time-to-botec/squiggle/node_modules/@stdlib/blas/ext/base/dnannsumkbn/README.md

199 lines
5.6 KiB
Markdown
Raw Normal View History

<!--
@license Apache-2.0
Copyright (c) 2020 The Stdlib Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
-->
# dnannsumkbn
> Calculate the sum of double-precision floating-point strided array elements, ignoring `NaN` values and using an improved KahanBabuška algorithm.
<section class="intro">
</section>
<!-- /.intro -->
<section class="usage">
## Usage
```javascript
var dnannsumkbn = require( '@stdlib/blas/ext/base/dnannsumkbn' );
```
#### dnannsumkbn( N, x, strideX, out, strideOut )
Computes the sum of double-precision floating-point strided array elements, ignoring `NaN` values and using an improved KahanBabuška algorithm.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
var out = new Float64Array( 2 );
var v = dnannsumkbn( x.length, x, 1, out, 1 );
// returns <Float64Array>[ 1.0, 3 ]
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: input [`Float64Array`][@stdlib/array/float64].
- **strideX**: index increment for `x`.
- **out**: output [`Float64Array`][@stdlib/array/float64] whose first element is the sum and whose second element is the number of non-NaN elements.
- **strideOut**: index increment for `out`.
The `N` and `stride` parameters determine which elements are accessed at runtime. For example, to compute the sum of every other element in `x`,
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );
var x = new Float64Array( [ 1.0, 2.0, NaN, -7.0, NaN, 3.0, 4.0, 2.0 ] );
var out = new Float64Array( 2 );
var N = floor( x.length / 2 );
var v = dnannsumkbn( N, x, 2, out, 1 );
// returns <Float64Array>[ 5.0, 2 ]
```
Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
<!-- eslint-disable stdlib/capitalized-comments -->
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );
var x0 = new Float64Array( [ 2.0, 1.0, NaN, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var out0 = new Float64Array( 4 );
var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*2 ); // start at 3rd element
var N = floor( x0.length / 2 );
var v = dnannsumkbn( N, x1, 2, out1, 1 );
// returns <Float64Array>[ 5.0, 4 ]
```
#### dnannsumkbn.ndarray( N, x, strideX, offsetX, out, strideOut, offsetOut )
Computes the sum of double-precision floating-point strided array elements, ignoring `NaN` values and using an improved KahanBabuška algorithm and alternative indexing semantics.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
var out = new Float64Array( 2 );
var v = dnannsumkbn.ndarray( x.length, x, 1, 0, out, 1, 0 );
// returns <Float64Array>[ 1.0, 3 ]
```
The function has the following additional parameters:
- **offsetX**: starting index for `x`.
- **offsetOut**: starting index for `out`.
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 sum of every other value in `x` starting from the second value
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );
var x = new Float64Array( [ 2.0, 1.0, NaN, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var out = new Float64Array( 4 );
var N = floor( x.length / 2 );
var v = dnannsumkbn.ndarray( N, x, 2, 1, out, 2, 1 );
// returns <Float64Array>[ 0.0, 5.0, 0.0, 4 ]
```
</section>
<!-- /.usage -->
<section class="notes">
## Notes
- If `N <= 0`, both functions return a sum equal to `0.0`.
</section>
<!-- /.notes -->
<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var dnannsumkbn = require( '@stdlib/blas/ext/base/dnannsumkbn' );
var x;
var i;
x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
if ( randu() < 0.2 ) {
x[ i ] = NaN;
} else {
x[ i ] = round( randu()*100.0 );
}
}
console.log( x );
var out = new Float64Array( 2 );
dnannsumkbn( x.length, x, 1, out, 1 );
console.log( out );
```
</section>
<!-- /.examples -->
* * *
<section class="references">
## References
- Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 3951. doi:[10.1002/zamm.19740540106][@neumaier:1974a].
</section>
<!-- /.references -->
<section class="links">
[@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106
</section>
<!-- /.links -->