Skip to content

Commit 71e9995

Browse files
kgrytekgryte
committed
Add strided interface to compute an arithmetic mean using the KBN algorithm
1 parent 62a685f commit 71e9995

34 files changed

+3371
-0
lines changed

‎lib/node_modules/@stdlib/stats/base/smeankbn/README.md

+198
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,198 @@
1+
<!--
2+
3+
@license Apache-2.0
4+
5+
Copyright (c) 2020 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+
# smeankbn
22+
23+
> Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm.
24+
25+
<section class="intro>">
26+
27+
The [arithmetic mean][arithmetic-mean] is defined as
28+
29+
<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->
30+
31+
<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
32+
<img src="" alt="Equation for the arithmetic mean.">
33+
<br>
34+
</div>
35+
36+
<!-- </equation> -->
37+
38+
</section>
39+
40+
<!-- /.intro -->
41+
42+
<section class="usage">
43+
44+
## Usage
45+
46+
```javascript
47+
var smeankbn = require( '@stdlib/stats/base/smeankbn' );
48+
```
49+
50+
#### smeankbn( N, x, stride )
51+
52+
Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array `x` using an improved Kahan–Babuška algorithm.
53+
54+
```javascript
55+
var Float32Array = require( '@stdlib/array/float32' );
56+
57+
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
58+
var N = x.length;
59+
60+
var v = smeankbn( N, x, 1 );
61+
// returns ~0.3333
62+
```
63+
64+
The function accepts the following parameters:
65+
66+
- **N**: number of indexed elements.
67+
- **x**: input [`Float32Array`][@stdlib/array/float32].
68+
- **stride**: index increment for `x`.
69+
70+
The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [arithmetic mean][arithmetic-mean] of every other element in `x`,
71+
72+
```javascript
73+
var Float32Array = require( '@stdlib/array/float32' );
74+
var floor = require( '@stdlib/math/base/special/floor' );
75+
76+
var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
77+
var N = floor( x.length / 2 );
78+
79+
var v = smeankbn( N, x, 2 );
80+
// returns 1.25
81+
```
82+
83+
Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
84+
85+
<!-- eslint-disable stdlib/capitalized-comments -->
86+
87+
```javascript
88+
var Float32Array = require( '@stdlib/array/float32' );
89+
var floor = require( '@stdlib/math/base/special/floor' );
90+
91+
var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
92+
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
93+
94+
var N = floor( x0.length / 2 );
95+
96+
var v = smeankbn( N, x1, 2 );
97+
// returns 1.25
98+
```
99+
100+
#### smeankbn.ndarray( N, x, stride, offset )
101+
102+
Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using an improved Kahan–Babuška algorithm and alternative indexing semantics.
103+
104+
```javascript
105+
var Float32Array = require( '@stdlib/array/float32' );
106+
107+
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
108+
var N = x.length;
109+
110+
var v = smeankbn.ndarray( N, x, 1, 0 );
111+
// returns ~0.33333
112+
```
113+
114+
The function accepts the following additional parameters:
115+
116+
- **offset**: starting index for `x`.
117+
118+
While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [arithmetic mean][arithmetic-mean] for every other value in `x` starting from the second value
119+
120+
```javascript
121+
var Float32Array = require( '@stdlib/array/float32' );
122+
var floor = require( '@stdlib/math/base/special/floor' );
123+
124+
var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
125+
var N = floor( x.length / 2 );
126+
127+
var v = smeankbn.ndarray( N, x, 2, 1 );
128+
// returns 1.25
129+
```
130+
131+
</section>
132+
133+
<!-- /.usage -->
134+
135+
<section class="notes">
136+
137+
## Notes
138+
139+
- If `N <= 0`, both functions return `NaN`.
140+
141+
</section>
142+
143+
<!-- /.notes -->
144+
145+
<section class="examples">
146+
147+
## Examples
148+
149+
<!-- eslint no-undef: "error" -->
150+
151+
```javascript
152+
var randu = require( '@stdlib/random/base/randu' );
153+
var round = require( '@stdlib/math/base/special/round' );
154+
var Float32Array = require( '@stdlib/array/float32' );
155+
var smeankbn = require( '@stdlib/stats/base/smeankbn' );
156+
157+
var x;
158+
var i;
159+
160+
x = new Float32Array( 10 );
161+
for ( i = 0; i < x.length; i++ ) {
162+
x[ i ] = round( (randu()*100.0) - 50.0 );
163+
}
164+
console.log( x );
165+
166+
var v = smeankbn( x.length, x, 1 );
167+
console.log( v );
168+
```
169+
170+
</section>
171+
172+
<!-- /.examples -->
173+
174+
* * *
175+
176+
<section class="references">
177+
178+
## References
179+
180+
- Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106][@neumaier:1974a].
181+
182+
</section>
183+
184+
<!-- /.references -->
185+
186+
<section class="links">
187+
188+
[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
189+
190+
[@stdlib/array/float32]: https://github.com/stdlib-js/stdlib
191+
192+
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
193+
194+
[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106
195+
196+
</section>
197+
198+
<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/smeankbn/benchmark/benchmark.js

+96
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,96 @@
1+
/**
2+
* @license Apache-2.0
3+
*
4+
* Copyright (c) 2020 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 randu = require( '@stdlib/random/base/randu' );
25+
var isnan = require( '@stdlib/math/base/assert/is-nan' );
26+
var pow = require( '@stdlib/math/base/special/pow' );
27+
var Float32Array = require( '@stdlib/array/float32' );
28+
var pkg = require( './../package.json' ).name;
29+
var smeankbn = require( './../lib/smeankbn.js' );
30+
31+
32+
// FUNCTIONS //
33+
34+
/**
35+
* Creates a benchmark function.
36+
*
37+
* @private
38+
* @param {PositiveInteger} len - array length
39+
* @returns {Function} benchmark function
40+
*/
41+
function createBenchmark( len ) {
42+
var x;
43+
var i;
44+
45+
x = new Float32Array( len );
46+
for ( i = 0; i < x.length; i++ ) {
47+
x[ i ] = ( randu()*20.0 ) - 10.0;
48+
}
49+
return benchmark;
50+
51+
function benchmark( b ) {
52+
var v;
53+
var i;
54+
55+
b.tic();
56+
for ( i = 0; i < b.iterations; i++ ) {
57+
v = smeankbn( x.length, x, 1 );
58+
if ( isnan( v ) ) {
59+
b.fail( 'should not return NaN' );
60+
}
61+
}
62+
b.toc();
63+
if ( isnan( v ) ) {
64+
b.fail( 'should not return NaN' );
65+
}
66+
b.pass( 'benchmark finished' );
67+
b.end();
68+
}
69+
}
70+
71+
72+
// MAIN //
73+
74+
/**
75+
* Main execution sequence.
76+
*
77+
* @private
78+
*/
79+
function main() {
80+
var len;
81+
var min;
82+
var max;
83+
var f;
84+
var i;
85+
86+
min = 1; // 10^min
87+
max = 6; // 10^max
88+
89+
for ( i = min; i <= max; i++ ) {
90+
len = pow( 10, i );
91+
f = createBenchmark( len );
92+
bench( pkg+':len='+len, f );
93+
}
94+
}
95+
96+
main();

0 commit comments

Comments
 (0)