feat: add ndarray/diagonal

lib/node_modules/@stdlib/ndarray/diagonal/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# diagonal
+
+> Return a **read-only** view of the diagonal of a matrix (or stack of matrices).
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro section element. -->
+
+<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."> -->
+
+```math
+D_k = \{\, A_{i,j} : j - i = k \,\}
+```
+
+<!-- <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). For example, given the matrix
+
+<!-- <equation class="equation" label="eq:diagonal_example" align="center" raw="A = \begin{bmatrix} a_{0,0} & a_{0,1} & a_{0,2} \\ a_{1,0} & a_{1,1} & a_{1,2} \\ a_{2,0} & a_{2,1} & a_{2,2} \end{bmatrix}" alt="Example matrix."> -->
+
+```math
+A = \begin{bmatrix} a_{0,0} & a_{0,1} & a_{0,2} \\ a_{1,0} & a_{1,1} & a_{1,2} \\ a_{2,0} & a_{2,1} & a_{2,2} \end{bmatrix}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="A = \begin{bmatrix} a_{0,0} & a_{0,1} & a_{0,2} \\ a_{1,0} & a_{1,1} & a_{1,2} \\ a_{2,0} & a_{2,1} & a_{2,2} \end{bmatrix}" data-equation="eq:diagonal_example">
+    <img src="" alt="Example matrix.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+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} ]`.
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## 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 <ndarray>[ [ 1.0, 2.0, 3.0 ], [ 4.0, 5.0, 6.0 ], [ 7.0, 8.0, 9.0 ] ]
+
+var y = diagonal( x );
+// returns <ndarray>[ 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]`.
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+## 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]`.
+
+</section>
+
+<!-- /.notes -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```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 ) );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<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/ctor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/ctor
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/ndarray/diagonal/benchmark/benchmark.js

@@ -0,0 +1,196 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var isndarrayLike = require( '@stdlib/assert/is-ndarray-like' );
+var empty = require( '@stdlib/ndarray/empty' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var diagonal = require( './../lib' );
+
+
+// MAIN //
+
+bench( format( '%s:ndims=2', pkg ), function benchmark( b ) {
+	var values;
+	var v;
+	var i;
+
+	/* eslint-disable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	values = [
+		empty( [ 2, 2 ], { 'dtype': 'float64' } ),
+		empty( [ 2, 2 ], { 'dtype': 'float32' } ),
+		empty( [ 2, 2 ], { 'dtype': 'int32' } ),
+		empty( [ 2, 2 ], { 'dtype': 'complex128' } ),
+		empty( [ 2, 2 ], { 'dtype': 'generic' } )
+	];
+
+	/* eslint-enable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = diagonal( values[ i%values.length ] );
+		if ( typeof v !== 'object' ) {
+			b.fail( 'should return an ndarray' );
+		}
+	}
+	b.toc();
+	if ( !isndarrayLike( v ) ) {
+		b.fail( 'should return an ndarray' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( format( '%s:ndims=3', pkg ), function benchmark( b ) {
+	var values;
+	var v;
+	var i;
+
+	/* eslint-disable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	values = [
+		empty( [ 2, 2, 2 ], { 'dtype': 'float64' } ),
+		empty( [ 2, 2, 2 ], { 'dtype': 'float32' } ),
+		empty( [ 2, 2, 2 ], { 'dtype': 'int32' } ),
+		empty( [ 2, 2, 2 ], { 'dtype': 'complex128' } ),
+		empty( [ 2, 2, 2 ], { 'dtype': 'generic' } )
+	];
+
+	/* eslint-enable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = diagonal( values[ i%values.length ] );
+		if ( typeof v !== 'object' ) {
+			b.fail( 'should return an ndarray' );
+		}
+	}
+	b.toc();
+	if ( !isndarrayLike( v ) ) {
+		b.fail( 'should return an ndarray' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( format( '%s:ndims=3,dims=[0,2]', pkg ), function benchmark( b ) {
+	var values;
+	var opts;
+	var v;
+	var i;
+
+	/* eslint-disable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	values = [
+		empty( [ 2, 2, 2 ], { 'dtype': 'float64' } ),
+		empty( [ 2, 2, 2 ], { 'dtype': 'float32' } ),
+		empty( [ 2, 2, 2 ], { 'dtype': 'int32' } ),
+		empty( [ 2, 2, 2 ], { 'dtype': 'complex128' } ),
+		empty( [ 2, 2, 2 ], { 'dtype': 'generic' } )
+	];
+
+	/* eslint-enable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	opts = {
+		'dims': [ 0, 2 ]
+	};
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = diagonal( values[ i%values.length ], opts );
+		if ( typeof v !== 'object' ) {
+			b.fail( 'should return an ndarray' );
+		}
+	}
+	b.toc();
+	if ( !isndarrayLike( v ) ) {
+		b.fail( 'should return an ndarray' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( format( '%s:ndims=4', pkg ), function benchmark( b ) {
+	var values;
+	var v;
+	var i;
+
+	/* eslint-disable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	values = [
+		empty( [ 2, 2, 2, 2 ], { 'dtype': 'float64' } ),
+		empty( [ 2, 2, 2, 2 ], { 'dtype': 'float32' } ),
+		empty( [ 2, 2, 2, 2 ], { 'dtype': 'int32' } ),
+		empty( [ 2, 2, 2, 2 ], { 'dtype': 'complex128' } ),
+		empty( [ 2, 2, 2, 2 ], { 'dtype': 'generic' } )
+	];
+
+	/* eslint-enable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = diagonal( values[ i%values.length ] );
+		if ( typeof v !== 'object' ) {
+			b.fail( 'should return an ndarray' );
+		}
+	}
+	b.toc();
+	if ( !isndarrayLike( v ) ) {
+		b.fail( 'should return an ndarray' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( format( '%s:ndims=5', pkg ), function benchmark( b ) {
+	var values;
+	var v;
+	var i;
+
+	/* eslint-disable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	values = [
+		empty( [ 2, 2, 2, 2, 2 ], { 'dtype': 'float64' } ),
+		empty( [ 2, 2, 2, 2, 2 ], { 'dtype': 'float32' } ),
+		empty( [ 2, 2, 2, 2, 2 ], { 'dtype': 'int32' } ),
+		empty( [ 2, 2, 2, 2, 2 ], { 'dtype': 'complex128' } ),
+		empty( [ 2, 2, 2, 2, 2 ], { 'dtype': 'generic' } )
+	];
+
+	/* eslint-enable object-curly-newline, stdlib/line-closing-bracket-spacing */
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = diagonal( values[ i%values.length ] );
+		if ( typeof v !== 'object' ) {
+			b.fail( 'should return an ndarray' );
+		}
+	}
+	b.toc();
+	if ( !isndarrayLike( v ) ) {
+		b.fail( 'should return an ndarray' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});