feat: add lapack/base/iladlr

lib/node_modules/@stdlib/lapack/base/iladlr/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# iladlr
+
+> Find the index of the last non-zero row in a matrix `A`.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var iladlr = require( '@stdlib/lapack/base/iladlr' );
+```
+
+#### iladlr( order, M, N, A, LDA )
+
+Returns the index of the last non-zero row in a matrix `A`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 0.0, 0.0 ] );
+
+/*
+    A = [
+        [ 1.0, 2.0 ],
+        [ 3.0, 4.0 ],
+        [ 0.0, 0.0 ]
+    ]
+*/
+
+var out = iladlr( 'row-major', 3, 2, A, 2 );
+// returns 1
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **M**: number of rows in `A`.
+-   **N**: number of columns in `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial array:
+var A0 = new Float64Array( [ 9999.0, 1.0, 2.0, 3.0, 4.0, 0.0, 0.0 ] );
+
+// Create an offset view:
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var out = iladlr( 'row-major', 3, 2, A1, 2 );
+// returns 1
+```
+
+#### iladlr.ndarray( M, N, A, strideA1, strideA2, offsetA )
+
+Returns the index of the last non-zero row in a matrix `A` using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 0.0, 0.0 ] );
+
+/*
+    A = [
+        [ 1.0, 2.0 ],
+        [ 3.0, 4.0 ],
+        [ 0.0, 0.0 ]
+    ]
+*/
+
+var out = iladlr.ndarray( 3, 2, A, 2, 1, 0 );
+// returns 1
+```
+
+The function has the following parameters:
+
+-   **M**: number of rows in `A`.
+-   **N**: number of columns in `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **strideA1**: stride of the first dimension of `A`.
+-   **strideA2**: stride of the second dimension of `A`.
+-   **offsetA**: starting index for `A`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 9999.0, 1.0, 2.0, 3.0, 4.0, 0.0, 0.0 ] );
+
+/*
+    A = [
+        [ 1.0, 2.0 ],
+        [ 3.0, 4.0 ],
+        [ 0.0, 0.0 ]
+    ]
+*/
+
+var out = iladlr.ndarray( 3, 2, A, 2, 1, 1 );
+// returns 1
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   This routine is commonly used throughout LAPACK to shrink work domains (e.g., before bulge-chasing, deflation, or when trimming Householder panels), thus ensuring that higher-level routines operate only on numerically relevant sub-matrices.
+-   `iladlr()` corresponds to the [LAPACK][lapack] routine [`iladlr`][lapack-iladlr].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var Float64Array = require( '@stdlib/array/float64' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var iladlr = require( '@stdlib/lapack/base/iladlr' );
+
+var shape = [ 3, 3 ];
+var order = 'row-major';
+var strides = shape2strides( shape, order );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 0.0, 0.0, 0.0 ] );
+console.log( ndarray2array( A, shape, strides, 0, order ) );
+
+var out = iladlr( order, shape[ 0 ], shape[ 1 ], A, strides[ 0 ] );
+console.log( out );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- 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">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-iladlr]: https://www.netlib.org/lapack/explore-html/da/d60/group__ilalr_gadb53a9bd5cc7a6e3bbca7bf4eca32208.html
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/lapack/base/iladlr/benchmark/benchmark.js

@@ -0,0 +1,111 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var zeros = require( '@stdlib/array/zeros' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pkg = require( './../package.json' ).name;
+var iladlr = require( './../lib/iladlr.js' );
+
+
+// VARIABLES //
+
+var LAYOUTS = [
+	'row-major',
+	'column-major'
+];
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {string} order - storage layout
+* @param {PositiveInteger} N - number of elements along each dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( order, N ) {
+	var A = zeros( N*N, 'float64' );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var z;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			A[ 0 ] = i;
+			z = iladlr( order, N, N, A, N );
+			if ( isnan( z ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var min;
+	var max;
+	var ord;
+	var N;
+	var f;
+	var i;
+	var k;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( k = 0; k < LAYOUTS.length; k++ ) {
+		ord = LAYOUTS[ k ];
+		for ( i = min; i <= max; i++ ) {
+			N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+			f = createBenchmark( ord, N );
+			bench( pkg+'::square_matrix:order='+ord+',size='+(N*N), f );
+		}
+	}
+}
+
+main();