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# drot

> Apply a plane rotation.

<section class="intro">

This BLAS level 1 routine applies a real plane rotation to real double-precision floating-point vectors. The plane rotation is applied to `N` points, where the points to be rotated are contained in vectors `x` and `y` and where the cosine and sine of the angle of rotation are `c` and `s`, respectively. The operation is as follows:

<!-- <equation class="equation" label="eq:drot" align="center" raw="\begin{bmatrix}x_i \\ y_i\end{bmatrix} = \begin{bmatrix} c & s \\ -s & c\end{bmatrix}\begin{bmatrix} x_i \\ y_i \end{bmatrix}" alt="Plane rotation"> -->

<!-- </equation> -->

where `x_i` and `y_i` are the individual elements on which the rotation is applied.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### drot( N, x, strideX, y, strideY, c, s )

Applies a plane rotation.

```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( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );

drot( x.length, x, 1, y, 1, 0.8, 0.6 );
// x => <Float64Array>[ ~4.4, ~5.8, 7.2, 8.6, 10.0 ]
// y => <Float64Array>[ ~4.2, 4.4, 4.6, 4.8, 5.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: first input [`Float64Array`][mdn-float64array].
-   **strideX**: index increment for `x`.
-   **y**: second input [`Float64Array`][mdn-float64array].
-   **strideY**: index increment for `y`.
-   **c**: cosine of the angle of rotation.
-   **s**: sine of the angle of rotation.

The `N` and stride parameters determine how values in the strided arrays are accessed at runtime. For example, to apply a plane rotation to every other element,

```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 ] );

drot( 3, x, 2, y, 2, 0.8, 0.6 );
// x => <Float64Array>[ 5.0, 2.0, 7.8, 4.0, 10.6, 6.0 ]
// y => <Float64Array>[ ~5.0, 8.0, 5.4, 10.0, ~5.8, 12.0 ]
```

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

drot( 3, x1, -2, y1, 1, 0.8, 0.6 );
// x0 => <Float64Array>[ 1.0, ~8.8, 3.0, 9.8, 5.0, 10.8 ]
// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 4.4, 6.4, ~8.4 ]
```

#### drot.ndarray( N, x, strideX, offsetX, y, strideY, offsetY, c, s )

Applies a plane rotation 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( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );

drot.ndarray( 4, x, 1, 1, y, 1, 1, 0.8, 0.6 );
// x => <Float64Array>[ 1.0, ~5.8, 7.2, 8.6, 10.0 ]
// y => <Float64Array>[ 6.0, 4.4, ~4.6, ~4.8, 5.0 ]
```

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 apply a plane rotation to every other element starting from the second element,

```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 ] );

drot.ndarray( 3, x, 2, 1, y, 2, 1, 0.8, 0.6 );
// x => <Float64Array>[ 1.0, 6.4, 3.0, 9.2, 5.0, 12.0 ]
// y => <Float64Array>[ 7.0, 5.2, 9.0, 5.6, 11.0, ~6.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions leave `x` and `y` unchanged.
-   `drot()` corresponds to the [BLAS][blas] level 1 function [`drot`][drot].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 500, opts );
console.log( x );

var y = discreteUniform( x.length, 0, 255, opts );
console.log( y );

// Apply a plane rotation:
drot( x.length, x, 1, y, 1, 0.8, 0.6 );
console.log( x );
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/drot.h"
```

#### c_drot( N, \*X, strideX, \*Y, strideY, c, s )

Applies a plane rotation.

```c
double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
double y[] = { 6.0, 7.0, 8.0, 9.0, 10.0 };

c_drot( 5, x, 1, y, 1, 0.8, 0.6 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[inout] double*` first input array.
-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
-   **Y**: `[inout] double*` second input array.
-   **strideY**: `[in] CBLAS_INT` index increment for `Y`.
-   **c**: `[in] double` cosine of the angle of rotation.
-   **s**: `[in] double` sine of the angle of rotation.

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

#### c_drot_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY, c, s )

Applies a plane rotation using alternative indexing semantics.

```c
double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
double y[] = { 6.0, 7.0, 8.0, 9.0, 10.0 };

c_drot_ndarray( 5, x, 1, 0, y, 1, 0, 0.8, 0.6 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[inout] double*` first input array.
-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
-   **Y**: `[inout] double*` second input array.
-   **strideY**: `[in] CBLAS_INT` index increment for `Y`.
-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
-   **c**: `[in] double` cosine of the angle of rotation.
-   **s**: `[in] double` sine of the angle of rotation.

```c
void c_drot_ndarray( const CBLAS_INT N, double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, const double c, const double s );
```

</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/drot.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays:
    double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
    double y[] = { 6.0, 7.0, 8.0, 9.0, 10.0 };

    // Specify the number of elements:
    const int N = 3;

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

    // Specify angle of rotation:
    const double c = 0.8;
    const double s = 0.6;

    // Apply plane rotation:
    c_drot( N, x, strideX, y, strideY, c, s );

    // Print the result:
    for ( int i = 0; i < 5; i++ ) {
        printf( "x[ %i ] = %lf, y[ %i ] = %lf\n", i, x[ i ], i, y[ i ] );
    }

    // Apply plane rotation:
    c_drot_ndarray( N, x, strideX, 0, y, strideY, 4, c, s );

    // Print the result:
    for ( int i = 0; i < 5; i++ ) {
        printf( "x[ %i ] = %lf, y[ %i ] = %lf\n", i, x[ i ], 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">

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

[drot]: https://www.netlib.org/lapack/explore-html/d1/d45/group__rot_gae48ef017306866ac2d5a8c5a52617858.html#gae48ef017306866ac2d5a8c5a5261785

[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

</section>

<!-- /.links -->
