numpy.std#

numpy.std(a,axis=None,dtype=None,out=None,ddof=0,keepdims=<novalue>,*,where=<novalue>,mean=<novalue>,correction=<novalue>)[source]#

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 theflattened array by default, otherwise over the specified axis.

Parameters:
aarray_like

Calculate the standard deviation of these values.

axisNone or int or tuple of ints, optional

Axis or axes along which the standard deviation is computed. Thedefault is to compute the standard deviation of the flattened array.If this is a tuple of ints, a standard deviation is performed overmultiple axes, instead of a single axis or all the axes as before.

dtypedtype, optional

Type to use in computing the standard deviation. For arrays ofinteger type the default is float64, for arrays of float types it isthe same as the array type.

outndarray, optional

Alternative output array in which to place the result. It must havethe same shape as the expected output but the type (of the calculatedvalues) will be cast if necessary.SeeOutput type determination for more details.

ddof{int, float}, optional

Means Delta Degrees of Freedom. The divisor used in calculationsisN-ddof, whereN represents the number of elements.By defaultddof is zero. See Notes for details about use ofddof.

keepdimsbool, optional

If this is set to True, the axes which are reduced are leftin the result as dimensions with size one. With this option,the result will broadcast correctly against the input array.

If the default value is passed, thenkeepdims will not bepassed through to thestd method of sub-classes ofndarray, however any non-default value will be. If thesub-class’ method does not implementkeepdims anyexceptions will be raised.

wherearray_like of bool, optional

Elements to include in the standard deviation.Seereduce for details.

New in version 1.20.0.

meanarray_like, optional

Provide the mean to prevent its recalculation. The mean should havea shape as if it was calculated withkeepdims=True.The axis for the calculation of the mean should be the same as used inthe call to this std function.

New in version 2.0.0.

correction{int, float}, optional

Array API compatible name for theddof parameter. Only one of themcan be provided at the same time.

New in version 2.0.0.

Returns:
standard_deviationndarray, see dtype parameter above.

Ifout is None, return a new array containing the standard deviation,otherwise return a reference to the output array.

Notes

There are several common variants of the array standard deviationcalculation. Assuming the inputa is a one-dimensional NumPy arrayandmean is either provided as an argument or computed asa.mean(), NumPy computes the standard deviation of an array as:

N=len(a)d2=abs(a-mean)**2# abs is for complex `a`var=d2.sum()/(N-ddof)# note use of `ddof`std=var**0.5

Different values of the argumentddof are useful in differentcontexts. NumPy’s defaultddof=0 corresponds with the expression:

\[\sqrt{\frac{\sum_i{|a_i - \bar{a}|^2 }}{N}}\]

which is sometimes called the “population standard deviation” in the fieldof statistics because it applies the definition of standard deviation toa as ifa were a complete population of possible observations.

Many other libraries define the standard deviation of an arraydifferently, e.g.:

\[\sqrt{\frac{\sum_i{|a_i - \bar{a}|^2 }}{N - 1}}\]

In statistics, the resulting quantity is sometimes called the “samplestandard deviation” because ifa is a random sample from a largerpopulation, this calculation provides the square root of an unbiasedestimate of the variance of the population. The use of\(N-1\) in thedenominator is often called “Bessel’s correction” because it corrects forbias (toward lower values) in the variance estimate introduced when thesample mean ofa is used in place of the true mean of the population.The resulting estimate of the standard deviation is still biased, but lessthan it would have been without the correction. For this quantity, useddof=1.

Note that, for complex numbers,std takes the absolutevalue before squaring, so that the result is always real and nonnegative.

For floating-point input, the standard deviation is computed using the sameprecision the input has. Depending on the input data, this can causethe results to be inaccurate, especially for float32 (see example below).Specifying a higher-accuracy accumulator using thedtype keyword canalleviate this issue.

Examples

>>>importnumpyasnp>>>a=np.array([[1,2],[3,4]])>>>np.std(a)1.1180339887498949 # may vary>>>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)np.float32(0.45000005)

Computing the standard deviation in float64 is more accurate:

>>>np.std(a,dtype=np.float64)0.44999999925494177 # may vary

Specifying a where argument:

>>>a=np.array([[14,8,11,10],[7,9,10,11],[10,15,5,10]])>>>np.std(a)2.614064523559687 # may vary>>>np.std(a,where=[[True],[True],[False]])2.0

Using the mean keyword to save computation time:

>>>importnumpyasnp>>>fromtimeitimporttimeit>>>a=np.array([[14,8,11,10],[7,9,10,11],[10,15,5,10]])>>>mean=np.mean(a,axis=1,keepdims=True)>>>>>>g=globals()>>>n=10000>>>t1=timeit("std = np.std(a, axis=1, mean=mean)",globals=g,number=n)>>>t2=timeit("std = np.std(a, axis=1)",globals=g,number=n)>>>print(f'Percentage execution time saved{100*(t2-t1)/t2:.0f}%')Percentage execution time saved 30%
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