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# saxpby

> Multiply a single-precision floating-point strided array `x` by a constant and add the result to a single-precision floating-point strided array `y` multiplied by a constant.

<section class="intro">

This BLAS extension implements the operation

<!-- <equation class="equation" label="eq:axpby" align="center" raw="\mathbf{y} = \alpha \mathbf{x} + \beta \mathbf{y}" alt="Equation for axpby operation."> -->

<!-- </equation> -->

This API is complementary to the package [`@stdlib/blas/base/saxpy`][@stdlib/blas/base/saxpy] and is a common BLAS extension in libraries such as Intel MKL, OpenBLAS, and others.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var saxpby = require( '@stdlib/blas/ext/base/saxpby' );
```

#### saxpby( N, alpha, x, strideX, beta, y, strideY )

Multiplies a single-precision floating-point strided array `x` by a constant and adds the result to a single-precision floating-point strided array `y` multiplied by a constant.

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float32Array( [ 2.0, 3.0, 4.0, 5.0, 6.0 ] );

saxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
// y => <Float32Array>[ 9.0, 16.0, 23.0, 30.0, 37.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alpha**: first scalar constant.
-   **x**: input [`Float32Array`][@stdlib/array/float32].
-   **strideX**: stride length for `x`.
-   **beta**: second scalar constant.
-   **y**: output [`Float32Array`][@stdlib/array/float32].
-   **strideY**: stride length for `y`.

The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to multiply every other element of `x` by `alpha` and add to every other element of `y` multiplied by `beta`:

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

saxpby( 3, 5.0, x, 2, 2.0, y, 2 );
// y => <Float32Array>[ 19.0, 8.0, 33.0, 10.0, 47.0, 12.0 ]
```

Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.

```javascript
var Float32Array = require( '@stdlib/array/float32' );

// Initial arrays...
var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

saxpby( 3, 5.0, x1, 1, 2.0, y1, 1 );
// y0 => <Float32Array>[ 7.0, 8.0, 28.0, 35.0, 42.0, 12.0 ]
```

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

Multiplies a single-precision floating-point strided array `x` by a constant and adds the result to a single-precision floating-point strided array `y` multiplied by a constant using alternative indexing semantics.

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float32Array( [ 2.0, 3.0, 4.0, 5.0, 6.0 ] );

saxpby.ndarray( x.length, 5.0, x, 1, 0, 2.0, y, 1, 0 );
// y => <Float32Array>[ 9.0, 16.0, 23.0, 30.0, 37.0 ]
```

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 multiply the last three elements of `x` by `alpha` and add to the last three elements of `y` multiplied by `beta`:

```javascript
var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float32Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );

saxpby.ndarray( 3, 5.0, x, 1, x.length-3, 2.0, y, 1, y.length-3 );
// y => <Float32Array>[ 6.0, 7.0, 31.0, 38.0, 45.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `y` unchanged.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var saxpby = require( '@stdlib/blas/ext/base/saxpby' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float32'
});
console.log( x );

var y = discreteUniform( 10, -100, 100, {
    'dtype': 'float32'
});
console.log( y );

saxpby( x.length, 5.0, x, 1, 2.0, y, 1 );
console.log( y );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<section class="intro">

</section>

<!-- /.intro -->

<section class="usage">

### Usage

```c
#include "stdlib/blas/ext/base/saxpby.h"
```

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

Multiplies a single-precision floating-point strided array `x` by a constant and adds the result to a single-precision floating-point strided array `y` multiplied by a constant.

```c
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
float y[] = { 2.0f, 3.0f, 4.0f, 5.0f };

stdlib_strided_saxpby( 4, 5.0f, x, 1, 2.0f, y, 1 );
```

The function accepts the following arguments:

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

```c
void stdlib_strided_saxpby( const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const float beta, float *Y, const CBLAS_INT strideY );
```

<!--lint disable maximum-heading-length-->

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

<!--lint enable maximum-heading-length-->

Multiplies a single-precision floating-point strided array `x` by a constant and adds the result to a single-precision floating-point strided array `y` multiplied by a constant using alternative indexing semantics.

```c
const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
float y[] = { 2.0f, 3.0f, 4.0f, 5.0f };

stdlib_strided_saxpby_ndarray( 4, 5.0f, x, 1, 0, 2.0f, y, 1, 0 );
```

The function accepts the following arguments:

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

```c
void stdlib_strided_saxpby_ndarray( const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const float beta, float *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

### Examples

```c
#include "stdlib/blas/ext/base/saxpby.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays:
    const float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
    float y[] = { 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f };

    // Specify the number of indexed elements:
    const int N = 8;

    // Specify strides:
    const int strideX = 1;
    const int strideY = 1;

    // Multiply `x` by a constant and add to `y` multiplied by a constant:
    stdlib_strided_saxpby( N, 5.0f, x, strideX, 2.0f, y, strideY );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %i ] = %f\n", i, y[ i ] );
    }
}
```

</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="links">

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

[@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/array-float32

[@stdlib/blas/base/saxpy]: https://github.com/stdlib-js/blas/tree/main/base/saxpy

<!-- <related-links> -->

<!-- </related-links> -->

</section>

<!-- /.links -->
