# diagonal
> Return a 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
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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/base/diagonal' );
```
#### diagonal( x, dims, k, writable )
Returns a view of the diagonal of a matrix (or stack of matrices) `x`.
```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, [ 0, 1 ], 0, false );
// returns [ 1.0, 5.0, 9.0 ]
```
The function accepts the following arguments:
- **x**: input ndarray.
- **dims**: dimension indices defining the plane from which to extract the diagonal.
- **k**: diagonal offset.
- **writable**: boolean indicating whether the returned ndarray should be writable.
## Notes
- The order of the dimension indices contained in `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]`.
- The diagonal offset `k` 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.
- The returned ndarray is a **view** of the input ndarray. Accordingly, writing to the original ndarray will **mutate** the returned ndarray and vice versa.
- The `writable` parameter **only** applies to ndarray constructors supporting **read-only** instances.
## Examples
```javascript
var uniform = require( '@stdlib/random/uniform' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var diagonal = require( '@stdlib/ndarray/base/diagonal' );
// Create a stack of matrices:
var x = uniform( [ 2, 3, 3 ], -10.0, 10.0, {
'dtype': 'float64'
});
console.log( ndarray2array( x ) );
// Extract the main diagonals from the stack:
var y = diagonal( x, [ 1, 2 ], 0, false );
console.log( ndarray2array( y ) );
// Extract super-diagonals from the stack:
y = diagonal( x, [ 1, 2 ], 1, false );
console.log( ndarray2array( y ) );
// Extract sub-diagonals from the stack:
y = diagonal( x, [ 1, 2 ], -1, false );
console.log( ndarray2array( y ) );
```