# diagonal
> Return a **read-only** view of the diagonal of a matrix (or stack of matrices).
For an `M`-by-`N` matrix `A`, the `k`-th diagonal is defined as
-->
where `k = 0` corresponds to the main diagonal, `k > 0` corresponds to the super-diagonals (above the main diagonal), and `k < 0` corresponds to the sub-diagonals (below the main diagonal). For example, given the matrix
the main diagonal is `[ a_{0,0}, a_{1,1}, a_{2,2} ]`, the super-diagonal `k = 1` is `[ a_{0,1}, a_{1,2} ]`, and the sub-diagonal `k = -1` is `[ a_{1,0}, a_{2,1} ]`.
## Usage
```javascript
var diagonal = require( '@stdlib/ndarray/diagonal' );
```
#### diagonal( x\[, options] )
Returns a read-only view of the diagonal of a matrix (or stack of matrices).
```javascript
var array = require( '@stdlib/ndarray/array' );
var x = array( [ [ 1.0, 2.0, 3.0 ], [ 4.0, 5.0, 6.0 ], [ 7.0, 8.0, 9.0 ] ] );
// returns [ [ 1.0, 2.0, 3.0 ], [ 4.0, 5.0, 6.0 ], [ 7.0, 8.0, 9.0 ] ]
var y = diagonal( x );
// returns [ 1.0, 5.0, 9.0 ]
```
The function accepts the following arguments:
- **x**: input [`ndarray`][@stdlib/ndarray/ctor].
- **options**: function options.
The function accepts the following options:
- **k**: diagonal offset. The diagonal offset is interpreted as `column - row`. Accordingly, when `k = 0`, the function returns the main diagonal; when `k > 0`, the function returns the diagonal above the main diagonal; and when `k < 0`, the function returns the diagonal below the main diagonal. Default: `0`.
- **dims**: dimension indices defining the plane from which to extract the diagonal. Must contain exactly two unique dimension indices. The first element specifies the row-like dimension. The second element specifies the column-like dimension. If a dimension index is provided as an integer less than zero, the dimension index is resolved relative to the last dimension, with the last dimension corresponding to the value `-1`. Default: `[-2, -1]`.
## Notes
- The order of the dimension indices contained in `options.dims` matters. The first element specifies the row-like dimension. The second element specifies the column-like dimension.
- Each provided dimension index must reside on the interval `[-ndims, ndims-1]`.
## Examples
```javascript
var uniform = require( '@stdlib/random/uniform' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var diagonal = require( '@stdlib/ndarray/diagonal' );
// Create a stack of matrices:
var x = uniform( [ 2, 3, 3 ], -10.0, 10.0 );
console.log( ndarray2array( x ) );
// Extract the main diagonals from the stack:
var y = diagonal( x );
console.log( ndarray2array( y ) );
// Extract super-diagonals from the stack:
y = diagonal( x, {
'k': 1
});
console.log( ndarray2array( y ) );
// Extract sub-diagonals from the stack:
y = diagonal( x, {
'k': -1
});
console.log( ndarray2array( y ) );
```
[@stdlib/ndarray/ctor]: https://github.com/stdlib-js/ndarray/tree/main/ctor