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# fillDiagonal

> Fill a specified diagonal of a matrix (or stack of matrices) with a scalar value.

<section class="intro">

For an `M`-by-`N` matrix `A`, the `k`-th diagonal is defined as

<!-- <equation class="equation" label="eq:diagonal_definition" align="center" raw="D_k = \{\, A_{i,j} : j - i = k \,\}" alt="Definition of the k-th diagonal of a matrix."> -->

<div class="equation" align="center" data-raw-text="D_k = \{\, A_{i,j} : j - i = k \,\}" data-equation="eq:diagonal_definition">
    <img src="" alt="Definition of the k-th diagonal of a matrix.">
    <br>
</div>

<!-- </equation> -->

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).

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var fillDiagonal = require( '@stdlib/ndarray/base/fill-diagonal' );
```

#### fillDiagonal( x, value, dims, k )

Fills a specified diagonal of a matrix (or stack of matrices) with a scalar value.

```javascript
var zeros = require( '@stdlib/ndarray/zeros' );

var x = zeros( [ 3, 3 ] );
// returns <ndarray>[ [ 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0 ] ]

var out = fillDiagonal( x, 1.0, [ 0, 1 ], 0 );
// returns <ndarray>[ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ]

var bool = ( out === x );
// returns true
```

The function accepts the following arguments:

-   **x**: input ndarray.
-   **value**: scalar value.
-   **dims**: dimension indices defining the plane in which to fill the diagonal.
-   **k**: diagonal offset.

</section>

<!-- /.usage -->

<section class="notes">

## 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 fills the main diagonal; when `k > 0`, the function fills the diagonal above the main diagonal; and when `k < 0`, the function fills the diagonal below the main diagonal.
-   If `value` is a number and `x` has a complex [data type][@stdlib/ndarray/dtypes], the function fills an input ndarray with a complex number whose real component equals the provided scalar `value` and whose imaginary component is zero.
-   A `value` must be able to safely cast to the input ndarray [data type][@stdlib/ndarray/dtypes]. Scalar values having floating-point data types (both real and complex) are allowed to downcast to a lower precision data type of the same kind (e.g., a scalar double-precision floating-point number can be used to fill a `'float32'` input ndarray).
-   The function **mutates** the input ndarray in-place.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var zeros = require( '@stdlib/ndarray/zeros' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var fillDiagonal = require( '@stdlib/ndarray/base/fill-diagonal' );

// Create a stack of matrices:
var x = zeros( [ 2, 3, 3 ] );

// Fill main diagonals:
fillDiagonal( x, 1.0, [ 1, 2 ], 0 );
console.log( ndarray2array( x ) );

// Fill super-diagonals:
fillDiagonal( x, 2.0, [ 1, 2 ], 1 );
console.log( ndarray2array( x ) );

// Fill sub-diagonals:
fillDiagonal( x, 3.0, [ 1, 2 ], -1 );
console.log( ndarray2array( x ) );
```

</section>

<!-- /.examples -->

<section class="references">

</section>

<!-- /.references -->

<!-- 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">

[@stdlib/ndarray/dtypes]: https://github.com/stdlib-js/ndarray/tree/main/dtypes

</section>

<!-- /.links -->
