Skip to content

Commit 1a840e0

Browse files
iampratik13iampratik13
committed
feat: add stats/base/ndarray/variancetk
--- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: passed - task: lint_package_json status: passed - task: lint_repl_help status: passed - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: passed - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: passed - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: passed - task: lint_license_headers status: passed ---
1 parent 49457c5 commit 1a840e0

File tree

11 files changed

+981
-0
lines changed

11 files changed

+981
-0
lines changed

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

Lines changed: 200 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,200 @@
1+
<!--
2+
3+
@license Apache-2.0
4+
5+
Copyright (c) 2026 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+
# variancetk
22+
23+
> Calculate the [variance][variance] of a one-dimensional ndarray using textbook algorithm.
24+
25+
<section class="intro">
26+
27+
The population [variance][variance] of a finite size population of size `N` is given by
28+
29+
<!-- <equation class="equation" label="eq:population_variance" align="center" raw="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" alt="Equation for the population variance."> -->
30+
31+
```math
32+
\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2
33+
```
34+
35+
<!-- <div class="equation" align="center" data-raw-text="\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2" data-equation="eq:population_variance">
36+
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/variancetk/docs/img/equation_population_variance.svg" alt="Equation for the population variance.">
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/variancetk/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 [variance][variance] 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 [variance][variance], the result is biased and yields an **uncorrected sample variance**. To compute a **corrected sample variance** for a sample of size `n`,
58+
59+
<!-- <equation class="equation" label="eq:corrected_sample_variance" 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 variance."> -->
60+
61+
```math
62+
s^2 = \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^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2" data-equation="eq:corrected_sample_variance">
66+
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@08ca32895957967bd760a4fe02d61762432a0b72/lib/node_modules/@stdlib/stats/strided/variancetk/docs/img/equation_corrected_sample_variance.svg" alt="Equation for computing a corrected sample variance.">
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/variancetk/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 variance and population variance. 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 variancetk = require( '@stdlib/stats/base/ndarray/variancetk' );
99+
```
100+
101+
#### variancetk( arrays )
102+
103+
Computes the [variance][variance] of a one-dimensional ndarray using textbook algorithm.
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': 'generic'
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 = variancetk( [ x, correction ] );
118+
// returns ~4.3333
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 specifying the degrees of freedom adjustment. Providing a non-zero degrees of freedom adjustment has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `N-c` where `N` is the number of elements in the input ndarray and `c` corresponds to the provided degrees of freedom adjustment. When computing the [variance][variance] 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 [variance][variance], 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 `N` corresponds to the number of elements in the input ndarray and `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 ndarray = require( '@stdlib/ndarray/base/ctor' );
149+
var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
150+
var ndarray2array = require( '@stdlib/ndarray/to-array' );
151+
var variancetk = require( '@stdlib/stats/base/ndarray/variancetk' );
152+
153+
var opts = {
154+
'dtype': 'float64'
155+
};
156+
157+
var xbuf = discreteUniform( 10, -50, 50, opts );
158+
var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
159+
console.log( ndarray2array( x ) );
160+
161+
var correction = scalar2ndarray( 1.0, opts );
162+
var v = variancetk( [ x, correction ] );
163+
console.log( v );
164+
```
165+
166+
</section>
167+
168+
<!-- /.examples -->
169+
170+
* * *
171+
172+
<section class="references">
173+
174+
## References
175+
176+
- Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." _Journal of the American Statistical Association_ 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:[10.2307/2286154][@ling:1974a].
177+
178+
</section>
179+
180+
<!-- /.references -->
181+
182+
<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
183+
184+
<section class="related">
185+
186+
</section>
187+
188+
<!-- /.related -->
189+
190+
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
191+
192+
<section class="links">
193+
194+
[variance]: https://en.wikipedia.org/wiki/Variance
195+
196+
[@ling:1974a]: https://doi.org/10.2307/2286154
197+
198+
</section>
199+
200+
<!-- /.links -->

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

Lines changed: 112 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,112 @@
1+
/**
2+
* @license Apache-2.0
3+
*
4+
* Copyright (c) 2026 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 format = require( '@stdlib/string/format' );
30+
var pkg = require( './../package.json' ).name;
31+
var variancetk = require( './../lib' );
32+
33+
34+
// VARIABLES //
35+
36+
var options = {
37+
'dtype': 'generic'
38+
};
39+
40+
41+
// FUNCTIONS //
42+
43+
/**
44+
* Creates a benchmark function.
45+
*
46+
* @private
47+
* @param {PositiveInteger} len - array length
48+
* @returns {Function} benchmark function
49+
*/
50+
function createBenchmark( len ) {
51+
var correction;
52+
var xbuf;
53+
var x;
54+
55+
xbuf = uniform( len, -10.0, 10.0, options );
56+
x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
57+
correction = scalar2ndarray( 1.0, options );
58+
59+
return benchmark;
60+
61+
/**
62+
* Benchmark function.
63+
*
64+
* @private
65+
* @param {Benchmark} b - benchmark instance
66+
*/
67+
function benchmark( b ) {
68+
var v;
69+
var i;
70+
71+
b.tic();
72+
for ( i = 0; i < b.iterations; i++ ) {
73+
v = variancetk( [ x, correction ] );
74+
if ( isnan( v ) ) {
75+
b.fail( 'should not return NaN' );
76+
}
77+
}
78+
b.toc();
79+
if ( isnan( v ) ) {
80+
b.fail( 'should not return NaN' );
81+
}
82+
b.pass( 'benchmark finished' );
83+
b.end();
84+
}
85+
}
86+
87+
88+
// MAIN //
89+
90+
/**
91+
* Main execution sequence.
92+
*
93+
* @private
94+
*/
95+
function main() {
96+
var len;
97+
var min;
98+
var max;
99+
var f;
100+
var i;
101+
102+
min = 1; // 10^min
103+
max = 6; // 10^max
104+
105+
for ( i = min; i <= max; i++ ) {
106+
len = pow( 10, i );
107+
f = createBenchmark( len );
108+
bench( format( '%s:len=%d', pkg, len ), f );
109+
}
110+
}
111+
112+
main();

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

Lines changed: 43 additions & 0 deletions
Loading

0 commit comments

Comments
 (0)