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1"""
2Utilities that manipulate strides to achieve desirable effects.
4An explanation of strides can be found in the "ndarray.rst" file in the
5NumPy reference guide.
7"""
8import numpy as np
9from numpy.core.overrides import array_function_dispatch
11__all__ = ['broadcast_to', 'broadcast_arrays']
14class DummyArray:
15 """Dummy object that just exists to hang __array_interface__ dictionaries
16 and possibly keep alive a reference to a base array.
17 """
19 def __init__(self, interface, base=None):
20 self.__array_interface__ = interface
21 self.base = base
24def _maybe_view_as_subclass(original_array, new_array):
25 if type(original_array) is not type(new_array):
26 # if input was an ndarray subclass and subclasses were OK,
27 # then view the result as that subclass.
28 new_array = new_array.view(type=type(original_array))
29 # Since we have done something akin to a view from original_array, we
30 # should let the subclass finalize (if it has it implemented, i.e., is
31 # not None).
32 if new_array.__array_finalize__:
33 new_array.__array_finalize__(original_array)
34 return new_array
37def as_strided(x, shape=None, strides=None, subok=False, writeable=True):
38 """
39 Create a view into the array with the given shape and strides.
41 .. warning:: This function has to be used with extreme care, see notes.
43 Parameters
44 ----------
45 x : ndarray
46 Array to create a new.
47 shape : sequence of int, optional
48 The shape of the new array. Defaults to ``x.shape``.
49 strides : sequence of int, optional
50 The strides of the new array. Defaults to ``x.strides``.
51 subok : bool, optional
52 .. versionadded:: 1.10
54 If True, subclasses are preserved.
55 writeable : bool, optional
56 .. versionadded:: 1.12
58 If set to False, the returned array will always be readonly.
59 Otherwise it will be writable if the original array was. It
60 is advisable to set this to False if possible (see Notes).
62 Returns
63 -------
64 view : ndarray
66 See also
67 --------
68 broadcast_to: broadcast an array to a given shape.
69 reshape : reshape an array.
71 Notes
72 -----
73 ``as_strided`` creates a view into the array given the exact strides
74 and shape. This means it manipulates the internal data structure of
75 ndarray and, if done incorrectly, the array elements can point to
76 invalid memory and can corrupt results or crash your program.
77 It is advisable to always use the original ``x.strides`` when
78 calculating new strides to avoid reliance on a contiguous memory
79 layout.
81 Furthermore, arrays created with this function often contain self
82 overlapping memory, so that two elements are identical.
83 Vectorized write operations on such arrays will typically be
84 unpredictable. They may even give different results for small, large,
85 or transposed arrays.
86 Since writing to these arrays has to be tested and done with great
87 care, you may want to use ``writeable=False`` to avoid accidental write
88 operations.
90 For these reasons it is advisable to avoid ``as_strided`` when
91 possible.
92 """
93 # first convert input to array, possibly keeping subclass
94 x = np.array(x, copy=False, subok=subok)
95 interface = dict(x.__array_interface__)
96 if shape is not None:
97 interface['shape'] = tuple(shape)
98 if strides is not None:
99 interface['strides'] = tuple(strides)
101 array = np.asarray(DummyArray(interface, base=x))
102 # The route via `__interface__` does not preserve structured
103 # dtypes. Since dtype should remain unchanged, we set it explicitly.
104 array.dtype = x.dtype
106 view = _maybe_view_as_subclass(x, array)
108 if view.flags.writeable and not writeable:
109 view.flags.writeable = False
111 return view
114def _broadcast_to(array, shape, subok, readonly):
115 shape = tuple(shape) if np.iterable(shape) else (shape,)
116 array = np.array(array, copy=False, subok=subok)
117 if not shape and array.shape:
118 raise ValueError('cannot broadcast a non-scalar to a scalar array')
119 if any(size < 0 for size in shape):
120 raise ValueError('all elements of broadcast shape must be non-'
121 'negative')
122 extras = []
123 it = np.nditer(
124 (array,), flags=['multi_index', 'refs_ok', 'zerosize_ok'] + extras,
125 op_flags=['readonly'], itershape=shape, order='C')
126 with it:
127 # never really has writebackifcopy semantics
128 broadcast = it.itviews[0]
129 result = _maybe_view_as_subclass(array, broadcast)
130 # In a future version this will go away
131 if not readonly and array.flags._writeable_no_warn:
132 result.flags.writeable = True
133 result.flags._warn_on_write = True
134 return result
137def _broadcast_to_dispatcher(array, shape, subok=None):
138 return (array,)
141@array_function_dispatch(_broadcast_to_dispatcher, module='numpy')
142def broadcast_to(array, shape, subok=False):
143 """Broadcast an array to a new shape.
145 Parameters
146 ----------
147 array : array_like
148 The array to broadcast.
149 shape : tuple
150 The shape of the desired array.
151 subok : bool, optional
152 If True, then sub-classes will be passed-through, otherwise
153 the returned array will be forced to be a base-class array (default).
155 Returns
156 -------
157 broadcast : array
158 A readonly view on the original array with the given shape. It is
159 typically not contiguous. Furthermore, more than one element of a
160 broadcasted array may refer to a single memory location.
162 Raises
163 ------
164 ValueError
165 If the array is not compatible with the new shape according to NumPy's
166 broadcasting rules.
168 Notes
169 -----
170 .. versionadded:: 1.10.0
172 Examples
173 --------
174 >>> x = np.array([1, 2, 3])
175 >>> np.broadcast_to(x, (3, 3))
176 array([[1, 2, 3],
177 [1, 2, 3],
178 [1, 2, 3]])
179 """
180 return _broadcast_to(array, shape, subok=subok, readonly=True)
183def _broadcast_shape(*args):
184 """Returns the shape of the arrays that would result from broadcasting the
185 supplied arrays against each other.
186 """
187 # use the old-iterator because np.nditer does not handle size 0 arrays
188 # consistently
189 b = np.broadcast(*args[:32])
190 # unfortunately, it cannot handle 32 or more arguments directly
191 for pos in range(32, len(args), 31):
192 # ironically, np.broadcast does not properly handle np.broadcast
193 # objects (it treats them as scalars)
194 # use broadcasting to avoid allocating the full array
195 b = broadcast_to(0, b.shape)
196 b = np.broadcast(b, *args[pos:(pos + 31)])
197 return b.shape
200def _broadcast_arrays_dispatcher(*args, subok=None):
201 return args
204@array_function_dispatch(_broadcast_arrays_dispatcher, module='numpy')
205def broadcast_arrays(*args, subok=False):
206 """
207 Broadcast any number of arrays against each other.
209 Parameters
210 ----------
211 `*args` : array_likes
212 The arrays to broadcast.
214 subok : bool, optional
215 If True, then sub-classes will be passed-through, otherwise
216 the returned arrays will be forced to be a base-class array (default).
218 Returns
219 -------
220 broadcasted : list of arrays
221 These arrays are views on the original arrays. They are typically
222 not contiguous. Furthermore, more than one element of a
223 broadcasted array may refer to a single memory location. If you need
224 to write to the arrays, make copies first. While you can set the
225 ``writable`` flag True, writing to a single output value may end up
226 changing more than one location in the output array.
228 .. deprecated:: 1.17
229 The output is currently marked so that if written to, a deprecation
230 warning will be emitted. A future version will set the
231 ``writable`` flag False so writing to it will raise an error.
233 Examples
234 --------
235 >>> x = np.array([[1,2,3]])
236 >>> y = np.array([[4],[5]])
237 >>> np.broadcast_arrays(x, y)
238 [array([[1, 2, 3],
239 [1, 2, 3]]), array([[4, 4, 4],
240 [5, 5, 5]])]
242 Here is a useful idiom for getting contiguous copies instead of
243 non-contiguous views.
245 >>> [np.array(a) for a in np.broadcast_arrays(x, y)]
246 [array([[1, 2, 3],
247 [1, 2, 3]]), array([[4, 4, 4],
248 [5, 5, 5]])]
250 """
251 # nditer is not used here to avoid the limit of 32 arrays.
252 # Otherwise, something like the following one-liner would suffice:
253 # return np.nditer(args, flags=['multi_index', 'zerosize_ok'],
254 # order='C').itviews
256 args = [np.array(_m, copy=False, subok=subok) for _m in args]
258 shape = _broadcast_shape(*args)
260 if all(array.shape == shape for array in args):
261 # Common case where nothing needs to be broadcasted.
262 return args
264 return [_broadcast_to(array, shape, subok=subok, readonly=False)
265 for array in args]