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

# -*- coding: utf-8 -*-
# MegEngine is Licensed under the Apache License, Version 2.0 (the "License")
#
# Copyright (c) 2014-2021 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.
from typing import Iterable, Optional, Sequence, Tuple, Union

import numpy as np

from ..core._imperative_rt import CompNode
from ..core._imperative_rt.core2 import SymbolVar, apply, dtype_promotion
from ..core._wrap import as_device
from ..core.ops import builtin
from ..core.ops.builtin import Copy, Identity
from ..core.ops.special import Const
from ..core.tensor.array_method import _broadcast, _remove_axis
from ..core.tensor.utils import astensor1d, convert_inputs, get_device
from ..device import get_default_device
from ..tensor import Tensor
from .elemwise import ceil

__all__ = [
    "arange",
    "broadcast_to",
    "concat",
    "cond_take",
    "cumsum",
    "expand_dims",
    "eye",
    "flatten",
    "full",
    "full_like",
    "gather",
    "linspace",
    "ones",
    "ones_like",
    "repeat",
    "reshape",
    "roll",
    "split",
    "squeeze",
    "stack",
    "scatter",
    "tile",
    "copy",
    "transpose",
    "where",
    "zeros",
    "zeros_like",
]


def eye(N, M=None, *, dtype="float32", device: Optional[CompNode] = None) -> Tensor:
    r"""Returns a 2D tensor with ones on the diagonal and zeros elsewhere.

    Args:
        shape: a list, tuple or integer defining the shape of the output tensor.
        dtype: the desired data type of the output tensor. Default: ``float32``.
        device: the desired device of the output tensor. Default: if ``None``,
            use the default device (see :func:`~.megengine.get_default_device`).

    Returns:
        eye matrix.

    Examples:

        .. testcode::

            import numpy as np
            import megengine.functional as F

            out = F.eye(4, 6, dtype=np.float32)
            print(out.numpy())

        Outputs:

        .. testoutput::

            [[1. 0. 0. 0. 0. 0.]
             [0. 1. 0. 0. 0. 0.]
             [0. 0. 1. 0. 0. 0.]
             [0. 0. 0. 1. 0. 0.]]
    """
    if M is not None:
        if isinstance(N, Tensor) or isinstance(M, Tensor):
            shape = astensor1d((N, M))
        else:
            shape = Tensor([N, M], dtype="int32", device=device)
    elif isinstance(N, Tensor):
        shape = N
    else:
        shape = Tensor(N, dtype="int32", device=device)
    op = builtin.Eye(k=0, dtype=dtype, comp_node=device)
    (result,) = apply(op, shape)
    return result


def full(
    shape: Union[int, tuple, list],
    value: Union[bool, int, float, Tensor],
    dtype=None,
    device=None,
) -> Tensor:
    r"""Creates a tensor of shape ``shape`` filled with ``value``.

    Args:
        shape: output tensor shape.
        value: fill value.
        dtype: output tensor data type. If ``dtype`` is ``None``, the output tensor
            data type must be inferred from ``value``. If the value is an ``int``,
            the output tensor data type must be the default integer data type. If the
            value is a ``float``, the output tensor data type must be the default
            floating-point data type. If the value is a ``bool``, the output tensor 
            must have boolean data type. Default: ``None``.
        device: device on which to place the created tensor. Default: ``None``.

    Returns:
        a tensor where every element is equal to ``value``.

    Examples:

        .. testcode::

            import numpy as np
            import megengine.functional as F

            out = F.full([2,3], 1.5)
            print(out.numpy())

        Outputs:

        .. testoutput::

            [[1.5 1.5 1.5]
             [1.5 1.5 1.5]]
    """

    if isinstance(shape, int):
        shape = (shape,)
    if device is None:
        device = get_default_device()
    (x,) = Const(value, dtype=dtype, device=device)()
    if type(shape) in (list, tuple) and len(shape) == 0:
        return x
    return broadcast_to(x, shape)


def ones(
    shape: Union[int, Tuple[int, ...]],
    *,
    dtype="float32",
    device: Optional[CompNode] = None
) -> Tensor:
    r"""Returns a new tensor having a specified shape and filled with ones.

    Args:
        shape (int or sequence of ints): the shape of the output tensor.

    Keyword args:
        dtype (:attr:`.Tensor.dtype`): output tensor data type. Default: ``float32``.
        device (:attr:`.Tensor.device`): device on which to place the created tensor. Default: ``None``.

    Returns:
        a tensor containing ones.

    Examples:

        .. testcode::

            import megengine.functional as F

            out = F.ones(5)
            print(out.numpy())
            out = F.ones((5, ), dtype='int32')
            print(out.numpy())
            out = F.ones((2, 2))
            print(out.numpy())
            out = F.ones([2, 1])
            print(out.numpy())

        Outputs:

        .. testoutput::

            [1. 1. 1. 1. 1.]
            [1 1 1 1 1]
            [[1. 1.]
             [1. 1.]]
            [[1.]
             [1.]]
    """
    return full(shape, 1.0, dtype=dtype, device=device)


def zeros(shape, dtype="float32", device=None) -> Tensor:
    r"""Returns a zero tensor with given shape.

    Args:
        shape: a list, tuple or integer defining the shape of the output tensor.
        dtype: the desired data type of the output tensor. Default: ``float32``.
        device: the desired device of the output tensor. Default: if ``None``,
            use the default device (see :func:`~.megengine.get_default_device`).
    """
    return full(shape, 0.0, dtype=dtype, device=device)


def zeros_like(inp: Union[Tensor, SymbolVar]) -> Union[Tensor, SymbolVar]:
    r"""Returns a zero tensor with the same shape as input tensor.

    Args:
        inp: input tensor.

    Return:
        output tensor.

    Examples:

        .. testcode::

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

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

        Outputs:

        .. testoutput::

            [[0 0 0]
             [0 0 0]]

    """
    return full_like(inp, 0.0)


def ones_like(inp: Union[Tensor, SymbolVar]) -> Union[Tensor, SymbolVar]:
    r"""Returns a ones tensor with the same shape as input tensor.

    Args:
        inp: input tensor.

    Return:
        output tensor.

    Examples:

        .. testcode::

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

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

        Outputs:

        .. testoutput::

            [[1 1 1]
             [1 1 1]]
    """
    return full_like(inp, 1.0)


def full_like(
    inp: Union[Tensor, SymbolVar], value: Union[int, float]
) -> Union[Tensor, SymbolVar]:
    r"""Returns a tensor filled with given value with the same shape as input tensor.

    Args:
        inp: input tensor.
        value: target value.

    Return:
        output tensor.

    Examples:

        .. testcode::

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

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

        Outputs:

        .. testoutput::

            [[2 2 2]
             [2 2 2]]

    """
    (x,) = Const(value, dtype=inp.dtype, device=inp.device)(inp)
    if inp.ndim == 0:
        return x
    return broadcast_to(x, inp.shape)


def broadcast_to(inp: Tensor, shape: Union[int, Iterable[int]]) -> Tensor:
    r"""Broadcasts a tensor to given shape.

    Args:
        inp: input tensor.
        shape: target shape.

    Returns:
        output tensor.

    Examples:

        .. testcode::

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

            data = tensor(np.arange(0, 3, dtype=np.float32).reshape(3))
            out = F.broadcast_to(data, (2, 3))
            print(out.numpy())

        Outputs:

        .. testoutput::

            [[0. 1. 2.]
             [0. 1. 2.]]
    """
    return _broadcast(inp, shape)


def concat(inps: Iterable[Tensor], axis: int = 0, device=None) -> Tensor:
    r"""Concat some tensors

    Args:
        inps: input tensors to concat.
        axis: over which dimension the tensors are concatenated. Default: 0
        device: which device output will be. Default: None

    Returns:
        output tensor.

    Examples:

        .. testcode::

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

            data1 = tensor(np.arange(0, 6, dtype=np.float32).reshape((2, 3)))
            data2 = tensor(np.arange(6, 12, dtype=np.float32).reshape((2, 3)))
            out = F.concat([data1, data2])
            print(out.numpy())

        Outputs:

        .. testoutput::

            [[ 0.  1.  2.]
             [ 3.  4.  5.]
             [ 6.  7.  8.]
             [ 9. 10. 11.]]
    """
    if len(inps) == 1:
        return inps[0]

    # FIXME: remove this convert_inputs
    inps = convert_inputs(*inps, device=device)
    if device is None:
        device = get_device(inps)
    device = as_device(device)
    (result,) = apply(builtin.Concat(axis=axis, comp_node=device.to_c()), *inps)
    return result


def stack(inps, axis=0, device=None):
    r"""Concats a sequence of tensors along a new axis.
    The input tensors must have the same shape.

    Args:
        inps: input tensors.
        axis: which axis will be concatenated.
        device: the device output will be. Default: None

    Returns:
        output concatenated tensor.

    Examples:

        .. testcode::

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

            x1 = tensor(np.arange(0, 3, dtype=np.float32).reshape((3)))
            x2 = tensor(np.arange(6, 9, dtype=np.float32).reshape((3)))
            out = F.stack([x1, x2], axis=0)
            print(out.numpy())

        Outputs:

        .. testoutput::

            [[0. 1. 2.]
             [6. 7. 8.]]
    """
    if len(inps) > 0 and not isinstance(inps[0].shape, inps[0].__class__):
        shapes = {arr.shape for arr in inps}
        if len(shapes) != 1:
            raise ValueError("All input tensors must have the same shape")

    inps = [expand_dims(inp, axis=axis) for inp in inps]
    return concat(inps, axis=axis, device=device)


def split(inp, nsplits_or_sections, axis=0):
    r"""Splits the input tensor into several smaller tensors.
    When nsplits_or_sections is int, the last tensor may be smaller than others.

    Args:
        inp: input tensor.
        nsplits_or_sections: number of sub tensors or sections information list.
        axis: which axis will be splited.

    Returns:
        output tensor list.

    Examples:

        .. testcode::

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

            x = tensor(np.random.random((10, 20)), dtype=np.float32)
            y = F.split(x, 3)
            z = F.split(x, [6, 17], axis=1)

            print([i.numpy().shape for i in y])
            print([i.numpy().shape for i in z])

        Outputs:

        .. testoutput::

            [(4, 20), (3, 20), (3, 20)]
            [(10, 6), (10, 11), (10, 3)]
    """
    ndim = len(inp.shape)
    if axis >= ndim:
        raise ValueError("Invalid axis {}".format(axis))

    Ntotal = inp.shape[axis]

    if isinstance(nsplits_or_sections, Sequence):
        Nsections = len(nsplits_or_sections) + 1
        is_array = True
    else:
        Nsections = int(nsplits_or_sections)
        is_array = False

    if is_array:
        partitions = []
        div_points = [0] + list(nsplits_or_sections) + [Ntotal]
        for i in range(1, len(div_points)):
            if div_points[i - 1] > div_points[i]:
                raise ValueError(
                    "Invalid nsplits_or_secions: {}".format(nsplits_or_sections)
                )
            partitions.append(div_points[i] - div_points[i - 1])
    else:  # scalar
        if Nsections <= 0:
            raise ValueError("Number sections must be larger than 0")
        if Nsections > Ntotal:
            raise ValueError(
                "The size {} at dim {} cannot be split into {} sections".format(
                    Ntotal, axis, Nsections
                )
            )
        partitions = []
        for i in range(Nsections):
            section_size = (Ntotal + Nsections - i - 1) // Nsections
            partitions.append(section_size)

    partitions = [
        part
        if isinstance(part, (SymbolVar, Tensor))
        else Const(part, dtype="int32", device=inp.device)(inp)[0]
        for part in partitions
    ]
    op = builtin.Split(axis=axis)
    return apply(op, inp, *partitions)


def _get_idx(index, axis):
    index_dims = len(index.shape)
    idx = []
    for i in range(index_dims):
        if i != axis:
            shape = [1] * index_dims
            shape[i] = index.shape[i]
            arange = linspace(
                0, index.shape[i] - 1, index.shape[i], device=index.device,
            )
            arange = (
                broadcast_to(arange.reshape(*shape), index.shape)
                .reshape(-1)
                .astype(np.int32)
            )
            idx.append(arange)
        else:
            idx.append(index.reshape(-1))
    return tuple(idx)


def gather(inp: Tensor, axis: int, index: Tensor) -> Tensor:
    # TODO: rewrite doc
    r"""
    Gathers data from input tensor on axis using index.

    For a 3-D tensor, the output is specified by:

    .. code-block::

       out[i][j][k] = inp[index[i][j][k]][j][k] # if axis == 0
       out[i][j][k] = inp[i][index[i][j][k]][k] # if axis == 1
       out[i][j][k] = inp[i][j][index[i][j][k]] # if axis == 2

    if input tensor is a n-dimensional tensor with size
    :math:`(x_0,x_1,...,x_{i-1},x_i,x_{i+1},...,x_{n-1})` and axis=i,
    then index must be a n-dimensional tensor with size
    :math:`(x_0,x_1,...,x_{i-1},y,x_{i+1},...,x_{n-1})` where :math:`y\ge 1` and
    output will have the same size as index.

    Args:
        inp: input tensor.
        axis: along which axis to index.
        index: indices of elements to gather.

    Return:
        output tensor.

    Examples:

        .. testcode::

            import megengine.functional as F
            from megengine import tensor

            inp = tensor([
                [1,2], [3,4], [5,6],
            ])
            index = tensor([[0,2], [1,0]])
            oup = F.gather(inp, 0, index)
            print(oup.numpy())

        Outputs:

        .. testoutput::

            [[1 6]
             [3 2]]
    """
    input_shape = inp.shape
    index_shape = index.shape
    input_dims = len(input_shape)
    index_dims = len(index_shape)
    if input_dims != index_dims:
        raise ValueError(
            "The index tensor must have same dimensions as input tensor, "
            "But the input dims:{}, the index dims:{}".format(input_dims, index_dims)
        )

    if axis < 0 or axis >= input_dims:
        raise ValueError(
            "Index axis {} is output of bounds, should in range [0 {})".format(
                axis, input_dims
            )
        )

    for i in range(input_dims):
        if i != axis and input_shape[i] != index_shape[i]:
            raise ValueError(
                "The input {} and index {} must have the same size apart from axis {}".format(
                    input_shape, index_shape, axis
                )
            )

    idx = _get_idx(index, axis)
    return inp[idx].reshape(index.shape)  # pylint: disable=no-member


def scatter(inp: Tensor, axis: int, index: Tensor, source: Tensor) -> Tensor:
    # TODO: rewrite doc
    r"""
    Writes all values from the tensor source into input tensor
    at the indices specified in the index tensor.

    For each value in source, its output index is specified by its index
    in source for ``axis != dimension`` and by the corresponding value in
    index for ``axis = dimension``.

    For a 3-D tensor, input tensor is updated as:

    .. code-block::

       inp[index[i][j][k]][j][k] = source[i][j][k]  # if axis == 0
       inp[i][index[i][j][k]][k] = source[i][j][k]  # if axis == 1
       inp[i][j][index[i][j][k]] = source[i][j][k]  # if axis == 2

    ``inp``, ``index`` and ``source`` should have same number of dimensions.

    It is also required that ``source.shape(d) <= inp.shape(d)`` and ``index.shape(d) == source.shape(d)``
    for all dimensions ``d``.

    Moreover, the values of index must be between ``0`` and ``inp.shape(axis) - 1`` inclusive.

    Note:
        Please notice that, due to performance issues, the result is uncertain on the GPU device
        if scattering different positions from source to the same destination position
        regard to index tensor.

        Check the following examples, the oup[0][2] is maybe
        from source[0][2] which value is 0.2256 or source[1][2] which value is 0.5339
        if set the index[1][2] from 1 to 0.

    Args:
        inp: inp tensor which to be scattered.
        axis: axis along which to index.
        index: indices of elements to scatter.
        source: source element(s) to scatter.

    Return:
        output tensor.

    Examples:

        .. testcode::

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

            inp = tensor(np.zeros(shape=(3,5),dtype=np.float32))
            source = tensor([[0.9935,0.9465,0.2256,0.8926,0.4396],[0.7723,0.0718,0.5939,0.357,0.4576]])
            index = tensor([[0,2,0,2,1],[2,0,1,1,2]])
            oup = F.scatter(inp, 0, index,source)
            print(oup.numpy())

        Outputs:

        .. testoutput::

            [[0.9935 0.0718 0.2256 0.     0.    ]
             [0.     0.     0.5939 0.357  0.4396]
             [0.7723 0.9465 0.     0.8926 0.4576]]
    """
    input_shape = inp.shape
    index_shape = index.shape
    source_shape = source.shape
    input_dims = len(input_shape)
    index_dims = len(index_shape)
    source_dims = len(source_shape)

    if input_dims != index_dims or input_dims != source_dims:
        raise ValueError("The input, source and index tensor must have same dimensions")

    if axis < 0 or axis >= input_dims:
        raise ValueError(
            "Index axis {} is output of bounds, should in range [0 {})".format(
                axis, input_dims
            )
        )

    for i in range(source_dims):
        if source_shape[i] > input_shape[i]:
            raise ValueError(
                "The each shape size for source {} must be less than or equal to input {} ".format(
                    source_shape, input_shape
                )
            )

    for i in range(index_dims):
        if index_shape[i] != source_shape[i]:
            raise ValueError(
                "The each shape size for index {} must be equal to source {} ".format(
                    index_shape, source_shape
                )
            )

    for i in range(index_dims):
        if i != axis and index_shape[i] > input_shape[i]:
            raise ValueError(
                "The index {} must be less than or equal to input {} size apart from axis {}".format(
                    index_shape, input_shape, axis
                )
            )

    idx = _get_idx(index, axis)
    inp[idx] = source.flatten()
    return inp


def where(mask: Tensor, x: Tensor, y: Tensor) -> Tensor:
    r"""Selects elements either from Tensor x or Tensor y, according to mask.

    .. math::

        \textrm{out}_i = x_i \textrm{ if } \textrm{mask}_i \textrm{ is True else } y_i

    Args:
        mask: a mask used for choosing ``x`` or ``y``.
        x: first choice.
        y: second choice.

    Returns:
        output tensor.

    Examples:

        .. testcode::

            import numpy as np
            from megengine import tensor
            import megengine.functional as F
            mask = tensor(np.array([[True, False], [False, True]], dtype=np.bool))
            x = tensor(np.array([[1, np.inf], [np.nan, 4]],
                dtype=np.float32))
            y = tensor(np.array([[5, 6], [7, 8]], dtype=np.float32))
            out = F.where(mask, x, y)
            print(out.numpy())

        Outputs:

        .. testoutput::

            [[1. 6.]
             [7. 4.]]
    """

    if not isinstance(x, Tensor):
        raise TypeError("input x must be a tensor")
    if not isinstance(y, Tensor):
        raise TypeError("input y must be a tensor")
    if not isinstance(mask, Tensor):
        raise TypeError("mask must be a tensor")
    if mask.dtype != np.bool_:
        raise ValueError("mask must be bool")
    if x.device != mask.device:
        raise ValueError("ambiguous device: {} vs {}".format(x.device, mask.device))

    dtype = dtype_promotion(x, y)
    if x.dtype != dtype:
        x = x.astype(dtype)
    if y.dtype != dtype:
        y = y.astype(dtype)

    v0, index0 = cond_take(mask, x)
    v1, index1 = cond_take(~mask, y)

    out = concat([v0, v1])

    out[index0] = v0
    out[index1] = v1
    out = out.reshape(x.shape)
    return out


def cond_take(mask: Tensor, x: Tensor) -> Tensor:
    r"""Takes elements from data if specific condition is satisfied on mask.
    This operator has two outputs: the first is the elements taken,
    and the second is the indices corresponding to those elements;
    they are both 1-dimensional. High-dimension input would first be flattened.

    Args:
        mask: condition param; must be the same shape with data.
        x: input tensor from which to take elements.

    Examples:

        .. testcode::

            import numpy as np
            from megengine import tensor
            import megengine.functional as F
            mask = tensor(np.array([[True, False], [False, True]], dtype=np.bool_))
            x = tensor(np.array([[1, np.inf], [np.nan, 4]],
                dtype=np.float32))
            v, index = F.cond_take(mask, x)
            print(v.numpy(), index.numpy())

        Outputs:

        .. testoutput::

            [1. 4.] [0 3]
    """
    if not isinstance(x, (Tensor, SymbolVar)):
        raise TypeError("input must be a tensor")
    if not isinstance(mask, (Tensor, SymbolVar)):
        raise TypeError("mask must be a tensor")
    if mask.dtype != np.bool_:
        raise ValueError("mask must be bool")
    if x.device != mask.device:
        raise ValueError("ambiguous device: {} vs {}".format(x.device, mask.device))

    op = builtin.CondTake()
    v, index = apply(op, x, mask)
    return v, index


def transpose(inp: Tensor, pattern: Iterable[int]) -> Tensor:
    r"""Swaps shapes and strides according to given pattern.

    Args:
        inp: input tensor.
        pattern: a list of integers including 0, 1, ... , ``ndim``-1,
            and any number of ``'x'`` char in dimensions where this tensor should be broadcasted.
            For examples:

            * (``'x'``) -> make a 0d (scalar) into a 1d vector
            * (0, 1) -> identity for 2d vectors
            * (1, 0) -> inverts the first and second dimensions
            * (``'x'``, 0) -> make a row out of a 1d vector (N to 1xN)
            * (0, ``'x'``) -> make a column out of a 1d vector (N to Nx1)
            * (2, 0, 1) -> AxBxC to CxAxB
            * (0, ``'x'``, 1) -> AxB to Ax1xB
            * (1, ``'x'``, 0) -> AxB to Bx1xA
            * (1,) -> this removes dimensions 0. It must be a broadcastable dimension (1xA to A)

    Returns:
        output tensor.

    Examples:

        .. testcode::

            import numpy as np
            from megengine import tensor
            import megengine.functional as F
            x = tensor(np.array([[1, 1], [0, 0]], dtype=np.int32))
            out = F.transpose(x, (1, 0))
            print(out.numpy())

        Outputs:

        .. testoutput::

            [[1 0]
            [1 0]]
    """
    return inp.transpose(list(-1 if _ == "x" else _ for _ in pattern))


def reshape(inp: Tensor, target_shape: Iterable[int]) -> Tensor:
    r"""Reshapes a tensor to given target shape; total number of logical elements must
    remain unchanged

    Args:
        inp: input tensor.
        target_shape: target shape, it can contain an element of -1 representing ``unspec_axis``.

    Examples:

        .. testcode::

            import numpy as np
            from megengine import tensor
            import megengine.functional as F
            x = tensor(np.arange(12, dtype=np.int32))
            out = F.reshape(x, (3, 4))
            print(out.numpy())

        Outputs:

        .. testoutput::

            [[ 0  1  2  3]
             [ 4  5  6  7]
             [ 8  9 10 11]]
    """
    return inp.reshape(target_shape)


def flatten(inp: Tensor, start_axis: int = 0, end_axis: int = -1) -> Tensor:
    r"""Reshapes the tensor by flattening the sub-tensor from dimension ``start_axis`` to dimension ``end_axis``.

    Args:
        inp: input tensor.
        start_axis: start dimension that the sub-tensor to be flattened. Default: 0
        end_axis: end dimension that the sub-tensor to be flattened. Default: -1

    Returns:
        output tensor.

    Examples:

        .. testcode::

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

            inp_shape = (2, 2, 3, 3)
            x = tensor(
                np.arange(36, dtype=np.int32).reshape(inp_shape),
            )
            out = F.flatten(x, 2)
            print(x.numpy().shape)
            print(out.numpy().shape)

        Outputs:

        .. testoutput::

            (2, 2, 3, 3)
            (2, 2, 9)
    """
    target_shape = tuple(inp.shape[i] for i in range(start_axis)) + (-1,)
    if end_axis != -1:
        target_shape += (*inp.shape[end_axis + 1 :],)
    return inp.reshape(*target_shape)


def expand_dims(inp: Tensor, axis: Union[int, Sequence[int]]) -> Tensor:
    r"""Adds dimension before given axis.

    Args:
        inp: input tensor.
        axis: place of new axes.

    Returns:
        output tensor.

    Examples:

        .. testcode::

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

            x = tensor([1, 2])
            out = F.expand_dims(x, 0)
            print(out.numpy().shape)

        Outputs:

        .. testoutput::

            (1, 2)
    """

    def get_axes():
        try:
            return [int(axis)]
        except (TypeError, ValueError):
            pass
        return list(map(int, axis))

    axis = get_axes()
    try:
        ndim = inp.ndim + len(axis)
        axis = sorted(i + ndim if i < 0 else i for i in axis)
    except ValueError:
        if any([ind < 0 for ind in axis]):
            raise IndexError(
                "Does not support negative index when tensor's ndim is unknown"
            )
        axis = sorted(axis)
    assert axis, "axis could not be empty"
    if inp._isscalar():
        assert axis[0] == 0, "invalid axis {} for ndim 0".format(axis[0])
        if len(axis) == 1:
            inp = copy(inp, device=None)
            inp._unsetscalar()
            return inp
        axis = axis[1:]
    op = builtin.AddAxis(axis=axis)
    (result,) = apply(op, inp)
    return result


def squeeze(inp: Tensor, axis: Optional[Union[int, Sequence[int]]] = None) -> Tensor:
    r"""Removes dimension of shape 1.

    Args:
        inp: input tensor.
        axis: place of axis to be removed.

    Returns:
        output tensor.

    Examples:

        .. testcode::

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

            x = tensor(np.array([1, 2], dtype=np.int32).reshape(1, 1, 2, 1))
            out = F.squeeze(x, 3)
            print(out.numpy().shape)

        Outputs:

        .. testoutput::

            (1, 1, 2)
    """
    return _remove_axis(inp, axis)


def linspace(
    start: Union[int, float, Tensor],
    stop: Union[int, float, Tensor],
    num: Union[int, Tensor],
    dtype="float32",
    device: Optional[CompNode] = None,
) -> Tensor:
    r"""Returns equally spaced numbers over a specified interval.

    Args:
        start: starting value of the squence, shoule be scalar.
        stop: last value of the squence, shoule be scalar.
        num: number of values to generate.
        dtype: result data type.

    Returns:
        generated tensor.

    Examples:

        .. testcode::

            import numpy as np
            import megengine.functional as F

            a = F.linspace(3, 10, 5)
            print(a.numpy())

        Outputs:

        .. testoutput::

            [ 3.    4.75  6.5   8.25 10.  ]
    """
    for item in (start, stop, num):
        cur_device = getattr(item, "device", None)
        if device is None:
            device = cur_device
        else:
            if not (cur_device is None or device == cur_device):
                raise ("ambiguous device for linspace opr")

    is_symbolvar = list(isinstance(x, SymbolVar) for x in [start, stop, num])
    if any(is_symbolvar) and not all(is_symbolvar):
        raise TypeError("start, stop and num should all be VarNode or none of them")

    if not isinstance(start, (Tensor, SymbolVar)):
        start = Tensor(start, device=device)
    if not isinstance(stop, (Tensor, SymbolVar)):
        stop = Tensor(stop, device=device)
    if not isinstance(num, (Tensor, SymbolVar)):
        num = Tensor(num, device=device)

    op = builtin.Linspace(comp_node=device)
    (result,) = apply(op, start, stop, num)
    if np.dtype(dtype) != np.float32:
        return result.astype(dtype)
    return result


def arange(
    start: Union[int, float, Tensor] = 0,
    stop: Optional[Union[int, float, Tensor]] = None,
    step: Union[int, float, Tensor] = 1,
    dtype="float32",
    device: Optional[CompNode] = None,
) -> Tensor:
    r"""Returns evenly spaced values within the half-open interval ``[start, stop)`` as a one-dimensional tensor. 

    Note:
        This function cannot guarantee that the interval does not include the stop value in those cases 
        where step is not an integer and floating-point rounding errors affect the length of the output tensor.

    Args:
        start: if ``stop`` is specified, the start of interval (inclusive); otherwise, 
            the end of the interval (exclusive). If ``stop`` is not specified, the default starting value is ``0``. 
        stop: the end of the interval. Default: ``None``.
        step: the distance between two adjacent elements ( ``out[i+1] - out[i]`` ). Must not be 0 ; 
            may be negative, this results i an empty tensor if stop >= start . Default: 1 . 

    Keyword args:
        dtype( :attr:`.Tensor.dtype` ): output tensor data type. Default: ``float32``.
        device( :attr:`.Tensor.device` ): device on which to place the created tensor. Default: ``None``.

    Returns:
        A one-dimensional tensor containing evenly spaced values.

        The length of the output tensor must be ``ceil((stop-start)/step)`` 
        if ``stop - start`` and ``step`` have the same sign, and length 0 otherwise.

    Examples:

        >>> F.arange(5)
        Tensor([0. 1. 2. 3. 4.], device=xpux:0)
        >>> F.arange(1, 4)
        Tensor([1. 2. 3.], device=xpux:0)

    """
    if stop is None:
        start, stop = 0, start

    start = Tensor(start, dtype="float32")
    stop = Tensor(stop, dtype="float32")
    step = Tensor(step, dtype="float32")

    num = ceil((stop - start) / step)
    stop = start + step * (num - 1)
    result = linspace(start, stop, num, device=device)
    if np.dtype(dtype) != np.float32:
        return result.astype(dtype)
    return result


def repeat(inp: Tensor, repeats: int, axis: Optional[int] = None):
    r"""Repeat elements of an array.

    Args:
        inp: input tensor.
        repeats: the number of repetitions for each element.
        axis: the axis along which to repeat values. By default, use the
            flattened input array, and return a flat output array.

    Returns:
        output tensor.

    Examples:

        .. testcode::

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

            x = tensor([[1, 2], [3, 4]], np.int32)
            y = F.repeat(x, 2, axis=0)
            print(y.numpy())

        Outputs:

        .. testoutput::

            [[1 2]
             [1 2]
             [3 4]
             [3 4]]
    """
    if axis is None:
        inp = inp.reshape(-1)  # flatten
        axis = 0
    if inp._isscalar():
        inp._unsetscalar()
    shape = astensor1d(inp.shape, inp, dtype="int32", device=inp.device)
    # assume inp.ndim is not changed during trace
    max_axis = len(shape) - 1
    assert axis >= 0 and axis <= max_axis
    assert repeats >= 1

    base_shape, bcast_shape, target_shape = [], [], []
    if axis != 0:
        target_shape.append(shape[:axis])
    base_shape.extend([shape[: axis + 1], [1,]])
    bcast_shape.extend([shape[: axis + 1], [repeats,]])
    target_shape.extend(
        [shape[axis] * repeats,]
    )
    if axis + 1 <= max_axis:
        base_shape.append(shape[axis + 1 :])
        bcast_shape.append(shape[axis + 1 :])
        target_shape.append(shape[axis + 1 :])

    out = broadcast_to(inp.reshape(concat(base_shape)), concat(bcast_shape)).reshape(
        concat(target_shape)
    )
    return out


def _tile_one_dim(inp, rep, axis):
    shape = astensor1d(inp.shape, inp, dtype="int32", device=inp.device)
    # assume inp.ndim is not changed during trace
    max_axis = len(shape) - 1

    base_shape, bcast_shape, target_shape = [], [], []

    if axis != 0:
        base_shape.append(shape[:axis])
        bcast_shape.append(shape[:axis])
        target_shape.append(shape[:axis])
    base_shape.extend([[1,], shape[axis:]])
    bcast_shape.extend([rep, shape[axis:]])
    target_shape.append(shape[axis] * rep)
    if axis + 1 <= max_axis:
        target_shape.append(shape[axis + 1 :])

    out = broadcast_to(inp.reshape(concat(base_shape)), concat(bcast_shape)).reshape(
        concat(target_shape)
    )
    return out


def tile(inp: Tensor, reps: Iterable[int]):
    r"""Construct an array by repeating ``inp`` the number of times given by ``reps``. If reps has length d,
    the result will have dimension of ``max(d, inp.ndim)``. It is required that ``d >= inp.dim``. If ``inp.ndim < d``,
    ``inp`` is promoted to be ``d``-dimensional by prepending new axis.

    Args:
        inp: input tensor.
        reps: The number of repetitions of inp along each axis.

    Returns:
        output tensor.


    Examples:

        .. testcode::

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

            x = tensor([[1, 2], [3, 4]], np.int32)
            y = F.tile(x, (2,1))
            print(y.numpy())

        Outputs:

        .. testoutput::

            [[1 2]
             [3 4]
             [1 2]
             [3 4]]
    """
    shape = astensor1d(inp.shape, inp, dtype="int32", device=inp.device)
    reps = astensor1d(reps, inp, dtype="int32", device=inp.device)
    l_shape = len(shape)
    l_reps = len(reps)
    assert (
        l_reps >= l_shape
    ), "Number of dimensions of tiled dims can not be smaller than number of dimensions of tensor"

    for i in range(l_shape):
        rep = reps[i + (l_reps - l_shape)]
        inp = _tile_one_dim(inp, rep, i)

    if l_reps > l_shape:
        shape = inp.shape
        extra = reps[:-l_shape]
        extra_ones = ones_like(extra)
        base_shape = concat([extra_ones, shape])
        bcast_shape = concat([extra, shape])
        target_shape = concat([extra, shape])
        inp = broadcast_to(inp.reshape(base_shape), bcast_shape).reshape(target_shape)

    return inp


def copy(inp, device=None):
    r"""Copies tensor to another device.

    Args:
        inp: input tensor.
        device: destination device.

    Examples:

        .. testcode::

            import numpy as np
            import platform
            from megengine import tensor
            from megengine.device import get_device_count
            import megengine.functional as F

            x = tensor([1, 2, 3], np.int32)
            if 1 == get_device_count("gpu"):
                y = F.copy(x, "cpu1")
                print(y.numpy())
            else:
                y = F.copy(x, "xpu1")
                print(y.numpy())

        Outputs:

        .. testoutput::

            [1 2 3]
    """
    if device is None:
        return apply(Identity(), inp)[0]
    return apply(Copy(comp_node=as_device(device).to_c()), inp)[0]


def roll(
    inp: Tensor,
    shift: Union[int, Iterable[int]],
    axis: Optional[Union[int, Iterable[int]]] = None,
):
    r"""Roll the tensor along the given axis(or axes). Elements that are shifted
    beyond the last position are re-introduced at the first position.

    Args:
        inp: input tensor.
        shift: the number of places by which the elements of the tensor are
            shifted. If shift is a tuple, axis must be a tuple of the same size,
            and each axis will be rolled by the corresponding shift value.
        axis: axis along which to roll. If axis is not specified, the tensor
            will be flattened before rolling and then restored to the original shape.
            Duplicate axes is allowed if it is a tuple. Default: None.

    Examples:

        .. testcode::

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

            x = tensor([[1,2],[3,4],[5,6]], np.int32)
            y = F.roll(x, 1, 0)
            print(y.numpy())

        Outputs:

        .. testoutput::

            [[5 6]
            [1 2]
            [3 4]]
    """
    shp_bak = None
    if axis is None:
        shp_bak = inp.shape
        inp = inp.flatten()
        axis = 0
    shp = inp.shape
    dim = len(shp)
    if isinstance(shift, int):
        assert isinstance(axis, int)
        shift, axis = [shift,], [axis,]
    assert len(shift) == len(axis)
    out = inp
    for i in range(len(shift)):
        axis_ = axis[i]
        shift_ = shift[i]
        axis_normalized_ = axis_ + dim if axis_ < 0 else axis_
        assert (
            dim > axis_normalized_ >= 0
        ), "axis out of range (expected to be in range of [{}, {}], but got {})".format(
            -dim, dim - 1, axis_
        )
        if shift_ == 0:
            continue
        size = shp[axis_normalized_]
        shift_normalized_ = 0 if size == 0 else shift_ % size
        if shift_normalized_ > 0:
            a, b = split(out, [size - shift_normalized_,], axis=axis_normalized_)
        else:
            a, b = split(out, [-shift_normalized_,], axis=axis_normalized_)
        out = concat((b, a), axis=axis_normalized_)
    if shp_bak is not None:
        out = out.reshape(shp_bak)
    return out


def cumsum(inp: Tensor, axis: int):
    r"""Computes the cumulative sum of elements along given axis.

    Args:
        inp: input tensor.
        axis: axis along which cumsum is performed.

    Examples:

        .. testcode::

            from megengine import tensor
            import megengine.functional as F

            x = tensor([[1, 2, 3], [4, 5, 6]], "int32")
            y = F.cumsum(x, 1)
            print(y.numpy())

        Outputs:

        .. testoutput::

            [[ 1  3  6]
            [ 4  9 15]]
    """
    assert isinstance(inp, Tensor), "input of cumsum must be type of Tensor"
    assert axis >= 0 and axis < inp.ndim, "input axis {} out of bound".format(axis)
    op = builtin.Cumsum(axis=axis, exclusive=False, reverse=False)
    return apply(op, inp)[0]