# srotm
> Apply a modified Givens plane rotation.
## Usage
```javascript
var srotm = require( '@stdlib/blas/base/srotm' );
```
#### srotm( N, x, strideX, y, strideY, param )
Applies a modified Givens plane rotation.
```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 ] );
var param = new Float32Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
srotm( 2, x, 2, y, 1, param );
// x => [ ~-17.0, 2.0, ~-18.0, 4.0, 5.0 ]
// y => [ ~8.0, ~13.0, 8.0, 9.0, 10.0 ]
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: first input [`Float32Array`][mdn-float32array].
- **strideX**: index increment for `x`.
- **y**: second input [`Float32Array`][mdn-float32array].
- **strideY**: index increment for `y`.
- **param**: parameters for the modified Givens transformation
The `N` and stride parameters determine how values in the strided arrays are accessed at runtime. For example, to apply a modified Givens plane rotation to every other element,
```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 ] );
var param = new Float32Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
srotm( 3, x, 2, y, 2, param );
// x => [ ~-20.0, 2.0, ~-24.0, 4.0, ~-28.0, 6.0 ]
// y => [ ~9.0, 8.0, ~15.0, 10.0, ~21.0, 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 ] );
var y0 = new Float32Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
var param = new Float32Array( [ 1.0, 0.0, 2.0, 3.0, 0.0 ] );
// 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*3 ); // start at 4th element
srotm( 2, x1, 1, y1, 1, param );
// x0 => [ 1.0, ~9.0, ~10.0, 4.0, 5.0 ]
// y0 => [ 6.0, 7.0, 8.0, ~-2.0, ~-3.0 ]
```
#### srotm.ndarray( N, x, strideX, offsetX, y, strideY, offsetY, param )
Applies a modified Givens plane rotation 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( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
var param = new Float32Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
srotm.ndarray( 2, x, 1, 0, y, 2, 1, param );
// x => [ ~-20.0, ~-25.0, 3.0, 4.0, 5.0 ]
// y => [ 6.0, ~9.0, 8.0, ~13.0, 10.0 ]
```
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 modified Givens plane rotation to every other element starting from the second element,
```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 ] );
var param = new Float32Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );
srotm.ndarray( 3, x, 2, 1, y, 2, 1, param );
// x => [ 1.0, ~-22.0, 3.0, ~-26.0, 5.0, ~-30.0 ]
// y => [ 7.0, ~12.0, 9.0, ~18.0, 11.0, ~24.0 ]
```
## Notes
- If `N <= 0`, both functions leave `x` and `y` unchanged.
- `srotm()` corresponds to the [BLAS][blas] level 1 function [`srotm`][srotm].
## Examples
```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var srotm = require( '@stdlib/blas/base/srotm' );
var opts = {
'dtype': 'float32'
};
var x = discreteUniform( 10, 0, 500, opts );
console.log( x );
var y = discreteUniform( x.length, 0, 255, opts );
console.log( y );
var param = discreteUniform( 5, -5, 5, opts );
console.log( param );
// Apply a plane rotation:
srotm( x.length, x, 1, y, 1, param );
console.log( x );
console.log( y );
```
* * *
## C APIs
### Usage
```c
#include "stdlib/blas/base/srotm.h"
```
#### c_srotm( N, \*X, strideX, \*Y, strideY, param )
Applies a modified Givens plane rotation.
```c
float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f };
float y[] = { 6.0f, 7.0f, 8.0f, 9.0f, 10.0f };
const float param[5] = { 0.0f, 0.0f, 2.0f, -3.0f, 0.0f };
c_srotm( 5, x, 1, y, 1, param );
```
The function accepts the following arguments:
- **N**: `[in] CBLAS_INT` number of indexed elements.
- **X**: `[inout] float*` first input array.
- **strideX**: `[in] CBLAS_INT` index increment for `X`.
- **Y**: `[inout] float*` second input array.
- **strideY**: `[in] CBLAS_INT` index increment for `Y`.
- **param**: `[in] float` parameters for the modified Givens transformation.
```c
void c_srotm( const CBLAS_INT N, float *X, const CBLAS_INT strideX, float *Y, const CBLAS_INT strideY, const float *param );
```
#### c_srotm_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY, param )
Applies a modified Givens plane rotation using alternative indexing semantics.
```c
float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f };
float y[] = { 6.0f, 7.0f, 8.0f, 9.0f, 10.0f };
const float param[5] = { 0.0f, 0.0f, 2.0f, -3.0f, 0.0f };
c_srotm_ndarray( 5, x, 1, 0, y, 1, 0, param );
```
The function accepts the following arguments:
- **N**: `[in] CBLAS_INT` number of indexed elements.
- **X**: `[inout] float*` first input array.
- **strideX**: `[in] CBLAS_INT` index increment for `X`.
- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
- **Y**: `[inout] float*` second input array.
- **strideY**: `[in] CBLAS_INT` index increment for `Y`.
- **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
- **param**: `[in] float` parameters for the modified Givens transformation.
```c
void c_srotm_ndarray( const CBLAS_INT N, float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, float *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, const float *param );
```
### Examples
```c
#include "stdlib/blas/base/srotm.h"
#include
int main( void ) {
// Create strided arrays:
float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f };
float y[] = { 6.0f, 7.0f, 8.0f, 9.0f, 10.0f };
// Specify the number of elements:
const int N = 5;
// Specify stride lengths:
const int strideX = 1;
const int strideY = 1;
// Specify parameters for the modified Givens transformation:
const float param[5] = { 0.0f, 0.0f, 2.0f, -3.0f, 0.0f };
// Apply plane rotation:
c_srotm( N, x, strideX, y, strideY, param );
// Print the result:
for ( int i = 0; i < 5; i++ ) {
printf( "x[ %i ] = %f, y[ %i ] = %f\n", i, x[ i ], i, y[ i ] );
}
// Apply plane rotation:
c_srotm_ndarray( N, x, -strideX, N-1, y, -strideY, N-1, param );
// Print the result:
for ( int i = 0; i < 5; i++ ) {
printf( "x[ %i ] = %f, y[ %i ] = %f\n", i, x[ i ], i, y[ i ] );
}
}
```
[blas]: http://www.netlib.org/blas
[srotm]: https://www.netlib.org/lapack/explore-html/d1/d45/group__rot_gae48ef017306866ac2d5a8c5a52617858.html#gae48ef017306866ac2d5a8c5a5261785
[mdn-float32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float32Array
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray