stride_tricks.py

"""
Utilities that manipulate strides to achieve desirable effects.

An explanation of strides can be found in the "ndarray.rst" file in the
NumPy reference guide.

"""
from __future__ import division, absolute_import, print_function

import numpy as np

__all__ = ['broadcast_to', 'broadcast_arrays']


class DummyArray(object):
    """Dummy object that just exists to hang __array_interface__ dictionaries
    and possibly keep alive a reference to a base array.
    """

    def __init__(self, interface, base=None):
        self.__array_interface__ = interface
        self.base = base


def _maybe_view_as_subclass(original_array, new_array):
    if type(original_array) is not type(new_array):
        # if input was an ndarray subclass and subclasses were OK,
        # then view the result as that subclass.
        new_array = new_array.view(type=type(original_array))
        # Since we have done something akin to a view from original_array, we
        # should let the subclass finalize (if it has it implemented, i.e., is
        # not None).
        if new_array.__array_finalize__:
            new_array.__array_finalize__(original_array)
    return new_array


def as_strided(x, shape=None, strides=None, subok=False, writeable=True):
    """
    Create a view into the array with the given shape and strides.

    .. warning:: This function has to be used with extreme care, see notes.

    Parameters
    ----------
    x : ndarray
        Array to create a new.
    shape : sequence of int, optional
        The shape of the new array. Defaults to ``x.shape``.
    strides : sequence of int, optional
        The strides of the new array. Defaults to ``x.strides``.
    subok : bool, optional
        .. versionadded:: 1.10

        If True, subclasses are preserved.
    writeable : bool, optional
        .. versionadded:: 1.12

        If set to False, the returned array will always be readonly.
        Otherwise it will be writable if the original array was. It
        is advisable to set this to False if possible (see Notes).

    Returns
    -------
    view : ndarray

    See also
    --------
    broadcast_to: broadcast an array to a given shape.
    reshape : reshape an array.

    Notes
    -----
    ``as_strided`` creates a view into the array given the exact strides
    and shape. This means it manipulates the internal data structure of
    ndarray and, if done incorrectly, the array elements can point to
    invalid memory and can corrupt results or crash your program.
    It is advisable to always use the original ``x.strides`` when
    calculating new strides to avoid reliance on a contiguous memory
    layout.

    Furthermore, arrays created with this function often contain self
    overlapping memory, so that two elements are identical.
    Vectorized write operations on such arrays will typically be
    unpredictable. They may even give different results for small, large,
    or transposed arrays.
    Since writing to these arrays has to be tested and done with great
    care, you may want to use ``writeable=False`` to avoid accidental write
    operations.

    For these reasons it is advisable to avoid ``as_strided`` when
    possible.
    """
    # first convert input to array, possibly keeping subclass
    x = np.array(x, copy=False, subok=subok)
    interface = dict(x.__array_interface__)
    if shape is not None:
        interface['shape'] = tuple(shape)
    if strides is not None:
        interface['strides'] = tuple(strides)

    array = np.asarray(DummyArray(interface, base=x))
    # The route via `__interface__` does not preserve structured
    # dtypes. Since dtype should remain unchanged, we set it explicitly.
    array.dtype = x.dtype

    view = _maybe_view_as_subclass(x, array)

    if view.flags.writeable and not writeable:
        view.flags.writeable = False

    return view


def _broadcast_to(array, shape, subok, readonly):
    shape = tuple(shape) if np.iterable(shape) else (shape,)
    array = np.array(array, copy=False, subok=subok)
    if not shape and array.shape:
        raise ValueError('cannot broadcast a non-scalar to a scalar array')
    if any(size < 0 for size in shape):
        raise ValueError('all elements of broadcast shape must be non-'
                         'negative')
    needs_writeable = not readonly and array.flags.writeable
    extras = ['reduce_ok'] if needs_writeable else []
    op_flag = 'readwrite' if needs_writeable else 'readonly'
    broadcast = np.nditer(
        (array,), flags=['multi_index', 'refs_ok', 'zerosize_ok'] + extras,
        op_flags=[op_flag], itershape=shape, order='C').itviews[0]
    result = _maybe_view_as_subclass(array, broadcast)
    if needs_writeable and not result.flags.writeable:
        result.flags.writeable = True
    return result


def broadcast_to(array, shape, subok=False):
    """Broadcast an array to a new shape.

    Parameters
    ----------
    array : array_like
        The array to broadcast.
    shape : tuple
        The shape of the desired array.
    subok : bool, optional
        If True, then sub-classes will be passed-through, otherwise
        the returned array will be forced to be a base-class array (default).

    Returns
    -------
    broadcast : array
        A readonly view on the original array with the given shape. It is
        typically not contiguous. Furthermore, more than one element of a
        broadcasted array may refer to a single memory location.

    Raises
    ------
    ValueError
        If the array is not compatible with the new shape according to NumPy's
        broadcasting rules.

    Notes
    -----
    .. versionadded:: 1.10.0

    Examples
    --------
    >>> x = np.array([1, 2, 3])
    >>> np.broadcast_to(x, (3, 3))
    array([[1, 2, 3],
           [1, 2, 3],
           [1, 2, 3]])
    """
    return _broadcast_to(array, shape, subok=subok, readonly=True)


def _broadcast_shape(*args):
    """Returns the shape of the arrays that would result from broadcasting the
    supplied arrays against each other.
    """
    if not args:
        return ()
    # use the old-iterator because np.nditer does not handle size 0 arrays
    # consistently
    b = np.broadcast(*args[:32])
    # unfortunately, it cannot handle 32 or more arguments directly
    for pos in range(32, len(args), 31):
        # ironically, np.broadcast does not properly handle np.broadcast
        # objects (it treats them as scalars)
        # use broadcasting to avoid allocating the full array
        b = broadcast_to(0, b.shape)
        b = np.broadcast(b, *args[pos:(pos + 31)])
    return b.shape


def broadcast_arrays(*args, **kwargs):
    """
    Broadcast any number of arrays against each other.

    Parameters
    ----------
    `*args` : array_likes
        The arrays to broadcast.

    subok : bool, optional
        If True, then sub-classes will be passed-through, otherwise
        the returned arrays will be forced to be a base-class array (default).

    Returns
    -------
    broadcasted : list of arrays
        These arrays are views on the original arrays.  They are typically
        not contiguous.  Furthermore, more than one element of a
        broadcasted array may refer to a single memory location.  If you
        need to write to the arrays, make copies first.

    Examples
    --------
    >>> x = np.array([[1,2,3]])
    >>> y = np.array([[1],[2],[3]])
    >>> np.broadcast_arrays(x, y)
    [array([[1, 2, 3],
           [1, 2, 3],
           [1, 2, 3]]), array([[1, 1, 1],
           [2, 2, 2],
           [3, 3, 3]])]

    Here is a useful idiom for getting contiguous copies instead of
    non-contiguous views.

    >>> [np.array(a) for a in np.broadcast_arrays(x, y)]
    [array([[1, 2, 3],
           [1, 2, 3],
           [1, 2, 3]]), array([[1, 1, 1],
           [2, 2, 2],
           [3, 3, 3]])]

    """
    # nditer is not used here to avoid the limit of 32 arrays.
    # Otherwise, something like the following one-liner would suffice:
    # return np.nditer(args, flags=['multi_index', 'zerosize_ok'],
    #                  order='C').itviews

    subok = kwargs.pop('subok', False)
    if kwargs:
        raise TypeError('broadcast_arrays() got an unexpected keyword '
                        'argument {!r}'.format(kwargs.keys()[0]))
    args = [np.array(_m, copy=False, subok=subok) for _m in args]

    shape = _broadcast_shape(*args)

    if all(array.shape == shape for array in args):
        # Common case where nothing needs to be broadcasted.
        return args

    # TODO: consider making the results of broadcast_arrays readonly to match
    # broadcast_to. This will require a deprecation cycle.
    return [_broadcast_to(array, shape, subok=subok, readonly=False)
            for array in args]