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# Module containing non-deprecated functions borrowed from Numeric.
__docformat__ = "restructuredtext en"
# functions that are now methods
__all__ = ['take', 'reshape', 'choose', 'repeat', 'put',
'swapaxes', 'transpose', 'sort', 'argsort', 'argmax', 'argmin',
'searchsorted', 'alen',
'resize', 'diagonal', 'trace', 'ravel', 'nonzero', 'shape',
'compress', 'clip', 'sum', 'product', 'prod', 'sometrue', 'alltrue',
'any', 'all', 'cumsum', 'cumproduct', 'cumprod', 'ptp', 'ndim',
'rank', 'size', 'around', 'round_', 'mean', 'std', 'var', 'squeeze',
'amax', 'amin',
]
import multiarray as mu
import umath as um
import numerictypes as nt
from numeric import asarray, array, asanyarray, concatenate
_dt_ = nt.sctype2char
import types
try:
_gentype = types.GeneratorType
except AttributeError:
_gentype = types.NoneType
# save away Python sum
_sum_ = sum
# functions that are now methods
def _wrapit(obj, method, *args, **kwds):
try:
wrap = obj.__array_wrap__
except AttributeError:
wrap = None
result = getattr(asarray(obj),method)(*args, **kwds)
if wrap:
if not isinstance(result, mu.ndarray):
result = asarray(result)
result = wrap(result)
return result
def take(a, indices, axis=None, out=None, mode='raise'):
"""
Take elements from an array along an axis.
This function does the same thing as "fancy" indexing (indexing arrays
using arrays); however, it can be easier to use if you need elements
along a given axis.
Parameters
----------
a : array_like
The source array.
indices : array_like
The indices of the values to extract.
axis : int, optional
The axis over which to select values. By default, the flattened
input array is used.
out : ndarray, optional
If provided, the result will be placed in this array. It should
be of the appropriate shape and dtype.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices will behave.
* 'raise' -- raise an error (default)
* 'wrap' -- wrap around
* 'clip' -- clip to the range
'clip' mode means that all indices that are too large are replaced
by the index that addresses the last element along that axis. Note
that this disables indexing with negative numbers.
Returns
-------
subarray : ndarray
The returned array has the same type as `a`.
See Also
--------
ndarray.take : equivalent method
Examples
--------
>>> a = [4, 3, 5, 7, 6, 8]
>>> indices = [0, 1, 4]
>>> np.take(a, indices)
array([4, 3, 6])
In this example if `a` is an ndarray, "fancy" indexing can be used.
>>> a = np.array(a)
>>> a[indices]
array([4, 3, 6])
"""
try:
take = a.take
except AttributeError:
return _wrapit(a, 'take', indices, axis, out, mode)
return take(indices, axis, out, mode)
# not deprecated --- copy if necessary, view otherwise
def reshape(a, newshape, order='C'):
"""
Gives a new shape to an array without changing its data.
Parameters
----------
a : array_like
Array to be reshaped.
newshape : int or tuple of ints
The new shape should be compatible with the original shape. If
an integer, then the result will be a 1-D array of that length.
One shape dimension can be -1. In this case, the value is inferred
from the length of the array and remaining dimensions.
order : {'C', 'F'}, optional
Determines whether the array data should be viewed as in C
(row-major) order or FORTRAN (column-major) order.
Returns
-------
reshaped_array : ndarray
This will be a new view object if possible; otherwise, it will
be a copy.
See Also
--------
ndarray.reshape : Equivalent method.
Examples
--------
>>> a = np.array([[1,2,3], [4,5,6]])
>>> np.reshape(a, 6)
array([1, 2, 3, 4, 5, 6])
>>> np.reshape(a, 6, order='F')
array([1, 4, 2, 5, 3, 6])
>>> np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2
array([[1, 2],
[3, 4],
[5, 6]])
"""
try:
reshape = a.reshape
except AttributeError:
return _wrapit(a, 'reshape', newshape, order=order)
return reshape(newshape, order=order)
def choose(a, choices, out=None, mode='raise'):
"""
Construct an array from an index array and a set of arrays to choose from.
First of all, if confused or uncertain, definitely look at the Examples -
in its full generality, this function is less simple than it might
seem from the following code description (below ndi =
`numpy.lib.index_tricks`):
``np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)])``.
But this omits some subtleties. Here is a fully general summary:
Given an "index" array (`a`) of integers and a sequence of `n` arrays
(`choices`), `a` and each choice array are first broadcast, as necessary,
to arrays of a common shape; calling these *Ba* and *Bchoices[i], i =
0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape``
for each `i`. Then, a new array with shape ``Ba.shape`` is created as
follows:
* if ``mode=raise`` (the default), then, first of all, each element of
`a` (and thus `Ba`) must be in the range `[0, n-1]`; now, suppose that
`i` (in that range) is the value at the `(j0, j1, ..., jm)` position
in `Ba` - then the value at the same position in the new array is the
value in `Bchoices[i]` at that same position;
* if ``mode=wrap``, values in `a` (and thus `Ba`) may be any (signed)
integer; modular arithmetic is used to map integers outside the range
`[0, n-1]` back into that range; and then the new array is constructed
as above;
* if ``mode=clip``, values in `a` (and thus `Ba`) may be any (signed)
integer; negative integers are mapped to 0; values greater than `n-1`
are mapped to `n-1`; and then the new array is constructed as above.
Parameters
----------
a : int array
This array must contain integers in `[0, n-1]`, where `n` is the number
of choices, unless ``mode=wrap`` or ``mode=clip``, in which cases any
integers are permissible.
choices : sequence of arrays
Choice arrays. `a` and all of the choices must be broadcastable to the
same shape. If `choices` is itself an array (not recommended), then
its outermost dimension (i.e., the one corresponding to
``choices.shape[0]``) is taken as defining the "sequence".
out : array, optional
If provided, the result will be inserted into this array. It should
be of the appropriate shape and dtype.
mode : {'raise' (default), 'wrap', 'clip'}, optional
Specifies how indices outside `[0, n-1]` will be treated:
* 'raise' : an exception is raised
* 'wrap' : value becomes value mod `n`
* 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1
Returns
-------
merged_array : array
The merged result.
Raises
------
ValueError: shape mismatch
If `a` and each choice array are not all broadcastable to the same
shape.
See Also
--------
ndarray.choose : equivalent method
Notes
-----
To reduce the chance of misinterpretation, even though the following
"abuse" is nominally supported, `choices` should neither be, nor be
thought of as, a single array, i.e., the outermost sequence-like container
should be either a list or a tuple.
Examples
--------
>>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],
... [20, 21, 22, 23], [30, 31, 32, 33]]
>>> np.choose([2, 3, 1, 0], choices
... # the first element of the result will be the first element of the
... # third (2+1) "array" in choices, namely, 20; the second element
... # will be the second element of the fourth (3+1) choice array, i.e.,
... # 31, etc.
... )
array([20, 31, 12, 3])
>>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)
array([20, 31, 12, 3])
>>> # because there are 4 choice arrays
>>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)
array([20, 1, 12, 3])
>>> # i.e., 0
A couple examples illustrating how choose broadcasts:
>>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]
>>> choices = [-10, 10]
>>> np.choose(a, choices)
array([[ 10, -10, 10],
[-10, 10, -10],
[ 10, -10, 10]])
>>> # With thanks to Anne Archibald
>>> a = np.array([0, 1]).reshape((2,1,1))
>>> c1 = np.array([1, 2, 3]).reshape((1,3,1))
>>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))
>>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2
array([[[ 1, 1, 1, 1, 1],
[ 2, 2, 2, 2, 2],
[ 3, 3, 3, 3, 3]],
[[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5],
[-1, -2, -3, -4, -5]]])
"""
try:
choose = a.choose
except AttributeError:
return _wrapit(a, 'choose', choices, out=out, mode=mode)
return choose(choices, out=out, mode=mode)
def repeat(a, repeats, axis=None):
"""
Repeat elements of an array.
Parameters
----------
a : array_like
Input array.
repeats : {int, array of ints}
The number of repetitions for each element. `repeats` is broadcasted
to fit the shape of the given axis.
axis : int, optional
The axis along which to repeat values. By default, use the
flattened input array, and return a flat output array.
Returns
-------
repeated_array : ndarray
Output array which has the same shape as `a`, except along
the given axis.
See Also
--------
tile : Tile an array.
Examples
--------
>>> x = np.array([[1,2],[3,4]])
>>> np.repeat(x, 2)
array([1, 1, 2, 2, 3, 3, 4, 4])
>>> np.repeat(x, 3, axis=1)
array([[1, 1, 1, 2, 2, 2],
[3, 3, 3, 4, 4, 4]])
>>> np.repeat(x, [1, 2], axis=0)
array([[1, 2],
[3, 4],
[3, 4]])
"""
try:
repeat = a.repeat
except AttributeError:
return _wrapit(a, 'repeat', repeats, axis)
return repeat(repeats, axis)
def put(a, ind, v, mode='raise'):
"""
Replaces specified elements of an array with given values.
The indexing works on the flattened target array. `put` is roughly
equivalent to:
::
a.flat[ind] = v
Parameters
----------
a : ndarray
Target array.
ind : array_like
Target indices, interpreted as integers.
v : array_like
Values to place in `a` at target indices. If `v` is shorter than
`ind` it will be repeated as necessary.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices will behave.
* 'raise' -- raise an error (default)
* 'wrap' -- wrap around
* 'clip' -- clip to the range
'clip' mode means that all indices that are too large are replaced
by the index that addresses the last element along that axis. Note
that this disables indexing with negative numbers.
See Also
--------
putmask, place
Examples
--------
>>> a = np.arange(5)
>>> np.put(a, [0, 2], [-44, -55])
>>> a
array([-44, 1, -55, 3, 4])
>>> a = np.arange(5)
>>> np.put(a, 22, -5, mode='clip')
>>> a
array([ 0, 1, 2, 3, -5])
"""
return a.put(ind, v, mode)
def swapaxes(a, axis1, axis2):
"""
Interchange two axes of an array.
Parameters
----------
a : array_like
Input array.
axis1 : int
First axis.
axis2 : int
Second axis.
Returns
-------
a_swapped : ndarray
If `a` is an ndarray, then a view of `a` is returned; otherwise
a new array is created.
Examples
--------
>>> x = np.array([[1,2,3]])
>>> np.swapaxes(x,0,1)
array([[1],
[2],
[3]])
>>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
>>> x
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> np.swapaxes(x,0,2)
array([[[0, 4],
[2, 6]],
[[1, 5],
[3, 7]]])
"""
try:
swapaxes = a.swapaxes
except AttributeError:
return _wrapit(a, 'swapaxes', axis1, axis2)
return swapaxes(axis1, axis2)
def transpose(a, axes=None):
"""
Permute the dimensions of an array.
Parameters
----------
a : array_like
Input array.
axes : list of ints, optional
By default, reverse the dimensions, otherwise permute the axes
according to the values given.
Returns
-------
p : ndarray
`a` with its axes permuted. A view is returned whenever
possible.
See Also
--------
rollaxis
Examples
--------
>>> x = np.arange(4).reshape((2,2))
>>> x
array([[0, 1],
[2, 3]])
>>> np.transpose(x)
array([[0, 2],
[1, 3]])
>>> x = np.ones((1, 2, 3))
>>> np.transpose(x, (1, 0, 2)).shape
(2, 1, 3)
"""
try:
transpose = a.transpose
except AttributeError:
return _wrapit(a, 'transpose', axes)
return transpose(axes)
def sort(a, axis=-1, kind='quicksort', order=None):
"""
Return a sorted copy of an array.
Parameters
----------
a : array_like
Array to be sorted.
axis : int or None, optional
Axis along which to sort. If None, the array is flattened before
sorting. The default is -1, which sorts along the last axis.
kind : {'quicksort', 'mergesort', 'heapsort'}, optional
Sorting algorithm. Default is 'quicksort'.
order : list, optional
When `a` is a structured array, this argument specifies which fields
to compare first, second, and so on. This list does not need to
include all of the fields.
Returns
-------
sorted_array : ndarray
Array of the same type and shape as `a`.
See Also
--------
ndarray.sort : Method to sort an array in-place.
argsort : Indirect sort.
lexsort : Indirect stable sort on multiple keys.
searchsorted : Find elements in a sorted array.
Notes
-----
The various sorting algorithms are characterized by their average speed,
worst case performance, work space size, and whether they are stable. A
stable sort keeps items with the same key in the same relative
order. The three available algorithms have the following
properties:
=========== ======= ============= ============ =======
kind speed worst case work space stable
=========== ======= ============= ============ =======
'quicksort' 1 O(n^2) 0 no
'mergesort' 2 O(n*log(n)) ~n/2 yes
'heapsort' 3 O(n*log(n)) 0 no
=========== ======= ============= ============ =======
All the sort algorithms make temporary copies of the data when
sorting along any but the last axis. Consequently, sorting along
the last axis is faster and uses less space than sorting along
any other axis.
The sort order for complex numbers is lexicographic. If both the real
and imaginary parts are non-nan then the order is determined by the
real parts except when they are equal, in which case the order is
determined by the imaginary parts.
Previous to numpy 1.4.0 sorting real and complex arrays containing nan
values led to undefined behaviour. In numpy versions >= 1.4.0 nan
values are sorted to the end. The extended sort order is:
* Real: [R, nan]
* Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj]
where R is a non-nan real value. Complex values with the same nan
placements are sorted according to the non-nan part if it exists.
Non-nan values are sorted as before.
Examples
--------
>>> a = np.array([[1,4],[3,1]])
>>> np.sort(a) # sort along the last axis
array([[1, 4],
[1, 3]])
>>> np.sort(a, axis=None) # sort the flattened array
array([1, 1, 3, 4])
>>> np.sort(a, axis=0) # sort along the first axis
array([[1, 1],
[3, 4]])
Use the `order` keyword to specify a field to use when sorting a
structured array:
>>> dtype = [('name', 'S10'), ('height', float), ('age', int)]
>>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38),
... ('Galahad', 1.7, 38)]
>>> a = np.array(values, dtype=dtype) # create a structured array
>>> np.sort(a, order='height') # doctest: +SKIP
array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
('Lancelot', 1.8999999999999999, 38)],
dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])
Sort by age, then height if ages are equal:
>>> np.sort(a, order=['age', 'height']) # doctest: +SKIP
array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38),
('Arthur', 1.8, 41)],
dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])
"""
if axis is None:
a = asanyarray(a).flatten()
axis = 0
else:
a = asanyarray(a).copy()
a.sort(axis, kind, order)
return a
def argsort(a, axis=-1, kind='quicksort', order=None):
"""
Returns the indices that would sort an array.
Perform an indirect sort along the given axis using the algorithm specified
by the `kind` keyword. It returns an array of indices of the same shape as
`a` that index data along the given axis in sorted order.
Parameters
----------
a : array_like
Array to sort.
axis : int or None, optional
Axis along which to sort. The default is -1 (the last axis). If None,
the flattened array is used.
kind : {'quicksort', 'mergesort', 'heapsort'}, optional
Sorting algorithm.
order : list, optional
When `a` is an array with fields defined, this argument specifies
which fields to compare first, second, etc. Not all fields need be
specified.
Returns
-------
index_array : ndarray, int
Array of indices that sort `a` along the specified axis.
In other words, ``a[index_array]`` yields a sorted `a`.
See Also
--------
sort : Describes sorting algorithms used.
lexsort : Indirect stable sort with multiple keys.
ndarray.sort : Inplace sort.
Notes
-----
See `sort` for notes on the different sorting algorithms.
As of NumPy 1.4.0 `argsort` works with real/complex arrays containing
nan values. The enhanced sort order is documented in `sort`.
Examples
--------
One dimensional array:
>>> x = np.array([3, 1, 2])
>>> np.argsort(x)
array([1, 2, 0])
Two-dimensional array:
>>> x = np.array([[0, 3], [2, 2]])
>>> x
array([[0, 3],
[2, 2]])
>>> np.argsort(x, axis=0)
array([[0, 1],
[1, 0]])
>>> np.argsort(x, axis=1)
array([[0, 1],
[0, 1]])
Sorting with keys:
>>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '<i4'), ('y', '<i4')])
>>> x
array([(1, 0), (0, 1)],
dtype=[('x', '<i4'), ('y', '<i4')])
>>> np.argsort(x, order=('x','y'))
array([1, 0])
>>> np.argsort(x, order=('y','x'))
array([0, 1])
"""
try:
argsort = a.argsort
except AttributeError:
return _wrapit(a, 'argsort', axis, kind, order)
return argsort(axis, kind, order)
def argmax(a, axis=None):
"""
Indices of the maximum values along an axis.
Parameters
----------
a : array_like
Input array.
axis : int, optional
By default, the index is into the flattened array, otherwise
along the specified axis.
Returns
-------
index_array : ndarray of ints
Array of indices into the array. It has the same shape as `a.shape`
with the dimension along `axis` removed.
See Also
--------
ndarray.argmax, argmin
amax : The maximum value along a given axis.
unravel_index : Convert a flat index into an index tuple.
Notes
-----
In case of multiple occurrences of the maximum values, the indices
corresponding to the first occurrence are returned.
Examples
--------
>>> a = np.arange(6).reshape(2,3)
>>> a
array([[0, 1, 2],
[3, 4, 5]])
>>> np.argmax(a)
5
>>> np.argmax(a, axis=0)
array([1, 1, 1])
>>> np.argmax(a, axis=1)
array([2, 2])
>>> b = np.arange(6)
>>> b[1] = 5
>>> b
array([0, 5, 2, 3, 4, 5])
>>> np.argmax(b) # Only the first occurrence is returned.
1
"""
try:
argmax = a.argmax
except AttributeError:
return _wrapit(a, 'argmax', axis)
return argmax(axis)
def argmin(a, axis=None):
"""
Return the indices of the minimum values along an axis.
See Also
--------
argmax : Similar function. Please refer to `numpy.argmax` for detailed
documentation.
"""
try:
argmin = a.argmin
except AttributeError:
return _wrapit(a, 'argmin', axis)
return argmin(axis)
def searchsorted(a, v, side='left'):
"""
Find indices where elements should be inserted to maintain order.
Find the indices into a sorted array `a` such that, if the corresponding
elements in `v` were inserted before the indices, the order of `a` would
be preserved.
Parameters
----------
a : 1-D array_like
Input array, sorted in ascending order.
v : array_like
Values to insert into `a`.
side : {'left', 'right'}, optional
If 'left', the index of the first suitable location found is given. If
'right', return the last such index. If there is no suitable
index, return either 0 or N (where N is the length of `a`).
Returns
-------
indices : array of ints
Array of insertion points with the same shape as `v`.
See Also
--------
sort : Return a sorted copy of an array.
histogram : Produce histogram from 1-D data.
Notes
-----
Binary search is used to find the required insertion points.
As of Numpy 1.4.0 `searchsorted` works with real/complex arrays containing
`nan` values. The enhanced sort order is documented in `sort`.
Examples
--------
>>> np.searchsorted([1,2,3,4,5], 3)
2
>>> np.searchsorted([1,2,3,4,5], 3, side='right')
3
>>> np.searchsorted([1,2,3,4,5], [-10, 10, 2, 3])
array([0, 5, 1, 2])
"""
try:
searchsorted = a.searchsorted
except AttributeError:
return _wrapit(a, 'searchsorted', v, side)
return searchsorted(v, side)
def resize(a, new_shape):
"""
Return a new array with the specified shape.
If the new array is larger than the original array, then the new array
is filled with repeated copied of `a`. Note that this behavior is different
from a.resize(new_shape) which fills with zeros instead of repeated
copies of `a`.
Parameters
----------
a : array_like
Array to be resized.
new_shape : {tuple, int}
Shape of resized array.
Returns
-------
reshaped_array : ndarray
The new array is formed from the data in the old array, repeated
if necessary to fill out the required number of elements. The data
are repeated in the order that the data are stored in memory.
See Also
--------
ndarray.resize : resize an array in-place.
Examples
--------
>>> a=np.array([[0,1],[2,3]])
>>> np.resize(a,(1,4))
array([[0, 1, 2, 3]])
>>> np.resize(a,(2,4))
array([[0, 1, 2, 3],
[0, 1, 2, 3]])
"""
if isinstance(new_shape, (int, nt.integer)):
new_shape = (new_shape,)
a = ravel(a)
Na = len(a)
if not Na: return mu.zeros(new_shape, a.dtype.char)
total_size = um.multiply.reduce(new_shape)
n_copies = int(total_size / Na)
extra = total_size % Na
if total_size == 0:
return a[:0]
if extra != 0:
n_copies = n_copies+1
extra = Na-extra
a = concatenate( (a,)*n_copies)
if extra > 0:
a = a[:-extra]
return reshape(a, new_shape)
def squeeze(a):
"""
Remove single-dimensional entries from the shape of an array.
Parameters
----------
a : array_like
Input data.
Returns
-------
squeezed : ndarray
The input array, but with with all dimensions of length 1
removed. Whenever possible, a view on `a` is returned.
Examples
--------
>>> x = np.array([[[0], [1], [2]]])
>>> x.shape
(1, 3, 1)
>>> np.squeeze(x).shape
(3,)
"""
try:
squeeze = a.squeeze
except AttributeError:
return _wrapit(a, 'squeeze')
return squeeze()
def diagonal(a, offset=0, axis1=0, axis2=1):
"""
Return specified diagonals.
If `a` is 2-D, returns the diagonal of `a` with the given offset,
i.e., the collection of elements of the form `a[i,i+offset]`.
If `a` has more than two dimensions, then the axes specified
by `axis1` and `axis2` are used to determine the 2-D subarray
whose diagonal is returned. The shape of the resulting array
can be determined by removing `axis1` and `axis2` and appending
an index to the right equal to the size of the resulting diagonals.
Parameters
----------
a : array_like
Array from which the diagonals are taken.
offset : int, optional
Offset of the diagonal from the main diagonal. Can be both positive
and negative. Defaults to main diagonal (0).
axis1 : int, optional
Axis to be used as the first axis of the 2-D subarrays from which
the diagonals should be taken. Defaults to first axis (0).
axis2 : int, optional
Axis to be used as the second axis of the 2-D subarrays from which
the diagonals should be taken. Defaults to second axis (1).
Returns
-------
array_of_diagonals : ndarray
If `a` is 2-D, a 1-D array containing the diagonal is
returned. If `a` has larger dimensions, then an array of
diagonals is returned.
Raises
------
ValueError
If the dimension of `a` is less than 2.
See Also
--------
diag : Matlab workalike for 1-D and 2-D arrays.
diagflat : Create diagonal arrays.
trace : Sum along diagonals.
Examples
--------
>>> a = np.arange(4).reshape(2,2)
>>> a
array([[0, 1],
[2, 3]])
>>> a.diagonal()
array([0, 3])
>>> a.diagonal(1)
array([1])
>>> a = np.arange(8).reshape(2,2,2)
>>> a
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> a.diagonal(0,-2,-1)
array([[0, 3],
[4, 7]])
"""
return asarray(a).diagonal(offset, axis1, axis2)
def trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None):
"""
Return the sum along diagonals of the array.
If `a` is 2-D, the sum along its diagonal with the given offset
is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i.
If `a` has more than two dimensions, then the axes specified by axis1 and
axis2 are used to determine the 2-D sub-arrays whose traces are returned.
The shape of the resulting array is the same as that of `a` with `axis1`
and `axis2` removed.
Parameters
----------
a : array_like
Input array, from which the diagonals are taken.
offset : int, optional
Offset of the diagonal from the main diagonal. Can be both positive
and negative. Defaults to 0.
axis1, axis2 : int, optional
Axes to be used as the first and second axis of the 2-D sub-arrays
from which the diagonals should be taken. Defaults are the first two
axes of `a`.
dtype : dtype, optional
Determines the data-type of the returned array and of the accumulator
where the elements are summed. If dtype has the value None and `a` is
of integer type of precision less than the default integer
precision, then the default integer precision is used. Otherwise,
the precision is the same as that of `a`.
out : ndarray, optional
Array into which the output is placed. Its type is preserved and
it must be of the right shape to hold the output.
Returns
-------
sum_along_diagonals : ndarray
If `a` is 2-D, the sum along the diagonal is returned. If `a` has
larger dimensions, then an array of sums along diagonals is returned.
See Also
--------
diag, diagonal, diagflat
Examples
--------
>>> np.trace(np.eye(3))
3.0
>>> a = np.arange(8).reshape((2,2,2))
>>> np.trace(a)
array([6, 8])
>>> a = np.arange(24).reshape((2,2,2,3))
>>> np.trace(a).shape
(2, 3)
"""
return asarray(a).trace(offset, axis1, axis2, dtype, out)
def ravel(a, order='C'):
"""
Return a flattened array.
A 1-D array, containing the elements of the input, is returned. A copy is
made only if needed.
Parameters
----------
a : array_like
Input array. The elements in `a` are read in the order specified by
`order`, and packed as a 1-D array.
order : {'C','F'}, optional
The elements of `a` are read in this order. It can be either
'C' for row-major order, or `F` for column-major order.
By default, row-major order is used.
Returns
-------
1d_array : ndarray
Output of the same dtype as `a`, and of shape ``(a.size(),)``.
See Also
--------
ndarray.flat : 1-D iterator over an array.
ndarray.flatten : 1-D array copy of the elements of an array
in row-major order.
Notes
-----
In row-major order, the row index varies the slowest, and the column
index the quickest. This can be generalized to multiple dimensions,
where row-major order implies that the index along the first axis
varies slowest, and the index along the last quickest. The opposite holds
for Fortran-, or column-major, mode.
Examples
--------
If an array is in C-order (default), then `ravel` is equivalent
to ``reshape(-1)``:
>>> x = np.array([[1, 2, 3], [4, 5, 6]])
>>> print x.reshape(-1)
[1 2 3 4 5 6]
>>> print np.ravel(x)
[1 2 3 4 5 6]
When flattening using Fortran-order, however, we see
>>> print np.ravel(x, order='F')
[1 4 2 5 3 6]
"""
return asarray(a).ravel(order)
def nonzero(a):
"""
Return the indices of the elements that are non-zero.
Returns a tuple of arrays, one for each dimension of `a`, containing
the indices of the non-zero elements in that dimension. The
corresponding non-zero values can be obtained with::
a[nonzero(a)]
To group the indices by element, rather than dimension, use::
transpose(nonzero(a))
The result of this is always a 2-D array, with a row for
each non-zero element.
Parameters
----------
a : array_like
Input array.
Returns
-------
tuple_of_arrays : tuple
Indices of elements that are non-zero.
See Also
--------
flatnonzero :
Return indices that are non-zero in the flattened version of the input
array.
ndarray.nonzero :
Equivalent ndarray method.
Examples
--------
>>> x = np.eye(3)
>>> x
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
>>> np.nonzero(x)
(array([0, 1, 2]), array([0, 1, 2]))
>>> x[np.nonzero(x)]
array([ 1., 1., 1.])
>>> np.transpose(np.nonzero(x))
array([[0, 0],
[1, 1],
[2, 2]])
A common use for ``nonzero`` is to find the indices of an array, where
a condition is True. Given an array `a`, the condition `a` > 3 is a
boolean array and since False is interpreted as 0, np.nonzero(a > 3)
yields the indices of the `a` where the condition is true.
>>> a = np.array([[1,2,3],[4,5,6],[7,8,9]])
>>> a > 3
array([[False, False, False],
[ True, True, True],
[ True, True, True]], dtype=bool)
>>> np.nonzero(a > 3)
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
The ``nonzero`` method of the boolean array can also be called.
>>> (a > 3).nonzero()
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
"""
try:
nonzero = a.nonzero
except AttributeError:
res = _wrapit(a, 'nonzero')
else:
res = nonzero()
return res
def shape(a):
"""
Return the shape of an array.
Parameters
----------
a : array_like
Input array.
Returns
-------
shape : tuple of ints
The elements of the shape tuple give the lengths of the
corresponding array dimensions.
See Also
--------
alen
ndarray.shape : Equivalent array method.
Examples
--------
>>> np.shape(np.eye(3))
(3, 3)
>>> np.shape([[1, 2]])
(1, 2)
>>> np.shape([0])
(1,)
>>> np.shape(0)
()
>>> a = np.array([(1, 2), (3, 4)], dtype=[('x', 'i4'), ('y', 'i4')])
>>> np.shape(a)
(2,)
>>> a.shape
(2,)
"""
try:
result = a.shape
except AttributeError:
result = asarray(a).shape
return result
def compress(condition, a, axis=None, out=None):
"""
Return selected slices of an array along given axis.
When working along a given axis, a slice along that axis is returned in
`output` for each index where `condition` evaluates to True. When
working on a 1-D array, `compress` is equivalent to `extract`.
Parameters
----------
condition : 1-D array of bools
Array that selects which entries to return. If len(condition)
is less than the size of `a` along the given axis, then output is
truncated to the length of the condition array.
a : array_like
Array from which to extract a part.
axis : int, optional
Axis along which to take slices. If None (default), work on the
flattened array.
out : ndarray, optional
Output array. Its type is preserved and it must be of the right
shape to hold the output.
Returns
-------
compressed_array : ndarray
A copy of `a` without the slices along axis for which `condition`
is false.
See Also
--------
take, choose, diag, diagonal, select
ndarray.compress : Equivalent method.
numpy.doc.ufuncs : Section "Output arguments"
Examples
--------
>>> a = np.array([[1, 2], [3, 4], [5, 6]])
>>> a
array([[1, 2],
[3, 4],
[5, 6]])
>>> np.compress([0, 1], a, axis=0)
array([[3, 4]])
>>> np.compress([False, True, True], a, axis=0)
array([[3, 4],
[5, 6]])
>>> np.compress([False, True], a, axis=1)
array([[2],
[4],
[6]])
Working on the flattened array does not return slices along an axis but
selects elements.
>>> np.compress([False, True], a)
array([2])
"""
try:
compress = a.compress
except AttributeError:
return _wrapit(a, 'compress', condition, axis, out)
return compress(condition, axis, out)
def clip(a, a_min, a_max, out=None):
"""
Clip (limit) the values in an array.
Given an interval, values outside the interval are clipped to
the interval edges. For example, if an interval of ``[0, 1]``
is specified, values smaller than 0 become 0, and values larger
than 1 become 1.
Parameters
----------
a : array_like
Array containing elements to clip.
a_min : scalar or array_like
Minimum value.
a_max : scalar or array_like
Maximum value. If `a_min` or `a_max` are array_like, then they will
be broadcasted to the shape of `a`.
out : ndarray, optional
The results will be placed in this array. It may be the input
array for in-place clipping. `out` must be of the right shape
to hold the output. Its type is preserved.
Returns
-------
clipped_array : ndarray
An array with the elements of `a`, but where values
< `a_min` are replaced with `a_min`, and those > `a_max`
with `a_max`.
See Also
--------
numpy.doc.ufuncs : Section "Output arguments"
Examples
--------
>>> a = np.arange(10)
>>> np.clip(a, 1, 8)
array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])
>>> a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.clip(a, 3, 6, out=a)
array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
>>> a
array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
>>> np.clip(a, [3,4,1,1,1,4,4,4,4,4], 8)
array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])
"""
try:
clip = a.clip
except AttributeError:
return _wrapit(a, 'clip', a_min, a_max, out)
return clip(a_min, a_max, out)
def sum(a, axis=None, dtype=None, out=None):
"""
Sum of array elements over a given axis.
Parameters
----------
a : array_like
Elements to sum.
axis : integer, optional
Axis over which the sum is taken. By default `axis` is None,
and all elements are summed.
dtype : dtype, optional
The type of the returned array and of the accumulator in which
the elements are summed. By default, the dtype of `a` is used.
An exception is when `a` has an integer type with less precision
than the default platform integer. In that case, the default
platform integer is used instead.
out : ndarray, optional
Array into which the output is placed. By default, a new array is
created. If `out` is given, it must be of the appropriate shape
(the shape of `a` with `axis` removed, i.e.,
``numpy.delete(a.shape, axis)``). Its type is preserved. See
`doc.ufuncs` (Section "Output arguments") for more details.
Returns
-------
sum_along_axis : ndarray
An array with the same shape as `a`, with the specified
axis removed. If `a` is a 0-d array, or if `axis` is None, a scalar
is returned. If an output array is specified, a reference to
`out` is returned.
See Also
--------
ndarray.sum : Equivalent method.
cumsum : Cumulative sum of array elements.
trapz : Integration of array values using the composite trapezoidal rule.
mean, average
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
Examples
--------
>>> np.sum([0.5, 1.5])
2.0
>>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32)
1
>>> np.sum([[0, 1], [0, 5]])
6
>>> np.sum([[0, 1], [0, 5]], axis=0)
array([0, 6])
>>> np.sum([[0, 1], [0, 5]], axis=1)
array([1, 5])
If the accumulator is too small, overflow occurs:
>>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)
-128
"""
if isinstance(a, _gentype):
res = _sum_(a)
if out is not None:
out[...] = res
return out
return res
try:
sum = a.sum
except AttributeError:
return _wrapit(a, 'sum', axis, dtype, out)
return sum(axis, dtype, out)
def product (a, axis=None, dtype=None, out=None):
"""
Return the product of array elements over a given axis.
See Also
--------
prod : equivalent function; see for details.
"""
try:
prod = a.prod
except AttributeError:
return _wrapit(a, 'prod', axis, dtype, out)
return prod(axis, dtype, out)
def sometrue(a, axis=None, out=None):
"""
Check whether some values are true.
Refer to `any` for full documentation.
See Also
--------
any : equivalent function
"""
try:
any = a.any
except AttributeError:
return _wrapit(a, 'any', axis, out)
return any(axis, out)
def alltrue (a, axis=None, out=None):
"""
Check if all elements of input array are true.
See Also
--------
numpy.all : Equivalent function; see for details.
"""
try:
all = a.all
except AttributeError:
return _wrapit(a, 'all', axis, out)
return all(axis, out)
def any(a,axis=None, out=None):
"""
Test whether any array element along a given axis evaluates to True.
Returns single boolean unless `axis` is not ``None``
Parameters
----------
a : array_like
Input array or object that can be converted to an array.
axis : int, optional
Axis along which a logical OR is performed.
The default (`axis` = `None`) is to perform a logical OR
over a flattened input array. `axis` may be negative, in which
case it counts from the last to the first axis.
out : ndarray, optional
Alternative output array in which to place the result.
It must have the same shape as the expected output and
the type is preserved. See `doc.ufuncs` (Section
"Output arguments") for details.
Returns
-------
any : bool, ndarray
A new boolean or `ndarray` is returned unless `out` is
specified, in which case a reference to `out` is returned.
See Also
--------
ndarray.any : equivalent method
all : Test whether all array elements along a given axis evaluate
to True.
Notes
-----
Not a Number (NaN), positive infinity and negative infinity
evaluate to `True` because these are not equal to zero.
Examples
--------
>>> np.any([[True, False], [True, True]])
True
>>> np.any([[True, False], [False, False]], axis=0)
array([ True, False], dtype=bool)
>>> np.any([-1, 0, 5])
True
>>> np.any(np.nan)
True
>>> o=np.array([False])
>>> z=np.any([-1, 4, 5], out=o)
>>> z, o
(array([ True], dtype=bool), array([ True], dtype=bool))
>>> # Check now that z is a reference to o
>>> z is o
True
>>> id(z), id(o) # identity of z and o
(191614240, 191614240)
"""
try:
any = a.any
except AttributeError:
return _wrapit(a, 'any', axis, out)
return any(axis, out)
def all(a,axis=None, out=None):
"""
Test whether all array elements along a given axis evaluate to True.
Parameters
----------
a : array_like
Input array or object that can be converted to an array.
axis : int, optional
Axis along which a logical AND is performed.
The default (`axis` = `None`) is to perform a logical AND
over a flattened input array. `axis` may be negative, in which
case it counts from the last to the first axis.
out : ndarray, optional
Alternative output array in which to place the result.
It must have the same shape as the expected output and
the type is preserved. See `doc.ufuncs` (Section "Output
arguments") for more details.
Returns
-------
all : ndarray, bool
A new boolean or array is returned unless `out` is
specified, in which case a reference to `out` is returned.
See Also
--------
ndarray.all : equivalent method
any : Test whether any array element along a given axis evaluates to True.
Notes
-----
Not a Number (NaN), positive infinity and negative infinity
evaluate to `True` because these are not equal to zero.
Examples
--------
>>> np.all([[True,False],[True,True]])
False
>>> np.all([[True,False],[True,True]], axis=0)
array([ True, False], dtype=bool)
>>> np.all([-1, 4, 5])
True
>>> np.all([1.0, np.nan])
True
>>> o=np.array([False])
>>> z=np.all([-1, 4, 5], out=o)
>>> id(z), id(o), z
(28293632, 28293632, array([ True], dtype=bool))
"""
try:
all = a.all
except AttributeError:
return _wrapit(a, 'all', axis, out)
return all(axis, out)
def cumsum (a, axis=None, dtype=None, out=None):
"""
Return the cumulative sum of the elements along a given axis.
Parameters
----------
a : array_like
Input array.
axis : int, optional
Axis along which the cumulative sum is computed. The default
(None) is to compute the cumsum over the flattened array.
dtype : dtype, optional
Type of the returned array and of the accumulator in which the
elements are summed. If `dtype` is not specified, it defaults
to the dtype of `a`, unless `a` has an integer dtype with a
precision less than that of the default platform integer. In
that case, the default platform integer is used.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output
but the type will be cast if necessary. See `doc.ufuncs`
(Section "Output arguments") for more details.
Returns
-------
cumsum_along_axis : ndarray.
A new array holding the result is returned unless `out` is
specified, in which case a reference to `out` is returned. The
result has the same size as `a`, and the same shape as `a` if
`axis` is not None or `a` is a 1-d array.
See Also
--------
sum : Sum array elements.
trapz : Integration of array values using the composite trapezoidal rule.
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
Examples
--------
>>> a = np.array([[1,2,3], [4,5,6]])
>>> a
array([[1, 2, 3],
[4, 5, 6]])
>>> np.cumsum(a)
array([ 1, 3, 6, 10, 15, 21])
>>> np.cumsum(a, dtype=float) # specifies type of output value(s)
array([ 1., 3., 6., 10., 15., 21.])
>>> np.cumsum(a,axis=0) # sum over rows for each of the 3 columns
array([[1, 2, 3],
[5, 7, 9]])
>>> np.cumsum(a,axis=1) # sum over columns for each of the 2 rows
array([[ 1, 3, 6],
[ 4, 9, 15]])
"""
try:
cumsum = a.cumsum
except AttributeError:
return _wrapit(a, 'cumsum', axis, dtype, out)
return cumsum(axis, dtype, out)
def cumproduct(a, axis=None, dtype=None, out=None):
"""
Return the cumulative product over the given axis.
See Also
--------
cumprod : equivalent function; see for details.
"""
try:
cumprod = a.cumprod
except AttributeError:
return _wrapit(a, 'cumprod', axis, dtype, out)
return cumprod(axis, dtype, out)
def ptp(a, axis=None, out=None):
"""
Range of values (maximum - minimum) along an axis.
The name of the function comes from the acronym for 'peak to peak'.
Parameters
----------
a : array_like
Input values.
axis : int, optional
Axis along which to find the peaks. By default, flatten the
array.
out : array_like
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output,
but the type of the output values will be cast if necessary.
Returns
-------
ptp : ndarray
A new array holding the result, unless `out` was
specified, in which case a reference to `out` is returned.
Examples
--------
>>> x = np.arange(4).reshape((2,2))
>>> x
array([[0, 1],
[2, 3]])
>>> np.ptp(x, axis=0)
array([2, 2])
>>> np.ptp(x, axis=1)
array([1, 1])
"""
try:
ptp = a.ptp
except AttributeError:
return _wrapit(a, 'ptp', axis, out)
return ptp(axis, out)
def amax(a, axis=None, out=None):
"""
Return the maximum along an axis.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis along which to operate. By default flattened input is used.
out : ndarray, optional
Alternative output array in which to place the result. Must
be of the same shape and buffer length as the expected output.
See `doc.ufuncs` (Section "Output arguments") for more details.
Returns
-------
amax : ndarray
A new array or a scalar with the result, or a reference to `out`
if it was specified.
See Also
--------
nanmax : nan values are ignored instead of being propagated
fmax : same behavior as the C99 fmax function
argmax : Indices of the maximum values.
Notes
-----
NaN values are propagated, that is if at least one item is nan, the
corresponding max value will be nan as well. To ignore NaN values (matlab
behavior), please use nanmax.
Examples
--------
>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0, 1],
[2, 3]])
>>> np.amax(a)
3
>>> np.amax(a, axis=0)
array([2, 3])
>>> np.amax(a, axis=1)
array([1, 3])
>>> b = np.arange(5, dtype=np.float)
>>> b[2] = np.NaN
>>> np.amax(b)
nan
>>> np.nanmax(b)
4.0
"""
try:
amax = a.max
except AttributeError:
return _wrapit(a, 'max', axis, out)
return amax(axis, out)
def amin(a, axis=None, out=None):
"""
Return the minimum along an axis.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis along which to operate. By default a flattened input is used.
out : ndarray, optional
Alternative output array in which to place the result. Must
be of the same shape and buffer length as the expected output.
See `doc.ufuncs` (Section "Output arguments") for more details.
Returns
-------
amin : ndarray
A new array or a scalar with the result, or a reference to `out` if it
was specified.
See Also
--------
nanmin: nan values are ignored instead of being propagated
fmin: same behavior as the C99 fmin function
argmin: Return the indices of the minimum values.
amax, nanmax, fmax
Notes
-----
NaN values are propagated, that is if at least one item is nan, the
corresponding min value will be nan as well. To ignore NaN values (matlab
behavior), please use nanmin.
Examples
--------
>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0, 1],
[2, 3]])
>>> np.amin(a) # Minimum of the flattened array
0
>>> np.amin(a, axis=0) # Minima along the first axis
array([0, 1])
>>> np.amin(a, axis=1) # Minima along the second axis
array([0, 2])
>>> b = np.arange(5, dtype=np.float)
>>> b[2] = np.NaN
>>> np.amin(b)
nan
>>> np.nanmin(b)
0.0
"""
try:
amin = a.min
except AttributeError:
return _wrapit(a, 'min', axis, out)
return amin(axis, out)
def alen(a):
"""
Return the length of the first dimension of the input array.
Parameters
----------
a : array_like
Input array.
Returns
-------
l : int
Length of the first dimension of `a`.
See Also
--------
shape, size
Examples
--------
>>> a = np.zeros((7,4,5))
>>> a.shape[0]
7
>>> np.alen(a)
7
"""
try:
return len(a)
except TypeError:
return len(array(a,ndmin=1))
def prod(a, axis=None, dtype=None, out=None):
"""
Return the product of array elements over a given axis.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis over which the product is taken. By default, the product
of all elements is calculated.
dtype : data-type, optional
The data-type of the returned array, as well as of the accumulator
in which the elements are multiplied. By default, if `a` is of
integer type, `dtype` is the default platform integer. (Note: if
the type of `a` is unsigned, then so is `dtype`.) Otherwise,
the dtype is the same as that of `a`.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output, but the type of the
output values will be cast if necessary.
Returns
-------
product_along_axis : ndarray, see `dtype` parameter above.
An array shaped as `a` but with the specified axis removed.
Returns a reference to `out` if specified.
See Also
--------
ndarray.prod : equivalent method
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow. That means that, on a 32-bit platform:
>>> x = np.array([536870910, 536870910, 536870910, 536870910])
>>> np.prod(x) #random
16
Examples
--------
By default, calculate the product of all elements:
>>> np.prod([1.,2.])
2.0
Even when the input array is two-dimensional:
>>> np.prod([[1.,2.],[3.,4.]])
24.0
But we can also specify the axis over which to multiply:
>>> np.prod([[1.,2.],[3.,4.]], axis=1)
array([ 2., 12.])
If the type of `x` is unsigned, then the output type is
the unsigned platform integer:
>>> x = np.array([1, 2, 3], dtype=np.uint8)
>>> np.prod(x).dtype == np.uint
True
If `x` is of a signed integer type, then the output type
is the default platform integer:
>>> x = np.array([1, 2, 3], dtype=np.int8)
>>> np.prod(x).dtype == np.int
True
"""
try:
prod = a.prod
except AttributeError:
return _wrapit(a, 'prod', axis, dtype, out)
return prod(axis, dtype, out)
def cumprod(a, axis=None, dtype=None, out=None):
"""
Return the cumulative product of elements along a given axis.
Parameters
----------
a : array_like
Input array.
axis : int, optional
Axis along which the cumulative product is computed. By default the
input is flattened.
dtype : dtype, optional
Type of the returned array, as well as of the accumulator in which
the elements are multiplied. If dtype is not specified, it defaults
to the dtype of `a`, unless `a` has an integer dtype with a precision
less than that of the default platform integer. In that case, the
default platform integer is used instead.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output
but the type of the resulting values will be cast if necessary.
Returns
-------
cumprod : ndarray
A new array holding the result is returned unless `out` is
specified, in which case a reference to out is returned.
See Also
--------
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
Examples
--------
>>> a = np.array([1,2,3])
>>> np.cumprod(a) # intermediate results 1, 1*2
... # total product 1*2*3 = 6
array([1, 2, 6])
>>> a = np.array([[1, 2, 3], [4, 5, 6]])
>>> np.cumprod(a, dtype=float) # specify type of output
array([ 1., 2., 6., 24., 120., 720.])
The cumulative product for each column (i.e., over the rows of)
`a`:
>>> np.cumprod(a, axis=0)
array([[ 1, 2, 3],
[ 4, 10, 18]])
The cumulative product for each row (i.e. over the columns of)
`a`:
>>> np.cumprod(a,axis=1)
array([[ 1, 2, 6],
[ 4, 20, 120]])
"""
try:
cumprod = a.cumprod
except AttributeError:
return _wrapit(a, 'cumprod', axis, dtype, out)
return cumprod(axis, dtype, out)
def ndim(a):
"""
Return the number of dimensions of an array.
Parameters
----------
a : array_like
Input array. If it is not already an ndarray, a conversion is
attempted.
Returns
-------
number_of_dimensions : int
The number of dimensions in `a`. Scalars are zero-dimensional.
See Also
--------
ndarray.ndim : equivalent method
shape : dimensions of array
ndarray.shape : dimensions of array
Examples
--------
>>> np.ndim([[1,2,3],[4,5,6]])
2
>>> np.ndim(np.array([[1,2,3],[4,5,6]]))
2
>>> np.ndim(1)
0
"""
try:
return a.ndim
except AttributeError:
return asarray(a).ndim
def rank(a):
"""
Return the number of dimensions of an array.
If `a` is not already an array, a conversion is attempted.
Scalars are zero dimensional.
Parameters
----------
a : array_like
Array whose number of dimensions is desired. If `a` is not an array,
a conversion is attempted.
Returns
-------
number_of_dimensions : int
The number of dimensions in the array.
See Also
--------
ndim : equivalent function
ndarray.ndim : equivalent property
shape : dimensions of array
ndarray.shape : dimensions of array
Notes
-----
In the old Numeric package, `rank` was the term used for the number of
dimensions, but in Numpy `ndim` is used instead.
Examples
--------
>>> np.rank([1,2,3])
1
>>> np.rank(np.array([[1,2,3],[4,5,6]]))
2
>>> np.rank(1)
0
"""
try:
return a.ndim
except AttributeError:
return asarray(a).ndim
def size(a, axis=None):
"""
Return the number of elements along a given axis.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis along which the elements are counted. By default, give
the total number of elements.
Returns
-------
element_count : int
Number of elements along the specified axis.
See Also
--------
shape : dimensions of array
ndarray.shape : dimensions of array
ndarray.size : number of elements in array
Examples
--------
>>> a = np.array([[1,2,3],[4,5,6]])
>>> np.size(a)
6
>>> np.size(a,1)
3
>>> np.size(a,0)
2
"""
if axis is None:
try:
return a.size
except AttributeError:
return asarray(a).size
else:
try:
return a.shape[axis]
except AttributeError:
return asarray(a).shape[axis]
def around(a, decimals=0, out=None):
"""
Evenly round to the given number of decimals.
Parameters
----------
a : array_like
Input data.
decimals : int, optional
Number of decimal places to round to (default: 0). If
decimals is negative, it specifies the number of positions to
the left of the decimal point.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output, but the type of the output
values will be cast if necessary. See `doc.ufuncs` (Section
"Output arguments") for details.
Returns
-------
rounded_array : ndarray
An array of the same type as `a`, containing the rounded values.
Unless `out` was specified, a new array is created. A reference to
the result is returned.
The real and imaginary parts of complex numbers are rounded
separately. The result of rounding a float is a float.
See Also
--------
ndarray.round : equivalent method
ceil, fix, floor, rint, trunc
Notes
-----
For values exactly halfway between rounded decimal values, Numpy
rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,
-0.5 and 0.5 round to 0.0, etc. Results may also be surprising due
to the inexact representation of decimal fractions in the IEEE
floating point standard [1]_ and errors introduced when scaling
by powers of ten.
References
----------
.. [1] "Lecture Notes on the Status of IEEE 754", William Kahan,
http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
.. [2] "How Futile are Mindless Assessments of
Roundoff in Floating-Point Computation?", William Kahan,
http://www.cs.berkeley.edu/~wkahan/Mindless.pdf
Examples
--------
>>> np.around([0.37, 1.64])
array([ 0., 2.])
>>> np.around([0.37, 1.64], decimals=1)
array([ 0.4, 1.6])
>>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
array([ 0., 2., 2., 4., 4.])
>>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned
array([ 1, 2, 3, 11])
>>> np.around([1,2,3,11], decimals=-1)
array([ 0, 0, 0, 10])
"""
try:
round = a.round
except AttributeError:
return _wrapit(a, 'round', decimals, out)
return round(decimals, out)
def round_(a, decimals=0, out=None):
"""
Round an array to the given number of decimals.
Refer to `around` for full documentation.
See Also
--------
around : equivalent function
"""
try:
round = a.round
except AttributeError:
return _wrapit(a, 'round', decimals, out)
return round(decimals, out)
def mean(a, axis=None, dtype=None, out=None):
"""
Compute the arithmetic mean along the specified axis.
Returns the average of the array elements. The average is taken
over the flattened array by default, otherwise over the specified
axis. float64 intermediate and return values are used for integer
inputs.
Parameters
----------
a : array_like
Array containing numbers whose mean is desired. If `a` is not an
array, a conversion is attempted.
axis : int, optional
Axis along which the means are computed. The default is to compute
the mean of the flattened array.
dtype : dtype, optional
Type to use in computing the mean. For integer inputs, the default
is float64; for floating point, inputs it is the same as the input
dtype.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output but the type will be cast if
necessary. See `doc.ufuncs` for details.
Returns
-------
m : ndarray, see dtype parameter above
If `out=None`, returns a new array containing the mean values,
otherwise a reference to the output array is returned.
See Also
--------
average : Weighted average
Notes
-----
The arithmetic mean is the sum of the elements along the axis divided
by the number of elements.
Note that for floating-point input, the mean is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for float32 (see example below).
Specifying a higher-accuracy accumulator using the `dtype` keyword can
alleviate this issue.
Examples
--------
>>> a = np.array([[1, 2], [3, 4]])
>>> np.mean(a)
2.5
>>> np.mean(a, axis=0)
array([ 2., 3.])
>>> np.mean(a, axis=1)
array([ 1.5, 3.5])
In single precision, `mean` can be inaccurate:
>>> a = np.zeros((2, 512*512), dtype=np.float32)
>>> a[0, :] = 1.0
>>> a[1, :] = 0.1
>>> np.mean(a)
0.546875
Computing the mean in float64 is more accurate:
>>> np.mean(a, dtype=np.float64)
0.55000000074505806
"""
try:
mean = a.mean
except AttributeError:
return _wrapit(a, 'mean', axis, dtype, out)
return mean(axis, dtype, out)
def std(a, axis=None, dtype=None, out=None, ddof=0):
"""
Compute the standard deviation along the specified axis.
Returns the standard deviation, a measure of the spread of a distribution,
of the array elements. The standard deviation is computed for the
flattened array by default, otherwise over the specified axis.
Parameters
----------
a : array_like
Calculate the standard deviation of these values.
axis : int, optional
Axis along which the standard deviation is computed. The default is
to compute the standard deviation of the flattened array.
dtype : dtype, optional
Type to use in computing the standard deviation. For arrays of
integer type the default is float64, for arrays of float types it is
the same as the array type.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output but the type (of the calculated
values) will be cast if necessary.
ddof : int, optional
Means Delta Degrees of Freedom. The divisor used in calculations
is ``N - ddof``, where ``N`` represents the number of elements.
By default `ddof` is zero.
Returns
-------
standard_deviation : ndarray, see dtype parameter above.
If `out` is None, return a new array containing the standard deviation,
otherwise return a reference to the output array.
See Also
--------
var, mean
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
The standard deviation is the square root of the average of the squared
deviations from the mean, i.e., ``std = sqrt(mean(abs(x - x.mean())**2))``.
The mean is normally calculated as ``x.sum() / N``, where
``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof``
is used instead. In standard statistical practice, ``ddof=1`` provides an
unbiased estimator of the variance of the infinite population. ``ddof=0``
provides a maximum likelihood estimate of the variance for normally
distributed variables. The standard deviation computed in this function
is the square root of the estimated variance, so even with ``ddof=1``, it
will not be an unbiased estimate of the standard deviation per se.
Note that, for complex numbers, `std` takes the absolute
value before squaring, so that the result is always real and nonnegative.
For floating-point input, the *std* is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for float32 (see example below).
Specifying a higher-accuracy accumulator using the `dtype` keyword can
alleviate this issue.
Examples
--------
>>> a = np.array([[1, 2], [3, 4]])
>>> np.std(a)
1.1180339887498949
>>> np.std(a, axis=0)
array([ 1., 1.])
>>> np.std(a, axis=1)
array([ 0.5, 0.5])
In single precision, std() can be inaccurate:
>>> a = np.zeros((2,512*512), dtype=np.float32)
>>> a[0,:] = 1.0
>>> a[1,:] = 0.1
>>> np.std(a)
0.45172946707416706
Computing the standard deviation in float64 is more accurate:
>>> np.std(a, dtype=np.float64)
0.44999999925552653
"""
try:
std = a.std
except AttributeError:
return _wrapit(a, 'std', axis, dtype, out, ddof)
return std(axis, dtype, out, ddof)
def var(a, axis=None, dtype=None, out=None, ddof=0):
"""
Compute the variance along the specified axis.
Returns the variance of the array elements, a measure of the spread of a
distribution. The variance is computed for the flattened array by default,
otherwise over the specified axis.
Parameters
----------
a : array_like
Array containing numbers whose variance is desired. If `a` is not an
array, a conversion is attempted.
axis : int, optional
Axis along which the variance is computed. The default is to compute
the variance of the flattened array.
dtype : dtype, optional
Type to use in computing the variance. For arrays of integer type
the default is float32; for arrays of float types it is the same as
the array type.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output but the type is cast if
necessary.
ddof : int, optional
"Delta Degrees of Freedom": the divisor used in calculation is
``N - ddof``, where ``N`` represents the number of elements. By
default `ddof` is zero.
Returns
-------
variance : ndarray, see dtype parameter above
If out=None, returns a new array containing the variance; otherwise
a reference to the output array is returned.
See Also
--------
std : Standard deviation
mean : Average
numpy.doc.ufuncs : Section "Output arguments"
Notes
-----
The variance is the average of the squared deviations from the mean,
i.e., ``var = mean(abs(x - x.mean())**2)``.
The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
If, however, `ddof` is specified, the divisor ``N - ddof`` is used
instead. In standard statistical practice, ``ddof=1`` provides an
unbiased estimator of the variance of the infinite population. ``ddof=0``
provides a maximum likelihood estimate of the variance for normally
distributed variables.
Note that for complex numbers, the absolute value is taken before
squaring, so that the result is always real and nonnegative.
For floating-point input, the variance is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for float32 (see example below).
Specifying a higher-accuracy accumulator using the `dtype` keyword can
alleviate this issue.
Examples
--------
>>> a = np.array([[1,2],[3,4]])
>>> np.var(a)
1.25
>>> np.var(a,0)
array([ 1., 1.])
>>> np.var(a,1)
array([ 0.25, 0.25])
In single precision, var() can be inaccurate:
>>> a = np.zeros((2,512*512), dtype=np.float32)
>>> a[0,:] = 1.0
>>> a[1,:] = 0.1
>>> np.var(a)
0.20405951142311096
Computing the standard deviation in float64 is more accurate:
>>> np.var(a, dtype=np.float64)
0.20249999932997387
>>> ((1-0.55)**2 + (0.1-0.55)**2)/2
0.20250000000000001
"""
try:
var = a.var
except AttributeError:
return _wrapit(a, 'var', axis, dtype, out, ddof)
return var(axis, dtype, out, ddof)
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