generate.py

# class s_(object):

import functools
import numbers
import operator

import numpy

import cupy
from cupy._creation import from_data
from cupy._manipulation import join


class AxisConcatenator(object):
    """Translates slice objects to concatenation along an axis.

    For detailed documentation on usage, see :func:`cupy.r_`.
    This implementation is partially borrowed from NumPy's one.

    """

    def _output_obj(self, obj, ndim, ndmin, trans1d):
        k2 = ndmin - ndim
        if trans1d < 0:
            trans1d += k2 + 1
        defaxes = list(range(ndmin))
        k1 = trans1d
        axes = defaxes[:k1] + defaxes[k2:] + \
            defaxes[k1:k2]
        return obj.transpose(axes)

    def __init__(self, axis=0, matrix=False, ndmin=1, trans1d=-1):
        self.axis = axis
        self.trans1d = trans1d
        self.matrix = matrix
        self.ndmin = ndmin

    def __getitem__(self, key):
        trans1d = self.trans1d
        ndmin = self.ndmin
        objs = []
        arrays = []
        scalars = []
        if isinstance(key, str):
            raise NotImplementedError
        if not isinstance(key, tuple):
            key = (key,)

        for i, k in enumerate(key):
            if isinstance(k, slice):
                raise NotImplementedError
            elif isinstance(k, str):
                if i != 0:
                    raise ValueError(
                        'special directives must be the first entry.')
                raise NotImplementedError
            elif type(k) in numpy.ScalarType:
                newobj = from_data.array(k, ndmin=ndmin)
                scalars.append(i)
            else:
                newobj = from_data.array(k, copy=False, ndmin=ndmin)
                if ndmin > 1:
                    ndim = from_data.array(k, copy=False).ndim
                    if trans1d != -1 and ndim < ndmin:
                        newobj = self._output_obj(newobj, ndim, ndmin, trans1d)
                arrays.append(newobj)

            objs.append(newobj)

        final_dtype = numpy.result_type(*arrays, *[key[k] for k in scalars])
        if final_dtype is not None:
            for k in scalars:
                objs[k] = objs[k].astype(final_dtype)

        return join.concatenate(tuple(objs), axis=self.axis)

    def __len__(self):
        return 0


class CClass(AxisConcatenator):

    def __init__(self):
        super(CClass, self).__init__(-1, ndmin=2, trans1d=0)


c_ = CClass()
"""Translates slice objects to concatenation along the second axis.

This is a CuPy object that corresponds to :obj:`cupy.r_`, which is
useful because of its common occurrence. In particular, arrays will be
stacked along their last axis after being upgraded to at least 2-D with
1's post-pended to the shape (column vectors made out of 1-D arrays).

For detailed documentation, see :obj:`r_`.

This implementation is partially borrowed from NumPy's one.

Returns:
    cupy.ndarray: Joined array.

.. seealso:: :obj:`numpy.c_`

Examples
--------
>>> a = cupy.array([[1, 2, 3]], dtype=np.int32)
>>> b = cupy.array([[4, 5, 6]], dtype=np.int32)
>>> cupy.c_[a, 0, 0, b]
array([[1, 2, 3, 0, 0, 4, 5, 6]], dtype=int32)

"""


class RClass(AxisConcatenator):

    def __init__(self):
        super(RClass, self).__init__()


r_ = RClass()
"""Translates slice objects to concatenation along the first axis.

This is a simple way to build up arrays quickly.
If the index expression contains comma separated arrays, then stack
them along their first axis.

This object can build up from normal CuPy arrays.
Therefore, the other objects (e.g. writing strings like '2,3,4',
or using imaginary numbers like [1,2,3j],
or using string integers like '-1') are not implemented yet
compared with NumPy.

This implementation is partially borrowed from NumPy's one.

Returns:
    cupy.ndarray: Joined array.

.. seealso:: :obj:`numpy.r_`

Examples
--------
>>> a = cupy.array([1, 2, 3], dtype=np.int32)
>>> b = cupy.array([4, 5, 6], dtype=np.int32)
>>> cupy.r_[a, 0, 0, b]
array([1, 2, 3, 0, 0, 4, 5, 6], dtype=int32)

"""


def indices(dimensions, dtype=int):
    """Returns an array representing the indices of a grid.

    Computes an array where the subarrays contain index values 0,1,...
    varying only along the corresponding axis.

    Args:
        dimensions: The shape of the grid.
        dtype: Data type specifier. It is int by default.

    Returns:
        ndarray:
        The array of grid indices,
        ``grid.shape = (len(dimensions),) + tuple(dimensions)``.

    Examples
    --------
    >>> grid = cupy.indices((2, 3))
    >>> grid.shape
    (2, 2, 3)
    >>> grid[0]        # row indices
    array([[0, 0, 0],
           [1, 1, 1]])
    >>> grid[1]        # column indices
    array([[0, 1, 2],
           [0, 1, 2]])

    .. seealso:: :func:`numpy.indices`

    """
    dimensions = tuple(dimensions)
    N = len(dimensions)
    shape = (1,) * N
    res = cupy.empty((N,) + dimensions, dtype=dtype)
    for i, dim in enumerate(dimensions):
        res[i] = cupy.arange(dim, dtype=dtype).reshape(
            shape[:i] + (dim,) + shape[i + 1:]
        )
    return res


def ix_(*args):
    """Construct an open mesh from multiple sequences.

    This function takes N 1-D sequences and returns N outputs with N
    dimensions each, such that the shape is 1 in all but one dimension
    and the dimension with the non-unit shape value cycles through all
    N dimensions.

    Using `ix_` one can quickly construct index arrays that will index
    the cross product. ``a[cupy.ix_([1,3],[2,5])]`` returns the array
    ``[[a[1,2] a[1,5]], [a[3,2] a[3,5]]]``.

    Args:
        *args: 1-D sequences

    Returns:
        tuple of ndarrays:
        N arrays with N dimensions each, with N the number of input sequences.
        Together these arrays form an open mesh.

    Examples
    --------
    >>> a = cupy.arange(10).reshape(2, 5)
    >>> a
    array([[0, 1, 2, 3, 4],
           [5, 6, 7, 8, 9]])
    >>> ixgrid = cupy.ix_([0,1], [2,4])
    >>> ixgrid
    (array([[0],
           [1]]), array([[2, 4]]))

    .. warning::

        This function may synchronize the device.

    .. seealso:: :func:`numpy.ix_`

    """
    # TODO(niboshi): Avoid nonzero which may synchronize the device.
    out = []
    nd = len(args)
    for k, new in enumerate(args):
        new = from_data.asarray(new)
        if new.ndim != 1:
            raise ValueError('Cross index must be 1 dimensional')
        if new.size == 0:
            # Explicitly type empty arrays to avoid float default
            new = new.astype(numpy.intp)
        if cupy.issubdtype(new.dtype, cupy.bool_):
            new, = new.nonzero()  # may synchronize
        new = new.reshape((1,) * k + (new.size,) + (1,) * (nd - k - 1))
        out.append(new)
    return tuple(out)


def ravel_multi_index(multi_index, dims, mode='wrap', order='C'):
    """
    Converts a tuple of index arrays into an array of flat indices, applying
    boundary modes to the multi-index.

    Args:
        multi_index (tuple of cupy.ndarray) : A tuple of integer arrays, one
            array for each dimension.
        dims (tuple of ints): The shape of array into which the indices from
            ``multi_index`` apply.
        mode ('raise', 'wrap' or 'clip'), optional: Specifies how out-of-bounds
            indices are handled.  Can specify either one mode or a tuple of
            modes, one mode per index:

            - *'raise'* -- raise an error
            - *'wrap'* -- wrap around (default)
            - *'clip'* -- clip to the range

            In 'clip' mode, a negative index which would normally wrap will
            clip to 0 instead.
        order ('C' or 'F'), optional: Determines whether the multi-index should
            be viewed as indexing in row-major (C-style) or column-major
            (Fortran-style) order.

    Returns:
        raveled_indices (cupy.ndarray): An array of indices into the flattened
        version of an array of dimensions ``dims``.

    .. warning::

        This function may synchronize the device when ``mode == 'raise'``.

    Notes
    -----
    Note that the default `mode` (``'wrap'``) is different than in NumPy. This
    is done to avoid potential device synchronization.

    Examples
    --------
    >>> cupy.ravel_multi_index(cupy.asarray([[3,6,6],[4,5,1]]), (7,6))
    array([22, 41, 37])
    >>> cupy.ravel_multi_index(cupy.asarray([[3,6,6],[4,5,1]]), (7,6),
    ...                        order='F')
    array([31, 41, 13])
    >>> cupy.ravel_multi_index(cupy.asarray([[3,6,6],[4,5,1]]), (4,6),
    ...                        mode='clip')
    array([22, 23, 19])
    >>> cupy.ravel_multi_index(cupy.asarray([[3,6,6],[4,5,1]]), (4,4),
    ...                        mode=('clip', 'wrap'))
    array([12, 13, 13])
    >>> cupy.ravel_multi_index(cupy.asarray((3,1,4,1)), (6,7,8,9))
    array(1621)

    .. seealso:: :func:`numpy.ravel_multi_index`, :func:`unravel_index`
    """

    ndim = len(dims)
    if len(multi_index) != ndim:
        raise ValueError(
            "parameter multi_index must be a sequence of "
            "length {}".format(ndim))

    for d in dims:
        if not isinstance(d, numbers.Integral):
            raise TypeError(
                "{} object cannot be interpreted as an integer".format(
                    type(d)))

    if isinstance(mode, str):
        mode = (mode, ) * ndim

    if functools.reduce(operator.mul, dims) > cupy.iinfo(cupy.int64).max:
        raise ValueError("invalid dims: array size defined by dims is larger "
                         "than the maximum possible size")

    s = 1
    ravel_strides = [1] * ndim

    order = 'C' if order is None else order.upper()
    if order == 'C':
        for i in range(ndim - 2, -1, -1):
            s = s * dims[i + 1]
            ravel_strides[i] = s
    elif order == 'F':
        for i in range(1, ndim):
            s = s * dims[i - 1]
            ravel_strides[i] = s
    else:
        raise ValueError('order not understood')

    multi_index = cupy.broadcast_arrays(*multi_index)
    raveled_indices = cupy.zeros(multi_index[0].shape, dtype=cupy.int64)
    for d, stride, idx, _mode in zip(dims, ravel_strides, multi_index, mode):

        if not isinstance(idx, cupy.ndarray):
            raise TypeError("elements of multi_index must be cupy arrays")
        if not cupy.can_cast(idx, cupy.int64, 'same_kind'):
            raise TypeError(
                'multi_index entries could not be cast from dtype(\'{}\') to '
                'dtype(\'{}\') according to the rule \'same_kind\''.format(
                    idx.dtype, cupy.int64().dtype))
        idx = idx.astype(cupy.int64, copy=False)

        if _mode == "raise":
            if cupy.any(cupy.logical_or(idx >= d, idx < 0)):
                raise ValueError("invalid entry in coordinates array")
        elif _mode == "clip":
            idx = cupy.clip(idx, 0, d - 1)
        elif _mode == 'wrap':
            idx = idx % d
        else:
            raise ValueError('Unrecognized mode: {}'.format(_mode))
        raveled_indices += stride * idx
    return raveled_indices


def unravel_index(indices, dims, order='C'):
    """Converts array of flat indices into a tuple of coordinate arrays.

    Args:
        indices (cupy.ndarray): An integer array whose elements are indices
            into the flattened version of an array of dimensions :obj:`dims`.
        dims (tuple of ints): The shape of the array to use for unraveling
            indices.
        order ('C' or 'F'): Determines whether the indices should be viewed as
            indexing in row-major (C-style) or column-major (Fortran-style)
            order.

    Returns:
        tuple of ndarrays:
        Each array in the tuple has the same shape as the indices array.

    Examples
    --------
    >>> cupy.unravel_index(cupy.array([22, 41, 37]), (7, 6))
    (array([3, 6, 6]), array([4, 5, 1]))
    >>> cupy.unravel_index(cupy.array([31, 41, 13]), (7, 6), order='F')
    (array([3, 6, 6]), array([4, 5, 1]))

    .. warning::

        This function may synchronize the device.

    .. seealso:: :func:`numpy.unravel_index`, :func:`ravel_multi_index`

    """
    order = 'C' if order is None else order.upper()
    if order == 'C':
        dims = reversed(dims)
    elif order == 'F':
        pass
    else:
        raise ValueError('order not understood')

    if not cupy.can_cast(indices, cupy.int64, 'same_kind'):
        raise TypeError(
            'Iterator operand 0 dtype could not be cast '
            'from dtype(\'{}\') to dtype(\'{}\') '
            'according to the rule \'same_kind\''.format(
                indices.dtype, cupy.int64().dtype))

    if (indices < 0).any():  # synchronize!
        raise ValueError('invalid entry in index array')

    unraveled_coords = []
    for dim in dims:
        unraveled_coords.append(indices % dim)
        indices = indices // dim

    if (indices > 0).any():  # synchronize!
        raise ValueError('invalid entry in index array')

    if order == 'C':
        unraveled_coords = reversed(unraveled_coords)
    return tuple(unraveled_coords)


def mask_indices(n, mask_func, k=0):
    """
    Return the indices to access (n, n) arrays, given a masking function.

    Assume `mask_func` is a function that, for a square array a of
    size ``(n, n)`` with a possible offset argument `k`, when called
    as ``mask_func(a, k)`` returns a new array with zeros in certain
    locations (functions like :func:`~cupy.triu` or :func:`~cupy.tril` do
    precisely this). Then this function returns the indices where the non-zero
    values would be located.

    Args:
        n (int): The returned indices will be valid to access arrays
            of shape (n, n).
        mask_func (callable): A function whose call signature is
            similar to that of :func:`~cupy.triu`, :func:`~tril`.  That is,
            ``mask_func(x, k)`` returns a boolean array, shaped like
            `x`.  `k` is an optional argument to the function.
        k (scalar): An optional argument which is passed through to
            `mask_func`. Functions like :func:`~cupy.triu`, :func:`~cupy.tril`
            take a second argument that is interpreted as an offset.

    Returns:
        tuple of arrays: The `n` arrays of indices corresponding to
        the locations where ``mask_func(np.ones((n, n)), k)`` is
        True.

    .. warning::

        This function may synchronize the device.

    .. seealso:: :func:`numpy.mask_indices`
    """
    a = cupy.ones((n, n), dtype=cupy.int8)
    return mask_func(a, k).nonzero()


# TODO(okuta): Implement diag_indices


# TODO(okuta): Implement diag_indices_from


def tril_indices(n, k=0, m=None):
    """Returns the indices of the lower triangular matrix.
    Here, the first group of elements contains row coordinates
    of all indices and the second group of elements
    contains column coordinates.

    Parameters
    ----------
    n : int
        The row dimension of the arrays for which the returned
        indices will be valid.
    k : int, optional
        Diagonal above which to zero elements. `k = 0`
        (the default) is the main diagonal, `k < 0` is
        below it and `k > 0` is above.
    m : int, optional
        The column dimension of the arrays for which the
        returned arrays will be valid. By default, `m = n`.

    Returns
    -------
    y : tuple of ndarrays
        The indices for the triangle. The returned tuple
        contains two arrays, each with the indices along
        one dimension of the array.

    See Also
    --------
    numpy.tril_indices

    """

    tri_ = cupy.tri(n, m, k=k, dtype=bool)

    return tuple(cupy.broadcast_to(inds, tri_.shape)[tri_]
                 for inds in cupy.indices(tri_.shape, dtype=int))


def tril_indices_from(arr, k=0):
    """Returns the indices for the lower-triangle of arr.

    Parameters
    ----------
    arr : cupy.ndarray
          The indices are valid for square arrays
          whose dimensions are the same as arr.
    k : int, optional
        Diagonal offset.

    See Also
    --------
    numpy.tril_indices_from

    """

    if arr.ndim != 2:
        raise ValueError("input array must be 2-d")
    return tril_indices(arr.shape[-2], k=k, m=arr.shape[-1])


def triu_indices(n, k=0, m=None):
    """Returns the indices of the upper triangular matrix.
    Here, the first group of elements contains row coordinates
    of all indices and the second group of elements
    contains column coordinates.

    Parameters
    ----------
    n : int
        The size of the arrays for which the returned indices will
        be valid.
    k : int, optional
        Refers to the diagonal offset. By default, `k = 0` i.e.
        the main dialogal. The positive value of `k`
        denotes the diagonals above the main diagonal, while the negative
        value includes the diagonals below the main diagonal.
    m : int, optional
        The column dimension of the arrays for which the
        returned arrays will be valid. By default, `m = n`.

    Returns
    -------
    y : tuple of ndarrays
        The indices for the triangle. The returned tuple
        contains two arrays, each with the indices along
        one dimension of the array.

    See Also
    --------
    numpy.triu_indices

    """

    tri_ = ~cupy.tri(n, m, k=k - 1, dtype=bool)

    return tuple(cupy.broadcast_to(inds, tri_.shape)[tri_]
                 for inds in cupy.indices(tri_.shape, dtype=int))


def triu_indices_from(arr, k=0):
    """Returns indices for the upper-triangle of arr.

    Parameters
    ----------
    arr : cupy.ndarray
          The indices are valid for square arrays.
    k : int, optional
        Diagonal offset (see 'triu_indices` for details).

    Returns
    -------
    triu_indices_from : tuple of ndarrays
        Indices for the upper-triangle of `arr`.

    See Also
    --------
    numpy.triu_indices_from

    """

    if arr.ndim != 2:
        raise ValueError("input array must be 2-d")
    return triu_indices(arr.shape[-2], k=k, m=arr.shape[-1])