# inv
> Compute the [multiplicative inverse][multiplicative-inverse] for each element in a strided array.
The [multiplicative inverse][multiplicative-inverse] (or **reciprocal**) is defined as
## Usage
```javascript
var inv = require( '@stdlib/math/strided/special/inv' );
```
#### inv( N, x, strideX, y, strideY )
Computes the [multiplicative inverse][multiplicative-inverse] for each element in a strided array `x` and assigns the results to elements in a strided array `y`.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ -20.0, -1.0, 2.0, 4.0, 10.0 ] );
// Perform operation in-place:
inv( x.length, x, 1, x, 1 );
// x => [ -0.05, -1.0, 0.5, 0.25, 0.1 ]
```
The function accepts the following arguments:
- **N**: number of indexed elements.
- **x**: input array-like object.
- **strideX**: index increment for `x`.
- **y**: output array-like object.
- **strideY**: index increment for `y`.
The `N` and `stride` parameters determine which elements in `x` and `y` are accessed at runtime. For example, to index every other value in `x` and the first `N` elements of `y` in reverse order,
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ -20.0, -1.0, 2.0, 4.0, 10.0, 100.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
inv( 3, x, 2, y, -1 );
// y => [ 0.1, 0.5, -0.05, 0.0, 0.0, 0.0 ]
```
Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
// Initial arrays...
var x0 = new Float64Array( [ -20.0, -1.0, 2.0, 4.0, 10.0, 100.0 ] );
var y0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
// 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
inv( 3, x1, -2, y1, 1 );
// y0 => [ 0.0, 0.0, 0.0, 0.01, 0.25, -1.0 ]
```
#### inv.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )
Computes the [multiplicative inverse][multiplicative-inverse] for each element in a strided array `x` and assigns the results to elements in a strided array `y` using alternative indexing semantics.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ -20.0, -1.0, 2.0, 4.0, 10.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0 ] );
inv.ndarray( x.length, x, 1, 0, y, 1, 0 );
// y => [ -0.05, -1.0, 0.5, 0.25, 0.1 ]
```
The function accepts the following additional arguments:
- **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 `offsetX` and `offsetY` parameters support indexing semantics based on starting indices. For example, to index every other value in `x` starting from the second value and to index the last `N` elements in `y`,
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ -20.0, -1.0, 2.0, 4.0, 10.0, 100.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
inv.ndarray( 3, x, 2, 1, y, -1, y.length-1 );
// y => [ 0.0, 0.0, 0.0, 0.01, 0.25, -1.0 ]
```
## Examples
```javascript
var uniform = require( '@stdlib/random/base/uniform' ).factory;
var filledarray = require( '@stdlib/array/filled' );
var dtypes = require( '@stdlib/array/dtypes' );
var gfillBy = require( '@stdlib/blas/ext/base/gfill-by' );
var inv = require( '@stdlib/math/strided/special/inv' );
var dt;
var x;
var y;
var i;
dt = dtypes();
for ( i = 0; i < dt.length; i++ ) {
x = filledarray( 0.0, 10, dt[ i ] );
gfillBy( x.length, x, 1, uniform( -50.0, 50.0 ) );
console.log( x );
y = filledarray( 0.0, x.length, 'generic' );
console.log( y );
inv.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
console.log( y );
console.log( '' );
}
```
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
[multiplicative-inverse]: https://en.wikipedia.org/wiki/Multiplicative_inverse
