLY
    elif no_sort:
        mode = Mode.VALUE_IDX_NOSORT
    else:
        mode = Mode.VALUE_IDX_SORTED
    op = builtin.TopK(mode=mode)

    if not isinstance(k, (TensorBase, TensorWrapperBase)):
        (k,) = Const(k, dtype="int32", device=inp.device)(inp)

    if len(inp.shape) == 1:
        inp = inp.reshape(1, -1)
        res = apply(op, inp, k)
        if kth_only:
            tns = res[0]
        else:
            tns, ind = res[0][0], res[1][0]
    else:
        res = apply(op, inp, k)
        if kth_only:
            tns = res
        else:
            tns, ind = res[0], res[1]

    if descending:
        tns = -tns
    return tns, ind