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The purpose is to allow easier editing of the docstrings without requiring a re-compile. NOTE: Many of the methods of ndarray have corresponding functions. If you update these docstrings, please keep also the ones in core/fromnumeric.py, core/defmatrix.py up-to-date. � )�division�absolute_import�print_function)� add_newdocz numpy.coreZflatitera� Flat iterator object to iterate over arrays. A `flatiter` iterator is returned by ``x.flat`` for any array `x`. It allows iterating over the array as if it were a 1-D array, either in a for-loop or by calling its `next` method. Iteration is done in row-major, C-style order (the last index varying the fastest). The iterator can also be indexed using basic slicing or advanced indexing. See Also -------- ndarray.flat : Return a flat iterator over an array. ndarray.flatten : Returns a flattened copy of an array. Notes ----- A `flatiter` iterator can not be constructed directly from Python code by calling the `flatiter` constructor. Examples -------- >>> x = np.arange(6).reshape(2, 3) >>> fl = x.flat >>> type(fl) <type 'numpy.flatiter'> >>> for item in fl: ... print(item) ... 0 1 2 3 4 5 >>> fl[2:4] array([2, 3]) )�basez� A reference to the array that is iterated over. Examples -------- >>> x = np.arange(5) >>> fl = x.flat >>> fl.base is x True )Zcoordsz� An N-dimensional tuple of current coordinates. Examples -------- >>> x = np.arange(6).reshape(2, 3) >>> fl = x.flat >>> fl.coords (0, 0) >>> fl.next() 0 >>> fl.coords (0, 1) )�indexz� Current flat index into the array. Examples -------- >>> x = np.arange(6).reshape(2, 3) >>> fl = x.flat >>> fl.index 0 >>> fl.next() 0 >>> fl.index 1 )� __array__z2__array__(type=None) Get array from iterator )�copyz� copy() Get a copy of the iterator as a 1-D array. Examples -------- >>> x = np.arange(6).reshape(2, 3) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> fl = x.flat >>> fl.copy() array([0, 1, 2, 3, 4, 5]) Znditera* Efficient multi-dimensional iterator object to iterate over arrays. To get started using this object, see the :ref:`introductory guide to array iteration <arrays.nditer>`. Parameters ---------- op : ndarray or sequence of array_like The array(s) to iterate over. flags : sequence of str, optional Flags to control the behavior of the iterator. * "buffered" enables buffering when required. * "c_index" causes a C-order index to be tracked. * "f_index" causes a Fortran-order index to be tracked. * "multi_index" causes a multi-index, or a tuple of indices with one per iteration dimension, to be tracked. * "common_dtype" causes all the operands to be converted to a common data type, with copying or buffering as necessary. * "copy_if_overlap" causes the iterator to determine if read operands have overlap with write operands, and make temporary copies as necessary to avoid overlap. False positives (needless copying) are possible in some cases. * "delay_bufalloc" delays allocation of the buffers until a reset() call is made. Allows "allocate" operands to be initialized before their values are copied into the buffers. * "external_loop" causes the `values` given to be one-dimensional arrays with multiple values instead of zero-dimensional arrays. * "grow_inner" allows the `value` array sizes to be made larger than the buffer size when both "buffered" and "external_loop" is used. * "ranged" allows the iterator to be restricted to a sub-range of the iterindex values. * "refs_ok" enables iteration of reference types, such as object arrays. * "reduce_ok" enables iteration of "readwrite" operands which are broadcasted, also known as reduction operands. * "zerosize_ok" allows `itersize` to be zero. op_flags : list of list of str, optional This is a list of flags for each operand. At minimum, one of "readonly", "readwrite", or "writeonly" must be specified. * "readonly" indicates the operand will only be read from. * "readwrite" indicates the operand will be read from and written to. * "writeonly" indicates the operand will only be written to. * "no_broadcast" prevents the operand from being broadcasted. * "contig" forces the operand data to be contiguous. * "aligned" forces the operand data to be aligned. * "nbo" forces the operand data to be in native byte order. * "copy" allows a temporary read-only copy if required. * "updateifcopy" allows a temporary read-write copy if required. * "allocate" causes the array to be allocated if it is None in the `op` parameter. * "no_subtype" prevents an "allocate" operand from using a subtype. * "arraymask" indicates that this operand is the mask to use for selecting elements when writing to operands with the 'writemasked' flag set. The iterator does not enforce this, but when writing from a buffer back to the array, it only copies those elements indicated by this mask. * 'writemasked' indicates that only elements where the chosen 'arraymask' operand is True will be written to. * "overlap_assume_elementwise" can be used to mark operands that are accessed only in the iterator order, to allow less conservative copying when "copy_if_overlap" is present. op_dtypes : dtype or tuple of dtype(s), optional The required data type(s) of the operands. If copying or buffering is enabled, the data will be converted to/from their original types. order : {'C', 'F', 'A', 'K'}, optional Controls the iteration order. 'C' means C order, 'F' means Fortran order, 'A' means 'F' order if all the arrays are Fortran contiguous, 'C' order otherwise, and 'K' means as close to the order the array elements appear in memory as possible. This also affects the element memory order of "allocate" operands, as they are allocated to be compatible with iteration order. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur when making a copy or buffering. Setting this to 'unsafe' is not recommended, as it can adversely affect accumulations. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. op_axes : list of list of ints, optional If provided, is a list of ints or None for each operands. The list of axes for an operand is a mapping from the dimensions of the iterator to the dimensions of the operand. A value of -1 can be placed for entries, causing that dimension to be treated as "newaxis". itershape : tuple of ints, optional The desired shape of the iterator. This allows "allocate" operands with a dimension mapped by op_axes not corresponding to a dimension of a different operand to get a value not equal to 1 for that dimension. buffersize : int, optional When buffering is enabled, controls the size of the temporary buffers. Set to 0 for the default value. Attributes ---------- dtypes : tuple of dtype(s) The data types of the values provided in `value`. This may be different from the operand data types if buffering is enabled. finished : bool Whether the iteration over the operands is finished or not. has_delayed_bufalloc : bool If True, the iterator was created with the "delay_bufalloc" flag, and no reset() function was called on it yet. has_index : bool If True, the iterator was created with either the "c_index" or the "f_index" flag, and the property `index` can be used to retrieve it. has_multi_index : bool If True, the iterator was created with the "multi_index" flag, and the property `multi_index` can be used to retrieve it. index When the "c_index" or "f_index" flag was used, this property provides access to the index. Raises a ValueError if accessed and `has_index` is False. iterationneedsapi : bool Whether iteration requires access to the Python API, for example if one of the operands is an object array. iterindex : int An index which matches the order of iteration. itersize : int Size of the iterator. itviews Structured view(s) of `operands` in memory, matching the reordered and optimized iterator access pattern. multi_index When the "multi_index" flag was used, this property provides access to the index. Raises a ValueError if accessed accessed and `has_multi_index` is False. ndim : int The iterator's dimension. nop : int The number of iterator operands. operands : tuple of operand(s) The array(s) to be iterated over. shape : tuple of ints Shape tuple, the shape of the iterator. value Value of `operands` at current iteration. Normally, this is a tuple of array scalars, but if the flag "external_loop" is used, it is a tuple of one dimensional arrays. Notes ----- `nditer` supersedes `flatiter`. The iterator implementation behind `nditer` is also exposed by the NumPy C API. The Python exposure supplies two iteration interfaces, one which follows the Python iterator protocol, and another which mirrors the C-style do-while pattern. The native Python approach is better in most cases, but if you need the iterator's coordinates or index, use the C-style pattern. Examples -------- Here is how we might write an ``iter_add`` function, using the Python iterator protocol:: def iter_add_py(x, y, out=None): addop = np.add it = np.nditer([x, y, out], [], [['readonly'], ['readonly'], ['writeonly','allocate']]) for (a, b, c) in it: addop(a, b, out=c) return it.operands[2] Here is the same function, but following the C-style pattern:: def iter_add(x, y, out=None): addop = np.add it = np.nditer([x, y, out], [], [['readonly'], ['readonly'], ['writeonly','allocate']]) while not it.finished: addop(it[0], it[1], out=it[2]) it.iternext() return it.operands[2] Here is an example outer product function:: def outer_it(x, y, out=None): mulop = np.multiply it = np.nditer([x, y, out], ['external_loop'], [['readonly'], ['readonly'], ['writeonly', 'allocate']], op_axes=[range(x.ndim)+[-1]*y.ndim, [-1]*x.ndim+range(y.ndim), None]) for (a, b, c) in it: mulop(a, b, out=c) return it.operands[2] >>> a = np.arange(2)+1 >>> b = np.arange(3)+1 >>> outer_it(a,b) array([[1, 2, 3], [2, 4, 6]]) Here is an example function which operates like a "lambda" ufunc:: def luf(lamdaexpr, *args, **kwargs): "luf(lambdaexpr, op1, ..., opn, out=None, order='K', casting='safe', buffersize=0)" nargs = len(args) op = (kwargs.get('out',None),) + args it = np.nditer(op, ['buffered','external_loop'], [['writeonly','allocate','no_broadcast']] + [['readonly','nbo','aligned']]*nargs, order=kwargs.get('order','K'), casting=kwargs.get('casting','safe'), buffersize=kwargs.get('buffersize',0)) while not it.finished: it[0] = lamdaexpr(*it[1:]) it.iternext() return it.operands[0] >>> a = np.arange(5) >>> b = np.ones(5) >>> luf(lambda i,j:i*i + j/2, a, b) array([ 0.5, 1.5, 4.5, 9.5, 16.5]) )r a copy() Get a copy of the iterator in its current state. Examples -------- >>> x = np.arange(10) >>> y = x + 1 >>> it = np.nditer([x, y]) >>> it.next() (array(0), array(1)) >>> it2 = it.copy() >>> it2.next() (array(1), array(2)) )� debug_printzh debug_print() Print the current state of the `nditer` instance and debug info to stdout. )Zenable_external_loopz� enable_external_loop() When the "external_loop" was not used during construction, but is desired, this modifies the iterator to behave as if the flag was specified. )Ziternexta8 iternext() Check whether iterations are left, and perform a single internal iteration without returning the result. Used in the C-style pattern do-while pattern. For an example, see `nditer`. Returns ------- iternext : bool Whether or not there are iterations left. )Z remove_axiszw remove_axis(i) Removes axis `i` from the iterator. Requires that the flag "multi_index" be enabled. )Zremove_multi_indexz� remove_multi_index() When the "multi_index" flag was specified, this removes it, allowing the internal iteration structure to be optimized further. )�resetz@ reset() Reset the iterator to its initial state. Z broadcasta� Produce an object that mimics broadcasting. Parameters ---------- in1, in2, ... : array_like Input parameters. Returns ------- b : broadcast object Broadcast the input parameters against one another, and return an object that encapsulates the result. Amongst others, it has ``shape`` and ``nd`` properties, and may be used as an iterator. See Also -------- broadcast_arrays broadcast_to Examples -------- Manually adding two vectors, using broadcasting: >>> x = np.array([[1], [2], [3]]) >>> y = np.array([4, 5, 6]) >>> b = np.broadcast(x, y) >>> out = np.empty(b.shape) >>> out.flat = [u+v for (u,v) in b] >>> out array([[ 5., 6., 7.], [ 6., 7., 8.], [ 7., 8., 9.]]) Compare against built-in broadcasting: >>> x + y array([[5, 6, 7], [6, 7, 8], [7, 8, 9]]) )r a current index in broadcasted result Examples -------- >>> x = np.array([[1], [2], [3]]) >>> y = np.array([4, 5, 6]) >>> b = np.broadcast(x, y) >>> b.index 0 >>> b.next(), b.next(), b.next() ((1, 4), (1, 5), (1, 6)) >>> b.index 3 )Zitersa� tuple of iterators along ``self``'s "components." Returns a tuple of `numpy.flatiter` objects, one for each "component" of ``self``. See Also -------- numpy.flatiter Examples -------- >>> x = np.array([1, 2, 3]) >>> y = np.array([[4], [5], [6]]) >>> b = np.broadcast(x, y) >>> row, col = b.iters >>> row.next(), col.next() (1, 4) )�ndimz� Number of dimensions of broadcasted result. Alias for `nd`. .. versionadded:: 1.12.0 Examples -------- >>> x = np.array([1, 2, 3]) >>> y = np.array([[4], [5], [6]]) >>> b = np.broadcast(x, y) >>> b.ndim 2 )Znda# Number of dimensions of broadcasted result. For code intended for NumPy 1.12.0 and later the more consistent `ndim` is preferred. Examples -------- >>> x = np.array([1, 2, 3]) >>> y = np.array([[4], [5], [6]]) >>> b = np.broadcast(x, y) >>> b.nd 2 )Znumiterz� Number of iterators possessed by the broadcasted result. Examples -------- >>> x = np.array([1, 2, 3]) >>> y = np.array([[4], [5], [6]]) >>> b = np.broadcast(x, y) >>> b.numiter 2 )�shapez� Shape of broadcasted result. Examples -------- >>> x = np.array([1, 2, 3]) >>> y = np.array([[4], [5], [6]]) >>> b = np.broadcast(x, y) >>> b.shape (3, 3) )�sizez� Total size of broadcasted result. Examples -------- >>> x = np.array([1, 2, 3]) >>> y = np.array([[4], [5], [6]]) >>> b = np.broadcast(x, y) >>> b.size 9 )r a� reset() Reset the broadcasted result's iterator(s). Parameters ---------- None Returns ------- None Examples -------- >>> x = np.array([1, 2, 3]) >>> y = np.array([[4], [5], [6]] >>> b = np.broadcast(x, y) >>> b.index 0 >>> b.next(), b.next(), b.next() ((1, 4), (2, 4), (3, 4)) >>> b.index 3 >>> b.reset() >>> b.index 0 znumpy.core.multiarray�arraya� array(object, dtype=None, copy=True, order='K', subok=False, ndmin=0) Create an array. Parameters ---------- object : array_like An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence. dtype : data-type, optional The desired data-type for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence. This argument can only be used to 'upcast' the array. For downcasting, use the .astype(t) method. copy : bool, optional If true (default), then the object is copied. Otherwise, a copy will only be made if __array__ returns a copy, if obj is a nested sequence, or if a copy is needed to satisfy any of the other requirements (`dtype`, `order`, etc.). order : {'K', 'A', 'C', 'F'}, optional Specify the memory layout of the array. If object is not an array, the newly created array will be in C order (row major) unless 'F' is specified, in which case it will be in Fortran order (column major). If object is an array the following holds. ===== ========= =================================================== order no copy copy=True ===== ========= =================================================== 'K' unchanged F & C order preserved, otherwise most similar order 'A' unchanged F order if input is F and not C, otherwise C order 'C' C order C order 'F' F order F order ===== ========= =================================================== When ``copy=False`` and a copy is made for other reasons, the result is the same as if ``copy=True``, with some exceptions for `A`, see the Notes section. The default order is 'K'. 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). ndmin : int, optional Specifies the minimum number of dimensions that the resulting array should have. Ones will be pre-pended to the shape as needed to meet this requirement. Returns ------- out : ndarray An array object satisfying the specified requirements. See Also -------- empty, empty_like, zeros, zeros_like, ones, ones_like, full, full_like Notes ----- When order is 'A' and `object` is an array in neither 'C' nor 'F' order, and a copy is forced by a change in dtype, then the order of the result is not necessarily 'C' as expected. This is likely a bug. Examples -------- >>> np.array([1, 2, 3]) array([1, 2, 3]) Upcasting: >>> np.array([1, 2, 3.0]) array([ 1., 2., 3.]) More than one dimension: >>> np.array([[1, 2], [3, 4]]) array([[1, 2], [3, 4]]) Minimum dimensions 2: >>> np.array([1, 2, 3], ndmin=2) array([[1, 2, 3]]) Type provided: >>> np.array([1, 2, 3], dtype=complex) array([ 1.+0.j, 2.+0.j, 3.+0.j]) Data-type consisting of more than one element: >>> x = np.array([(1,2),(3,4)],dtype=[('a','<i4'),('b','<i4')]) >>> x['a'] array([1, 3]) Creating an array from sub-classes: >>> np.array(np.mat('1 2; 3 4')) array([[1, 2], [3, 4]]) >>> np.array(np.mat('1 2; 3 4'), subok=True) matrix([[1, 2], [3, 4]]) �emptya� empty(shape, dtype=float, order='C') Return a new array of given shape and type, without initializing entries. Parameters ---------- shape : int or tuple of int Shape of the empty array dtype : data-type, optional Desired output data-type. order : {'C', 'F'}, optional Whether to store multi-dimensional data in row-major (C-style) or column-major (Fortran-style) order in memory. Returns ------- out : ndarray Array of uninitialized (arbitrary) data of the given shape, dtype, and order. Object arrays will be initialized to None. See Also -------- empty_like, zeros, ones Notes ----- `empty`, unlike `zeros`, does not set the array values to zero, and may therefore be marginally faster. On the other hand, it requires the user to manually set all the values in the array, and should be used with caution. Examples -------- >>> np.empty([2, 2]) array([[ -9.74499359e+001, 6.69583040e-309], [ 2.13182611e-314, 3.06959433e-309]]) #random >>> np.empty([2, 2], dtype=int) array([[-1073741821, -1067949133], [ 496041986, 19249760]]) #random Z empty_likea� empty_like(a, dtype=None, order='K', subok=True) Return a new array with the same shape and type as a given array. Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. dtype : data-type, optional Overrides the data type of the result. .. versionadded:: 1.6.0 order : {'C', 'F', 'A', or 'K'}, optional Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if ``a`` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of ``a`` as closely as possible. .. versionadded:: 1.6.0 subok : bool, optional. If True, then the newly created array will use the sub-class type of 'a', otherwise it will be a base-class array. Defaults to True. Returns ------- out : ndarray Array of uninitialized (arbitrary) data with the same shape and type as `a`. See Also -------- ones_like : Return an array of ones with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. empty : Return a new uninitialized array. ones : Return a new array setting values to one. zeros : Return a new array setting values to zero. Notes ----- This function does *not* initialize the returned array; to do that use `zeros_like` or `ones_like` instead. It may be marginally faster than the functions that do set the array values. Examples -------- >>> a = ([1,2,3], [4,5,6]) # a is array-like >>> np.empty_like(a) array([[-1073741821, -1073741821, 3], #random [ 0, 0, -1073741821]]) >>> a = np.array([[1., 2., 3.],[4.,5.,6.]]) >>> np.empty_like(a) array([[ -2.00000715e+000, 1.48219694e-323, -2.00000572e+000],#random [ 4.38791518e-305, -2.00000715e+000, 4.17269252e-309]]) Zscalara� scalar(dtype, obj) Return a new scalar array of the given type initialized with obj. This function is meant mainly for pickle support. `dtype` must be a valid data-type descriptor. If `dtype` corresponds to an object descriptor, then `obj` can be any object, otherwise `obj` must be a string. If `obj` is not given, it will be interpreted as None for object type and as zeros for all other types. �zerosa� zeros(shape, dtype=float, order='C') Return a new array of given shape and type, filled with zeros. Parameters ---------- shape : int or sequence of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is `numpy.float64`. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. Returns ------- out : ndarray Array of zeros with the given shape, dtype, and order. See Also -------- zeros_like : Return an array of zeros with shape and type of input. ones_like : Return an array of ones with shape and type of input. empty_like : Return an empty array with shape and type of input. ones : Return a new array setting values to one. empty : Return a new uninitialized array. Examples -------- >>> np.zeros(5) array([ 0., 0., 0., 0., 0.]) >>> np.zeros((5,), dtype=np.int) array([0, 0, 0, 0, 0]) >>> np.zeros((2, 1)) array([[ 0.], [ 0.]]) >>> s = (2,2) >>> np.zeros(s) array([[ 0., 0.], [ 0., 0.]]) >>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype array([(0, 0), (0, 0)], dtype=[('x', '<i4'), ('y', '<i4')]) Z set_typeDictzuset_typeDict(dict) Set the internal dictionary that can look up an array type using a registered code. Z fromstringa fromstring(string, dtype=float, count=-1, sep='') A new 1-D array initialized from raw binary or text data in a string. Parameters ---------- string : str A string containing the data. dtype : data-type, optional The data type of the array; default: float. For binary input data, the data must be in exactly this format. count : int, optional Read this number of `dtype` elements from the data. If this is negative (the default), the count will be determined from the length of the data. sep : str, optional If not provided or, equivalently, the empty string, the data will be interpreted as binary data; otherwise, as ASCII text with decimal numbers. Also in this latter case, this argument is interpreted as the string separating numbers in the data; extra whitespace between elements is also ignored. Returns ------- arr : ndarray The constructed array. Raises ------ ValueError If the string is not the correct size to satisfy the requested `dtype` and `count`. See Also -------- frombuffer, fromfile, fromiter Examples -------- >>> np.fromstring('\x01\x02', dtype=np.uint8) array([1, 2], dtype=uint8) >>> np.fromstring('1 2', dtype=int, sep=' ') array([1, 2]) >>> np.fromstring('1, 2', dtype=int, sep=',') array([1, 2]) >>> np.fromstring('\x01\x02\x03\x04\x05', dtype=np.uint8, count=3) array([1, 2, 3], dtype=uint8) Zfromitera. fromiter(iterable, dtype, count=-1) Create a new 1-dimensional array from an iterable object. Parameters ---------- iterable : iterable object An iterable object providing data for the array. dtype : data-type The data-type of the returned array. count : int, optional The number of items to read from *iterable*. The default is -1, which means all data is read. Returns ------- out : ndarray The output array. Notes ----- Specify `count` to improve performance. It allows ``fromiter`` to pre-allocate the output array, instead of resizing it on demand. Examples -------- >>> iterable = (x*x for x in range(5)) >>> np.fromiter(iterable, np.float) array([ 0., 1., 4., 9., 16.]) Zfromfilea! fromfile(file, dtype=float, count=-1, sep='') Construct an array from data in a text or binary file. A highly efficient way of reading binary data with a known data-type, as well as parsing simply formatted text files. Data written using the `tofile` method can be read using this function. Parameters ---------- file : file or str Open file object or filename. dtype : data-type Data type of the returned array. For binary files, it is used to determine the size and byte-order of the items in the file. count : int Number of items to read. ``-1`` means all items (i.e., the complete file). sep : str Separator between items if file is a text file. Empty ("") separator means the file should be treated as binary. Spaces (" ") in the separator match zero or more whitespace characters. A separator consisting only of spaces must match at least one whitespace. See also -------- load, save ndarray.tofile loadtxt : More flexible way of loading data from a text file. Notes ----- Do not rely on the combination of `tofile` and `fromfile` for data storage, as the binary files generated are are not platform independent. In particular, no byte-order or data-type information is saved. Data can be stored in the platform independent ``.npy`` format using `save` and `load` instead. Examples -------- Construct an ndarray: >>> dt = np.dtype([('time', [('min', int), ('sec', int)]), ... ('temp', float)]) >>> x = np.zeros((1,), dtype=dt) >>> x['time']['min'] = 10; x['temp'] = 98.25 >>> x array([((10, 0), 98.25)], dtype=[('time', [('min', '<i4'), ('sec', '<i4')]), ('temp', '<f8')]) Save the raw data to disk: >>> import os >>> fname = os.tmpnam() >>> x.tofile(fname) Read the raw data from disk: >>> np.fromfile(fname, dtype=dt) array([((10, 0), 98.25)], dtype=[('time', [('min', '<i4'), ('sec', '<i4')]), ('temp', '<f8')]) The recommended way to store and load data: >>> np.save(fname, x) >>> np.load(fname + '.npy') array([((10, 0), 98.25)], dtype=[('time', [('min', '<i4'), ('sec', '<i4')]), ('temp', '<f8')]) Z frombuffera frombuffer(buffer, dtype=float, count=-1, offset=0) Interpret a buffer as a 1-dimensional array. Parameters ---------- buffer : buffer_like An object that exposes the buffer interface. dtype : data-type, optional Data-type of the returned array; default: float. count : int, optional Number of items to read. ``-1`` means all data in the buffer. offset : int, optional Start reading the buffer from this offset (in bytes); default: 0. Notes ----- If the buffer has data that is not in machine byte-order, this should be specified as part of the data-type, e.g.:: >>> dt = np.dtype(int) >>> dt = dt.newbyteorder('>') >>> np.frombuffer(buf, dtype=dt) The data of the resulting array will not be byteswapped, but will be interpreted correctly. Examples -------- >>> s = 'hello world' >>> np.frombuffer(s, dtype='S1', count=5, offset=6) array(['w', 'o', 'r', 'l', 'd'], dtype='|S1') Z concatenatea� concatenate((a1, a2, ...), axis=0) Join a sequence of arrays along an existing axis. Parameters ---------- a1, a2, ... : sequence of array_like The arrays must have the same shape, except in the dimension corresponding to `axis` (the first, by default). axis : int, optional The axis along which the arrays will be joined. Default is 0. Returns ------- res : ndarray The concatenated array. See Also -------- ma.concatenate : Concatenate function that preserves input masks. array_split : Split an array into multiple sub-arrays of equal or near-equal size. split : Split array into a list of multiple sub-arrays of equal size. hsplit : Split array into multiple sub-arrays horizontally (column wise) vsplit : Split array into multiple sub-arrays vertically (row wise) dsplit : Split array into multiple sub-arrays along the 3rd axis (depth). stack : Stack a sequence of arrays along a new axis. hstack : Stack arrays in sequence horizontally (column wise) vstack : Stack arrays in sequence vertically (row wise) dstack : Stack arrays in sequence depth wise (along third dimension) Notes ----- When one or more of the arrays to be concatenated is a MaskedArray, this function will return a MaskedArray object instead of an ndarray, but the input masks are *not* preserved. In cases where a MaskedArray is expected as input, use the ma.concatenate function from the masked array module instead. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> b = np.array([[5, 6]]) >>> np.concatenate((a, b), axis=0) array([[1, 2], [3, 4], [5, 6]]) >>> np.concatenate((a, b.T), axis=1) array([[1, 2, 5], [3, 4, 6]]) This function will not preserve masking of MaskedArray inputs. >>> a = np.ma.arange(3) >>> a[1] = np.ma.masked >>> b = np.arange(2, 5) >>> a masked_array(data = [0 -- 2], mask = [False True False], fill_value = 999999) >>> b array([2, 3, 4]) >>> np.concatenate([a, b]) masked_array(data = [0 1 2 2 3 4], mask = False, fill_value = 999999) >>> np.ma.concatenate([a, b]) masked_array(data = [0 -- 2 2 3 4], mask = [False True False False False False], fill_value = 999999) �inneraj inner(a, b) Inner product of two arrays. Ordinary inner product of vectors for 1-D arrays (without complex conjugation), in higher dimensions a sum product over the last axes. Parameters ---------- a, b : array_like If `a` and `b` are nonscalar, their last dimensions must match. Returns ------- out : ndarray `out.shape = a.shape[:-1] + b.shape[:-1]` Raises ------ ValueError If the last dimension of `a` and `b` has different size. See Also -------- tensordot : Sum products over arbitrary axes. dot : Generalised matrix product, using second last dimension of `b`. einsum : Einstein summation convention. Notes ----- For vectors (1-D arrays) it computes the ordinary inner-product:: np.inner(a, b) = sum(a[:]*b[:]) More generally, if `ndim(a) = r > 0` and `ndim(b) = s > 0`:: np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1)) or explicitly:: np.inner(a, b)[i0,...,ir-1,j0,...,js-1] = sum(a[i0,...,ir-1,:]*b[j0,...,js-1,:]) In addition `a` or `b` may be scalars, in which case:: np.inner(a,b) = a*b Examples -------- Ordinary inner product for vectors: >>> a = np.array([1,2,3]) >>> b = np.array([0,1,0]) >>> np.inner(a, b) 2 A multidimensional example: >>> a = np.arange(24).reshape((2,3,4)) >>> b = np.arange(4) >>> np.inner(a, b) array([[ 14, 38, 62], [ 86, 110, 134]]) An example where `b` is a scalar: >>> np.inner(np.eye(2), 7) array([[ 7., 0.], [ 0., 7.]]) ZfastCopyAndTransposez_fastCopyAndTranspose(a)Z correlatez cross_correlate(a,v, mode=0)ZarangeaT arange([start,] stop[, step,], dtype=None) Return evenly spaced values within a given interval. Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). For integer arguments the function is equivalent to the Python built-in `range <http://docs.python.org/lib/built-in-funcs.html>`_ function, but returns an ndarray rather than a list. When using a non-integer step, such as 0.1, the results will often not be consistent. It is better to use ``linspace`` for these cases. Parameters ---------- start : number, optional Start of interval. The interval includes this value. The default start value is 0. stop : number End of interval. The interval does not include this value, except in some cases where `step` is not an integer and floating point round-off affects the length of `out`. step : number, optional Spacing between values. For any output `out`, this is the distance between two adjacent values, ``out[i+1] - out[i]``. The default step size is 1. If `step` is specified, `start` must also be given. dtype : dtype The type of the output array. If `dtype` is not given, infer the data type from the other input arguments. Returns ------- arange : ndarray Array of evenly spaced values. For floating point arguments, the length of the result is ``ceil((stop - start)/step)``. Because of floating point overflow, this rule may result in the last element of `out` being greater than `stop`. See Also -------- linspace : Evenly spaced numbers with careful handling of endpoints. ogrid: Arrays of evenly spaced numbers in N-dimensions. mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions. Examples -------- >>> np.arange(3) array([0, 1, 2]) >>> np.arange(3.0) array([ 0., 1., 2.]) >>> np.arange(3,7) array([3, 4, 5, 6]) >>> np.arange(3,7,2) array([3, 5]) Z_get_ndarray_c_versionzS_get_ndarray_c_version() Return the compile time NDARRAY_VERSION number. � _reconstructzY_reconstruct(subtype, shape, dtype) Construct an empty array. Used by Pickles. Zset_string_functionzx set_string_function(f, repr=1) Internal method to set a function to be used when pretty printing arrays. Zset_numeric_opsaL set_numeric_ops(op1=func1, op2=func2, ...) Set numerical operators for array objects. Parameters ---------- op1, op2, ... : callable Each ``op = func`` pair describes an operator to be replaced. For example, ``add = lambda x, y: np.add(x, y) % 5`` would replace addition by modulus 5 addition. Returns ------- saved_ops : list of callables A list of all operators, stored before making replacements. Notes ----- .. WARNING:: Use with care! Incorrect usage may lead to memory errors. A function replacing an operator cannot make use of that operator. For example, when replacing add, you may not use ``+``. Instead, directly call ufuncs. Examples -------- >>> def add_mod5(x, y): ... return np.add(x, y) % 5 ... >>> old_funcs = np.set_numeric_ops(add=add_mod5) >>> x = np.arange(12).reshape((3, 4)) >>> x + x array([[0, 2, 4, 1], [3, 0, 2, 4], [1, 3, 0, 2]]) >>> ignore = np.set_numeric_ops(**old_funcs) # restore operators �wherea� where(condition, [x, y]) Return elements, either from `x` or `y`, depending on `condition`. If only `condition` is given, return ``condition.nonzero()``. Parameters ---------- condition : array_like, bool When True, yield `x`, otherwise yield `y`. x, y : array_like, optional Values from which to choose. `x`, `y` and `condition` need to be broadcastable to some shape. Returns ------- out : ndarray or tuple of ndarrays If both `x` and `y` are specified, the output array contains elements of `x` where `condition` is True, and elements from `y` elsewhere. If only `condition` is given, return the tuple ``condition.nonzero()``, the indices where `condition` is True. See Also -------- nonzero, choose Notes ----- If `x` and `y` are given and input arrays are 1-D, `where` is equivalent to:: [xv if c else yv for (c,xv,yv) in zip(condition,x,y)] Examples -------- >>> np.where([[True, False], [True, True]], ... [[1, 2], [3, 4]], ... [[9, 8], [7, 6]]) array([[1, 8], [3, 4]]) >>> np.where([[0, 1], [1, 0]]) (array([0, 1]), array([1, 0])) >>> x = np.arange(9.).reshape(3, 3) >>> np.where( x > 5 ) (array([2, 2, 2]), array([0, 1, 2])) >>> x[np.where( x > 3.0 )] # Note: result is 1D. array([ 4., 5., 6., 7., 8.]) >>> np.where(x < 5, x, -1) # Note: broadcasting. array([[ 0., 1., 2.], [ 3., 4., -1.], [-1., -1., -1.]]) Find the indices of elements of `x` that are in `goodvalues`. >>> goodvalues = [3, 4, 7] >>> ix = np.isin(x, goodvalues) >>> ix array([[False, False, False], [ True, True, False], [False, True, False]], dtype=bool) >>> np.where(ix) (array([1, 1, 2]), array([0, 1, 1])) Zlexsorta� lexsort(keys, axis=-1) Perform an indirect sort using a sequence of keys. Given multiple sorting keys, which can be interpreted as columns in a spreadsheet, lexsort returns an array of integer indices that describes the sort order by multiple columns. The last key in the sequence is used for the primary sort order, the second-to-last key for the secondary sort order, and so on. The keys argument must be a sequence of objects that can be converted to arrays of the same shape. If a 2D array is provided for the keys argument, it's rows are interpreted as the sorting keys and sorting is according to the last row, second last row etc. Parameters ---------- keys : (k, N) array or tuple containing k (N,)-shaped sequences The `k` different "columns" to be sorted. The last column (or row if `keys` is a 2D array) is the primary sort key. axis : int, optional Axis to be indirectly sorted. By default, sort over the last axis. Returns ------- indices : (N,) ndarray of ints Array of indices that sort the keys along the specified axis. See Also -------- argsort : Indirect sort. ndarray.sort : In-place sort. sort : Return a sorted copy of an array. Examples -------- Sort names: first by surname, then by name. >>> surnames = ('Hertz', 'Galilei', 'Hertz') >>> first_names = ('Heinrich', 'Galileo', 'Gustav') >>> ind = np.lexsort((first_names, surnames)) >>> ind array([1, 2, 0]) >>> [surnames[i] + ", " + first_names[i] for i in ind] ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich'] Sort two columns of numbers: >>> a = [1,5,1,4,3,4,4] # First column >>> b = [9,4,0,4,0,2,1] # Second column >>> ind = np.lexsort((b,a)) # Sort by a, then by b >>> print(ind) [2 0 4 6 5 3 1] >>> [(a[i],b[i]) for i in ind] [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)] Note that sorting is first according to the elements of ``a``. Secondary sorting is according to the elements of ``b``. A normal ``argsort`` would have yielded: >>> [(a[i],b[i]) for i in np.argsort(a)] [(1, 9), (1, 0), (3, 0), (4, 4), (4, 2), (4, 1), (5, 4)] Structured arrays are sorted lexically by ``argsort``: >>> x = np.array([(1,9), (5,4), (1,0), (4,4), (3,0), (4,2), (4,1)], ... dtype=np.dtype([('x', int), ('y', int)])) >>> np.argsort(x) # or np.argsort(x, order=('x', 'y')) array([2, 0, 4, 6, 5, 3, 1]) Zcan_casta� can_cast(from, totype, casting = 'safe') Returns True if cast between data types can occur according to the casting rule. If from is a scalar or array scalar, also returns True if the scalar value can be cast without overflow or truncation to an integer. Parameters ---------- from : dtype, dtype specifier, scalar, or array Data type, scalar, or array to cast from. totype : dtype or dtype specifier Data type to cast to. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. Returns ------- out : bool True if cast can occur according to the casting rule. Notes ----- Starting in NumPy 1.9, can_cast function now returns False in 'safe' casting mode for integer/float dtype and string dtype if the string dtype length is not long enough to store the max integer/float value converted to a string. Previously can_cast in 'safe' mode returned True for integer/float dtype and a string dtype of any length. See also -------- dtype, result_type Examples -------- Basic examples >>> np.can_cast(np.int32, np.int64) True >>> np.can_cast(np.float64, np.complex) True >>> np.can_cast(np.complex, np.float) False >>> np.can_cast('i8', 'f8') True >>> np.can_cast('i8', 'f4') False >>> np.can_cast('i4', 'S4') False Casting scalars >>> np.can_cast(100, 'i1') True >>> np.can_cast(150, 'i1') False >>> np.can_cast(150, 'u1') True >>> np.can_cast(3.5e100, np.float32) False >>> np.can_cast(1000.0, np.float32) True Array scalar checks the value, array does not >>> np.can_cast(np.array(1000.0), np.float32) True >>> np.can_cast(np.array([1000.0]), np.float32) False Using the casting rules >>> np.can_cast('i8', 'i8', 'no') True >>> np.can_cast('<i8', '>i8', 'no') False >>> np.can_cast('<i8', '>i8', 'equiv') True >>> np.can_cast('<i4', '>i8', 'equiv') False >>> np.can_cast('<i4', '>i8', 'safe') True >>> np.can_cast('<i8', '>i4', 'safe') False >>> np.can_cast('<i8', '>i4', 'same_kind') True >>> np.can_cast('<i8', '>u4', 'same_kind') False >>> np.can_cast('<i8', '>u4', 'unsafe') True Z promote_typesa� promote_types(type1, type2) Returns the data type with the smallest size and smallest scalar kind to which both ``type1`` and ``type2`` may be safely cast. The returned data type is always in native byte order. This function is symmetric and associative. Parameters ---------- type1 : dtype or dtype specifier First data type. type2 : dtype or dtype specifier Second data type. Returns ------- out : dtype The promoted data type. Notes ----- .. versionadded:: 1.6.0 Starting in NumPy 1.9, promote_types function now returns a valid string length when given an integer or float dtype as one argument and a string dtype as another argument. Previously it always returned the input string dtype, even if it wasn't long enough to store the max integer/float value converted to a string. See Also -------- result_type, dtype, can_cast Examples -------- >>> np.promote_types('f4', 'f8') dtype('float64') >>> np.promote_types('i8', 'f4') dtype('float64') >>> np.promote_types('>i8', '<c8') dtype('complex128') >>> np.promote_types('i4', 'S8') dtype('S11') Zmin_scalar_typea� min_scalar_type(a) For scalar ``a``, returns the data type with the smallest size and smallest scalar kind which can hold its value. For non-scalar array ``a``, returns the vector's dtype unmodified. Floating point values are not demoted to integers, and complex values are not demoted to floats. Parameters ---------- a : scalar or array_like The value whose minimal data type is to be found. Returns ------- out : dtype The minimal data type. Notes ----- .. versionadded:: 1.6.0 See Also -------- result_type, promote_types, dtype, can_cast Examples -------- >>> np.min_scalar_type(10) dtype('uint8') >>> np.min_scalar_type(-260) dtype('int16') >>> np.min_scalar_type(3.1) dtype('float16') >>> np.min_scalar_type(1e50) dtype('float64') >>> np.min_scalar_type(np.arange(4,dtype='f8')) dtype('float64') Z result_typea� result_type(*arrays_and_dtypes) Returns the type that results from applying the NumPy type promotion rules to the arguments. Type promotion in NumPy works similarly to the rules in languages like C++, with some slight differences. When both scalars and arrays are used, the array's type takes precedence and the actual value of the scalar is taken into account. For example, calculating 3*a, where a is an array of 32-bit floats, intuitively should result in a 32-bit float output. If the 3 is a 32-bit integer, the NumPy rules indicate it can't convert losslessly into a 32-bit float, so a 64-bit float should be the result type. By examining the value of the constant, '3', we see that it fits in an 8-bit integer, which can be cast losslessly into the 32-bit float. Parameters ---------- arrays_and_dtypes : list of arrays and dtypes The operands of some operation whose result type is needed. Returns ------- out : dtype The result type. See also -------- dtype, promote_types, min_scalar_type, can_cast Notes ----- .. versionadded:: 1.6.0 The specific algorithm used is as follows. Categories are determined by first checking which of boolean, integer (int/uint), or floating point (float/complex) the maximum kind of all the arrays and the scalars are. If there are only scalars or the maximum category of the scalars is higher than the maximum category of the arrays, the data types are combined with :func:`promote_types` to produce the return value. Otherwise, `min_scalar_type` is called on each array, and the resulting data types are all combined with :func:`promote_types` to produce the return value. The set of int values is not a subset of the uint values for types with the same number of bits, something not reflected in :func:`min_scalar_type`, but handled as a special case in `result_type`. Examples -------- >>> np.result_type(3, np.arange(7, dtype='i1')) dtype('int8') >>> np.result_type('i4', 'c8') dtype('complex128') >>> np.result_type(3.0, -2) dtype('float64') Z newbuffera newbuffer(size) Return a new uninitialized buffer object. Parameters ---------- size : int Size in bytes of returned buffer object. Returns ------- newbuffer : buffer object Returned, uninitialized buffer object of `size` bytes. � getbufferaa getbuffer(obj [,offset[, size]]) Create a buffer object from the given object referencing a slice of length size starting at offset. Default is the entire buffer. A read-write buffer is attempted followed by a read-only buffer. Parameters ---------- obj : object offset : int, optional size : int, optional Returns ------- buffer_obj : buffer Examples -------- >>> buf = np.getbuffer(np.ones(5), 1, 3) >>> len(buf) 3 >>> buf[0] '\x00' >>> buf <read-write buffer for 0x8af1e70, size 3, offset 1 at 0x8ba4ec0> �dota dot(a, b, out=None) Dot product of two arrays. For 2-D arrays it is equivalent to matrix multiplication, and for 1-D arrays to inner product of vectors (without complex conjugation). For N dimensions it is a sum product over the last axis of `a` and the second-to-last of `b`:: dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m]) Parameters ---------- a : array_like First argument. b : array_like Second argument. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for `dot(a,b)`. This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible. Returns ------- output : ndarray Returns the dot product of `a` and `b`. If `a` and `b` are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If `out` is given, then it is returned. Raises ------ ValueError If the last dimension of `a` is not the same size as the second-to-last dimension of `b`. See Also -------- vdot : Complex-conjugating dot product. tensordot : Sum products over arbitrary axes. einsum : Einstein summation convention. matmul : '@' operator as method with out parameter. Examples -------- >>> np.dot(3, 4) 12 Neither argument is complex-conjugated: >>> np.dot([2j, 3j], [2j, 3j]) (-13+0j) For 2-D arrays it is the matrix product: >>> a = [[1, 0], [0, 1]] >>> b = [[4, 1], [2, 2]] >>> np.dot(a, b) array([[4, 1], [2, 2]]) >>> a = np.arange(3*4*5*6).reshape((3,4,5,6)) >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3)) >>> np.dot(a, b)[2,3,2,1,2,2] 499128 >>> sum(a[2,3,2,:] * b[1,2,:,2]) 499128 �matmulap matmul(a, b, out=None) Matrix product of two arrays. The behavior depends on the arguments in the following way. - If both arguments are 2-D they are multiplied like conventional matrices. - If either argument is N-D, N > 2, it is treated as a stack of matrices residing in the last two indexes and broadcast accordingly. - If the first argument is 1-D, it is promoted to a matrix by prepending a 1 to its dimensions. After matrix multiplication the prepended 1 is removed. - If the second argument is 1-D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed. Multiplication by a scalar is not allowed, use ``*`` instead. Note that multiplying a stack of matrices with a vector will result in a stack of vectors, but matmul will not recognize it as such. ``matmul`` differs from ``dot`` in two important ways. - Multiplication by scalars is not allowed. - Stacks of matrices are broadcast together as if the matrices were elements. .. warning:: This function is preliminary and included in NumPy 1.10.0 for testing and documentation. Its semantics will not change, but the number and order of the optional arguments will. .. versionadded:: 1.10.0 Parameters ---------- a : array_like First argument. b : array_like Second argument. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for `dot(a,b)`. This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible. Returns ------- output : ndarray Returns the dot product of `a` and `b`. If `a` and `b` are both 1-D arrays then a scalar is returned; otherwise an array is returned. If `out` is given, then it is returned. Raises ------ ValueError If the last dimension of `a` is not the same size as the second-to-last dimension of `b`. If scalar value is passed. See Also -------- vdot : Complex-conjugating dot product. tensordot : Sum products over arbitrary axes. einsum : Einstein summation convention. dot : alternative matrix product with different broadcasting rules. Notes ----- The matmul function implements the semantics of the `@` operator introduced in Python 3.5 following PEP465. Examples -------- For 2-D arrays it is the matrix product: >>> a = [[1, 0], [0, 1]] >>> b = [[4, 1], [2, 2]] >>> np.matmul(a, b) array([[4, 1], [2, 2]]) For 2-D mixed with 1-D, the result is the usual. >>> a = [[1, 0], [0, 1]] >>> b = [1, 2] >>> np.matmul(a, b) array([1, 2]) >>> np.matmul(b, a) array([1, 2]) Broadcasting is conventional for stacks of arrays >>> a = np.arange(2*2*4).reshape((2,2,4)) >>> b = np.arange(2*2*4).reshape((2,4,2)) >>> np.matmul(a,b).shape (2, 2, 2) >>> np.matmul(a,b)[0,1,1] 98 >>> sum(a[0,1,:] * b[0,:,1]) 98 Vector, vector returns the scalar inner product, but neither argument is complex-conjugated: >>> np.matmul([2j, 3j], [2j, 3j]) (-13+0j) Scalar multiplication raises an error. >>> np.matmul([1,2], 3) Traceback (most recent call last): ... ValueError: Scalar operands are not allowed, use '*' instead Zc_einsuma c_einsum(subscripts, *operands, out=None, dtype=None, order='K', casting='safe') Evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional array operations can be represented in a simple fashion. This function provides a way to compute such summations. The best way to understand this function is to try the examples below, which show how many common NumPy functions can be implemented as calls to `einsum`. This is the core C function. Parameters ---------- subscripts : str Specifies the subscripts for summation. operands : list of array_like These are the arrays for the operation. out : ndarray, optional If provided, the calculation is done into this array. dtype : {data-type, None}, optional If provided, forces the calculation to use the data type specified. Note that you may have to also give a more liberal `casting` parameter to allow the conversions. Default is None. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the output. 'C' means it should be C contiguous. 'F' means it should be Fortran contiguous, 'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise. 'K' means it should be as close to the layout as the inputs as is possible, including arbitrarily permuted axes. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Setting this to 'unsafe' is not recommended, as it can adversely affect accumulations. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. Default is 'safe'. Returns ------- output : ndarray The calculation based on the Einstein summation convention. See Also -------- einsum, dot, inner, outer, tensordot Notes ----- .. versionadded:: 1.6.0 The subscripts string is a comma-separated list of subscript labels, where each label refers to a dimension of the corresponding operand. Repeated subscripts labels in one operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent to ``np.trace(a)``. Whenever a label is repeated, it is summed, so ``np.einsum('i,i', a, b)`` is equivalent to ``np.inner(a,b)``. If a label appears only once, it is not summed, so ``np.einsum('i', a)`` produces a view of ``a`` with no changes. The order of labels in the output is by default alphabetical. This means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while ``np.einsum('ji', a)`` takes its transpose. The output can be controlled by specifying output subscript labels as well. This specifies the label order, and allows summing to be disallowed or forced when desired. The call ``np.einsum('i->', a)`` is like ``np.sum(a, axis=-1)``, and ``np.einsum('ii->i', a)`` is like ``np.diag(a)``. The difference is that `einsum` does not allow broadcasting by default. To enable and control broadcasting, use an ellipsis. Default NumPy-style broadcasting is done by adding an ellipsis to the left of each term, like ``np.einsum('...ii->...i', a)``. To take the trace along the first and last axes, you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix product with the left-most indices instead of rightmost, you can do ``np.einsum('ij...,jk...->ik...', a, b)``. When there is only one operand, no axes are summed, and no output parameter is provided, a view into the operand is returned instead of a new array. Thus, taking the diagonal as ``np.einsum('ii->i', a)`` produces a view. An alternative way to provide the subscripts and operands is as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``. The examples below have corresponding `einsum` calls with the two parameter methods. .. versionadded:: 1.10.0 Views returned from einsum are now writeable whenever the input array is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now have the same effect as ``np.swapaxes(a, 0, 2)`` and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal of a 2D array. Examples -------- >>> a = np.arange(25).reshape(5,5) >>> b = np.arange(5) >>> c = np.arange(6).reshape(2,3) >>> np.einsum('ii', a) 60 >>> np.einsum(a, [0,0]) 60 >>> np.trace(a) 60 >>> np.einsum('ii->i', a) array([ 0, 6, 12, 18, 24]) >>> np.einsum(a, [0,0], [0]) array([ 0, 6, 12, 18, 24]) >>> np.diag(a) array([ 0, 6, 12, 18, 24]) >>> np.einsum('ij,j', a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum(a, [0,1], b, [1]) array([ 30, 80, 130, 180, 230]) >>> np.dot(a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum('...j,j', a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum('ji', c) array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum(c, [1,0]) array([[0, 3], [1, 4], [2, 5]]) >>> c.T array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum('..., ...', 3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum(3, [Ellipsis], c, [Ellipsis]) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.multiply(3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum('i,i', b, b) 30 >>> np.einsum(b, [0], b, [0]) 30 >>> np.inner(b,b) 30 >>> np.einsum('i,j', np.arange(2)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.einsum(np.arange(2)+1, [0], b, [1]) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.outer(np.arange(2)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.einsum('i...->...', a) array([50, 55, 60, 65, 70]) >>> np.einsum(a, [0,Ellipsis], [Ellipsis]) array([50, 55, 60, 65, 70]) >>> np.sum(a, axis=0) array([50, 55, 60, 65, 70]) >>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> np.einsum('ijk,jil->kl', a, b) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3]) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> np.tensordot(a,b, axes=([1,0],[0,1])) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> a = np.arange(6).reshape((3,2)) >>> b = np.arange(12).reshape((4,3)) >>> np.einsum('ki,jk->ij', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> np.einsum('ki,...k->i...', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> np.einsum('k...,jk', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> # since version 1.10.0 >>> a = np.zeros((3, 3)) >>> np.einsum('ii->i', a)[:] = 1 >>> a array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) Zvdota� vdot(a, b) Return the dot product of two vectors. The vdot(`a`, `b`) function handles complex numbers differently than dot(`a`, `b`). If the first argument is complex the complex conjugate of the first argument is used for the calculation of the dot product. Note that `vdot` handles multidimensional arrays differently than `dot`: it does *not* perform a matrix product, but flattens input arguments to 1-D vectors first. Consequently, it should only be used for vectors. Parameters ---------- a : array_like If `a` is complex the complex conjugate is taken before calculation of the dot product. b : array_like Second argument to the dot product. Returns ------- output : ndarray Dot product of `a` and `b`. Can be an int, float, or complex depending on the types of `a` and `b`. See Also -------- dot : Return the dot product without using the complex conjugate of the first argument. Examples -------- >>> a = np.array([1+2j,3+4j]) >>> b = np.array([5+6j,7+8j]) >>> np.vdot(a, b) (70-8j) >>> np.vdot(b, a) (70+8j) Note that higher-dimensional arrays are flattened! >>> a = np.array([[1, 4], [5, 6]]) >>> b = np.array([[4, 1], [2, 2]]) >>> np.vdot(a, b) 30 >>> np.vdot(b, a) 30 >>> 1*4 + 4*1 + 5*2 + 6*2 30 Zndarraya� ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None) An array object represents a multidimensional, homogeneous array of fixed-size items. An associated data-type object describes the format of each element in the array (its byte-order, how many bytes it occupies in memory, whether it is an integer, a floating point number, or something else, etc.) Arrays should be constructed using `array`, `zeros` or `empty` (refer to the See Also section below). The parameters given here refer to a low-level method (`ndarray(...)`) for instantiating an array. For more information, refer to the `numpy` module and examine the methods and attributes of an array. Parameters ---------- (for the __new__ method; see Notes below) shape : tuple of ints Shape of created array. dtype : data-type, optional Any object that can be interpreted as a numpy data type. buffer : object exposing buffer interface, optional Used to fill the array with data. offset : int, optional Offset of array data in buffer. strides : tuple of ints, optional Strides of data in memory. order : {'C', 'F'}, optional Row-major (C-style) or column-major (Fortran-style) order. Attributes ---------- T : ndarray Transpose of the array. data : buffer The array's elements, in memory. dtype : dtype object Describes the format of the elements in the array. flags : dict Dictionary containing information related to memory use, e.g., 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. flat : numpy.flatiter object Flattened version of the array as an iterator. The iterator allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for assignment examples; TODO). imag : ndarray Imaginary part of the array. real : ndarray Real part of the array. size : int Number of elements in the array. itemsize : int The memory use of each array element in bytes. nbytes : int The total number of bytes required to store the array data, i.e., ``itemsize * size``. ndim : int The array's number of dimensions. shape : tuple of ints Shape of the array. strides : tuple of ints The step-size required to move from one element to the next in memory. For example, a contiguous ``(3, 4)`` array of type ``int16`` in C-order has strides ``(8, 2)``. This implies that to move from element to element in memory requires jumps of 2 bytes. To move from row-to-row, one needs to jump 8 bytes at a time (``2 * 4``). ctypes : ctypes object Class containing properties of the array needed for interaction with ctypes. base : ndarray If the array is a view into another array, that array is its `base` (unless that array is also a view). The `base` array is where the array data is actually stored. See Also -------- array : Construct an array. zeros : Create an array, each element of which is zero. empty : Create an array, but leave its allocated memory unchanged (i.e., it contains "garbage"). dtype : Create a data-type. Notes ----- There are two modes of creating an array using ``__new__``: 1. If `buffer` is None, then only `shape`, `dtype`, and `order` are used. 2. If `buffer` is an object exposing the buffer interface, then all keywords are interpreted. No ``__init__`` method is needed because the array is fully initialized after the ``__new__`` method. Examples -------- These examples illustrate the low-level `ndarray` constructor. Refer to the `See Also` section above for easier ways of constructing an ndarray. First mode, `buffer` is None: >>> np.ndarray(shape=(2,2), dtype=float, order='F') array([[ -1.13698227e+002, 4.25087011e-303], [ 2.88528414e-306, 3.27025015e-309]]) #random Second mode: >>> np.ndarray((2,), buffer=np.array([1,2,3]), ... offset=np.int_().itemsize, ... dtype=int) # offset = 1*itemsize, i.e. skip first element array([2, 3]) )Z__array_interface__z Array protocol: Python side.)Z__array_finalize__zNone.)Z__array_priority__zArray priority.)Z__array_struct__z Array protocol: C-struct side.)Z_as_parameter_zrAllow the array to be interpreted as a ctypes object by returning the data-memory location as an integer )r a: Base object if memory is from some other object. Examples -------- The base of an array that owns its memory is None: >>> x = np.array([1,2,3,4]) >>> x.base is None True Slicing creates a view, whose memory is shared with x: >>> y = x[2:] >>> y.base is x True )�ctypesa� An object to simplify the interaction of the array with the ctypes module. This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library. Parameters ---------- None Returns ------- c : Python object Possessing attributes data, shape, strides, etc. See Also -------- numpy.ctypeslib Notes ----- Below are the public attributes of this object which were documented in "Guide to NumPy" (we have omitted undocumented public attributes, as well as documented private attributes): * data: A pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as self._array_interface_['data'][0]. * shape (c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to dtype('p') on this platform. This base-type could be c_int, c_long, or c_longlong depending on the platform. The c_intp type is defined accordingly in numpy.ctypeslib. The ctypes array contains the shape of the underlying array. * strides (c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array. * data_as(obj): Return the data pointer cast to a particular c-types object. For example, calling self._as_parameter_ is equivalent to self.data_as(ctypes.c_void_p). Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: self.data_as(ctypes.POINTER(ctypes.c_double)). * shape_as(obj): Return the shape tuple as an array of some other c-types type. For example: self.shape_as(ctypes.c_short). * strides_as(obj): Return the strides tuple as an array of some other c-types type. For example: self.strides_as(ctypes.c_longlong). Be careful using the ctypes attribute - especially on temporary arrays or arrays constructed on the fly. For example, calling ``(a+b).ctypes.data_as(ctypes.c_void_p)`` returns a pointer to memory that is invalid because the array created as (a+b) is deallocated before the next Python statement. You can avoid this problem using either ``c=a+b`` or ``ct=(a+b).ctypes``. In the latter case, ct will hold a reference to the array until ct is deleted or re-assigned. If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the as parameter attribute which will return an integer equal to the data attribute. Examples -------- >>> import ctypes >>> x array([[0, 1], [2, 3]]) >>> x.ctypes.data 30439712 >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long)) <ctypes.LP_c_long object at 0x01F01300> >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long)).contents c_long(0) >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_longlong)).contents c_longlong(4294967296L) >>> x.ctypes.shape <numpy.core._internal.c_long_Array_2 object at 0x01FFD580> >>> x.ctypes.shape_as(ctypes.c_long) <numpy.core._internal.c_long_Array_2 object at 0x01FCE620> >>> x.ctypes.strides <numpy.core._internal.c_long_Array_2 object at 0x01FCE620> >>> x.ctypes.strides_as(ctypes.c_longlong) <numpy.core._internal.c_longlong_Array_2 object at 0x01F01300> )�dataz?Python buffer object pointing to the start of the array's data.)�dtypeaR Data-type of the array's elements. Parameters ---------- None Returns ------- d : numpy dtype object See Also -------- numpy.dtype Examples -------- >>> x array([[0, 1], [2, 3]]) >>> x.dtype dtype('int32') >>> type(x.dtype) <type 'numpy.dtype'> )�imagz� The imaginary part of the array. Examples -------- >>> x = np.sqrt([1+0j, 0+1j]) >>> x.imag array([ 0. , 0.70710678]) >>> x.imag.dtype dtype('float64') )�itemsizez� Length of one array element in bytes. Examples -------- >>> x = np.array([1,2,3], dtype=np.float64) >>> x.itemsize 8 >>> x = np.array([1,2,3], dtype=np.complex128) >>> x.itemsize 16 )�flagsa� Information about the memory layout of the array. Attributes ---------- C_CONTIGUOUS (C) The data is in a single, C-style contiguous segment. F_CONTIGUOUS (F) The data is in a single, Fortran-style contiguous segment. OWNDATA (O) The array owns the memory it uses or borrows it from another object. WRITEABLE (W) The data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception. ALIGNED (A) The data and all elements are aligned appropriately for the hardware. UPDATEIFCOPY (U) This array is a copy of some other array. When this array is deallocated, the base array will be updated with the contents of this array. FNC F_CONTIGUOUS and not C_CONTIGUOUS. FORC F_CONTIGUOUS or C_CONTIGUOUS (one-segment test). BEHAVED (B) ALIGNED and WRITEABLE. CARRAY (CA) BEHAVED and C_CONTIGUOUS. FARRAY (FA) BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS. Notes ----- The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``), or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag names are only supported in dictionary access. Only the UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling `ndarray.setflags`. The array flags cannot be set arbitrarily: - UPDATEIFCOPY can only be set ``False``. - ALIGNED can only be set ``True`` if the data is truly aligned. - WRITEABLE can only be set ``True`` if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string. Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays. Even for contiguous arrays a stride for a given dimension ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1`` or the array has no elements. It does *not* generally hold that ``self.strides[-1] == self.itemsize`` for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for Fortran-style contiguous arrays is true. )�flata� A 1-D iterator over the array. This is a `numpy.flatiter` instance, which acts similarly to, but is not a subclass of, Python's built-in iterator object. See Also -------- flatten : Return a copy of the array collapsed into one dimension. flatiter Examples -------- >>> x = np.arange(1, 7).reshape(2, 3) >>> x array([[1, 2, 3], [4, 5, 6]]) >>> x.flat[3] 4 >>> x.T array([[1, 4], [2, 5], [3, 6]]) >>> x.T.flat[3] 5 >>> type(x.flat) <type 'numpy.flatiter'> An assignment example: >>> x.flat = 3; x array([[3, 3, 3], [3, 3, 3]]) >>> x.flat[[1,4]] = 1; x array([[3, 1, 3], [3, 1, 3]]) )�nbytesa? Total bytes consumed by the elements of the array. Notes ----- Does not include memory consumed by non-element attributes of the array object. Examples -------- >>> x = np.zeros((3,5,2), dtype=np.complex128) >>> x.nbytes 480 >>> np.prod(x.shape) * x.itemsize 480 )r z� Number of array dimensions. Examples -------- >>> x = np.array([1, 2, 3]) >>> x.ndim 1 >>> y = np.zeros((2, 3, 4)) >>> y.ndim 3 )�reala The real part of the array. Examples -------- >>> x = np.sqrt([1+0j, 0+1j]) >>> x.real array([ 1. , 0.70710678]) >>> x.real.dtype dtype('float64') See Also -------- numpy.real : equivalent function )r a� Tuple of array dimensions. Notes ----- May be used to "reshape" the array, as long as this would not require a change in the total number of elements Examples -------- >>> x = np.array([1, 2, 3, 4]) >>> x.shape (4,) >>> y = np.zeros((2, 3, 4)) >>> y.shape (2, 3, 4) >>> y.shape = (3, 8) >>> y array([[ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.]]) >>> y.shape = (3, 6) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: total size of new array must be unchanged )r a Number of elements in the array. Equivalent to ``np.prod(a.shape)``, i.e., the product of the array's dimensions. Examples -------- >>> x = np.zeros((3, 5, 2), dtype=np.complex128) >>> x.size 30 >>> np.prod(x.shape) 30 )�stridesa� Tuple of bytes to step in each dimension when traversing an array. The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a` is:: offset = sum(np.array(i) * a.strides) A more detailed explanation of strides can be found in the "ndarray.rst" file in the NumPy reference guide. Notes ----- Imagine an array of 32-bit integers (each 4 bytes):: x = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32) This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array `x` will be ``(20, 4)``. See Also -------- numpy.lib.stride_tricks.as_strided Examples -------- >>> y = np.reshape(np.arange(2*3*4), (2,3,4)) >>> y array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> y.strides (48, 16, 4) >>> y[1,1,1] 17 >>> offset=sum(y.strides * np.array((1,1,1))) >>> offset/y.itemsize 17 >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) >>> x.strides (32, 4, 224, 1344) >>> i = np.array([3,5,2,2]) >>> offset = sum(i * x.strides) >>> x[3,5,2,2] 813 >>> offset / x.itemsize 813 )�Ta� Same as self.transpose(), except that self is returned if self.ndim < 2. Examples -------- >>> x = np.array([[1.,2.],[3.,4.]]) >>> x array([[ 1., 2.], [ 3., 4.]]) >>> x.T array([[ 1., 3.], [ 2., 4.]]) >>> x = np.array([1.,2.,3.,4.]) >>> x array([ 1., 2., 3., 4.]) >>> x.T array([ 1., 2., 3., 4.]) )r z� a.__array__(|dtype) -> reference if type unchanged, copy otherwise. Returns either a new reference to self if dtype is not given or a new array of provided data type if dtype is different from the current dtype of the array. )Z__array_prepare__zLa.__array_prepare__(obj) -> Object of same type as ndarray object obj. )Z__array_wrap__zGa.__array_wrap__(obj) -> Object of same type as ndarray object a. )�__copy__a� a.__copy__([order]) Return a copy of the array. Parameters ---------- order : {'C', 'F', 'A'}, optional If order is 'C' (False) then the result is contiguous (default). If order is 'Fortran' (True) then the result has fortran order. If order is 'Any' (None) then the result has fortran order only if the array already is in fortran order. )� __deepcopy__z_a.__deepcopy__() -> Deep copy of array. Used if copy.deepcopy is called on an array. )� __reduce__z'a.__reduce__() For pickling. )� __setstate__af a.__setstate__(version, shape, dtype, isfortran, rawdata) For unpickling. Parameters ---------- version : int optional pickle version. If omitted defaults to 0. shape : tuple dtype : data-type isFortran : bool rawdata : string or list a binary string with the data (or a list if 'a' is an object array) )�allz� a.all(axis=None, out=None, keepdims=False) Returns True if all elements evaluate to True. Refer to `numpy.all` for full documentation. See Also -------- numpy.all : equivalent function )�anyz� a.any(axis=None, out=None, keepdims=False) Returns True if any of the elements of `a` evaluate to True. Refer to `numpy.any` for full documentation. See Also -------- numpy.any : equivalent function )�argmaxz� a.argmax(axis=None, out=None) Return indices of the maximum values along the given axis. Refer to `numpy.argmax` for full documentation. See Also -------- numpy.argmax : equivalent function )�argminz� a.argmin(axis=None, out=None) Return indices of the minimum values along the given axis of `a`. Refer to `numpy.argmin` for detailed documentation. See Also -------- numpy.argmin : equivalent function )�argsortz� a.argsort(axis=-1, kind='quicksort', order=None) Returns the indices that would sort this array. Refer to `numpy.argsort` for full documentation. See Also -------- numpy.argsort : equivalent function )Z argpartitiona! a.argpartition(kth, axis=-1, kind='introselect', order=None) Returns the indices that would partition this array. Refer to `numpy.argpartition` for full documentation. .. versionadded:: 1.8.0 See Also -------- numpy.argpartition : equivalent function )�astypea� a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) Copy of the array, cast to a specified type. Parameters ---------- dtype : str or dtype Typecode or data-type to which the array is cast. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout order of the result. 'C' means C order, 'F' means Fortran order, 'A' means 'F' order if all the arrays are Fortran contiguous, 'C' order otherwise, and 'K' means as close to the order the array elements appear in memory as possible. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'unsafe' for backwards compatibility. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. subok : bool, optional If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array. copy : bool, optional By default, astype always returns a newly allocated array. If this is set to false, and the `dtype`, `order`, and `subok` requirements are satisfied, the input array is returned instead of a copy. Returns ------- arr_t : ndarray Unless `copy` is False and the other conditions for returning the input array are satisfied (see description for `copy` input parameter), `arr_t` is a new array of the same shape as the input array, with dtype, order given by `dtype`, `order`. Notes ----- Starting in NumPy 1.9, astype method now returns an error if the string dtype to cast to is not long enough in 'safe' casting mode to hold the max value of integer/float array that is being casted. Previously the casting was allowed even if the result was truncated. Raises ------ ComplexWarning When casting from complex to float or int. To avoid this, one should use ``a.real.astype(t)``. Examples -------- >>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5]) >>> x.astype(int) array([1, 2, 2]) )�byteswapa] a.byteswap(inplace) Swap the bytes of the array elements Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place. Parameters ---------- inplace : bool, optional If ``True``, swap bytes in-place, default is ``False``. Returns ------- out : ndarray The byteswapped array. If `inplace` is ``True``, this is a view to self. Examples -------- >>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322'] Arrays of strings are not swapped >>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3') )�choosez� a.choose(choices, out=None, mode='raise') Use an index array to construct a new array from a set of choices. Refer to `numpy.choose` for full documentation. See Also -------- numpy.choose : equivalent function )�clipa a.clip(min=None, max=None, out=None) Return an array whose values are limited to ``[min, max]``. One of max or min must be given. Refer to `numpy.clip` for full documentation. See Also -------- numpy.clip : equivalent function )�compressz� a.compress(condition, axis=None, out=None) Return selected slices of this array along given axis. Refer to `numpy.compress` for full documentation. See Also -------- numpy.compress : equivalent function )�conjz� a.conj() Complex-conjugate all elements. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function )� conjugatez� a.conjugate() Return the complex conjugate, element-wise. Refer to `numpy.conjugate` for full documentation. See Also -------- numpy.conjugate : equivalent function )r aE a.copy(order='C') Return a copy of the array. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :func:numpy.copy are very similar, but have different default values for their order= arguments.) See also -------- numpy.copy numpy.copyto Examples -------- >>> x = np.array([[1,2,3],[4,5,6]], order='F') >>> y = x.copy() >>> x.fill(0) >>> x array([[0, 0, 0], [0, 0, 0]]) >>> y array([[1, 2, 3], [4, 5, 6]]) >>> y.flags['C_CONTIGUOUS'] True )�cumprodz� a.cumprod(axis=None, dtype=None, out=None) Return the cumulative product of the elements along the given axis. Refer to `numpy.cumprod` for full documentation. See Also -------- numpy.cumprod : equivalent function )�cumsumz� a.cumsum(axis=None, dtype=None, out=None) Return the cumulative sum of the elements along the given axis. Refer to `numpy.cumsum` for full documentation. See Also -------- numpy.cumsum : equivalent function )�diagonala� a.diagonal(offset=0, axis1=0, axis2=1) Return specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed. Refer to :func:`numpy.diagonal` for full documentation. See Also -------- numpy.diagonal : equivalent function )r a� a.dot(b, out=None) Dot product of two arrays. Refer to `numpy.dot` for full documentation. See Also -------- numpy.dot : equivalent function Examples -------- >>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]]) This array method can be conveniently chained: >>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]]) )�dumpz�a.dump(file) Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load. Parameters ---------- file : str A string naming the dump file. )�dumpsz� a.dumps() Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array. Parameters ---------- None )�filla\ a.fill(value) Fill the array with a scalar value. Parameters ---------- value : scalar All elements of `a` will be assigned this value. Examples -------- >>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.]) )�flattena� a.flatten(order='C') Return a copy of the array collapsed into one dimension. Parameters ---------- order : {'C', 'F', 'A', 'K'}, optional 'C' means to flatten in row-major (C-style) order. 'F' means to flatten in column-major (Fortran- style) order. 'A' means to flatten in column-major order if `a` is Fortran *contiguous* in memory, row-major order otherwise. 'K' means to flatten `a` in the order the elements occur in memory. The default is 'C'. Returns ------- y : ndarray A copy of the input array, flattened to one dimension. See Also -------- ravel : Return a flattened array. flat : A 1-D flat iterator over the array. Examples -------- >>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4]) )�getfielda� a.getfield(dtype, offset=0) Returns a field of the given array as a certain type. A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes. Parameters ---------- dtype : str or dtype The data type of the view. The dtype size of the view can not be larger than that of the array itself. offset : int Number of bytes to skip before beginning the element view. Examples -------- >>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]]) By choosing an offset of 8 bytes we can select the complex part of the array for our view: >>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]]) )�itema� a.item(*args) Copy an element of an array to a standard Python scalar and return it. Parameters ---------- \*args : Arguments (variable number and type) * none: in this case, the method only works for arrays with one element (`a.size == 1`), which element is copied into a standard Python scalar object and returned. * int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return. * tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array. Returns ------- z : Standard Python scalar object A copy of the specified element of the array as a suitable Python scalar Notes ----- When the data type of `a` is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned. `item` is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python's optimized math. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3 )�itemseta� a.itemset(*args) Insert scalar into an array (scalar is cast to array's dtype, if possible) There must be at least 1 argument, and define the last argument as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster than ``a[args] = item``. The item should be a scalar value and `args` must select a single item in the array `a`. Parameters ---------- \*args : Arguments If one argument: a scalar, only used in case `a` is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple. Notes ----- Compared to indexing syntax, `itemset` provides some speed increase for placing a scalar into a particular location in an `ndarray`, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when using `itemset` (and `item`) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration. Examples -------- >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]]) )�maxz� a.max(axis=None, out=None) Return the maximum along a given axis. Refer to `numpy.amax` for full documentation. See Also -------- numpy.amax : equivalent function )�meanz� a.mean(axis=None, dtype=None, out=None, keepdims=False) Returns the average of the array elements along given axis. Refer to `numpy.mean` for full documentation. See Also -------- numpy.mean : equivalent function )�minz� a.min(axis=None, out=None, keepdims=False) Return the minimum along a given axis. Refer to `numpy.amin` for full documentation. See Also -------- numpy.amin : equivalent function Z shares_memorya� shares_memory(a, b, max_work=None) Determine if two arrays share memory Parameters ---------- a, b : ndarray Input arrays max_work : int, optional Effort to spend on solving the overlap problem (maximum number of candidate solutions to consider). The following special values are recognized: max_work=MAY_SHARE_EXACT (default) The problem is solved exactly. In this case, the function returns True only if there is an element shared between the arrays. max_work=MAY_SHARE_BOUNDS Only the memory bounds of a and b are checked. Raises ------ numpy.TooHardError Exceeded max_work. Returns ------- out : bool See Also -------- may_share_memory Examples -------- >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9])) False Zmay_share_memorya1 may_share_memory(a, b, max_work=None) Determine if two arrays might share memory A return of True does not necessarily mean that the two arrays share any element. It just means that they *might*. Only the memory bounds of a and b are checked by default. Parameters ---------- a, b : ndarray Input arrays max_work : int, optional Effort to spend on solving the overlap problem. See `shares_memory` for details. Default for ``may_share_memory`` is to do a bounds check. Returns ------- out : bool See Also -------- shares_memory Examples -------- >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9])) False >>> x = np.zeros([3, 4]) >>> np.may_share_memory(x[:,0], x[:,1]) True )� newbyteorderaO arr.newbyteorder(new_order='S') Return the array with the same data viewed with a different byte order. Equivalent to:: arr.view(arr.dtype.newbytorder(new_order)) Changes are also made in all fields and sub-arrays of the array data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications below. `new_order` codes can be any of: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_arr : array New array object with the dtype reflecting given change to the byte order. )�nonzeroz� a.nonzero() Return the indices of the elements that are non-zero. Refer to `numpy.nonzero` for full documentation. See Also -------- numpy.nonzero : equivalent function )�prodz� a.prod(axis=None, dtype=None, out=None, keepdims=False) Return the product of the array elements over the given axis Refer to `numpy.prod` for full documentation. See Also -------- numpy.prod : equivalent function )�ptpz� a.ptp(axis=None, out=None) Peak to peak (maximum - minimum) value along a given axis. Refer to `numpy.ptp` for full documentation. See Also -------- numpy.ptp : equivalent function )�putz� a.put(indices, values, mode='raise') Set ``a.flat[n] = values[n]`` for all `n` in indices. Refer to `numpy.put` for full documentation. See Also -------- numpy.put : equivalent function Zcopytoa� copyto(dst, src, casting='same_kind', where=None) Copies values from one array to another, broadcasting as necessary. Raises a TypeError if the `casting` rule is violated, and if `where` is provided, it selects which elements to copy. .. versionadded:: 1.7.0 Parameters ---------- dst : ndarray The array into which values are copied. src : array_like The array from which values are copied. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur when copying. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. where : array_like of bool, optional A boolean array which is broadcasted to match the dimensions of `dst`, and selects elements to copy from `src` to `dst` wherever it contains the value True. Zputmaska� putmask(a, mask, values) Changes elements of an array based on conditional and input values. Sets ``a.flat[n] = values[n]`` for each n where ``mask.flat[n]==True``. If `values` is not the same size as `a` and `mask` then it will repeat. This gives behavior different from ``a[mask] = values``. Parameters ---------- a : array_like Target array. mask : array_like Boolean mask array. It has to be the same shape as `a`. values : array_like Values to put into `a` where `mask` is True. If `values` is smaller than `a` it will be repeated. See Also -------- place, put, take, copyto Examples -------- >>> x = np.arange(6).reshape(2, 3) >>> np.putmask(x, x>2, x**2) >>> x array([[ 0, 1, 2], [ 9, 16, 25]]) If `values` is smaller than `a` it is repeated: >>> x = np.arange(5) >>> np.putmask(x, x>1, [-33, -44]) >>> x array([ 0, 1, -33, -44, -33]) )�ravelz� a.ravel([order]) Return a flattened array. Refer to `numpy.ravel` for full documentation. See Also -------- numpy.ravel : equivalent function ndarray.flat : a flat iterator on the array. )�repeatz� a.repeat(repeats, axis=None) Repeat elements of an array. Refer to `numpy.repeat` for full documentation. See Also -------- numpy.repeat : equivalent function )�reshapez� a.reshape(shape, order='C') Returns an array containing the same data with a new shape. Refer to `numpy.reshape` for full documentation. See Also -------- numpy.reshape : equivalent function )�resizea: a.resize(new_shape, refcheck=True) Change shape and size of array in-place. Parameters ---------- new_shape : tuple of ints, or `n` ints Shape of resized array. refcheck : bool, optional If False, reference count will not be checked. Default is True. Returns ------- None Raises ------ ValueError If `a` does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist. SystemError If the `order` keyword argument is specified. This behaviour is a bug in NumPy. See Also -------- resize : Return a new array with the specified shape. Notes ----- This reallocates space for the data area if necessary. Only contiguous arrays (data elements consecutive in memory) can be resized. The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set `refcheck` to False. Examples -------- Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped: >>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]]) >>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]]) Enlarging an array: as above, but missing entries are filled with zeros: >>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]]) Referencing an array prevents resizing... >>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ... Unless `refcheck` is False: >>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]]) )�roundz� a.round(decimals=0, out=None) Return `a` with each element rounded to the given number of decimals. Refer to `numpy.around` for full documentation. See Also -------- numpy.around : equivalent function )� searchsorteda a.searchsorted(v, side='left', sorter=None) Find indices where elements of v should be inserted in a to maintain order. For full documentation, see `numpy.searchsorted` See Also -------- numpy.searchsorted : equivalent function )�setfielda� a.setfield(val, dtype, offset=0) Put a value into a specified place in a field defined by a data-type. Place `val` into `a`'s field defined by `dtype` and beginning `offset` bytes into the field. Parameters ---------- val : object Value to be placed in field. dtype : dtype object Data-type of the field in which to place `val`. offset : int, optional The number of bytes into the field at which to place `val`. Returns ------- None See Also -------- getfield Examples -------- >>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) )�setflagsa a.setflags(write=None, align=None, uic=None) Set array flags WRITEABLE, ALIGNED, and UPDATEIFCOPY, respectively. These Boolean-valued flags affect how numpy interprets the memory area used by `a` (see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The UPDATEIFCOPY flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.) Parameters ---------- write : bool, optional Describes whether or not `a` can be written to. align : bool, optional Describes whether or not `a` is aligned properly for its type. uic : bool, optional Describes whether or not `a` is a copy of another "base" array. Notes ----- Array flags provide information about how the memory area used for the array is to be interpreted. There are 6 Boolean flags in use, only three of which can be changed by the user: UPDATEIFCOPY, WRITEABLE, and ALIGNED. WRITEABLE (W) the data area can be written to; ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler); UPDATEIFCOPY (U) this array is a copy of some other array (referenced by .base). When this array is deallocated, the base array will be updated with the contents of this array. All flags can be accessed using their first (upper case) letter as well as the full name. Examples -------- >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: cannot set UPDATEIFCOPY flag to True )�sorta a.sort(axis=-1, kind='quicksort', order=None) Sort an array, in-place. Parameters ---------- axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'quicksort', 'mergesort', 'heapsort'}, optional Sorting algorithm. Default is 'quicksort'. order : str or list of str, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties. See Also -------- numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort. Notes ----- See ``sort`` for notes on the different sorting algorithms. Examples -------- >>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '<i4')]) )� partitiona� a.partition(kth, axis=-1, kind='introselect', order=None) Rearranges the elements in the array in such a way that value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined. .. versionadded:: 1.8.0 Parameters ---------- kth : int or sequence of ints Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once. axis : int, optional Axis along which to sort. Default is -1, which means sort along the last axis. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect'. order : str or list of str, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties. See Also -------- numpy.partition : Return a parititioned copy of an array. argpartition : Indirect partition. sort : Full sort. Notes ----- See ``np.partition`` for notes on the different algorithms. Examples -------- >>> a = np.array([3, 4, 2, 1]) >>> a.partition(3) >>> a array([2, 1, 3, 4]) >>> a.partition((1, 3)) array([1, 2, 3, 4]) )�squeezez� a.squeeze(axis=None) Remove single-dimensional entries from the shape of `a`. Refer to `numpy.squeeze` for full documentation. See Also -------- numpy.squeeze : equivalent function )�stda a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False) Returns the standard deviation of the array elements along given axis. Refer to `numpy.std` for full documentation. See Also -------- numpy.std : equivalent function )�sumz� a.sum(axis=None, dtype=None, out=None, keepdims=False) Return the sum of the array elements over the given axis. Refer to `numpy.sum` for full documentation. See Also -------- numpy.sum : equivalent function )�swapaxesz� a.swapaxes(axis1, axis2) Return a view of the array with `axis1` and `axis2` interchanged. Refer to `numpy.swapaxes` for full documentation. See Also -------- numpy.swapaxes : equivalent function )�takez� a.take(indices, axis=None, out=None, mode='raise') Return an array formed from the elements of `a` at the given indices. Refer to `numpy.take` for full documentation. See Also -------- numpy.take : equivalent function )�tofilea� a.tofile(fid, sep="", format="%s") Write array to a file as text or binary (default). Data is always written in 'C' order, independent of the order of `a`. The data produced by this method can be recovered using the function fromfile(). Parameters ---------- fid : file or str An open file object, or a string containing a filename. sep : str Separator between array items for text output. If "" (empty), a binary file is written, equivalent to ``file.write(a.tobytes())``. format : str Format string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using "format" % item. Notes ----- This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size. )�tolistay a.tolist() Return the array as a (possibly nested) list. Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible Python type. Parameters ---------- none Returns ------- y : list The possibly nested list of array elements. Notes ----- The array may be recreated, ``a = np.array(a.tolist())``. Examples -------- >>> a = np.array([1, 2]) >>> a.tolist() [1, 2] >>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]] a� a.{name}(order='C') Construct Python bytes containing the raw data bytes in the array. Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object can be produced in either 'C' or 'Fortran', or 'Any' order (the default is 'C'-order). 'Any' order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means 'Fortran' order. {deprecated} Parameters ---------- order : {{'C', 'F', None}}, optional Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array. Returns ------- s : bytes Python bytes exhibiting a copy of `a`'s raw data. Examples -------- >>> x = np.array([[0, 1], [2, 3]]) >>> x.tobytes() b'\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00' �tostringzbThis function is a compatibility alias for tobytes. Despite its name it returns bytes not strings.)�nameZ deprecated�tobytesz.. versionadded:: 1.9.0)�tracez� a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) Return the sum along diagonals of the array. Refer to `numpy.trace` for full documentation. See Also -------- numpy.trace : equivalent function )� transposea� a.transpose(*axes) Returns a view of the array with axes transposed. For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. Parameters ---------- axes : None, tuple of ints, or `n` ints * None or no argument: reverses the order of the axes. * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s `i`-th axis becomes `a.transpose()`'s `j`-th axis. * `n` ints: same as an n-tuple of the same ints (this form is intended simply as a "convenience" alternative to the tuple form) Returns ------- out : ndarray View of `a`, with axes suitably permuted. See Also -------- ndarray.T : Array property returning the array transposed. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]]) )�varz� a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False) Returns the variance of the array elements, along given axis. Refer to `numpy.var` for full documentation. See Also -------- numpy.var : equivalent function )�viewa� a.view(dtype=None, type=None) New view of array with the same data. Parameters ---------- dtype : data-type or ndarray sub-class, optional Data-type descriptor of the returned view, e.g., float32 or int16. The default, None, results in the view having the same data-type as `a`. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting the ``type`` parameter). type : Python type, optional Type of the returned view, e.g., ndarray or matrix. Again, the default None results in type preservation. Notes ----- ``a.view()`` is used two different ways: ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view of the array's memory with a different data-type. This can cause a reinterpretation of the bytes of memory. ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just returns an instance of `ndarray_subclass` that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory. For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance of ``a`` (shown by ``print(a)``). It also depends on exactly how ``a`` is stored in memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results. Examples -------- >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) Viewing array data using a different type and dtype: >>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print(type(y)) <class 'numpy.matrixlib.defmatrix.matrix'> Creating a view on a structured array so it can be used in calculations >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(-1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([ 2., 3.]) Making changes to the view changes the underlying array >>> xv[0,1] = 20 >>> print(x) [(1, 20) (3, 4)] Using a view to convert an array to a recarray: >>> z = x.view(np.recarray) >>> z.a array([1], dtype=int8) Views share data: >>> x[0] = (9, 10) >>> z[0] (9, 10) Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.: >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) >>> y = x[:, 0:2] >>> y array([[1, 2], [4, 5]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: new type not compatible with array. >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 2)], [(4, 5)]], dtype=[('width', '<i2'), ('length', '<i2')]) znumpy.core.umathZ frompyfunca5 frompyfunc(func, nin, nout) Takes an arbitrary Python function and returns a NumPy ufunc. Can be used, for example, to add broadcasting to a built-in Python function (see Examples section). Parameters ---------- func : Python function object An arbitrary Python function. nin : int The number of input arguments. nout : int The number of objects returned by `func`. Returns ------- out : ufunc Returns a NumPy universal function (``ufunc``) object. See Also -------- vectorize : evaluates pyfunc over input arrays using broadcasting rules of numpy Notes ----- The returned ufunc always returns PyObject arrays. Examples -------- Use frompyfunc to add broadcasting to the Python function ``oct``: >>> oct_array = np.frompyfunc(oct, 1, 1) >>> oct_array(np.array((10, 30, 100))) array([012, 036, 0144], dtype=object) >>> np.array((oct(10), oct(30), oct(100))) # for comparison array(['012', '036', '0144'], dtype='|S4') Z geterrobja� geterrobj() Return the current object that defines floating-point error handling. The error object contains all information that defines the error handling behavior in NumPy. `geterrobj` is used internally by the other functions that get and set error handling behavior (`geterr`, `seterr`, `geterrcall`, `seterrcall`). Returns ------- errobj : list The error object, a list containing three elements: [internal numpy buffer size, error mask, error callback function]. The error mask is a single integer that holds the treatment information on all four floating point errors. The information for each error type is contained in three bits of the integer. If we print it in base 8, we can see what treatment is set for "invalid", "under", "over", and "divide" (in that order). The printed string can be interpreted with * 0 : 'ignore' * 1 : 'warn' * 2 : 'raise' * 3 : 'call' * 4 : 'print' * 5 : 'log' See Also -------- seterrobj, seterr, geterr, seterrcall, geterrcall getbufsize, setbufsize Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> np.geterrobj() # first get the defaults [10000, 0, None] >>> def err_handler(type, flag): ... print("Floating point error (%s), with flag %s" % (type, flag)) ... >>> old_bufsize = np.setbufsize(20000) >>> old_err = np.seterr(divide='raise') >>> old_handler = np.seterrcall(err_handler) >>> np.geterrobj() [20000, 2, <function err_handler at 0x91dcaac>] >>> old_err = np.seterr(all='ignore') >>> np.base_repr(np.geterrobj()[1], 8) '0' >>> old_err = np.seterr(divide='warn', over='log', under='call', invalid='print') >>> np.base_repr(np.geterrobj()[1], 8) '4351' Z seterrobja seterrobj(errobj) Set the object that defines floating-point error handling. The error object contains all information that defines the error handling behavior in NumPy. `seterrobj` is used internally by the other functions that set error handling behavior (`seterr`, `seterrcall`). Parameters ---------- errobj : list The error object, a list containing three elements: [internal numpy buffer size, error mask, error callback function]. The error mask is a single integer that holds the treatment information on all four floating point errors. The information for each error type is contained in three bits of the integer. If we print it in base 8, we can see what treatment is set for "invalid", "under", "over", and "divide" (in that order). The printed string can be interpreted with * 0 : 'ignore' * 1 : 'warn' * 2 : 'raise' * 3 : 'call' * 4 : 'print' * 5 : 'log' See Also -------- geterrobj, seterr, geterr, seterrcall, geterrcall getbufsize, setbufsize Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> old_errobj = np.geterrobj() # first get the defaults >>> old_errobj [10000, 0, None] >>> def err_handler(type, flag): ... print("Floating point error (%s), with flag %s" % (type, flag)) ... >>> new_errobj = [20000, 12, err_handler] >>> np.seterrobj(new_errobj) >>> np.base_repr(12, 8) # int for divide=4 ('print') and over=1 ('warn') '14' >>> np.geterr() {'over': 'warn', 'divide': 'print', 'invalid': 'ignore', 'under': 'ignore'} >>> np.geterrcall() is err_handler True Zdigitizea� digitize(x, bins, right=False) Return the indices of the bins to which each value in input array belongs. Each index ``i`` returned is such that ``bins[i-1] <= x < bins[i]`` if `bins` is monotonically increasing, or ``bins[i-1] > x >= bins[i]`` if `bins` is monotonically decreasing. If values in `x` are beyond the bounds of `bins`, 0 or ``len(bins)`` is returned as appropriate. If right is True, then the right bin is closed so that the index ``i`` is such that ``bins[i-1] < x <= bins[i]`` or ``bins[i-1] >= x > bins[i]`` if `bins` is monotonically increasing or decreasing, respectively. Parameters ---------- x : array_like Input array to be binned. Prior to NumPy 1.10.0, this array had to be 1-dimensional, but can now have any shape. bins : array_like Array of bins. It has to be 1-dimensional and monotonic. right : bool, optional Indicating whether the intervals include the right or the left bin edge. Default behavior is (right==False) indicating that the interval does not include the right edge. The left bin end is open in this case, i.e., bins[i-1] <= x < bins[i] is the default behavior for monotonically increasing bins. Returns ------- out : ndarray of ints Output array of indices, of same shape as `x`. Raises ------ ValueError If `bins` is not monotonic. TypeError If the type of the input is complex. See Also -------- bincount, histogram, unique, searchsorted Notes ----- If values in `x` are such that they fall outside the bin range, attempting to index `bins` with the indices that `digitize` returns will result in an IndexError. .. versionadded:: 1.10.0 `np.digitize` is implemented in terms of `np.searchsorted`. This means that a binary search is used to bin the values, which scales much better for larger number of bins than the previous linear search. It also removes the requirement for the input array to be 1-dimensional. Examples -------- >>> x = np.array([0.2, 6.4, 3.0, 1.6]) >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0]) >>> inds = np.digitize(x, bins) >>> inds array([1, 4, 3, 2]) >>> for n in range(x.size): ... print(bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]]) ... 0.0 <= 0.2 < 1.0 4.0 <= 6.4 < 10.0 2.5 <= 3.0 < 4.0 1.0 <= 1.6 < 2.5 >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.]) >>> bins = np.array([0, 5, 10, 15, 20]) >>> np.digitize(x,bins,right=True) array([1, 2, 3, 4, 4]) >>> np.digitize(x,bins,right=False) array([1, 3, 3, 4, 5]) Zbincounta� bincount(x, weights=None, minlength=0) Count number of occurrences of each value in array of non-negative ints. The number of bins (of size 1) is one larger than the largest value in `x`. If `minlength` is specified, there will be at least this number of bins in the output array (though it will be longer if necessary, depending on the contents of `x`). Each bin gives the number of occurrences of its index value in `x`. If `weights` is specified the input array is weighted by it, i.e. if a value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead of ``out[n] += 1``. Parameters ---------- x : array_like, 1 dimension, nonnegative ints Input array. weights : array_like, optional Weights, array of the same shape as `x`. minlength : int, optional A minimum number of bins for the output array. .. versionadded:: 1.6.0 Returns ------- out : ndarray of ints The result of binning the input array. The length of `out` is equal to ``np.amax(x)+1``. Raises ------ ValueError If the input is not 1-dimensional, or contains elements with negative values, or if `minlength` is negative. TypeError If the type of the input is float or complex. See Also -------- histogram, digitize, unique Examples -------- >>> np.bincount(np.arange(5)) array([1, 1, 1, 1, 1]) >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7])) array([1, 3, 1, 1, 0, 0, 0, 1]) >>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23]) >>> np.bincount(x).size == np.amax(x)+1 True The input array needs to be of integer dtype, otherwise a TypeError is raised: >>> np.bincount(np.arange(5, dtype=np.float)) Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: array cannot be safely cast to required type A possible use of ``bincount`` is to perform sums over variable-size chunks of an array, using the ``weights`` keyword. >>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights >>> x = np.array([0, 1, 1, 2, 2, 2]) >>> np.bincount(x, weights=w) array([ 0.3, 0.7, 1.1]) Zravel_multi_indexa� ravel_multi_index(multi_index, dims, mode='raise', order='C') Converts a tuple of index arrays into an array of flat indices, applying boundary modes to the multi-index. Parameters ---------- multi_index : tuple of array_like 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', '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 (default) * 'wrap' -- wrap around * 'clip' -- clip to the range In 'clip' mode, a negative index which would normally wrap will clip to 0 instead. order : {'C', '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 : ndarray An array of indices into the flattened version of an array of dimensions ``dims``. See Also -------- unravel_index Notes ----- .. versionadded:: 1.6.0 Examples -------- >>> arr = np.array([[3,6,6],[4,5,1]]) >>> np.ravel_multi_index(arr, (7,6)) array([22, 41, 37]) >>> np.ravel_multi_index(arr, (7,6), order='F') array([31, 41, 13]) >>> np.ravel_multi_index(arr, (4,6), mode='clip') array([22, 23, 19]) >>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap')) array([12, 13, 13]) >>> np.ravel_multi_index((3,1,4,1), (6,7,8,9)) 1621 Z unravel_indexa� unravel_index(indices, dims, order='C') Converts a flat index or array of flat indices into a tuple of coordinate arrays. Parameters ---------- indices : array_like An integer array whose elements are indices into the flattened version of an array of dimensions ``dims``. Before version 1.6.0, this function accepted just one index value. dims : tuple of ints The shape of the array to use for unraveling ``indices``. order : {'C', 'F'}, optional Determines whether the indices should be viewed as indexing in row-major (C-style) or column-major (Fortran-style) order. .. versionadded:: 1.6.0 Returns ------- unraveled_coords : tuple of ndarray Each array in the tuple has the same shape as the ``indices`` array. See Also -------- ravel_multi_index Examples -------- >>> np.unravel_index([22, 41, 37], (7,6)) (array([3, 6, 6]), array([4, 5, 1])) >>> np.unravel_index([31, 41, 13], (7,6), order='F') (array([3, 6, 6]), array([4, 5, 1])) >>> np.unravel_index(1621, (6,7,8,9)) (3, 1, 4, 1) Z add_docstringz� add_docstring(obj, docstring) Add a docstring to a built-in obj if possible. If the obj already has a docstring raise a RuntimeError If this routine does not know how to add a docstring to the object raise a TypeError Z_add_newdoc_ufuncaI add_ufunc_docstring(ufunc, new_docstring) Replace the docstring for a ufunc with new_docstring. This method will only work if the current docstring for the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.) Parameters ---------- ufunc : numpy.ufunc A ufunc whose current doc is NULL. new_docstring : string The new docstring for the ufunc. Notes ----- This method allocates memory for new_docstring on the heap. Technically this creates a mempory leak, since this memory will not be reclaimed until the end of the program even if the ufunc itself is removed. However this will only be a problem if the user is repeatedly creating ufuncs with no documentation, adding documentation via add_newdoc_ufunc, and then throwing away the ufunc. Zpackbitsa packbits(myarray, axis=None) Packs the elements of a binary-valued array into bits in a uint8 array. The result is padded to full bytes by inserting zero bits at the end. Parameters ---------- myarray : array_like An array of integers or booleans whose elements should be packed to bits. axis : int, optional The dimension over which bit-packing is done. ``None`` implies packing the flattened array. Returns ------- packed : ndarray Array of type uint8 whose elements represent bits corresponding to the logical (0 or nonzero) value of the input elements. The shape of `packed` has the same number of dimensions as the input (unless `axis` is None, in which case the output is 1-D). See Also -------- unpackbits: Unpacks elements of a uint8 array into a binary-valued output array. Examples -------- >>> a = np.array([[[1,0,1], ... [0,1,0]], ... [[1,1,0], ... [0,0,1]]]) >>> b = np.packbits(a, axis=-1) >>> b array([[[160],[64]],[[192],[32]]], dtype=uint8) Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000, and 32 = 0010 0000. Z unpackbitsaG unpackbits(myarray, axis=None) Unpacks elements of a uint8 array into a binary-valued output array. Each element of `myarray` represents a bit-field that should be unpacked into a binary-valued output array. The shape of the output array is either 1-D (if `axis` is None) or the same shape as the input array with unpacking done along the axis specified. Parameters ---------- myarray : ndarray, uint8 type Input array. axis : int, optional Unpacks along this axis. Returns ------- unpacked : ndarray, uint8 type The elements are binary-valued (0 or 1). See Also -------- packbits : Packs the elements of a binary-valued array into bits in a uint8 array. Examples -------- >>> a = np.array([[2], [7], [23]], dtype=np.uint8) >>> a array([[ 2], [ 7], [23]], dtype=uint8) >>> b = np.unpackbits(a, axis=1) >>> b array([[0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8) Zufunca� Functions that operate element by element on whole arrays. To see the documentation for a specific ufunc, use `info`. For example, ``np.info(np.sin)``. Because ufuncs are written in C (for speed) and linked into Python with NumPy's ufunc facility, Python's help() function finds this page whenever help() is called on a ufunc. A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`. Calling ufuncs: =============== op(*x[, out], where=True, **kwargs) Apply `op` to the arguments `*x` elementwise, broadcasting the arguments. The broadcasting rules are: * Dimensions of length 1 may be prepended to either array. * Arrays may be repeated along dimensions of length 1. Parameters ---------- *x : array_like Input arrays. out : ndarray, None, or tuple of ndarray and None, optional Alternate array object(s) in which to put the result; if provided, it must have a shape that the inputs broadcast to. A tuple of arrays (possible only as a keyword argument) must have length equal to the number of outputs; use `None` for outputs to be allocated by the ufunc. where : array_like, optional Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`. Returns ------- r : ndarray or tuple of ndarray `r` will have the shape that the arrays in `x` broadcast to; if `out` is provided, `r` will be equal to `out`. If the function has more than one output, then the result will be a tuple of arrays. )�identityaD The identity value. Data attribute containing the identity element for the ufunc, if it has one. If it does not, the attribute value is None. Examples -------- >>> np.add.identity 0 >>> np.multiply.identity 1 >>> np.power.identity 1 >>> print(np.exp.identity) None )�nargsa� The number of arguments. Data attribute containing the number of arguments the ufunc takes, including optional ones. Notes ----- Typically this value will be one more than what you might expect because all ufuncs take the optional "out" argument. Examples -------- >>> np.add.nargs 3 >>> np.multiply.nargs 3 >>> np.power.nargs 3 >>> np.exp.nargs 2 )�ninz� The number of inputs. Data attribute containing the number of arguments the ufunc treats as input. Examples -------- >>> np.add.nin 2 >>> np.multiply.nin 2 >>> np.power.nin 2 >>> np.exp.nin 1 )�noutae The number of outputs. Data attribute containing the number of arguments the ufunc treats as output. Notes ----- Since all ufuncs can take output arguments, this will always be (at least) 1. Examples -------- >>> np.add.nout 1 >>> np.multiply.nout 1 >>> np.power.nout 1 >>> np.exp.nout 1 )Zntypesau The number of types. The number of numerical NumPy types - of which there are 18 total - on which the ufunc can operate. See Also -------- numpy.ufunc.types Examples -------- >>> np.add.ntypes 18 >>> np.multiply.ntypes 18 >>> np.power.ntypes 17 >>> np.exp.ntypes 7 >>> np.remainder.ntypes 14 )�typesa\ Returns a list with types grouped input->output. Data attribute listing the data-type "Domain-Range" groupings the ufunc can deliver. The data-types are given using the character codes. See Also -------- numpy.ufunc.ntypes Examples -------- >>> np.add.types ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G', 'OO->O'] >>> np.multiply.types ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G', 'OO->O'] >>> np.power.types ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G', 'OO->O'] >>> np.exp.types ['f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O'] >>> np.remainder.types ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'OO->O'] )�reduceaQ reduce(a, axis=0, dtype=None, out=None, keepdims=False) Reduces `a`'s dimension by one, by applying ufunc along one axis. Let :math:`a.shape = (N_0, ..., N_i, ..., N_{M-1})`. Then :math:`ufunc.reduce(a, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` = the result of iterating `j` over :math:`range(N_i)`, cumulatively applying ufunc to each :math:`a[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`. For a one-dimensional array, reduce produces results equivalent to: :: r = op.identity # op = ufunc for i in range(len(A)): r = op(r, A[i]) return r For example, add.reduce() is equivalent to sum(). Parameters ---------- a : array_like The array to act on. axis : None or int or tuple of ints, optional Axis or axes along which a reduction is performed. The default (`axis` = 0) is perform a reduction over the first dimension of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is `None`, a reduction is performed over all the axes. If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. For operations which are either not commutative or not associative, doing a reduction over multiple axes is not well-defined. The ufuncs do not currently raise an exception in this case, but will likely do so in the future. dtype : data-type code, optional The type used to represent the intermediate results. Defaults to the data-type of the output array if this is provided, or the data-type of the input array if no output array is provided. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If not provided or `None`, a freshly-allocated array is returned. For consistency with :ref:`ufunc.__call__`, if given as a keyword, this may be wrapped in a 1-element tuple. .. versionchanged:: 1.13.0 Tuples are allowed for keyword argument. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. .. versionadded:: 1.7.0 Returns ------- r : ndarray The reduced array. If `out` was supplied, `r` is a reference to it. Examples -------- >>> np.multiply.reduce([2,3,5]) 30 A multi-dimensional array example: >>> X = np.arange(8).reshape((2,2,2)) >>> X array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> np.add.reduce(X, 0) array([[ 4, 6], [ 8, 10]]) >>> np.add.reduce(X) # confirm: default axis value is 0 array([[ 4, 6], [ 8, 10]]) >>> np.add.reduce(X, 1) array([[ 2, 4], [10, 12]]) >>> np.add.reduce(X, 2) array([[ 1, 5], [ 9, 13]]) )� accumulateac accumulate(array, axis=0, dtype=None, out=None, keepdims=None) Accumulate the result of applying the operator to all elements. For a one-dimensional array, accumulate produces results equivalent to:: r = np.empty(len(A)) t = op.identity # op = the ufunc being applied to A's elements for i in range(len(A)): t = op(t, A[i]) r[i] = t return r For example, add.accumulate() is equivalent to np.cumsum(). For a multi-dimensional array, accumulate is applied along only one axis (axis zero by default; see Examples below) so repeated use is necessary if one wants to accumulate over multiple axes. Parameters ---------- array : array_like The array to act on. axis : int, optional The axis along which to apply the accumulation; default is zero. dtype : data-type code, optional The data-type used to represent the intermediate results. Defaults to the data-type of the output array if such is provided, or the the data-type of the input array if no output array is provided. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If not provided or `None`, a freshly-allocated array is returned. For consistency with :ref:`ufunc.__call__`, if given as a keyword, this may be wrapped in a 1-element tuple. .. versionchanged:: 1.13.0 Tuples are allowed for keyword argument. keepdims : bool Has no effect. Deprecated, and will be removed in future. Returns ------- r : ndarray The accumulated values. If `out` was supplied, `r` is a reference to `out`. Examples -------- 1-D array examples: >>> np.add.accumulate([2, 3, 5]) array([ 2, 5, 10]) >>> np.multiply.accumulate([2, 3, 5]) array([ 2, 6, 30]) 2-D array examples: >>> I = np.eye(2) >>> I array([[ 1., 0.], [ 0., 1.]]) Accumulate along axis 0 (rows), down columns: >>> np.add.accumulate(I, 0) array([[ 1., 0.], [ 1., 1.]]) >>> np.add.accumulate(I) # no axis specified = axis zero array([[ 1., 0.], [ 1., 1.]]) Accumulate along axis 1 (columns), through rows: >>> np.add.accumulate(I, 1) array([[ 1., 1.], [ 0., 1.]]) )Zreduceata� reduceat(a, indices, axis=0, dtype=None, out=None) Performs a (local) reduce with specified slices over a single axis. For i in ``range(len(indices))``, `reduceat` computes ``ufunc.reduce(a[indices[i]:indices[i+1]])``, which becomes the i-th generalized "row" parallel to `axis` in the final result (i.e., in a 2-D array, for example, if `axis = 0`, it becomes the i-th row, but if `axis = 1`, it becomes the i-th column). There are three exceptions to this: * when ``i = len(indices) - 1`` (so for the last index), ``indices[i+1] = a.shape[axis]``. * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is simply ``a[indices[i]]``. * if ``indices[i] >= len(a)`` or ``indices[i] < 0``, an error is raised. The shape of the output depends on the size of `indices`, and may be larger than `a` (this happens if ``len(indices) > a.shape[axis]``). Parameters ---------- a : array_like The array to act on. indices : array_like Paired indices, comma separated (not colon), specifying slices to reduce. axis : int, optional The axis along which to apply the reduceat. dtype : data-type code, optional The type used to represent the intermediate results. Defaults to the data type of the output array if this is provided, or the data type of the input array if no output array is provided. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If not provided or `None`, a freshly-allocated array is returned. For consistency with :ref:`ufunc.__call__`, if given as a keyword, this may be wrapped in a 1-element tuple. .. versionchanged:: 1.13.0 Tuples are allowed for keyword argument. Returns ------- r : ndarray The reduced values. If `out` was supplied, `r` is a reference to `out`. Notes ----- A descriptive example: If `a` is 1-D, the function `ufunc.accumulate(a)` is the same as ``ufunc.reduceat(a, indices)[::2]`` where `indices` is ``range(len(array) - 1)`` with a zero placed in every other element: ``indices = zeros(2 * len(a) - 1)``, ``indices[1::2] = range(1, len(a))``. Don't be fooled by this attribute's name: `reduceat(a)` is not necessarily smaller than `a`. Examples -------- To take the running sum of four successive values: >>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2] array([ 6, 10, 14, 18]) A 2-D example: >>> x = np.linspace(0, 15, 16).reshape(4,4) >>> x array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [ 12., 13., 14., 15.]]) :: # reduce such that the result has the following five rows: # [row1 + row2 + row3] # [row4] # [row2] # [row3] # [row1 + row2 + row3 + row4] >>> np.add.reduceat(x, [0, 3, 1, 2, 0]) array([[ 12., 15., 18., 21.], [ 12., 13., 14., 15.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [ 24., 28., 32., 36.]]) :: # reduce such that result has the following two columns: # [col1 * col2 * col3, col4] >>> np.multiply.reduceat(x, [0, 3], 1) array([[ 0., 3.], [ 120., 7.], [ 720., 11.], [ 2184., 15.]]) )Zoutera� outer(A, B, **kwargs) Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`. Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of ``op.outer(A, B)`` is an array of dimension M + N such that: .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] = op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}]) For `A` and `B` one-dimensional, this is equivalent to:: r = empty(len(A),len(B)) for i in range(len(A)): for j in range(len(B)): r[i,j] = op(A[i], B[j]) # op = ufunc in question Parameters ---------- A : array_like First array B : array_like Second array kwargs : any Arguments to pass on to the ufunc. Typically `dtype` or `out`. Returns ------- r : ndarray Output array See Also -------- numpy.outer Examples -------- >>> np.multiply.outer([1, 2, 3], [4, 5, 6]) array([[ 4, 5, 6], [ 8, 10, 12], [12, 15, 18]]) A multi-dimensional example: >>> A = np.array([[1, 2, 3], [4, 5, 6]]) >>> A.shape (2, 3) >>> B = np.array([[1, 2, 3, 4]]) >>> B.shape (1, 4) >>> C = np.multiply.outer(A, B) >>> C.shape; C (2, 3, 1, 4) array([[[[ 1, 2, 3, 4]], [[ 2, 4, 6, 8]], [[ 3, 6, 9, 12]]], [[[ 4, 8, 12, 16]], [[ 5, 10, 15, 20]], [[ 6, 12, 18, 24]]]]) )ZataE at(a, indices, b=None) Performs unbuffered in place operation on operand 'a' for elements specified by 'indices'. For addition ufunc, this method is equivalent to `a[indices] += b`, except that results are accumulated for elements that are indexed more than once. For example, `a[[0,0]] += 1` will only increment the first element once because of buffering, whereas `add.at(a, [0,0], 1)` will increment the first element twice. .. versionadded:: 1.8.0 Parameters ---------- a : array_like The array to perform in place operation on. indices : array_like or tuple Array like index object or slice object for indexing into first operand. If first operand has multiple dimensions, indices can be a tuple of array like index objects or slice objects. b : array_like Second operand for ufuncs requiring two operands. Operand must be broadcastable over first operand after indexing or slicing. Examples -------- Set items 0 and 1 to their negative values: >>> a = np.array([1, 2, 3, 4]) >>> np.negative.at(a, [0, 1]) >>> print(a) array([-1, -2, 3, 4]) :: Increment items 0 and 1, and increment item 2 twice: >>> a = np.array([1, 2, 3, 4]) >>> np.add.at(a, [0, 1, 2, 2], 1) >>> print(a) array([2, 3, 5, 4]) :: Add items 0 and 1 in first array to second array, and store results in first array: >>> a = np.array([1, 2, 3, 4]) >>> b = np.array([1, 2]) >>> np.add.at(a, [0, 1], b) >>> print(a) array([2, 4, 3, 4]) r a� dtype(obj, align=False, copy=False) Create a data type object. A numpy array is homogeneous, and contains elements described by a dtype object. A dtype object can be constructed from different combinations of fundamental numeric types. Parameters ---------- obj Object to be converted to a data type object. align : bool, optional Add padding to the fields to match what a C compiler would output for a similar C-struct. Can be ``True`` only if `obj` is a dictionary or a comma-separated string. If a struct dtype is being created, this also sets a sticky alignment flag ``isalignedstruct``. copy : bool, optional Make a new copy of the data-type object. If ``False``, the result may just be a reference to a built-in data-type object. See also -------- result_type Examples -------- Using array-scalar type: >>> np.dtype(np.int16) dtype('int16') Structured type, one field name 'f1', containing int16: >>> np.dtype([('f1', np.int16)]) dtype([('f1', '<i2')]) Structured type, one field named 'f1', in itself containing a structured type with one field: >>> np.dtype([('f1', [('f1', np.int16)])]) dtype([('f1', [('f1', '<i2')])]) Structured type, two fields: the first field contains an unsigned int, the second an int32: >>> np.dtype([('f1', np.uint), ('f2', np.int32)]) dtype([('f1', '<u4'), ('f2', '<i4')]) Using array-protocol type strings: >>> np.dtype([('a','f8'),('b','S10')]) dtype([('a', '<f8'), ('b', '|S10')]) Using comma-separated field formats. The shape is (2,3): >>> np.dtype("i4, (2,3)f8") dtype([('f0', '<i4'), ('f1', '<f8', (2, 3))]) Using tuples. ``int`` is a fixed type, 3 the field's shape. ``void`` is a flexible type, here of size 10: >>> np.dtype([('hello',(np.int,3)),('world',np.void,10)]) dtype([('hello', '<i4', 3), ('world', '|V10')]) Subdivide ``int16`` into 2 ``int8``'s, called x and y. 0 and 1 are the offsets in bytes: >>> np.dtype((np.int16, {'x':(np.int8,0), 'y':(np.int8,1)})) dtype(('<i2', [('x', '|i1'), ('y', '|i1')])) Using dictionaries. Two fields named 'gender' and 'age': >>> np.dtype({'names':['gender','age'], 'formats':['S1',np.uint8]}) dtype([('gender', '|S1'), ('age', '|u1')]) Offsets in bytes, here 0 and 25: >>> np.dtype({'surname':('S25',0),'age':(np.uint8,25)}) dtype([('surname', '|S25'), ('age', '|u1')]) )� alignmentz� The required alignment (bytes) of this data-type according to the compiler. More information is available in the C-API section of the manual. )� byteordera� A character indicating the byte-order of this data-type object. One of: === ============== '=' native '<' little-endian '>' big-endian '|' not applicable === ============== All built-in data-type objects have byteorder either '=' or '|'. Examples -------- >>> dt = np.dtype('i2') >>> dt.byteorder '=' >>> # endian is not relevant for 8 bit numbers >>> np.dtype('i1').byteorder '|' >>> # or ASCII strings >>> np.dtype('S2').byteorder '|' >>> # Even if specific code is given, and it is native >>> # '=' is the byteorder >>> import sys >>> sys_is_le = sys.byteorder == 'little' >>> native_code = sys_is_le and '<' or '>' >>> swapped_code = sys_is_le and '>' or '<' >>> dt = np.dtype(native_code + 'i2') >>> dt.byteorder '=' >>> # Swapped code shows up as itself >>> dt = np.dtype(swapped_code + 'i2') >>> dt.byteorder == swapped_code True )�charzDA unique character code for each of the 21 different built-in types.)�descra, PEP3118 interface description of the data-type. The format is that required by the 'descr' key in the PEP3118 `__array_interface__` attribute. Warning: This attribute exists specifically for PEP3118 compliance, and is not a datatype description compatible with `np.dtype`. )�fieldsaX Dictionary of named fields defined for this data type, or ``None``. The dictionary is indexed by keys that are the names of the fields. Each entry in the dictionary is a tuple fully describing the field:: (dtype, offset[, title]) If present, the optional title can be any object (if it is a string or unicode then it will also be a key in the fields dictionary, otherwise it's meta-data). Notice also that the first two elements of the tuple can be passed directly as arguments to the ``ndarray.getfield`` and ``ndarray.setfield`` methods. See Also -------- ndarray.getfield, ndarray.setfield Examples -------- >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) >>> print(dt.fields) {'grades': (dtype(('float64',(2,))), 16), 'name': (dtype('|S16'), 0)} )r ax Bit-flags describing how this data type is to be interpreted. Bit-masks are in `numpy.core.multiarray` as the constants `ITEM_HASOBJECT`, `LIST_PICKLE`, `ITEM_IS_POINTER`, `NEEDS_INIT`, `NEEDS_PYAPI`, `USE_GETITEM`, `USE_SETITEM`. A full explanation of these flags is in C-API documentation; they are largely useful for user-defined data-types. )Z hasobjecta� Boolean indicating whether this dtype contains any reference-counted objects in any fields or sub-dtypes. Recall that what is actually in the ndarray memory representing the Python object is the memory address of that object (a pointer). Special handling may be required, and this attribute is useful for distinguishing data types that may contain arbitrary Python objects and data-types that won't. )� isbuiltina1 Integer indicating how this dtype relates to the built-in dtypes. Read-only. = ======================================================================== 0 if this is a structured array type, with fields 1 if this is a dtype compiled into numpy (such as ints, floats etc) 2 if the dtype is for a user-defined numpy type A user-defined type uses the numpy C-API machinery to extend numpy to handle a new array type. See :ref:`user.user-defined-data-types` in the NumPy manual. = ======================================================================== Examples -------- >>> dt = np.dtype('i2') >>> dt.isbuiltin 1 >>> dt = np.dtype('f8') >>> dt.isbuiltin 1 >>> dt = np.dtype([('field1', 'f8')]) >>> dt.isbuiltin 0 )Zisnativeza Boolean indicating whether the byte order of this dtype is native to the platform. )Zisalignedstructz� Boolean indicating whether the dtype is a struct which maintains field alignment. This flag is sticky, so when combining multiple structs together, it is preserved and produces new dtypes which are also aligned. )r z� The element size of this data-type object. For 18 of the 21 types this number is fixed by the data-type. For the flexible data-types, this number can be anything. )�kindae A character code (one of 'biufcmMOSUV') identifying the general kind of data. = ====================== b boolean i signed integer u unsigned integer f floating-point c complex floating-point m timedelta M datetime O object S (byte-)string U Unicode V void = ====================== )rW zt A bit-width name for this data-type. Un-sized flexible data-type objects do not have this attribute. )�namesaw Ordered list of field names, or ``None`` if there are no fields. The names are ordered according to increasing byte offset. This can be used, for example, to walk through all of the named fields in offset order. Examples -------- >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) >>> dt.names ('name', 'grades') )�numz� A unique number for each of the 21 different built-in types. These are roughly ordered from least-to-most precision. )r zj Shape tuple of the sub-array if this data type describes a sub-array, and ``()`` otherwise. )r z� Number of dimensions of the sub-array if this data type describes a sub-array, and ``0`` otherwise. .. versionadded:: 1.13.0 )�strz7The array-protocol typestring of this data-type object.)Zsubdtypea� Tuple ``(item_dtype, shape)`` if this `dtype` describes a sub-array, and None otherwise. The *shape* is the fixed shape of the sub-array described by this data type, and *item_dtype* the data type of the array. If a field whose dtype object has this attribute is retrieved, then the extra dimensions implied by *shape* are tacked on to the end of the retrieved array. )�typez?The type object used to instantiate a scalar of this data-type.)r@ a� newbyteorder(new_order='S') Return a new dtype with a different byte order. Changes are also made in all fields and sub-arrays of the data type. Parameters ---------- new_order : string, optional Byte order to force; a value from the byte order specifications below. The default value ('S') results in swapping the current byte order. `new_order` codes can be any of: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) The code does a case-insensitive check on the first letter of `new_order` for these alternatives. For example, any of '>' or 'B' or 'b' or 'brian' are valid to specify big-endian. Returns ------- new_dtype : dtype New dtype object with the given change to the byte order. Notes ----- Changes are also made in all fields and sub-arrays of the data type. Examples -------- >>> import sys >>> sys_is_le = sys.byteorder == 'little' >>> native_code = sys_is_le and '<' or '>' >>> swapped_code = sys_is_le and '>' or '<' >>> native_dt = np.dtype(native_code+'i2') >>> swapped_dt = np.dtype(swapped_code+'i2') >>> native_dt.newbyteorder('S') == swapped_dt True >>> native_dt.newbyteorder() == swapped_dt True >>> native_dt == swapped_dt.newbyteorder('S') True >>> native_dt == swapped_dt.newbyteorder('=') True >>> native_dt == swapped_dt.newbyteorder('N') True >>> native_dt == native_dt.newbyteorder('|') True >>> np.dtype('<i2') == native_dt.newbyteorder('<') True >>> np.dtype('<i2') == native_dt.newbyteorder('L') True >>> np.dtype('>i2') == native_dt.newbyteorder('>') True >>> np.dtype('>i2') == native_dt.newbyteorder('B') True Zbusdaycalendara� busdaycalendar(weekmask='1111100', holidays=None) A business day calendar object that efficiently stores information defining valid days for the busday family of functions. The default valid days are Monday through Friday ("business days"). A busdaycalendar object can be specified with any set of weekly valid days, plus an optional "holiday" dates that always will be invalid. Once a busdaycalendar object is created, the weekmask and holidays cannot be modified. .. versionadded:: 1.7.0 Parameters ---------- weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates, no matter which weekday they fall upon. Holiday dates may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. Returns ------- out : busdaycalendar A business day calendar object containing the specified weekmask and holidays values. See Also -------- is_busday : Returns a boolean array indicating valid days. busday_offset : Applies an offset counted in valid days. busday_count : Counts how many valid days are in a half-open date range. Attributes ---------- Note: once a busdaycalendar object is created, you cannot modify the weekmask or holidays. The attributes return copies of internal data. weekmask : (copy) seven-element array of bool holidays : (copy) sorted array of datetime64[D] Examples -------- >>> # Some important days in July ... bdd = np.busdaycalendar( ... holidays=['2011-07-01', '2011-07-04', '2011-07-17']) >>> # Default is Monday to Friday weekdays ... bdd.weekmask array([ True, True, True, True, True, False, False], dtype='bool') >>> # Any holidays already on the weekend are removed ... bdd.holidays array(['2011-07-01', '2011-07-04'], dtype='datetime64[D]') )Zweekmaskz?A copy of the seven-element boolean mask indicating valid days.)Zholidaysz?A copy of the holiday array indicating additional invalid days.Z is_busdaya is_busday(dates, weekmask='1111100', holidays=None, busdaycal=None, out=None) Calculates which of the given dates are valid days, and which are not. .. versionadded:: 1.7.0 Parameters ---------- dates : array_like of datetime64[D] The array of dates to process. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of bool, optional If provided, this array is filled with the result. Returns ------- out : array of bool An array with the same shape as ``dates``, containing True for each valid day, and False for each invalid day. See Also -------- busdaycalendar: An object that specifies a custom set of valid days. busday_offset : Applies an offset counted in valid days. busday_count : Counts how many valid days are in a half-open date range. Examples -------- >>> # The weekdays are Friday, Saturday, and Monday ... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'], ... holidays=['2011-07-01', '2011-07-04', '2011-07-17']) array([False, False, True], dtype='bool') Z busday_offseta) busday_offset(dates, offsets, roll='raise', weekmask='1111100', holidays=None, busdaycal=None, out=None) First adjusts the date to fall on a valid day according to the ``roll`` rule, then applies offsets to the given dates counted in valid days. .. versionadded:: 1.7.0 Parameters ---------- dates : array_like of datetime64[D] The array of dates to process. offsets : array_like of int The array of offsets, which is broadcast with ``dates``. roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding', 'modifiedfollowing', 'modifiedpreceding'}, optional How to treat dates that do not fall on a valid day. The default is 'raise'. * 'raise' means to raise an exception for an invalid day. * 'nat' means to return a NaT (not-a-time) for an invalid day. * 'forward' and 'following' mean to take the first valid day later in time. * 'backward' and 'preceding' mean to take the first valid day earlier in time. * 'modifiedfollowing' means to take the first valid day later in time unless it is across a Month boundary, in which case to take the first valid day earlier in time. * 'modifiedpreceding' means to take the first valid day earlier in time unless it is across a Month boundary, in which case to take the first valid day later in time. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of datetime64[D], optional If provided, this array is filled with the result. Returns ------- out : array of datetime64[D] An array with a shape from broadcasting ``dates`` and ``offsets`` together, containing the dates with offsets applied. See Also -------- busdaycalendar: An object that specifies a custom set of valid days. is_busday : Returns a boolean array indicating valid days. busday_count : Counts how many valid days are in a half-open date range. Examples -------- >>> # First business day in October 2011 (not accounting for holidays) ... np.busday_offset('2011-10', 0, roll='forward') numpy.datetime64('2011-10-03','D') >>> # Last business day in February 2012 (not accounting for holidays) ... np.busday_offset('2012-03', -1, roll='forward') numpy.datetime64('2012-02-29','D') >>> # Third Wednesday in January 2011 ... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed') numpy.datetime64('2011-01-19','D') >>> # 2012 Mother's Day in Canada and the U.S. ... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun') numpy.datetime64('2012-05-13','D') >>> # First business day on or after a date ... np.busday_offset('2011-03-20', 0, roll='forward') numpy.datetime64('2011-03-21','D') >>> np.busday_offset('2011-03-22', 0, roll='forward') numpy.datetime64('2011-03-22','D') >>> # First business day after a date ... np.busday_offset('2011-03-20', 1, roll='backward') numpy.datetime64('2011-03-21','D') >>> np.busday_offset('2011-03-22', 1, roll='backward') numpy.datetime64('2011-03-23','D') Z busday_counta� busday_count(begindates, enddates, weekmask='1111100', holidays=[], busdaycal=None, out=None) Counts the number of valid days between `begindates` and `enddates`, not including the day of `enddates`. If ``enddates`` specifies a date value that is earlier than the corresponding ``begindates`` date value, the count will be negative. .. versionadded:: 1.7.0 Parameters ---------- begindates : array_like of datetime64[D] The array of the first dates for counting. enddates : array_like of datetime64[D] The array of the end dates for counting, which are excluded from the count themselves. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of int, optional If provided, this array is filled with the result. Returns ------- out : array of int An array with a shape from broadcasting ``begindates`` and ``enddates`` together, containing the number of valid days between the begin and end dates. See Also -------- busdaycalendar: An object that specifies a custom set of valid days. is_busday : Returns a boolean array indicating valid days. busday_offset : Applies an offset counted in valid days. Examples -------- >>> # Number of weekdays in January 2011 ... np.busday_count('2011-01', '2011-02') 21 >>> # Number of weekdays in 2011 ... np.busday_count('2011', '2012') 260 >>> # Number of Saturdays in 2011 ... np.busday_count('2011', '2012', weekmask='Sat') 53 Znormalize_axis_indexaz normalize_axis_index(axis, ndim, msg_prefix=None) Normalizes an axis index, `axis`, such that is a valid positive index into the shape of array with `ndim` dimensions. Raises an AxisError with an appropriate message if this is not possible. Used internally by all axis-checking logic. .. versionadded:: 1.13.0 Parameters ---------- axis : int The un-normalized index of the axis. Can be negative ndim : int The number of dimensions of the array that `axis` should be normalized against msg_prefix : str A prefix to put before the message, typically the name of the argument Returns ------- normalized_axis : int The normalized axis index, such that `0 <= normalized_axis < ndim` Raises ------ AxisError If the axis index is invalid, when `-ndim <= axis < ndim` is false. Examples -------- >>> normalize_axis_index(0, ndim=3) 0 >>> normalize_axis_index(1, ndim=3) 1 >>> normalize_axis_index(-1, ndim=3) 2 >>> normalize_axis_index(3, ndim=3) Traceback (most recent call last): ... AxisError: axis 3 is out of bounds for array of dimension 3 >>> normalize_axis_index(-4, ndim=3, msg_prefix='axes_arg') Traceback (most recent call last): ... AxisError: axes_arg: axis -4 is out of bounds for array of dimension 3 znumpy.lib.index_tricksZmgridag `nd_grid` instance which returns a dense multi-dimensional "meshgrid". An instance of `numpy.lib.index_tricks.nd_grid` which returns an dense (or fleshed out) mesh-grid when indexed, so that each returned argument has the same shape. The dimensions and number of the output arrays are equal to the number of indexing dimensions. If the step length is not a complex number, then the stop is not inclusive. However, if the step length is a **complex number** (e.g. 5j), then the integer part of its magnitude is interpreted as specifying the number of points to create between the start and stop values, where the stop value **is inclusive**. Returns ---------- mesh-grid `ndarrays` all of the same dimensions See Also -------- numpy.lib.index_tricks.nd_grid : class of `ogrid` and `mgrid` objects ogrid : like mgrid but returns open (not fleshed out) mesh grids r_ : array concatenator Examples -------- >>> np.mgrid[0:5,0:5] array([[[0, 0, 0, 0, 0], [1, 1, 1, 1, 1], [2, 2, 2, 2, 2], [3, 3, 3, 3, 3], [4, 4, 4, 4, 4]], [[0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4]]]) >>> np.mgrid[-1:1:5j] array([-1. , -0.5, 0. , 0.5, 1. ]) Zogrida� `nd_grid` instance which returns an open multi-dimensional "meshgrid". An instance of `numpy.lib.index_tricks.nd_grid` which returns an open (i.e. not fleshed out) mesh-grid when indexed, so that only one dimension of each returned array is greater than 1. The dimension and number of the output arrays are equal to the number of indexing dimensions. If the step length is not a complex number, then the stop is not inclusive. However, if the step length is a **complex number** (e.g. 5j), then the integer part of its magnitude is interpreted as specifying the number of points to create between the start and stop values, where the stop value **is inclusive**. Returns ---------- mesh-grid `ndarrays` with only one dimension :math:`\neq 1` See Also -------- np.lib.index_tricks.nd_grid : class of `ogrid` and `mgrid` objects mgrid : like `ogrid` but returns dense (or fleshed out) mesh grids r_ : array concatenator Examples -------- >>> from numpy import ogrid >>> ogrid[-1:1:5j] array([-1. , -0.5, 0. , 0.5, 1. ]) >>> ogrid[0:5,0:5] [array([[0], [1], [2], [3], [4]]), array([[0, 1, 2, 3, 4]])] znumpy.core.numerictypesZgenericai Base class for numpy scalar types. Class from which most (all?) numpy scalar types are derived. For consistency, exposes the same API as `ndarray`, despite many consequent attributes being either "get-only," or completely irrelevant. This is the class from which it is strongly suggested users should derive custom scalar types. )r" a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r a7 Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r zPointer to start of data.)r zGet array data-descriptor.)r zThe integer value of flags.)r zA 1-D view of the scalar.)r z!The imaginary part of the scalar.)r z#The length of one element in bytes.)r z"The length of the scalar in bytes.)r z The number of array dimensions.)r z The real part of the scalar.)r zTuple of array dimensions.)r z&The number of elements in the gentype.)r! z'Tuple of bytes steps in each dimension.)r' a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r( a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r) a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r* a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r+ a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r, a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r- a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r. a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r/ a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r0 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r2 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r3 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r4 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r5 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r6 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r7 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r8 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r9 a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r: a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r; a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r< a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r= a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r> a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r? a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r@ a� newbyteorder(new_order='S') Return a new `dtype` with a different byte order. Changes are also made in all fields and sub-arrays of the data type. The `new_order` code can be any from the following: * 'S' - swap dtype from current to opposite endian * {'<', 'L'} - little endian * {'>', 'B'} - big endian * {'=', 'N'} - native order * {'|', 'I'} - ignore (no change to byte order) Parameters ---------- new_order : str, optional Byte order to force; a value from the byte order specifications above. The default value ('S') results in swapping the current byte order. The code does a case-insensitive check on the first letter of `new_order` for the alternatives above. For example, any of 'B' or 'b' or 'biggish' are valid to specify big-endian. Returns ------- new_dtype : dtype New `dtype` object with the given change to the byte order. )rA a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rB a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rC a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rD a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rE a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rF a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rG a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rH a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rI a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rJ a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rK a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rL a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rM a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rO a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rP a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rQ a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rR a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rS a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rT a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rU a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rV a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rY a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )rZ a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r[ a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. )r\ a? Not implemented (virtual attribute) Class generic exists solely to derive numpy scalars from, and possesses, albeit unimplemented, all the attributes of the ndarray class so as to provide a uniform API. See Also -------- The corresponding attribute of the derived class of interest. Zbool_z;NumPy's Boolean type. Character code: ``?``. Alias: bool8Z complex64zR Complex number type composed of two 32 bit floats. Character code: 'F'. Z complex128zq Complex number type composed of two 64 bit floats. Character code: 'D'. Python complex compatible. Z complex256zS Complex number type composed of two 128-bit floats. Character code: 'G'. Zfloat32zP 32-bit floating-point number. Character code 'f'. C float compatible. Zfloat64zU 64-bit floating-point number. Character code 'd'. Python float compatible. Zfloat96z Zfloat128z[ 128-bit floating-point number. Character code: 'g'. C long float compatible. Zint8z78-bit integer. Character code ``b``. C char compatible.Zint16z916-bit integer. Character code ``h``. C short compatible.Zint32z532-bit integer. Character code 'i'. C int compatible.�int64z:64-bit integer. Character code 'l'. Python int compatible.Zobject_z(Any Python object. Character code: 'O'.N) �__doc__� __future__r r r Z numpy.libr Z tobytesdoc�format� rs rs �D/opt/alt/python37/lib64/python3.7/site-packages/numpy/add_newdocs.py�<module> s� ) i , %h,: 32 I$IH;*EJj2.C Iy _5w g G * > E ( + & * : . '$ * ( \ 3 H 8 7 # F 6 j*>9 NG8)+)- , \ Q k @ DS + H> 1X>1 ) % !