npm package: @stdlib/lapack-base-dlassq
Description: Return an updated sum of squares represented in scaled form.
Author: The Stdlib Authors
Latest version: 0.1.1

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# dlassq

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Return an updated sum of squares represented in scaled form.

<section class="intro">

This routine returns the values $s_{textrm{out}}$ and $\\textrm{ss}_{\\textrm{out}}$ such that

<!-- <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"> -->

<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">
    <img src="" alt="Sum of squares represented in scaled form">
    <br>
</div>

<!-- </equation> -->

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.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/lapack-base-dlassq
```

</section>

<section class="usage">

## Usage

```javascript
var dlassq = require( '@stdlib/lapack-base-dlassq' );
```

#### dlassq( N, X, strideX, scale, sumsq )

Returns an updated sum of squares represented in scaled form.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );

var out = dlassq( 4, X, 1, 1.0, 0.0 );
// returns <Float64Array>[ 1.0, 30.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **X**: input [`Float64Array`][mdn-float64array].
-   **strideX**: stride length for `X`.
-   **scale**: scaling factor.
-   **sumsq**: basic sum of squares from which output is factored out.

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' );

// Initial array:
var X0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );

// Create an offset view:
var X1 = new Float64Array( X0.buffer, X0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

// Compute the sum of squares:
var out = dlassq( X1.length, X1, 1, 1.0, 0.0 );
// returns <Float64Array>[ 1.0, 30.0 ]
```

The returned [`Float64Array`][mdn-float64array] contains an updated scale factor and an updated sum of squares, respectively.

#### dlassq.ndarray( N, X, sx, ox, scale, sumsq, out, so, oo )

Returns an updated sum of squares represented in scaled form using alternative indexing semantics.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
var out = new Float64Array( [ 0.0, 0.0 ] );

dlassq.ndarray( 4, X, 1, 0, 1.0, 0.0, out, 1, 0 );
// out => <Float64Array>[ 1.0, 30.0 ]
```

The function has the following additional parameters:

-   **ox**: starting index for `X`.
-   **out**: output [`Float64Array`][mdn-float64array].
-   **so**: stride length for `out`.
-   **oo**: starting index for `out`.

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,

<!-- eslint-disable max-len -->

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var X = new Float64Array( [ 1.0, 0.0, 2.0, 0.0, 3.0, 0.0, 4.0 ] );
var out = new Float64Array( [ 0.0, 0.0, 999.9, 0.0, 999.9 ] );

dlassq.ndarray( 4, X, 2, 0, 1.0, 0.0, out, 2, 1 );
// out => <Float64Array>[ 0.0, 1.0, 999.9, 30.0, 999.9 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   `dlassq()` corresponds to the [LAPACK][LAPACK] function [`dlassq`][lapack-dlassq].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var dlassq = require( '@stdlib/lapack-base-dlassq' );

var X = discreteUniform( 10, -10, 10, {
    'dtype': 'float64'
});
console.log( X );

var out = dlassq( X.length, X, 1, 1.0, 0.0 );
console.log( out );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
TODO
```

#### TODO

TODO.

```c
TODO
```

TODO

```c
TODO
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
TODO
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

* * *

<section class="references">

## References

-   Blue, James L. 1978. "A Portable Fortran Program to Find the Euclidean Norm of a Vector." _ACM Transactions on Mathematical Software_ 4 (1). New York, NY, USA: Association for Computing Machinery: 15–23. doi:[10.1145/355769.355771][@blue:1978a].
-   Anderson, Edward. 2017. "Algorithm 978: Safe Scaling in the Level 1 BLAS." _ACM Transactions on Mathematical Software_ 44 (1). New York, NY, USA: Association for Computing Machinery: 1–28. doi:[10.1145/3061665][@anderson:2017a].

</section>

<!-- /.references -->

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<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[deno-url]: https://github.com/stdlib-js/lapack-base-dlassq/tree/deno
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/lapack-base-dlassq/main/LICENSE

[lapack]: https://www.netlib.org/lapack/explore-html/

[lapack-dlassq]: https://www.netlib.org/lapack/explore-html/d8/d76/group__lassq_gae8f40b0a34771b4f2d9c863de3af7be5.html#gae8f40b0a34771b4f2d9c863de3af7be5

[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

[@blue:1978a]: https://doi.org/10.1145/355769.355771

[@anderson:2017a]: https://doi.org/10.1145/3061665

</section>

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