Skip to content

Commit 02ef1d6

Browse files
iampratik13iampratik13
committed
feat/add-stats-base-ndarray-stdev
1 parent 94be096 commit 02ef1d6

File tree

11 files changed

+964
-0
lines changed

11 files changed

+964
-0
lines changed

‎lib/node_modules/@stdlib/stats/base/ndarray/stdev/README.md‎

Lines changed: 189 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,189 @@
1+
<!--
2+
3+
@license Apache-2.0
4+
5+
Copyright (c) 2025 The Stdlib Authors.
6+
7+
Licensed under the Apache License, Version 2.0 (the "License");
8+
you may not use this file except in compliance with the License.
9+
You may obtain a copy of the License at
10+
11+
http://www.apache.org/licenses/LICENSE-2.0
12+
13+
Unless required by applicable law or agreed to in writing, software
14+
distributed under the License is distributed on an "AS IS" BASIS,
15+
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
16+
See the License for the specific language governing permissions and
17+
limitations under the License.
18+
19+
-->
20+
21+
# stdev
22+
23+
> Calculate the [standard deviation][standard-deviation] of a one-dimensional ndarray.
24+
25+
<section class="intro">
26+
27+
The population [standard deviation][standard-deviation] of a finite size population of size `N` is given by
28+
29+
<!-- <equation class="equation" label="eq:population_standard_deviation" align="center" raw="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" alt="Equation for the population standard deviation."> -->
30+
31+
```math
32+
\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}
33+
```
34+
35+
<!-- <div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
36+
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/stdev/docs/img/equation_population_standard_deviation.svg" alt="Equation for the population standard deviation.">
37+
<br>
38+
</div> -->
39+
40+
<!-- </equation> -->
41+
42+
where the population mean is given by
43+
44+
<!-- <equation class="equation" label="eq:population_mean" align="center" raw="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean."> -->
45+
46+
```math
47+
\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i
48+
```
49+
50+
<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
51+
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/stdev/docs/img/equation_population_mean.svg" alt="Equation for the population mean.">
52+
<br>
53+
</div> -->
54+
55+
<!-- </equation> -->
56+
57+
Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`,
58+
59+
<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" alt="Equation for computing a corrected sample standard deviation."> -->
60+
61+
```math
62+
s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}
63+
```
64+
65+
<!-- <div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
66+
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/stdev/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for computing a corrected sample standard deviation.">
67+
<br>
68+
</div> -->
69+
70+
<!-- </equation> -->
71+
72+
where the sample mean is given by
73+
74+
<!-- <equation class="equation" label="eq:sample_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean."> -->
75+
76+
```math
77+
\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
78+
```
79+
80+
<!-- <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
81+
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/stdev/docs/img/equation_sample_mean.svg" alt="Equation for the sample mean.">
82+
<br>
83+
</div> -->
84+
85+
<!-- </equation> -->
86+
87+
The use of the term `n-1` is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample standard deviation and population standard deviation. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.
88+
89+
</section>
90+
91+
<!-- /.intro -->
92+
93+
<section class="usage">
94+
95+
## Usage
96+
97+
```javascript
98+
var stdev = require( '@stdlib/stats/base/ndarray/stdev' );
99+
```
100+
101+
#### stdev( arrays )
102+
103+
Computes the [standard deviation][standard-deviation] of a one-dimensional ndarray.
104+
105+
```javascript
106+
var ndarray = require( '@stdlib/ndarray/base/ctor' );
107+
var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
108+
109+
var opts = {
110+
'dtype': 'float64'
111+
};
112+
113+
var xbuf = [ 1.0, -2.0, 2.0 ];
114+
var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
115+
var correction = scalar2ndarray( 1.0, opts );
116+
117+
var v = stdev( [ x, correction ] );
118+
// returns ~2.0817
119+
```
120+
121+
The function has the following parameters:
122+
123+
- **arrays**: array-like object containing two elements: a one-dimensional input ndarray and a zero-dimensional ndarray (or ndarray-like object) specifying the degrees of freedom adjustment. Setting the correction value to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample [standard deviation][standard-deviation], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
124+
125+
</section>
126+
127+
<!-- /.usage -->
128+
129+
<section class="notes">
130+
131+
## Notes
132+
133+
- If provided an empty one-dimensional ndarray, the function returns `NaN`.
134+
- If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), the function returns `NaN`.
135+
136+
</section>
137+
138+
<!-- /.notes -->
139+
140+
<section class="examples">
141+
142+
## Examples
143+
144+
<!-- eslint no-undef: "error" -->
145+
146+
```javascript
147+
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
148+
var Float64Array = require( '@stdlib/array/float64' );
149+
var ndarray = require( '@stdlib/ndarray/base/ctor' );
150+
var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
151+
var ndarray2array = require( '@stdlib/ndarray/to-array' );
152+
var stdev = require( '@stdlib/stats/base/ndarray/stdev' );
153+
154+
var opts = {
155+
'dtype': 'float64'
156+
};
157+
158+
var xbuf = discreteUniform( 10, -50, 50, {
159+
'dtype': 'float64'
160+
});
161+
var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
162+
console.log( ndarray2array( x ) );
163+
164+
var correction = scalar2ndarray( 1.0, opts );
165+
var v = stdev( [ x, correction ] );
166+
console.log( v );
167+
```
168+
169+
</section>
170+
171+
<!-- /.examples -->
172+
173+
<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
174+
175+
<section class="related">
176+
177+
</section>
178+
179+
<!-- /.related -->
180+
181+
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
182+
183+
<section class="links">
184+
185+
[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation
186+
187+
</section>
188+
189+
<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/ndarray/stdev/benchmark/benchmark.js‎

Lines changed: 106 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,106 @@
1+
/**
2+
* @license Apache-2.0
3+
*
4+
* Copyright (c) 2025 The Stdlib Authors.
5+
*
6+
* Licensed under the Apache License, Version 2.0 (the "License");
7+
* you may not use this file except in compliance with the License.
8+
* You may obtain a copy of the License at
9+
*
10+
* http://www.apache.org/licenses/LICENSE-2.0
11+
*
12+
* Unless required by applicable law or agreed to in writing, software
13+
* distributed under the License is distributed on an "AS IS" BASIS,
14+
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
15+
* See the License for the specific language governing permissions and
16+
* limitations under the License.
17+
*/
18+
19+
'use strict';
20+
21+
// MODULES //
22+
23+
var bench = require( '@stdlib/bench' );
24+
var uniform = require( '@stdlib/random/array/uniform' );
25+
var isnan = require( '@stdlib/math/base/assert/is-nan' );
26+
var pow = require( '@stdlib/math/base/special/pow' );
27+
var ndarray = require( '@stdlib/ndarray/base/ctor' );
28+
var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
29+
var pkg = require( './../package.json' ).name;
30+
var stdev = require( './../lib' );
31+
32+
33+
// VARIABLES //
34+
35+
var options = {
36+
'dtype': 'float64'
37+
};
38+
39+
40+
// FUNCTIONS //
41+
42+
/**
43+
* Creates a benchmark function.
44+
*
45+
* @private
46+
* @param {PositiveInteger} len - array length
47+
* @returns {Function} benchmark function
48+
*/
49+
function createBenchmark( len ) {
50+
var correction;
51+
var xbuf;
52+
var x;
53+
54+
xbuf = uniform( len, -10.0, 10.0, options );
55+
x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
56+
correction = scalar2ndarray( 1.0, options );
57+
58+
return benchmark;
59+
60+
function benchmark( b ) {
61+
var v;
62+
var i;
63+
64+
b.tic();
65+
for ( i = 0; i < b.iterations; i++ ) {
66+
v = stdev( [ x, correction ] );
67+
if ( isnan( v ) ) {
68+
b.fail( 'should not return NaN' );
69+
}
70+
}
71+
b.toc();
72+
if ( isnan( v ) ) {
73+
b.fail( 'should not return NaN' );
74+
}
75+
b.pass( 'benchmark finished' );
76+
b.end();
77+
}
78+
}
79+
80+
81+
// MAIN //
82+
83+
/**
84+
* Main execution sequence.
85+
*
86+
* @private
87+
*/
88+
function main() {
89+
var len;
90+
var min;
91+
var max;
92+
var f;
93+
var i;
94+
95+
min = 1; // 10^min
96+
max = 6; // 10^max
97+
98+
for ( i = min; i <= max; i++ ) {
99+
len = pow( 10, i );
100+
f = createBenchmark( len );
101+
bench( pkg+':len='+len, f );
102+
}
103+
}
104+
105+
main();
106+

‎lib/node_modules/@stdlib/stats/base/ndarray/stdev/docs/img/equation_sample_mean.svg‎

Lines changed: 43 additions & 0 deletions
Loading

‎lib/node_modules/@stdlib/stats/base/ndarray/stdev/docs/repl.txt‎

Lines changed: 55 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,55 @@
1+
{{alias}}( arrays )
2+
Computes the standard deviation of a one-dimensional ndarray.
3+
4+
Parameters
5+
----------
6+
arrays: ArrayLikeObject<ndarray>
7+
Array-like object containing two elements: a one-dimensional input
8+
ndarray and a zero-dimensional ndarray (or ndarray-like object)
9+
specifying the degrees of freedom adjustment. Setting the correction
10+
value to a value other than `0` has the effect of adjusting the divisor
11+
during the calculation of the standard deviation according to `N - c`
12+
where `c` corresponds to the provided degrees of freedom adjustment.
13+
When computing the standard deviation of a population, setting this
14+
parameter to `0` is the standard choice (i.e., the provided array
15+
contains data constituting an entire population). When computing the
16+
corrected sample standard deviation, setting this parameter to `1` is
17+
the standard choice (i.e., the provided array contains data sampled from
18+
a larger population; this is commonly referred to as Bessel's
19+
correction).
20+
21+
Returns
22+
-------
23+
out: number
24+
The standard deviation.
25+
26+
Examples
27+
--------
28+
// Create input ndarray:
29+
> var xbuf = [ 1.0, -2.0, 2.0 ];
30+
> var dt = 'generic';
31+
> var sh = [ xbuf.length ];
32+
> var st = [ 1 ];
33+
> var oo = 0;
34+
> var ord = 'row-major';
35+
> var x = new {{alias:@stdlib/ndarray/ctor}}( dt, xbuf, sh, st, oo, ord );
36+
37+
// Create correction ndarray:
38+
> var opts = { 'dtype': 'float64' };
39+
> var correction = {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts );
40+
41+
// Compute the standard deviation:
42+
> {{alias}}( [ x, correction ] )
43+
~2.0817
44+
45+
// Using Float64Array buffer:
46+
> xbuf = new {{alias:@stdlib/array/float64}}( [ 1.0, -2.0, 3.0, 2.0, 5.0, -1.0 ] );
47+
> dt = 'float64';
48+
> sh = [ xbuf.length ];
49+
> x = new {{alias:@stdlib/ndarray/ctor}}( dt, xbuf, sh, st, oo, ord );
50+
> {{alias}}( [ x, correction ] )
51+
~2.3381
52+
53+
See Also
54+
--------
55+

0 commit comments

Comments
 (0)