# 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'):
"""Return an array formed from the elements of a at the given indices.
This function does the same thing as "fancy" indexing; however, it can
be easier to use if you need to specify a given axis.
Parameters
----------
a : array
The source array
indices : int array
The indices of the values to extract.
axis : {None, int}, optional
The axis over which to select values. None signifies that the
operation should be performed over the flattened array.
out : {None, array}, optional
If provided, the result will be inserted into 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
'wrap' -- wrap around
'clip' -- clip to the range
Returns
-------
subarray : array
The returned array has the same type as a.
See Also
--------
ndarray.take : equivalent method
"""
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'):
"""Returns an array containing the data of a, but with a new shape.
Parameters
----------
a : array
Array to be reshaped.
newshape : shape tuple or int
The new shape should be compatible with the original shape. If an
integer, then the result will be a 1D array of that length.
order : {'C', 'FORTRAN'}, optional
Determines whether the array data should be viewed as in C
(row-major) order or FORTRAN (column-major) order.
Returns
-------
reshaped_array : array
This will be a new view object if possible; otherwise, it will
be a copy.
See Also
--------
ndarray.reshape : Equivalent method.
"""
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'):
"""Use an index array to construct a new array from a set of
choices.
Given an array of integers and a set of n choice arrays, this function
will create a new array that merges each of the choice arrays. Where a
value in `a` is i, then the new array will have the value that
choices[i] contains in the same place.
Parameters
----------
a : int array
This array must contain integers in [0, n-1], where n is the number
of choices.
choices : sequence of arrays
Choice arrays. The index array and all of the choices should be
broadcastable to the same shape.
out : array, optional
If provided, the result will be inserted into 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
'wrap' : wrap around
'clip' : clip to the range
Returns
-------
merged_array : array
See Also
--------
ndarray.choose : equivalent method
Examples
--------
>>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],
... [20, 21, 22, 23], [30, 31, 32, 33]]
>>> choose([2, 3, 1, 0], choices)
array([20, 31, 12, 3])
>>> choose([2, 4, 1, 0], choices, mode='clip')
array([20, 31, 12, 3])
>>> choose([2, 4, 1, 0], choices, mode='wrap')
array([20, 1, 12, 3])
"""
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 : {integer, integer_array}
The number of repetitions for each element. If a plain integer, then
it is applied to all elements. If an array, it needs to be of the
same length as the chosen axis.
axis : {None, integer}, optional
The axis along which to repeat values. If None, then this function
will operated on the flattened array `a` and return a similarly flat
result.
Returns
-------
repeated_array : array
See Also
--------
ndarray.repeat : equivalent method
tile : tile an array
Examples
--------
>>> x = array([[1,2],[3,4]])
>>> repeat(x, 2)
array([1, 1, 2, 2, 3, 3, 4, 4])
>>> repeat(x, 3, axis=1)
array([[1, 1, 1, 2, 2, 2],
[3, 3, 3, 4, 4, 4]])
>>> 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'):
"""Set a.flat[n] = v[n] for all n in ind.
If v is shorter than ind, it will repeat.
Parameters
----------
a : array_like (contiguous)
Target array.
ind : array_like
Target indices, interpreted as integers.
v : array_like
Values to place in `a` at target indices.
mode : {'raise', 'wrap', 'clip'}, optional
Specifies how out-of-bounds indices will behave.
'raise' -- raise an error
'wrap' -- wrap around
'clip' -- clip to the range
Notes
-----
If v is shorter than mask it will be repeated as necessary. In particular v
can be a scalar or length 1 array. The routine put is the equivalent of the
following (although the loop is in C for speed):
ind = array(indices, copy=False)
v = array(values, copy=False).astype(a.dtype)
for i in ind: a.flat[i] = v[i]
Examples
--------
>>> x = np.arange(5)
>>> np.put(x,[0,2,4],[-1,-2,-3])
>>> print x
[-1 1 -2 3 -3]
"""
return a.put(ind, v, mode)
def swapaxes(a, axis1, axis2):
"""Return a view of array a with axis1 and axis2 interchanged.
Parameters
----------
a : array_like
Input array.
axis1 : int
First axis.
axis2 : int
Second axis.
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):
"""Return a view of the array with dimensions permuted.
Parameters
----------
a : array_like
Input array.
axes : {None, list of int}, optional
If None (the default), reverse dimensions, otherwise permute
axes according to the values given.
Examples
--------
>>> x = np.arange(4).reshape((2,2))
>>> x
array([[0, 1],
[2, 3]])
>>> np.transpose(x)
array([[0, 2],
[1, 3]])
>>> np.transpose(x,(0,1)) # no change, axes are kept in current order
array([[0, 1],
[2, 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 copy of 'a' sorted along the given axis.
Perform an inplace sort along the given axis using the algorithm
specified by the kind keyword.
Parameters
----------
a : array
Array to be sorted.
axis : {None, int} optional
Axis along which to sort. None indicates that the flattened
array should be used.
kind : {'quicksort', 'mergesort', 'heapsort'}, optional
Sorting algorithm to use.
order : {None, list type}, 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
-------
sorted_array : array of same type as a
See Also
--------
argsort : Indirect sort.
lexsort : Indirect stable sort on multiple keys.
searchsorted : Find keys in sorted array.
Notes
-----
The various sorts are characterized by average speed, worst case
performance, need for work space, 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
the sort is not along the last axis. Consequently, sorts along
the last axis are faster and use less space than sorts along
other axis.
"""
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 array of indices that index 'a' in sorted order.
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
Array to be sorted.
axis : {None, int} optional
Axis along which to sort. None indicates that the flattened
array should be used.
kind : {'quicksort', 'mergesort', 'heapsort'}, optional
Sorting algorithm to use.
order : {None, list type}, 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 : {integer_array}
Array of indices that sort 'a' along the specified axis.
See Also
--------
lexsort : Indirect stable sort with multiple keys.
sort : Inplace sort.
Notes
-----
The various sorts are characterized by average speed, worst case
performance, need for work space, 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
the sort is not along the last axis. Consequently, sorts along
the last axis are faster and use less space than sorts along
other axis.
"""
try:
argsort = a.argsort
except AttributeError:
return _wrapit(a, 'argsort', axis, kind, order)
return argsort(axis, kind, order)
def argmax(a, axis=None):
"""Returns array of indices of the maximum values of along the given axis.
Parameters
----------
a : {array_like}
Array to look in.
axis : {None, integer}
If None, the index is into the flattened array, otherwise along
the specified axis
Returns
-------
index_array : {integer_array}
Examples
--------
>>> a = arange(6).reshape(2,3)
>>> argmax(a)
5
>>> argmax(a,0)
array([1, 1, 1])
>>> argmax(a,1)
array([2, 2])
"""
try:
argmax = a.argmax
except AttributeError:
return _wrapit(a, 'argmax', axis)
return argmax(axis)
def argmin(a, axis=None):
"""Return array of indices to the minimum values along the given axis.
Parameters
----------
a : {array_like}
Array to look in.
axis : {None, integer}
If None, the index is into the flattened array, otherwise along
the specified axis
Returns
-------
index_array : {integer_array}
Examples
--------
>>> a = arange(6).reshape(2,3)
>>> argmin(a)
0
>>> argmin(a,0)
array([0, 0, 0])
>>> argmin(a,1)
array([0, 0])
"""
try:
argmin = a.argmin
except AttributeError:
return _wrapit(a, 'argmin', axis)
return argmin(axis)
def searchsorted(a, v, side='left'):
"""Return indices where keys in v should be inserted to maintain order.
Find the indices into a sorted array such that if the corresponding keys in
v were inserted before the indices the order of a would be preserved. If
side='left', then the first such index is returned. If side='right', then
the last such index is returned. If there is no such index because the key
is out of bounds, then the length of a is returned, i.e., the key would need
to be appended. The returned index array has the same shape as v.
Parameters
----------
a : 1-d array
Array must be sorted in ascending order.
v : array or list type
Array of keys to be searched for in a.
side : {'left', 'right'}, optional
If 'left', the index of the first location where the key could be
inserted is found, if 'right', the index of the last such element is
returned. If the is no such element, then either 0 or N is returned,
where N is the size of the array.
Returns
-------
indices : integer array
Array of insertion points with the same shape as v.
See Also
--------
sort : Inplace sort.
histogram : Produce histogram from 1-d data.
Notes
-----
The array a must be 1-d and is assumed to be sorted in ascending
order. Searchsorted uses binary search to find the required
insertion points.
Examples
--------
>>> searchsorted([1,2,3,4,5],[6,4,0])
array([5, 3, 0])
"""
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.
The original array's total size can be any size. The new array is
filled with repeated copies of a.
Note that a.resize(new_shape) will fill the array with 0's beyond
current definition of a.
Parameters
----------
a : {array_like}
Array to be reshaped.
new_shape : {tuple}
Shape of reshaped array.
Returns
-------
reshaped_array : {array}
The new array is formed from the data in the old array, repeated if
necessary to fill out the required number of elements, with the new
shape.
"""
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 a.
Examples
--------
>>> x = array([[[1,1,1],[2,2,2],[3,3,3]]])
>>> x.shape
(1, 3, 3)
>>> squeeze(x).shape
(3, 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 self 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 whis the diagonals are taken.
offset : {0, integer}, optional
Offset of the diagonal from the main diagonal. Can be both positive
and negative. Defaults to main diagonal.
axis1 : {0, integer}, 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.
axis2 : {1, integer}, 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.
Returns
-------
array_of_diagonals : array of same type as a
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.
See Also
--------
diag : Matlab workalike for 1-d and 2-d arrays.
diagflat : Create diagonal arrays.
trace : Sum along diagonals.
Examples
--------
>>> a = arange(4).reshape(2,2)
>>> a
array([[0, 1],
[2, 3]])
>>> a.diagonal()
array([0, 3])
>>> a.diagonal(1)
array([1])
>>> a = 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, returns the sum along the diagonal of self 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 trace 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 whis the diagonals are taken.
offset : {0, integer}, optional
Offset of the diagonal from the main diagonal. Can be both positive
and negative. Defaults to main diagonal.
axis1 : {0, integer}, 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.
axis2 : {1, integer}, 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.
dtype : {None, dtype}, optional
Determines the 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 : {None, array}, optional
Array into which the sum can be placed. Its type is preserved and
it must be of the right shape to hold the output.
Returns
-------
sum_along_diagonals : array
If a is 2-d, a 0-d array containing the diagonal is
returned. If a has larger dimensions, then an array of
diagonals is returned.
Examples
--------
>>> trace(eye(3))
3.0
>>> a = arange(8).reshape((2,2,2))
>>> trace(a)
array([6, 8])
"""
return asarray(a).trace(offset, axis1, axis2, dtype, out)
def ravel(a, order='C'):
"""Return a 1d array containing the elements of a (copy only if needed).
Returns the elements of a as a 1d array. The elements in the new array
are taken in the order specified by the order keyword. The new array is
a view of a if possible, otherwise it is a copy.
Parameters
----------
a : {array_like}
order : {'C','F'}, optional
If order is 'C' the elements are taken in row major order. If order
is 'F' they are taken in column major order.
Returns
-------
1d_array : {array}
See Also
--------
ndarray.flat : 1d iterator over the array.
ndarray.flatten : 1d array copy of the elements of a in C order.
Examples
--------
>>> x = array([[1,2,3],[4,5,6]])
>>> x
array([[1, 2, 3],
[4, 5, 6]])
>>> ravel(x)
array([1, 2, 3, 4, 5, 6])
"""
return asarray(a).ravel(order)
def nonzero(a):
"""Return the indices of the elements of a which are not zero.
Parameters
----------
a : {array_like}
Returns
-------
tuple_of_arrays : {tuple}
Examples
--------
>>> eye(3)[nonzero(eye(3))]
array([ 1., 1., 1.])
>>> nonzero(eye(3))
(array([0, 1, 2]), array([0, 1, 2]))
>>> eye(3)[nonzero(eye(3))]
array([ 1., 1., 1.])
"""
try:
nonzero = a.nonzero
except AttributeError:
res = _wrapit(a, 'nonzero')
else:
res = nonzero()
return res
def shape(a):
"""Return the shape of a.
Parameters
----------
a : {array_like}
Array whose shape is desired. If a is not an array, a conversion is
attempted.
Returns
-------
tuple_of_integers :
The elements of the tuple are the length of the corresponding array
dimension.
Examples
--------
>>> shape(eye(3))
(3, 3)
>>> shape([[1,2]])
(1, 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.
Parameters
----------
condition : {array}
Boolean 1-d array selecting which entries to return. If len(condition)
is less than the size of a along the axis, then output is truncated
to length of condition array.
a : {array_type}
Array from which to extract a part.
axis : {None, integer}
Axis along which to take slices. If None, work on the flattened array.
out : array, optional
Output array. Its type is preserved and it must be of the right
shape to hold the output.
Returns
-------
compressed_array : array
A copy of a, without the slices along axis for which condition is false.
Examples
--------
>>> a = np.array([[1, 2], [3, 4]])
>>> np.compress([0, 1], a, axis=0)
array([[3, 4]])
>>> np.compress([1], a, axis=1)
array([[1],
[3]])
>>> np.compress([0,1,1], a)
array([2, 3])
"""
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):
"""Return an array whose values are limited to [a_min, a_max].
Parameters
----------
a : {array_like}
Array containing elements to clip.
a_min :
Minimum value
a_max :
Maximum value
out : array, optional
The results will be placed in this array. It may be the input array for
inplace clipping.
Returns
-------
clipped_array : {array}
A new array whose elements are same as for a, but values
< a_min are replaced with a_min, and > a_max with a_max.
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])
"""
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):
"""Return the sum of the array elements over the given axis
Parameters
----------
a : {array_type}
Array containing elements whose sum is desired. If a is not an array, a
conversion is attempted.
axis : {None, integer}
Axis over which the sum is taken. If None is used, then the sum is
over all the array elements.
dtype : {None, dtype}, optional
Determines the type of the returned array and of the accumulator
where the elements are summed. If dtype has the value None and the
type of a is an integer type of precision less than the default
platform integer, then the default platform integer precision is
used. Otherwise, the dtype is the same as that of a.
out : {None, array}, optional
Array into which the sum can be placed. Its type is preserved and
it must be of the right shape to hold the output.
Returns
-------
sum_along_axis : {array, scalar}, see dtype parameter above.
Returns an array whose shape is the same as a with the specified
axis removed. Returns a 0d array when a is 1d or axis=None.
Returns a reference to the specified output array if specified.
See Also
--------
ndarray.sum : equivalent method
Examples
--------
>>> sum([0.5, 1.5])
2.0
>>> sum([0.5, 1.5], dtype=N.int32)
1
>>> sum([[0, 1], [0, 5]])
6
>>> sum([[0, 1], [0, 5]], axis=1)
array([1, 5])
>>> ones(128, dtype=int8).sum(dtype=int8) # overflow!
-128
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
"""
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 the array elements over the given axis
Parameters
----------
a : {array_like}
Array containing elements whose product is desired. If a is not an array, a
conversion is attempted.
axis : {None, integer}
Axis over which the product is taken. If None is used, then the
product is over all the array elements.
dtype : {None, dtype}, optional
Determines the type of the returned array and of the accumulator
where the elements are multiplied. If dtype has the value None and
the type of a is an integer type of precision less than the default
platform integer, then the default platform integer precision is
used. Otherwise, the dtype is the same as that of a.
out : {None, array}, 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.
Returns
-------
product_along_axis : {array, scalar}, see dtype parameter above.
Returns an array whose shape is the same as a with the specified
axis removed. Returns a 0d array when a is 1d or axis=None.
Returns a reference to the specified output array if specified.
See Also
--------
ndarray.prod : equivalent method
Examples
--------
>>> product([1.,2.])
2.0
>>> product([1.,2.], dtype=int32)
2
>>> product([[1.,2.],[3.,4.]])
24.0
>>> product([[1.,2.],[3.,4.]], axis=1)
array([ 2., 12.])
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
"""
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):
"""
Assert whether some values are true.
`sometrue` performs a logical_or over the given axis.
Parameters
----------
a : array_like
Array on which to operate.
axis : {None, integer}
Axis to perform the operation over.
If `None` (default), perform over flattened array.
out : {None, array}, optional
Array into which the product can be placed. Its type is preserved
and it must be of the right shape to hold the output.
See Also
--------
ndarray.any : equivalent method
Examples
--------
>>> b = numpy.array([True, False, True, True])
>>> numpy.sometrue(b)
True
>>> a = numpy.array([1, 5, 2, 7])
>>> numpy.sometrue(a >= 5)
True
"""
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 of the elements of `a` are true.
Performs a logical_and over the given axis and returns the result
Parameters
----------
a : array_like
axis : {None, integer}
Axis to perform the operation over.
If None, perform over flattened array.
out : {None, array}, optional
Array into which the product can be placed. Its type is preserved
and it must be of the right shape to hold the output.
See Also
--------
ndarray.all : equivalent method
"""
try:
all = a.all
except AttributeError:
return _wrapit(a, 'all', axis, out)
return all(axis, out)
def any(a,axis=None, out=None):
"""Check if any of the elements of `a` are true.
Performs a logical_or over the given axis and returns the result
Parameters
----------
a : array_like
axis : {None, integer}
Axis to perform the operation over.
If None, perform over flattened array and return a scalar.
out : {None, array}, optional
Array into which the product can be placed. Its type is preserved
and it must be of the right shape to hold the output.
See Also
--------
ndarray.any : equivalent method
"""
try:
any = a.any
except AttributeError:
return _wrapit(a, 'any', axis, out)
return any(axis, out)
def all(a,axis=None, out=None):
"""Check if all of the elements of `a` are true.
Performs a logical_and over the given axis and returns the result
Parameters
----------
a : array_like
axis : {None, integer}
Axis to perform the operation over.
If None, perform over flattened array and return a scalar.
out : {None, array}, optional
Array into which the product can be placed. Its type is preserved
and it must be of the right shape to hold the output.
See Also
--------
ndarray.all : equivalent method
"""
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 or object that can be converted to an array.
axis : {None, -1, int}, optional
Axis along which the sum is computed. The default
(`axis` = `None`) is to compute over the flattened array.
dtype : {None, 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.
Returns
-------
cumsum : ndarray.
A new array holding the result is returned unless `out` is
specified, in which case a reference to `out` is returned.
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
Examples
--------
>>> import numpy
>>> a=numpy.array([[1,2,3],[4,5,6]])
>>> numpy.cumsum(a) # cumulative sum = intermediate summing results & total sum. Default axis=None results in raveling the array first.
array([ 1, 3, 6, 10, 15, 21])
>>> numpy.cumsum(a,dtype=float) # specifies type of output value(s)
array([ 1., 3., 6., 10., 15., 21.])
>>> numpy.cumsum(a,axis=0) # sum over rows for each of the 3 columns
array([[1, 2, 3],
[5, 7, 9]])
>>> numpy.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
"""
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):
"""Return (maximum - minimum) along the the given dimension
(i.e. peak-to-peak value).
Parameters
----------
a : array_like
Input values.
axis : {None, int}, optional
Axis along which to find the peaks. If None (default) the
flattened array is used.
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 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,0)
array([2, 2])
>>> np.ptp(x,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 a given axis.
Parameters
----------
a : array_like
Input data.
axis : {None, int}, optional
Axis along which to operate. By default, ``axis`` is None and the
flattened input is used.
out : array_like, optional
Alternative output array in which to place the result. Must
be of the same shape and buffer length as the expected output.
Returns
-------
amax : array_like
New array holding the result, unless ``out`` was specified.
Examples
--------
>>> x = np.arange(4).reshape((2,2))
>>> x
array([[0, 1],
[2, 3]])
>>> np.amax(x,0)
array([2, 3])
>>> np.amax(x,1)
array([1, 3])
"""
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 a given axis.
Parameters
----------
a : array_like
Input data.
axis : {None, int}, optional
Axis along which to operate. By default, ``axis`` is None and the
flattened input is used.
out : array_like, optional
Alternative output array in which to place the result. Must
be of the same shape and buffer length as the expected output.
Returns
-------
amin : array_like
New array holding the result, unless ``out`` was specified.
Examples
--------
>>> x = np.arange(4).reshape((2,2))
>>> x
array([[0, 1],
[2, 3]])
>>> np.amin(x,0)
array([0, 1])
>>> np.amin(x,1)
array([0, 2])
"""
try:
amin = a.min
except AttributeError:
return _wrapit(a, 'min', axis, out)
return amin(axis, out)
def alen(a):
"""
Return the length of a Python object interpreted as an array
of at least 1 dimension.
Parameters
----------
a : array_like
Returns
-------
alen : int
Length of the first dimension of `a`.
Examples
--------
>>> z = numpy.zeros((7,4,5))
>>> z.shape[0]
7
>>> numpy.alen(z)
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 the array elements over the given axis
Parameters
----------
a : {array_like}
Array containing elements whose product is desired. If a is not an array, a
conversion is attempted.
axis : {None, integer}
Axis over which the product is taken. If None is used, then the
product is over all the array elements.
dtype : {None, dtype}, optional
Determines the type of the returned array and of the accumulator
where the elements are multiplied. If dtype has the value None and
the type of a is an integer type of precision less than the default
platform integer, then the default platform integer precision is
used. Otherwise, the dtype is the same as that of a.
out : {None, array}, 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.
Returns
-------
product_along_axis : {array, scalar}, see dtype parameter above.
Returns an array whose shape is the same as a with the specified
axis removed. Returns a 0d array when a is 1d or axis=None.
Returns a reference to the specified output array if specified.
See Also
--------
ndarray.prod : equivalent method
Examples
--------
>>> prod([1.,2.])
2.0
>>> prod([1.,2.], dtype=int32)
2
>>> prod([[1.,2.],[3.,4.]])
24.0
>>> prod([[1.,2.],[3.,4.]], axis=1)
array([ 2., 12.])
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
"""
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 the elements along the given axis.
The cumulative product is taken over the flattened array by
default, otherwise over the specified axis.
Parameters
----------
a : array-like
Input array or object that can be converted to an array.
axis : {None, -1, int}, optional
Axis along which the product is computed. The default
(`axis` = `None`) is to compute over the flattened array.
dtype : {None, dtype}, optional
Type of the returned array and of the accumulator
where the elements are multiplied. If `dtype` has the value `None` and
the type of `a` is an integer type of precision less than the default
platform integer, then the default platform integer precision is
used. 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 and buffer length as the expected output
but the type 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.
Notes
-----
Arithmetic is modular when using integer types, and no error is
raised on overflow.
Examples
--------
>>> a=numpy.array([[1,2,3],[4,5,6]])
>>> a=numpy.array([1,2,3])
>>> numpy.cumprod(a) # intermediate results 1, 1*2
... # total product 1*2*3 = 6
array([1, 2, 6])
>>> a=numpy.array([[1,2,3],[4,5,6]])
>>> numpy.cumprod(a,dtype=float) # specify type of output
array([ 1., 2., 6., 24., 120., 720.])
>>> numpy.cumprod(a,axis=0) # for each of the 3 columns:
... # product and intermediate results
array([[ 1, 2, 3],
[ 4, 10, 18]])
>>> numpy.cumprod(a,axis=1) # for each of the two rows:
... # product and intermediate results
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 a.
If a is not already an array, a conversion is attempted. Scalars are zero
dimensional.
Parameters
----------
a : {array_like}
Array whose number of dimensions are desired. If a is not an
array, a conversion is attempted.
Returns
-------
number_of_dimensions : {integer}
Returns the number of dimensions.
See Also
--------
rank : equivalent function.
ndarray.ndim : equivalent method
shape : dimensions of array
ndarray.shape : dimensions of array
Examples
--------
>>> ndim([[1,2,3],[4,5,6]])
2
>>> ndim(array([[1,2,3],[4,5,6]]))
2
>>> ndim(1)
0
"""
try:
return a.ndim
except AttributeError:
return asarray(a).ndim
def rank(a):
"""Return the number of dimensions of a.
In old Numeric, rank was the term used for the number of dimensions. 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 : {integer}
Returns the number of dimensions.
See Also
--------
ndim : equivalent function
ndarray.ndim : equivalent method
shape : dimensions of array
ndarray.shape : dimensions of array
Examples
--------
>>> rank([[1,2,3],[4,5,6]])
2
>>> rank(array([[1,2,3],[4,5,6]]))
2
>>> rank(1)
0
"""
try:
return a.ndim
except AttributeError:
return asarray(a).ndim
def size(a, axis=None):
"""Return the number of elements along given axis.
Parameters
----------
a : {array_like}
Array whose axis size is desired. If a is not an array, a
conversion is attempted.
axis : {None, integer}, optional
Axis along which the elements are counted. None means all
elements in the array.
Returns
-------
element_count : {integer}
Count of elements along specified axis.
See Also
--------
shape : dimensions of array
ndarray.shape : dimensions of array
ndarray.size : number of elements in array
Examples
--------
>>> a = array([[1,2,3],[4,5,6]])
>>> size(a)
6
>>> size(a,1)
3
>>> 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):
"""Round a to the given number of decimals.
The real and imaginary parts of complex numbers are rounded separately. The
result of rounding a float is a float so the type must be cast if integers
are desired. Nothing is done if the input is an integer array and the
decimals parameter has a value >= 0.
Parameters
----------
a : {array_like}
Array containing numbers whose rounded values are desired. If a is
not an array, a conversion is attempted.
decimals : {0, int}, optional
Number of decimal places to round to. When decimals is negative it
specifies the number of positions to the left of the decimal point.
out : {None, array}, 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. Numpy rounds floats to floats by default.
Returns
-------
rounded_array : {array}
If out=None, returns a new array of the same type as a containing
the rounded values, otherwise a reference to the output array is
returned.
See Also
--------
round_ : equivalent function
ndarray.round : equivalent method
Notes
-----
Numpy rounds to even. 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 IEEE floating point and the
errors introduced when scaling by powers of ten.
Examples
--------
>>> around([.5, 1.5, 2.5, 3.5, 4.5])
array([ 0., 2., 2., 4., 4.])
>>> around([1,2,3,11], decimals=1)
array([ 1, 2, 3, 11])
>>> 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 a to the given number of decimals.
The real and imaginary parts of complex numbers are rounded separately. The
result of rounding a float is a float so the type must be cast if integers
are desired. Nothing is done if the input is an integer array and the
decimals parameter has a value >= 0.
Parameters
----------
a : {array_like}
Array containing numbers whose rounded values are desired. If a is
not an array, a conversion is attempted.
decimals : {0, integer}, optional
Number of decimal places to round to. When decimals is negative it
specifies the number of positions to the left of the decimal point.
out : {None, array}, 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.
Returns
-------
rounded_array : {array}
If out=None, returns a new array of the same type as a containing
the rounded values, otherwise a reference to the output array is
returned.
See Also
--------
around : equivalent function
ndarray.round : equivalent method
Notes
-----
Numpy rounds to even. 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 IEEE floating point and the
errors introduced when scaling by powers of ten.
Examples
--------
>>> round_([.5, 1.5, 2.5, 3.5, 4.5])
array([ 0., 2., 2., 4., 4.])
>>> round_([1,2,3,11], decimals=1)
array([ 1, 2, 3, 11])
>>> round_([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 mean(a, axis=None, dtype=None, out=None):
"""Compute the 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. The dtype returned for integer type arrays is float.
Parameters
----------
a : {array_like}
Array containing numbers whose mean is desired. If a is not an
array, a conversion is attempted.
axis : {None, integer}, optional
Axis along which the means are computed. The default is to compute
the mean of the flattened array.
dtype : {None, dtype}, optional
Type to use in computing the mean. For arrays of integer type the
default is float32, for arrays of float types it is the same as the
array type.
out : {None, array}, 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.
Returns
-------
mean : {array, scalar}, 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 mean is the sum of the elements along the axis divided by the
number of elements.
Examples
--------
>>> a = array([[1,2],[3,4]])
>>> mean(a)
2.5
>>> mean(a,0)
array([ 2., 3.])
>>> mean(a,1)
array([ 1.5, 3.5])
"""
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 of the array elements, a measure of the
spread of a distribution. The standard deviation is computed for the
flattened array by default, otherwise over the specified axis.
Parameters
----------
a : {array_like}
Array containing numbers whose standard deviation is desired. If a
is not an array, a conversion is attempted.
axis : {None, integer}, optional
Axis along which the standard deviation is computed. The default is
to compute the standard deviation of the flattened array.
dtype : {None, dtype}, optional
Type to use in computing the standard deviation. For arrays of
integer type the default is float32, for arrays of float types it is
the same as the array type.
out : {None, array}, 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.
ddof : {0, integer}
Means Delta Degrees of Freedom. The divisor used in calculations
is N-ddof.
Returns
-------
standard_deviation : {array, scalar}, see dtype parameter above.
If out=None, returns a new array containing the standard deviation,
otherwise a reference to the output array is returned.
See Also
--------
var : Variance
mean : Average
Notes
-----
The standard deviation is the square root of the average of the squared
deviations from the mean, i.e. var = sqrt(mean(abs(x - x.mean())**2)).
The computed standard deviation is computed by dividing by the number of
elements, N-ddof. The option ddof defaults to zero, that is, a
biased estimate. Note that for complex numbers std takes the absolute
value before squaring, so that the result is always real and nonnegative.
Examples
--------
>>> a = array([[1,2],[3,4]])
>>> std(a)
1.1180339887498949
>>> std(a,0)
array([ 1., 1.])
>>> std(a,1)
array([ 0.5, 0.5])
"""
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 : {None, integer}, optional
Axis along which the variance is computed. The default is to compute
the variance of the flattened array.
dtype : {None, 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 : {None, array}, 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.
ddof : {0, integer},
Means Delta Degrees of Freedom. The divisor used in calculation is
N - ddof.
Returns
-------
variance : {array, scalar}, 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
Notes
-----
The variance is the average of the squared deviations from the mean,
i.e. var = mean(abs(x - x.mean())**2). The computed variance is biased,
i.e., the mean is computed by dividing by the number of elements, N,
rather than by N-1. Note that for complex numbers the absolute value is
taken before squaring, so that the result is always real and nonnegative.
Examples
--------
>>> a = array([[1,2],[3,4]])
>>> var(a)
1.25
>>> var(a,0)
array([ 1., 1.])
>>> var(a,1)
array([ 0.25, 0.25])
"""
try:
var = a.var
except AttributeError:
return _wrapit(a, 'var', axis, dtype, out, ddof)
return var(axis, dtype, out, ddof)
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