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# daxpy

> Multiply a vector `x` by a constant `alpha` and add the result to `y`.

<section class="usage">

## Usage

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

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

Multiplies a vector `x` by a constant `alpha` and adds the result to `y`.

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

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = 5.0;

daxpy( x.length, alpha, x, 1, y, 1 );
// y => <Float64Array>[ 6.0, 11.0, 16.0, 21.0, 26.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alpha**: scalar constant.
-   **x**: input [`Float64Array`][mdn-float64array].
-   **strideX**: index increment for `x`.
-   **y**: input [`Float64Array`][mdn-float64array].
-   **strideY**: index increment for `y`.

The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to multiply every other value in `x` by `alpha` and add the result to the first `N` elements of `y` in reverse order,

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

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

var alpha = 5.0;

daxpy( 3, alpha, x, 2, y, -1 );
// y => <Float64Array>[ 26.0, 16.0, 6.0, 1.0, 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 Float64Array = require( '@stdlib/array/float64' );

// Initial arrays...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

daxpy( 3, 5.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]
```

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

Multiplies a vector `x` by a constant `alpha` and adds the result to `y` using alternative indexing semantics.

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

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = 5.0;

daxpy.ndarray( x.length, alpha, x, 1, 0, y, 1, 0 );
// y => <Float64Array>[ 6.0, 11.0, 16.0, 21.0, 26.0 ]
```

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 every other value in `x` by a constant `alpha` starting from the second value and add to the last `N` elements in `y` where `x[i] -> y[n]`, `x[i+2] -> y[n-1]`,...,

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

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

var alpha = 5.0;

daxpy.ndarray( 3, alpha, x, 2, 1, y, -1, y.length-1 );
// y => <Float64Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

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

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );

var y = discreteUniform( x.length, 0, 10, opts );
console.log( y );

daxpy.ndarray( x.length, 5.0, x, 1, 0, y, -1, y.length-1 );
console.log( y );
```

</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/daxpy.h"
```

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

Multiplies a vector `X` by a constant and adds the result to `Y`.

```c
const double x[] = { 1.0, 2.0, 3.0, 4.0 };
double y[] = { 0.0, 0.0, 0.0, 0.0 };

c_daxpy( 4, 5.0, x, 1, y, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alpha**: `[in] double` scalar constant.
-   **X**: `[in] double*` input array.
-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
-   **Y**: `[inout] double*` output array.
-   **strideY**: `[in] CBLAS_INT` index increment for `Y`.

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

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

Multiplies a vector `X` by a constant and adds the result to `Y` using alternative indexing semantics.

```c
const double x[] = { 1.0, 2.0, 3.0, 4.0 };
double y[] = { 0.0, 0.0, 0.0, 0.0 };

c_daxpy_ndarray( 4, 5.0, x, 1, 0, y, 1, 0 );
```

The function accepts the following arguments:

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

```c
void c_daxpy_ndarray( const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *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/daxpy.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[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

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

    // Specify stride lengths:
    const int strideX = 2;
    const int strideY = -2;

    // Compute `a*x + y`:
    c_daxpy( N, 5.0, x, strideX, y, strideY );

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

    // Compute `a*x + y`:
    c_daxpy_ndarray( N, 5.0, x, strideX, 1, y, strideY, 7 );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %i ] = %lf\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">

* * *

## See Also

-   <span class="package-name">[`@stdlib/blas/base/dasum`][@stdlib/blas/base/dasum]</span><span class="delimiter">: </span><span class="description">compute the sum of absolute values (L1 norm).</span>
-   <span class="package-name">[`@stdlib/blas/base/gaxpy`][@stdlib/blas/base/gaxpy]</span><span class="delimiter">: </span><span class="description">multiply a vector `x` by a constant and add the result to `y`.</span>
-   <span class="package-name">[`@stdlib/blas/base/saxpy`][@stdlib/blas/base/saxpy]</span><span class="delimiter">: </span><span class="description">multiply a vector `x` by a constant and add the result to `y`.</span>

</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">

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

[daxpy]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html

[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

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

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

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

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

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

</section>

<!-- /.links -->
