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feat: add lapack/base/dlassq
PR-URL: #2668 Ref: #2464 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com>
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‎lib/node_modules/@stdlib/lapack/base/dlassq/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2024 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dlassq
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> Return an updated sum of squares represented in scaled form.
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<section class="intro">
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This routine returns the values $s_{textrm{out}}$ and $\textrm{ss}_{\textrm{out}}$ such that
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<!-- <equation class="equation" label="eq:sum_of_squares" align="center" raw="s_{\textrm{out}}^2 \cdot \textrm{ss}_{\textrm{out}} = x_0^2 + \ldots + x_{N-1}^2 + s_{\textrm{in}}^2 \cdot \textrm{ss}_{\textrm{in}}" alt="Sum of squares represented in scaled form"> -->
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<div class="equation" align="center" data-raw-text="s_{\textrm{out}}^2 \cdot \textrm{ss}_{\textrm{out}} = x_0^2 + \ldots + x_{N-1}^2 + s_{\textrm{in}}^2 \cdot \textrm{ss}_{\textrm{in}}" data-equation="eq:sum_of_squares">
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<img src="" alt="Sum of squares represented in scaled form">
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<br>
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</div>
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<!-- </equation> -->
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where $x_i = X_{(i-1) \cdot \textrm{sx}}$ and $\textrm{sx}$ is the stride of `X`. The value of $\textrm{ss}_{\textrm{in}}$ is assumed to be nonnegative.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var dlassq = require( '@stdlib/lapack/base/dlassq' );
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```
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#### dlassq( N, X, strideX, scale, sumsq )
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Returns an updated sum of squares represented in scaled form.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
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var out = dlassq( 4, X, 1, 1.0, 0.0 );
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// returns <Float64Array>[ 1.0, 30.0 ]
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **X**: input [`Float64Array`][mdn-float64array].
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- **strideX**: stride length for `X`.
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- **scale**: scaling factor.
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- **sumsq**: basic sum of squares from which output is factored out.
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial array:
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var X0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
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// Create an offset view:
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var X1 = new Float64Array( X0.buffer, X0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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// Compute the sum of squares:
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var out = dlassq( X1.length, X1, 1, 1.0, 0.0 );
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// returns <Float64Array>[ 1.0, 30.0 ]
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```
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The returned [`Float64Array`][mdn-float64array] contains an updated scale factor and an updated sum of squares, respectively.
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#### dlassq.ndarray( N, X, sx, ox, scale, sumsq, out, so, oo )
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Returns an updated sum of squares represented in scaled form using alternative indexing semantics.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
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var out = new Float64Array( [ 0.0, 0.0 ] );
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dlassq.ndarray( 4, X, 1, 0, 1.0, 0.0, out, 1, 0 );
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// out => <Float64Array>[ 1.0, 30.0 ]
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```
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The function has the following additional parameters:
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- **ox**: starting index for `X`.
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- **out**: output [`Float64Array`][mdn-float64array]
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- **so**: stride length for `out`.
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- **oo**: starting index for `out`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
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<!-- eslint-disable max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var X = new Float64Array( [ 1.0, 0.0, 2.0, 0.0, 3.0, 0.0, 4.0 ] );
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var out = new Float64Array( [ 0.0, 0.0, 999.9, 0.0, 999.9 ] );
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dlassq.ndarray( 4, X, 2, 0, 1.0, 0.0, out, 2, 1 );
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// out => <Float64Array>[ 0.0, 1.0, 999.9, 30.0, 999.9 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- `dlassq()` corresponds to the [LAPACK][LAPACK] function [`dlassq`][lapack-dlassq].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var dlassq = require( '@stdlib/lapack/base/dlassq' );
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var X = discreteUniform( 10, -10, 10, {
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'dtype': 'float64'
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});
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console.log( X );
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var out = dlassq( X.length, X, 1, 1.0, 0.0 );
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console.log( out );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[lapack]: https://www.netlib.org/lapack/explore-html/
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[lapack-dlassq]: https://www.netlib.org/lapack/explore-html/d8/d76/group__lassq_gae8f40b0a34771b4f2d9c863de3af7be5.html#gae8f40b0a34771b4f2d9c863de3af7be5
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/lapack/base/dlassq/benchmark/benchmark.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var pkg = require( './../package.json' ).name;
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var dlassq = require( './../lib/dlassq.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float64'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var x = uniform( len, -100.0, 100.0, options );
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return benchmark;
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function benchmark( b ) {
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var out;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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out = dlassq( x.length, x, 1, 1.0, 0.0 );
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if ( isnan( out[ 0 ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( out[ 1 ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

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