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feat: add ndarray/diagonal
PR-URL: #11900 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com> Closes: stdlib-js/metr-issue-tracker#497
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‎lib/node_modules/@stdlib/ndarray/diagonal/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# diagonal
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> Return a **read-only** view of the diagonal of a matrix (or stack of matrices).
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro section element. -->
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<section class="intro">
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For an `M`-by-`N` matrix `A`, the `k`-th diagonal is defined as
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<!-- <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."> -->
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```math
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D_k = \{\, A_{i,j} : j - i = k \,\}
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```
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<!-- <div class="equation" align="center" data-raw-text="D_k = \{\, A_{i,j} : j - i = k \,\}" data-equation="eq:diagonal_definition">
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<img src="" alt="Definition of the k-th diagonal of a matrix.">
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<br>
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</div> -->
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<!-- </equation> -->
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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
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<!-- <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."> -->
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```math
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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}
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```
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<!-- <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">
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<img src="" alt="Example matrix.">
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<br>
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</div> -->
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<!-- </equation> -->
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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} ]`.
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var diagonal = require( '@stdlib/ndarray/diagonal' );
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```
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#### diagonal( x\[, options] )
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Returns a read-only view of the diagonal of a matrix (or stack of matrices).
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```javascript
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var array = require( '@stdlib/ndarray/array' );
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var x = array( [ [ 1.0, 2.0, 3.0 ], [ 4.0, 5.0, 6.0 ], [ 7.0, 8.0, 9.0 ] ] );
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// returns <ndarray>[ [ 1.0, 2.0, 3.0 ], [ 4.0, 5.0, 6.0 ], [ 7.0, 8.0, 9.0 ] ]
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var y = diagonal( x );
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// returns <ndarray>[ 1.0, 5.0, 9.0 ]
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```
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The function accepts the following arguments:
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- **x**: input [`ndarray`][@stdlib/ndarray/ctor].
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- **options**: function options.
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The function accepts the following options:
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- **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`.
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- **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]`.
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</section>
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<!-- /.usage -->
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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## Notes
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- 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.
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- Each provided dimension index must reside on the interval `[-ndims, ndims-1]`.
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</section>
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<!-- /.notes -->
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<!-- Package usage examples. -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var uniform = require( '@stdlib/random/uniform' );
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var ndarray2array = require( '@stdlib/ndarray/to-array' );
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var diagonal = require( '@stdlib/ndarray/diagonal' );
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// Create a stack of matrices:
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var x = uniform( [ 2, 3, 3 ], -10.0, 10.0 );
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console.log( ndarray2array( x ) );
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// Extract the main diagonals from the stack:
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var y = diagonal( x );
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console.log( ndarray2array( y ) );
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// Extract super-diagonals from the stack:
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y = diagonal( x, {
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'k': 1
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});
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console.log( ndarray2array( y ) );
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// Extract sub-diagonals from the stack:
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y = diagonal( x, {
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'k': -1
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});
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console.log( ndarray2array( y ) );
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```
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</section>
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<!-- /.examples -->
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<!-- 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. -->
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<section class="references">
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</section>
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<!-- /.references -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[@stdlib/ndarray/ctor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/ctor
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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

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

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