In [ 98 ]: a.std() # standard deviation
Out[98]: 0.70710678118654757
In [ 99 ]: a.cumsum() # running cumulative sum
Out[99]: array([ 0. , 0.5, 1.5, 3. , 5. ])
Another major feature is the (vectorized) mathematical operations defined on ndarray
objects:
In [ 100 ]: a * 2
Out[100]: array([ 0., 1., 2., 3., 4.])
In [ 101 ]: a ** 2
Out[101]: array([ 0. , 0.25, 1. , 2.25, 4. ])
In [ 102 ]: np.sqrt(a)
Out[102]: array([ 0. , 0.70710678, 1. , 1.22474487, 1.41421356
])
The transition to more than one dimension is seamless, and all features presented so far
carry over to the more general cases. In particular, the indexing system is made consistent
across all dimensions:
In [ 103 ]: b = np.array([a, a * 2 ])
b
Out[103]: array([[ 0. , 0.5, 1. , 1.5, 2. ],
[ 0. , 1. , 2. , 3. , 4. ]])
In [ 104 ]: b[ 0 ] # first row
Out[104]: array([ 0. , 0.5, 1. , 1.5, 2. ])
In [ 105 ]: b[ 0 , 2 ] # third element of first row
Out[105]: 1.0
In [ 106 ]: b.sum()
Out[106]: 15.0
In contrast to our list object-based approach to constructing arrays, the numpy.ndarray
class knows axes explicitly. Selecting either rows or columns from a matrix is essentially
the same:
In [ 107 ]: b.sum(axis= 0 )
# sum along axis 0, i.e. column-wise sum
Out[107]: array([ 0. , 1.5, 3. , 4.5, 6. ])
In [ 108 ]: b.sum(axis= 1 )
# sum along axis 1, i.e. row-wise sum
Out[108]: array([ 5., 10.])
There are a number of ways to initialize (instantiate) a numpy.ndarray object. One is as
presented before, via np.array. However, this assumes that all elements of the array are
already available. In contrast, one would maybe like to have the numpy.ndarray objects
instantiated first to populate them later with results generated during the execution of
code. To this end, we can use the following functions:
In [ 109 ]: c = np.zeros(( 2 , 3 , 4 ), dtype=‘i’, order=‘C’) # also: np.ones()
c
Out[109]: array([[[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]],
[[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]], dtype=int32)
In [ 110 ]: d = np.ones_like(c, dtype=‘f16’, order=‘C’) # also: np.zeros_like()
d
Out[110]: array([[[ 1.0, 1.0, 1.0, 1.0],
[ 1.0, 1.0, 1.0, 1.0],
[ 1.0, 1.0, 1.0, 1.0]],
