standardize

mdtools.statistics.standardize(x, axis=None, dtype=None, inplace=False, ddof=0)[source]

Standardize a distribution.

Standardize a distribution such that its mean is zero and its standard deviation is one.

Parameters:

x (array_like) – Input array.
axis (int or None, optional) – The axis along which to compute the sample mean and standard deviation. By default, the flattened input array is used.
dtype (data-type, optional) – The dtype of the output array. This dtype is also used to compute the mean and standard deviation. Note that computing means and standard deviations can be inaccurate when using the floating-point dtype numpy.float32 or less. See numpy.mean() for more details.
inplace (bool, optional) – If True, change the input array inplace if possible (the given dtype must be castable to the dtype of x and x must already be a numpy.ndarray).
ddof (int, optional) – Delta Degrees of Freedom. When calculating the standard deviation, the used divisor is N - ddof, where N represents the number of elements. See numpy.std() for more details.

Returns:

x_standardized (numpy.ndarray) – The standardized input distribution: (x - np.mean(x)) / np.std(x).

See also

numpy.mean(): Compute the arithmetic mean along the specified axis
numpy.std(): Compute the standard deviation along the specified axis
mdtools.statistics.center(): Center a distribution around its sample mean

Examples

>>> a = np.arange(24).reshape(2,3,4)
>>> mdt.stats.standardize(a)
array([[[-1.66132477, -1.51686175, -1.37239873, -1.2279357 ],
        [-1.08347268, -0.93900965, -0.79454663, -0.65008361],
        [-0.50562058, -0.36115756, -0.21669454, -0.07223151]],

       [[ 0.07223151,  0.21669454,  0.36115756,  0.50562058],
        [ 0.65008361,  0.79454663,  0.93900965,  1.08347268],
        [ 1.2279357 ,  1.37239873,  1.51686175,  1.66132477]]])
>>> mdt.stats.standardize(a, axis=0)
array([[[-1., -1., -1., -1.],
        [-1., -1., -1., -1.],
        [-1., -1., -1., -1.]],

       [[ 1.,  1.,  1.,  1.],
        [ 1.,  1.,  1.,  1.],
        [ 1.,  1.,  1.,  1.]]])
>>> mdt.stats.standardize(a, axis=1)
array([[[-1.22474487, -1.22474487, -1.22474487, -1.22474487],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [ 1.22474487,  1.22474487,  1.22474487,  1.22474487]],

       [[-1.22474487, -1.22474487, -1.22474487, -1.22474487],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [ 1.22474487,  1.22474487,  1.22474487,  1.22474487]]])
>>> mdt.stats.standardize(a, axis=2)
array([[[-1.34164079, -0.4472136 ,  0.4472136 ,  1.34164079],
        [-1.34164079, -0.4472136 ,  0.4472136 ,  1.34164079],
        [-1.34164079, -0.4472136 ,  0.4472136 ,  1.34164079]],

       [[-1.34164079, -0.4472136 ,  0.4472136 ,  1.34164079],
        [-1.34164079, -0.4472136 ,  0.4472136 ,  1.34164079],
        [-1.34164079, -0.4472136 ,  0.4472136 ,  1.34164079]]])

>>> a = np.arange(3, dtype=np.float64)
>>> a
array([0., 1., 2.])
>>> b = mdt.stats.standardize(a, inplace=True)
>>> b
array([-1.22474487,  0.        ,  1.22474487])
>>> b is a
True
>>> b[0] = 1
>>> a
array([1.        , 0.        , 1.22474487])