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import functools |
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import numbers |
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import operator |
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import numpy |
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import cupy |
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from cupy._creation import from_data |
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from cupy._manipulation import join |
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class AxisConcatenator(object): |
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"""Translates slice objects to concatenation along an axis. |
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For detailed documentation on usage, see :func:`cupy.r_`. |
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This implementation is partially borrowed from NumPy's one. |
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""" |
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def _output_obj(self, obj, ndim, ndmin, trans1d): |
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k2 = ndmin - ndim |
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if trans1d < 0: |
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trans1d += k2 + 1 |
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defaxes = list(range(ndmin)) |
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k1 = trans1d |
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axes = defaxes[:k1] + defaxes[k2:] + \ |
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defaxes[k1:k2] |
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return obj.transpose(axes) |
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def __init__(self, axis=0, matrix=False, ndmin=1, trans1d=-1): |
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self.axis = axis |
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self.trans1d = trans1d |
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self.matrix = matrix |
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self.ndmin = ndmin |
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def __getitem__(self, key): |
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trans1d = self.trans1d |
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ndmin = self.ndmin |
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objs = [] |
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arrays = [] |
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scalars = [] |
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if isinstance(key, str): |
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raise NotImplementedError |
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if not isinstance(key, tuple): |
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key = (key,) |
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for i, k in enumerate(key): |
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if isinstance(k, slice): |
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raise NotImplementedError |
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elif isinstance(k, str): |
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if i != 0: |
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raise ValueError( |
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'special directives must be the first entry.') |
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raise NotImplementedError |
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elif type(k) in numpy.ScalarType: |
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newobj = from_data.array(k, ndmin=ndmin) |
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scalars.append(i) |
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else: |
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newobj = from_data.array(k, copy=False, ndmin=ndmin) |
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if ndmin > 1: |
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ndim = from_data.array(k, copy=False).ndim |
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if trans1d != -1 and ndim < ndmin: |
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newobj = self._output_obj(newobj, ndim, ndmin, trans1d) |
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arrays.append(newobj) |
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objs.append(newobj) |
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final_dtype = numpy.result_type(*arrays, *[key[k] for k in scalars]) |
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if final_dtype is not None: |
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for k in scalars: |
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objs[k] = objs[k].astype(final_dtype) |
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return join.concatenate(tuple(objs), axis=self.axis) |
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def __len__(self): |
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return 0 |
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class CClass(AxisConcatenator): |
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def __init__(self): |
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super(CClass, self).__init__(-1, ndmin=2, trans1d=0) |
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c_ = CClass() |
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"""Translates slice objects to concatenation along the second axis. |
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This is a CuPy object that corresponds to :obj:`cupy.r_`, which is |
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useful because of its common occurrence. In particular, arrays will be |
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stacked along their last axis after being upgraded to at least 2-D with |
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1's post-pended to the shape (column vectors made out of 1-D arrays). |
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For detailed documentation, see :obj:`r_`. |
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This implementation is partially borrowed from NumPy's one. |
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Returns: |
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cupy.ndarray: Joined array. |
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.. seealso:: :obj:`numpy.c_` |
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Examples |
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-------- |
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>>> a = cupy.array([[1, 2, 3]], dtype=np.int32) |
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>>> b = cupy.array([[4, 5, 6]], dtype=np.int32) |
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>>> cupy.c_[a, 0, 0, b] |
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array([[1, 2, 3, 0, 0, 4, 5, 6]], dtype=int32) |
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""" |
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class RClass(AxisConcatenator): |
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def __init__(self): |
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super(RClass, self).__init__() |
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r_ = RClass() |
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"""Translates slice objects to concatenation along the first axis. |
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This is a simple way to build up arrays quickly. |
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If the index expression contains comma separated arrays, then stack |
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them along their first axis. |
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This object can build up from normal CuPy arrays. |
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Therefore, the other objects (e.g. writing strings like '2,3,4', |
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or using imaginary numbers like [1,2,3j], |
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or using string integers like '-1') are not implemented yet |
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compared with NumPy. |
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This implementation is partially borrowed from NumPy's one. |
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Returns: |
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cupy.ndarray: Joined array. |
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.. seealso:: :obj:`numpy.r_` |
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Examples |
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-------- |
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>>> a = cupy.array([1, 2, 3], dtype=np.int32) |
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>>> b = cupy.array([4, 5, 6], dtype=np.int32) |
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>>> cupy.r_[a, 0, 0, b] |
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array([1, 2, 3, 0, 0, 4, 5, 6], dtype=int32) |
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""" |
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def indices(dimensions, dtype=int): |
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"""Returns an array representing the indices of a grid. |
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Computes an array where the subarrays contain index values 0,1,... |
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varying only along the corresponding axis. |
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Args: |
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dimensions: The shape of the grid. |
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dtype: Data type specifier. It is int by default. |
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Returns: |
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ndarray: |
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The array of grid indices, |
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``grid.shape = (len(dimensions),) + tuple(dimensions)``. |
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Examples |
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-------- |
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>>> grid = cupy.indices((2, 3)) |
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>>> grid.shape |
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(2, 2, 3) |
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>>> grid[0] # row indices |
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array([[0, 0, 0], |
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[1, 1, 1]]) |
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>>> grid[1] # column indices |
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array([[0, 1, 2], |
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[0, 1, 2]]) |
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.. seealso:: :func:`numpy.indices` |
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""" |
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dimensions = tuple(dimensions) |
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N = len(dimensions) |
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shape = (1,) * N |
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res = cupy.empty((N,) + dimensions, dtype=dtype) |
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for i, dim in enumerate(dimensions): |
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res[i] = cupy.arange(dim, dtype=dtype).reshape( |
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shape[:i] + (dim,) + shape[i + 1:] |
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) |
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return res |
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def ix_(*args): |
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"""Construct an open mesh from multiple sequences. |
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This function takes N 1-D sequences and returns N outputs with N |
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dimensions each, such that the shape is 1 in all but one dimension |
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and the dimension with the non-unit shape value cycles through all |
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N dimensions. |
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Using `ix_` one can quickly construct index arrays that will index |
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the cross product. ``a[cupy.ix_([1,3],[2,5])]`` returns the array |
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``[[a[1,2] a[1,5]], [a[3,2] a[3,5]]]``. |
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Args: |
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*args: 1-D sequences |
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Returns: |
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tuple of ndarrays: |
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N arrays with N dimensions each, with N the number of input sequences. |
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Together these arrays form an open mesh. |
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Examples |
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-------- |
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>>> a = cupy.arange(10).reshape(2, 5) |
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>>> a |
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array([[0, 1, 2, 3, 4], |
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[5, 6, 7, 8, 9]]) |
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>>> ixgrid = cupy.ix_([0,1], [2,4]) |
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>>> ixgrid |
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(array([[0], |
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[1]]), array([[2, 4]])) |
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.. warning:: |
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This function may synchronize the device. |
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.. seealso:: :func:`numpy.ix_` |
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""" |
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out = [] |
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nd = len(args) |
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for k, new in enumerate(args): |
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new = from_data.asarray(new) |
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if new.ndim != 1: |
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raise ValueError('Cross index must be 1 dimensional') |
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if new.size == 0: |
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new = new.astype(numpy.intp) |
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if cupy.issubdtype(new.dtype, cupy.bool_): |
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new, = new.nonzero() |
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new = new.reshape((1,) * k + (new.size,) + (1,) * (nd - k - 1)) |
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out.append(new) |
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return tuple(out) |
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def ravel_multi_index(multi_index, dims, mode='wrap', order='C'): |
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""" |
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Converts a tuple of index arrays into an array of flat indices, applying |
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boundary modes to the multi-index. |
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Args: |
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multi_index (tuple of cupy.ndarray) : A tuple of integer arrays, one |
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array for each dimension. |
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dims (tuple of ints): The shape of array into which the indices from |
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``multi_index`` apply. |
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mode ('raise', 'wrap' or 'clip'), optional: Specifies how out-of-bounds |
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indices are handled. Can specify either one mode or a tuple of |
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modes, one mode per index: |
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- *'raise'* -- raise an error |
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- *'wrap'* -- wrap around (default) |
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- *'clip'* -- clip to the range |
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In 'clip' mode, a negative index which would normally wrap will |
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clip to 0 instead. |
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order ('C' or 'F'), optional: Determines whether the multi-index should |
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be viewed as indexing in row-major (C-style) or column-major |
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(Fortran-style) order. |
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Returns: |
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raveled_indices (cupy.ndarray): An array of indices into the flattened |
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version of an array of dimensions ``dims``. |
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.. warning:: |
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This function may synchronize the device when ``mode == 'raise'``. |
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Notes |
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----- |
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Note that the default `mode` (``'wrap'``) is different than in NumPy. This |
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is done to avoid potential device synchronization. |
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Examples |
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-------- |
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>>> cupy.ravel_multi_index(cupy.asarray([[3,6,6],[4,5,1]]), (7,6)) |
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array([22, 41, 37]) |
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>>> cupy.ravel_multi_index(cupy.asarray([[3,6,6],[4,5,1]]), (7,6), |
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... order='F') |
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array([31, 41, 13]) |
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>>> cupy.ravel_multi_index(cupy.asarray([[3,6,6],[4,5,1]]), (4,6), |
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... mode='clip') |
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array([22, 23, 19]) |
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>>> cupy.ravel_multi_index(cupy.asarray([[3,6,6],[4,5,1]]), (4,4), |
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... mode=('clip', 'wrap')) |
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array([12, 13, 13]) |
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>>> cupy.ravel_multi_index(cupy.asarray((3,1,4,1)), (6,7,8,9)) |
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array(1621) |
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.. seealso:: :func:`numpy.ravel_multi_index`, :func:`unravel_index` |
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""" |
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ndim = len(dims) |
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if len(multi_index) != ndim: |
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raise ValueError( |
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"parameter multi_index must be a sequence of " |
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"length {}".format(ndim)) |
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for d in dims: |
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if not isinstance(d, numbers.Integral): |
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raise TypeError( |
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"{} object cannot be interpreted as an integer".format( |
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type(d))) |
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if isinstance(mode, str): |
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mode = (mode, ) * ndim |
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if functools.reduce(operator.mul, dims) > cupy.iinfo(cupy.int64).max: |
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raise ValueError("invalid dims: array size defined by dims is larger " |
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"than the maximum possible size") |
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s = 1 |
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ravel_strides = [1] * ndim |
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order = 'C' if order is None else order.upper() |
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if order == 'C': |
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for i in range(ndim - 2, -1, -1): |
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s = s * dims[i + 1] |
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ravel_strides[i] = s |
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elif order == 'F': |
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for i in range(1, ndim): |
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s = s * dims[i - 1] |
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ravel_strides[i] = s |
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else: |
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raise ValueError('order not understood') |
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multi_index = cupy.broadcast_arrays(*multi_index) |
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raveled_indices = cupy.zeros(multi_index[0].shape, dtype=cupy.int64) |
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for d, stride, idx, _mode in zip(dims, ravel_strides, multi_index, mode): |
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if not isinstance(idx, cupy.ndarray): |
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raise TypeError("elements of multi_index must be cupy arrays") |
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if not cupy.can_cast(idx, cupy.int64, 'same_kind'): |
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raise TypeError( |
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'multi_index entries could not be cast from dtype(\'{}\') to ' |
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'dtype(\'{}\') according to the rule \'same_kind\''.format( |
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idx.dtype, cupy.int64().dtype)) |
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idx = idx.astype(cupy.int64, copy=False) |
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if _mode == "raise": |
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if cupy.any(cupy.logical_or(idx >= d, idx < 0)): |
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raise ValueError("invalid entry in coordinates array") |
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elif _mode == "clip": |
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idx = cupy.clip(idx, 0, d - 1) |
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elif _mode == 'wrap': |
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idx = idx % d |
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else: |
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raise ValueError('Unrecognized mode: {}'.format(_mode)) |
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raveled_indices += stride * idx |
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return raveled_indices |
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def unravel_index(indices, dims, order='C'): |
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"""Converts array of flat indices into a tuple of coordinate arrays. |
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Args: |
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indices (cupy.ndarray): An integer array whose elements are indices |
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into the flattened version of an array of dimensions :obj:`dims`. |
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dims (tuple of ints): The shape of the array to use for unraveling |
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indices. |
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order ('C' or 'F'): Determines whether the indices should be viewed as |
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indexing in row-major (C-style) or column-major (Fortran-style) |
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order. |
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Returns: |
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tuple of ndarrays: |
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Each array in the tuple has the same shape as the indices array. |
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Examples |
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-------- |
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>>> cupy.unravel_index(cupy.array([22, 41, 37]), (7, 6)) |
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(array([3, 6, 6]), array([4, 5, 1])) |
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>>> cupy.unravel_index(cupy.array([31, 41, 13]), (7, 6), order='F') |
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(array([3, 6, 6]), array([4, 5, 1])) |
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.. warning:: |
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This function may synchronize the device. |
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.. seealso:: :func:`numpy.unravel_index`, :func:`ravel_multi_index` |
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""" |
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order = 'C' if order is None else order.upper() |
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if order == 'C': |
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dims = reversed(dims) |
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elif order == 'F': |
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pass |
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else: |
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raise ValueError('order not understood') |
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if not cupy.can_cast(indices, cupy.int64, 'same_kind'): |
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raise TypeError( |
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'Iterator operand 0 dtype could not be cast ' |
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'from dtype(\'{}\') to dtype(\'{}\') ' |
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'according to the rule \'same_kind\''.format( |
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indices.dtype, cupy.int64().dtype)) |
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if (indices < 0).any(): |
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raise ValueError('invalid entry in index array') |
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unraveled_coords = [] |
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for dim in dims: |
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unraveled_coords.append(indices % dim) |
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indices = indices // dim |
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if (indices > 0).any(): |
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raise ValueError('invalid entry in index array') |
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if order == 'C': |
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unraveled_coords = reversed(unraveled_coords) |
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return tuple(unraveled_coords) |
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def mask_indices(n, mask_func, k=0): |
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""" |
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Return the indices to access (n, n) arrays, given a masking function. |
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Assume `mask_func` is a function that, for a square array a of |
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size ``(n, n)`` with a possible offset argument `k`, when called |
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as ``mask_func(a, k)`` returns a new array with zeros in certain |
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locations (functions like :func:`~cupy.triu` or :func:`~cupy.tril` do |
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precisely this). Then this function returns the indices where the non-zero |
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values would be located. |
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Args: |
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n (int): The returned indices will be valid to access arrays |
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of shape (n, n). |
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mask_func (callable): A function whose call signature is |
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similar to that of :func:`~cupy.triu`, :func:`~tril`. That is, |
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``mask_func(x, k)`` returns a boolean array, shaped like |
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`x`. `k` is an optional argument to the function. |
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k (scalar): An optional argument which is passed through to |
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`mask_func`. Functions like :func:`~cupy.triu`, :func:`~cupy.tril` |
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take a second argument that is interpreted as an offset. |
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Returns: |
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tuple of arrays: The `n` arrays of indices corresponding to |
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the locations where ``mask_func(np.ones((n, n)), k)`` is |
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True. |
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.. warning:: |
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This function may synchronize the device. |
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.. seealso:: :func:`numpy.mask_indices` |
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""" |
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a = cupy.ones((n, n), dtype=cupy.int8) |
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return mask_func(a, k).nonzero() |
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def tril_indices(n, k=0, m=None): |
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"""Returns the indices of the lower triangular matrix. |
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Here, the first group of elements contains row coordinates |
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of all indices and the second group of elements |
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contains column coordinates. |
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Parameters |
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---------- |
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n : int |
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The row dimension of the arrays for which the returned |
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indices will be valid. |
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k : int, optional |
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Diagonal above which to zero elements. `k = 0` |
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(the default) is the main diagonal, `k < 0` is |
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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]) |
|
|
|