npm package: @stdlib/blas-base-zaxpy
Description: Scale a double-precision complex floating-point vector by a double-precision complex floating-point constant and add the result to a double-precision complex floating-point vector.
Author: The Stdlib Authors
Latest version: 0.2.1

<!--

@license Apache-2.0

Copyright (c) 2024 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.

-->


<details>
  <summary>
    About stdlib...
  </summary>
  <p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p>
  <p>The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.</p>
  <p>When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.</p>
  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href="https://github.com/stdlib-js/stdlib">GitHub</a>, and please consider <a href="https://opencollective.com/stdlib">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>
</details>

# zaxpy

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

> Scale a double-precision complex floating-point vector by a double-precision complex floating-point constant and add the result to a double-precision complex floating-point vector.

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-base-zaxpy
```

</section>

<section class="usage">

## Usage

```javascript
var zaxpy = require( '@stdlib/blas-base-zaxpy' );
```

#### zaxpy( N, alpha, x, strideX, y, strideY )

Scales values from `x` by `alpha` and adds the result to `y`.

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex128( 2.0, 2.0 );

zaxpy( 3, alpha, x, 1, y, 1 );
// y => <Complex128Array>[ -1.0, 7.0, -1.0, 15.0, -1.0, 23.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alpha**: scalar [`Complex128`][@stdlib/complex/float64/ctor] constant.
-   **x**: first input [`Complex128Array`][@stdlib/array/complex128].
-   **strideX**: stride length for `x`.
-   **y**: second input [`Complex128Array`][@stdlib/array/complex128].
-   **strideY**: stride length for `y`.

The `N` and stride parameters determine how elements from `x` are scaled by `alpha` and added to `y`. For example, to scale every other element in `x` by `alpha` and add the result to every other element of `y`,

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex128( 2.0, 2.0 );

zaxpy( 2, alpha, x, 2, y, 2 );
// y => <Complex128Array>[ -1.0, 7.0, 1.0, 1.0, -1.0, 23.0, 1.0, 1.0 ]
```

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 Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

// Initial arrays...
var x0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y0 = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

// Define a scalar constant:
var alpha = new Complex128( 2.0, 2.0 );

// Create offset views...
var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Complex128Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

// Perform operation:
zaxpy( 2, alpha, x1, 1, y1, 1 );
// y0 => <Complex128Array>[ 1.0, 1.0, 1.0, 1.0, -1.0, 15.0, -1.0, 23.0 ]
```

#### zaxpy.ndarray( N, alpha, x, strideX, offsetX, y, strideY, offsetY )

Scales values from `x` by `alpha` and adds the result to `y` using alternative indexing semantics.

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex128( 2.0, 2.0 );

zaxpy.ndarray( 3, alpha, x, 1, 0, y, 1, 0 );
// y => <Complex128Array>[ -1.0, 7.0, -1.0, 15.0, -1.0, 23.0 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.
-   **offsetY**: starting index for `y`.

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, to scale elements in the first input strided array starting from the second element and add the result to the second input array starting from the second element,

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex128( 2.0, 2.0 );

zaxpy.ndarray( 3, alpha, x, 1, 1, y, 1, 1 );
// y => <Complex128Array>[ 1.0, 1.0, -1.0, 15.0, -1.0, 23.0, -1.0, 31.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0` or `alpha == 0`, both functions return `y` unchanged.
-   `zaxpy()` corresponds to the [BLAS][blas] level 1 function [`zaxpy`][zaxpy].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var zcopy = require( '@stdlib/blas-base-zcopy' );
var zeros = require( '@stdlib/array-zeros' );
var logEach = require( '@stdlib/console-log-each' );
var zaxpy = require( '@stdlib/blas-base-zaxpy' );

function rand() {
    return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

var x = filledarrayBy( 10, 'complex128', rand );
var y = filledarrayBy( 10, 'complex128', rand );
var yc1 = zcopy( y.length, y, 1, zeros( y.length, 'complex128' ), 1 );

var alpha = new Complex128( 2.0, 2.0 );

// Perform operation:
zaxpy( x.length, alpha, x, 1, yc1, 1 );

// Print the results:
logEach( '(%s)*(%s) + (%s) = %s', alpha, x, y, yc1 );

var yc2 = zcopy( y.length, y, 1, zeros( y.length, 'complex128' ), 1 );

// Perform operation using alternative indexing semantics:
zaxpy.ndarray( x.length, alpha, x, 1, 0, yc2, 1, 0 );

// Print the results:
logEach( '(%s)*(%s) + (%s) = %s', alpha, x, y, yc2 );
```

</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
#include "stdlib/blas/base/zaxpy.h"
```

#### c_zaxpy( N, alpha, \*X, strideX, \*Y, strideY )

Scales values from `X` by `alpha` and adds the result to `Y`.

```c
#include "stdlib/complex/float64/ctor.h"

const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
double y[] = { -1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0, -8.0 };
const stdlib_complex128_t alpha = stdlib_complex128( 2.0, 2.0 );

c_zaxpy( 4, alpha, (void *)x, 1, (void *)y, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alpha**: `[in] stdlib_complex128_t` scalar constant.
-   **X**: `[in] void*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **Y**: `[inout] void*` output array.
-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.

```c
void c_zaxpy( const CBLAS_INT N, const stdlib_complex128_t alpha, const void *X, const CBLAS_INT strideX, void *Y, const CBLAS_INT strideY );
```

#### c_zaxpy_ndarray( N, alpha, \*X, strideX, offsetX, \*Y, strideY, offsetY )

Scales values from `X` by `alpha` and adds the result to `Y` using alternative indexing semantics.

```c
#include "stdlib/complex/float64/ctor.h"

const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
double y[] = { -1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0, -8.0 };
const stdlib_complex128_t alpha = stdlib_complex128( 2.0, 2.0 );

c_zaxpy_ndarray( 4, alpha, (void *)x, 1, 0, (void *)y, 1, 0 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alpha**: `[in] stdlib_complex128_t` scalar constant.
-   **X**: `[in] void*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
-   **Y**: `[inout] void*` output array.
-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.

```c
void c_zaxpy_ndarray( const CBLAS_INT N, const stdlib_complex128_t alpha, const void *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, void *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
```

</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
#include "stdlib/blas/base/zaxpy.h"
#include "stdlib/complex/float64/ctor.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
    double y[] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };

    // Create a complex scalar:
    const stdlib_complex128_t alpha = stdlib_complex128( 2.0, 2.0 );

    // Specify the number of elements:
    const int N = 4;

    // Specify stride lengths:
    const int strideX = 1;
    const int strideY = 1;

    // Perform operation:
    c_zaxpy( N, alpha, (void *)x, strideX, (void *)y, strideY );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "zaxpy[ %i ] = %lf + %lfj\n", i, y[ i*2 ], y[ (i*2)+1 ] );
    }

    // Perform operation using alternative indexing semantics:
    c_zaxpy_ndarray( N, alpha, (void *)x, strideX, 0, (void *)y, strideY, 0 );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "zaxpy[ %i ] = %lf + %lfj\n", i, y[ i*2 ], y[ (i*2)+1 ] );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->


<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

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

<!-- /.stdlib -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[npm-image]: http://img.shields.io/npm/v/@stdlib/blas-base-zaxpy.svg
[npm-url]: https://npmjs.org/package/@stdlib/blas-base-zaxpy

[test-image]: https://github.com/stdlib-js/blas-base-zaxpy/actions/workflows/test.yml/badge.svg?branch=v0.2.1
[test-url]: https://github.com/stdlib-js/blas-base-zaxpy/actions/workflows/test.yml?query=branch:v0.2.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-base-zaxpy/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/blas-base-zaxpy?branch=main

<!--

[dependencies-image]: https://img.shields.io/david/stdlib-js/blas-base-zaxpy.svg
[dependencies-url]: https://david-dm.org/stdlib-js/blas-base-zaxpy/main

-->

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg
[chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/blas-base-zaxpy/tree/deno
[deno-readme]: https://github.com/stdlib-js/blas-base-zaxpy/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/blas-base-zaxpy/tree/umd
[umd-readme]: https://github.com/stdlib-js/blas-base-zaxpy/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/blas-base-zaxpy/tree/esm
[esm-readme]: https://github.com/stdlib-js/blas-base-zaxpy/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/blas-base-zaxpy/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-base-zaxpy/main/LICENSE

[blas]: http://www.netlib.org/blas

[zaxpy]: https://www.netlib.org/lapack/explore-html/d5/d4b/group__axpy_gaf603daa00d5c723d0e409d9b2d011bf4.html

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

[@stdlib/array/complex128]: https://www.npmjs.com/package/@stdlib/array-complex128

[@stdlib/complex/float64/ctor]: https://www.npmjs.com/package/@stdlib/complex-float64-ctor

</section>

<!-- /.links -->