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"""
This is only meant to add docs to objects defined in C-extension modules.
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.
"""
from __future__ import division, absolute_import, print_function
from numpy.lib import add_newdoc
###############################################################################
#
# flatiter
#
# flatiter needs a toplevel description
#
###############################################################################
add_newdoc('numpy.core', 'flatiter',
"""
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])
""")
# flatiter attributes
add_newdoc('numpy.core', 'flatiter', ('base',
"""
A reference to the array that is iterated over.
Examples
--------
>>> x = np.arange(5)
>>> fl = x.flat
>>> fl.base is x
True
"""))
add_newdoc('numpy.core', 'flatiter', ('coords',
"""
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)
"""))
add_newdoc('numpy.core', 'flatiter', ('index',
"""
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
"""))
# flatiter functions
add_newdoc('numpy.core', 'flatiter', ('__array__',
"""__array__(type=None) Get array from iterator
"""))
add_newdoc('numpy.core', 'flatiter', ('copy',
"""
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])
"""))
###############################################################################
#
# nditer
#
###############################################################################
add_newdoc('numpy.core', 'nditer',
"""
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.
* "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.
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])
""")
# nditer methods
add_newdoc('numpy.core', 'nditer', ('copy',
"""
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))
"""))
add_newdoc('numpy.core', 'nditer', ('debug_print',
"""
debug_print()
Print the current state of the `nditer` instance and debug info to stdout.
"""))
add_newdoc('numpy.core', 'nditer', ('enable_external_loop',
"""
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.
"""))
add_newdoc('numpy.core', 'nditer', ('iternext',
"""
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.
"""))
add_newdoc('numpy.core', 'nditer', ('remove_axis',
"""
remove_axis(i)
Removes axis `i` from the iterator. Requires that the flag "multi_index"
be enabled.
"""))
add_newdoc('numpy.core', 'nditer', ('remove_multi_index',
"""
remove_multi_index()
When the "multi_index" flag was specified, this removes it, allowing
the internal iteration structure to be optimized further.
"""))
add_newdoc('numpy.core', 'nditer', ('reset',
"""
reset()
Reset the iterator to its initial state.
"""))
###############################################################################
#
# broadcast
#
###############################################################################
add_newdoc('numpy.core', 'broadcast',
"""
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]])
""")
# attributes
add_newdoc('numpy.core', 'broadcast', ('index',
"""
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
"""))
add_newdoc('numpy.core', 'broadcast', ('iters',
"""
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)
"""))
add_newdoc('numpy.core', 'broadcast', ('ndim',
"""
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
"""))
add_newdoc('numpy.core', 'broadcast', ('nd',
"""
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
"""))
add_newdoc('numpy.core', 'broadcast', ('numiter',
"""
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
"""))
add_newdoc('numpy.core', 'broadcast', ('shape',
"""
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)
"""))
add_newdoc('numpy.core', 'broadcast', ('size',
"""
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
"""))
add_newdoc('numpy.core', 'broadcast', ('reset',
"""
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
"""))
###############################################################################
#
# numpy functions
#
###############################################################################
add_newdoc('numpy.core.multiarray', 'array',
"""
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]])
""")
add_newdoc('numpy.core.multiarray', 'empty',
"""
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
""")
add_newdoc('numpy.core.multiarray', 'empty_like',
"""
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]])
""")
add_newdoc('numpy.core.multiarray', 'scalar',
"""
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.
""")
add_newdoc('numpy.core.multiarray', 'zeros',
"""
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')])
""")
add_newdoc('numpy.core.multiarray', 'set_typeDict',
"""set_typeDict(dict)
Set the internal dictionary that can look up an array type using a
registered code.
""")
add_newdoc('numpy.core.multiarray', 'fromstring',
"""
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)
""")
add_newdoc('numpy.core.multiarray', 'fromiter',
"""
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.])
""")
add_newdoc('numpy.core.multiarray', 'fromfile',
"""
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')])
""")
add_newdoc('numpy.core.multiarray', 'frombuffer',
"""
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')
""")
add_newdoc('numpy.core.multiarray', 'concatenate',
"""
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)
""")
add_newdoc('numpy.core', 'inner',
"""
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.]])
""")
add_newdoc('numpy.core', 'fastCopyAndTranspose',
"""_fastCopyAndTranspose(a)""")
add_newdoc('numpy.core.multiarray', 'correlate',
"""cross_correlate(a,v, mode=0)""")
add_newdoc('numpy.core.multiarray', 'arange',
"""
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])
""")
add_newdoc('numpy.core.multiarray', '_get_ndarray_c_version',
"""_get_ndarray_c_version()
Return the compile time NDARRAY_VERSION number.
""")
add_newdoc('numpy.core.multiarray', '_reconstruct',
"""_reconstruct(subtype, shape, dtype)
Construct an empty array. Used by Pickles.
""")
add_newdoc('numpy.core.multiarray', 'set_string_function',
"""
set_string_function(f, repr=1)
Internal method to set a function to be used when pretty printing arrays.
""")
add_newdoc('numpy.core.multiarray', 'set_numeric_ops',
"""
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
""")
add_newdoc('numpy.core.multiarray', 'where',
"""
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` and `y` need to have the same
shape as `condition`.
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.in1d(x.ravel(), goodvalues).reshape(x.shape)
>>> ix
array([[False, False, False],
[ True, True, False],
[False, True, False]], dtype=bool)
>>> np.where(ix)
(array([1, 1, 2]), array([0, 1, 1]))
""")
add_newdoc('numpy.core.multiarray', 'lexsort',
"""
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])
""")
add_newdoc('numpy.core.multiarray', 'can_cast',
"""
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
""")
add_newdoc('numpy.core.multiarray', 'promote_types',
"""
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')
""")
add_newdoc('numpy.core.multiarray', 'min_scalar_type',
"""
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')
""")
add_newdoc('numpy.core.multiarray', 'result_type',
"""
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')
""")
add_newdoc('numpy.core.multiarray', 'newbuffer',
"""
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.
""")
add_newdoc('numpy.core.multiarray', 'getbuffer',
"""
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>
""")
add_newdoc('numpy.core', 'dot',
"""
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
""")
add_newdoc('numpy.core', 'matmul',
"""
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
""")
add_newdoc('numpy.core', 'c_einsum',
"""
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.]])
""")
add_newdoc('numpy.core', 'vdot',
"""
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
""")
##############################################################################
#
# Documentation for ndarray attributes and methods
#
##############################################################################
##############################################################################
#
# ndarray object
#
##############################################################################
add_newdoc('numpy.core.multiarray', 'ndarray',
"""
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])
""")
##############################################################################
#
# ndarray attributes
#
##############################################################################
add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_interface__',
"""Array protocol: Python side."""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_finalize__',
"""None."""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_priority__',
"""Array priority."""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_struct__',
"""Array protocol: C-struct side."""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('_as_parameter_',
"""Allow the array to be interpreted as a ctypes object by returning the
data-memory location as an integer
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('base',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('ctypes',
"""
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>
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('data',
"""Python buffer object pointing to the start of the array's data."""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('dtype',
"""
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'>
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('imag',
"""
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')
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('itemsize',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('flags',
"""
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.
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('flat',
"""
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]])
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('nbytes',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('ndim',
"""
Number of array dimensions.
Examples
--------
>>> x = np.array([1, 2, 3])
>>> x.ndim
1
>>> y = np.zeros((2, 3, 4))
>>> y.ndim
3
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('real',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('shape',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('size',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('strides',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('T',
"""
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.])
"""))
##############################################################################
#
# ndarray methods
#
##############################################################################
add_newdoc('numpy.core.multiarray', 'ndarray', ('__array__',
""" 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.
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_prepare__',
"""a.__array_prepare__(obj) -> Object of same type as ndarray object obj.
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_wrap__',
"""a.__array_wrap__(obj) -> Object of same type as ndarray object a.
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__copy__',
"""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.
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__deepcopy__',
"""a.__deepcopy__() -> Deep copy of array.
Used if copy.deepcopy is called on an array.
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__reduce__',
"""a.__reduce__()
For pickling.
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('__setstate__',
"""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)
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('all',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('any',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('argmax',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('argmin',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('argsort',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('argpartition',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('astype',
"""
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])
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('byteswap',
"""
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')
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('choose',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('clip',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('compress',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('conj',
"""
a.conj()
Complex-conjugate all elements.
Refer to `numpy.conjugate` for full documentation.
See Also
--------
numpy.conjugate : equivalent function
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('conjugate',
"""
a.conjugate()
Return the complex conjugate, element-wise.
Refer to `numpy.conjugate` for full documentation.
See Also
--------
numpy.conjugate : equivalent function
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('copy',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('cumprod',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('cumsum',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('diagonal',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('dot',
"""
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.]])
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('dump',
"""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.
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('dumps',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('fill',
"""
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.])
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('flatten',
"""
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])
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('getfield',
"""
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.]])
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('item',
"""
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
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('itemset',
"""
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]])
"""))
add_newdoc('numpy.core.multiarray', 'ndarray', ('max',
"""
a.max(axis=None, out=None)
Return the maximum along a given axis.
Refer to `numpy.amax` for full documentation.
</