feat: add lapack/base/dlacn2

lib/node_modules/@stdlib/lapack/base/dlacn2/README.md

@@ -0,0 +1,275 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 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.
+
+-->
+
+# dlacn2
+
+> Estimate the 1-norm of a square, real matrix `A`, reverse communication is used for evaluating matrix-vector products.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dlacn2 = require( '@stdlib/lapack/base/dlacn2' );
+```
+
+#### dlacn2( N, V, X, ISGN, EST, KASE, ISAVE )
+
+Estimates the 1-norm of a square, real matrix `A`, reverse communication is used for evaluating matrix-vector products.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var V = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var ISGN = new Int32Array( [ 1, 1, 1, 1 ] );
+var EST = new Float64Array( [ 0.0 ] );
+var KASE = new Int32Array( [ 0 ] );
+var ISAVE = new Int32Array( [ 0, 0, 0, 0, 0] );
+
+ISGN = dlacn2( 4, V, X, ISGN, EST, KASE, ISAVE );
+// ISGN => <Int32Array>[ 1, 1, 1, 1 ]
+```
+
+The function has the following parameters:
+
+-   **N**: order of matrix `A`.
+-   **V** [`Float64Array`][mdn-float64array], on final return `V=A*W`, where `W` is not returned.
+-   **X** input [`Float64Array`][mdn-float64array].
+-   **ISGN** [`Int32Array`][mdn-int32array] of signs.
+-   **EST** [`Float64Array`][mdn-float64array] containing estimate of lower bound of 1-norm of `A`.
+-   **KASE** [`Int32Array`][mdn-int32array] containing value KASE to control overwritting of `X`.
+-   **ISAVE** [`Int32Array`][mdn-int32array] for internal storage.
+
+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' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+// Initial arrays...
+var V0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+var X0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+var ISGN0 = new Int32Array( [ 1, 1, 1, 1, 1 ] );
+var EST0 = new Float64Array( [ 0.0, 0.0 ] );
+var KASE0 = new Int32Array( [ 0, 0 ] );
+var ISAVE0 = new Int32Array( [ 0, 0, 0, 0, 0 ] );
+
+// Create offset views...
+var V1 = new Float64Array( V0.buffer, V0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var X1 = new Float64Array( X0.buffer, X0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var ISGN1 = new Int32Array( ISGN0.buffer, ISGN0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var EST1 = new Float64Array( EST0.buffer, EST0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var KASE1 = new Int32Array( KASE0.buffer, KASE0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var ISAVE1 = new Int32Array( ISAVE0.buffer, ISAVE0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+ISGN1 = dlacn2( 4, V1, X1, ISGN1, EST1, KASE1, ISAVE1 );
+// ISGN0 => <Int32Array>[ 1, 1, 1, 1, 1 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dlacn2.ndarray( N, V, sv, ov, X, sx, ox, I, si, oi, E, oe, K, ok, S, ss, os )
+
+Estimates the 1-norm of a square, real matrix `A`, reverse communication is used for evaluating matrix-vector products using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var V = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var I = new Int32Array( [ 1, 1, 1, 1 ] );
+var E = new Float64Array( [ 0.0 ] );
+var K = new Int32Array( [ 0 ] );
+var S = new Int32Array( [ 0, 0, 0 ] );
+
+I = dlacn2.ndarray( 4, V, 1, 0, X, 1, 0, I, 1, 0, E, 0, K, 0, S, 1, 0 );
+// I => <Int32Array>[ 1, 1, 1, 1 ]
+```
+
+The function has the following additional parameters:
+
+-   **sv**: stride length for `V`.
+-   **ov**: starting index of `V`.
+-   **sx**: stride length for `X`.
+-   **ox**: starting index of `X`.
+-   **si**: stride length for `I`.
+-   **oi**: starting index of `I`.
+-   **oe**: starting index of `E`.
+-   **ok**: starting index of `K`.
+-   **ss**: stride length for `S`.
+-   **os**: starting index of `S`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var V = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var I = new Int32Array( [ 0, 1, 1, 1, 1 ] );
+var E = new Float64Array( [ 0.0, 0.0 ] );
+var K = new Int32Array( [ 0, 0 ] );
+var S = new Int32Array( [ 0, 0, 0 ] );
+
+I = dlacn2.ndarray( 4, V, 1, 0, X, 1, 0, I, 1, 1, E, 1, K, 1, S, 1, 1 );
+// I => <Int32Array>[ 0, 1, 1, 1, 1 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlacn2()` corresponds to the [LAPACK][lapack] routine [`dlacn2`][lapack-dlacn2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var dlacn2 = require( '@stdlib/lapack/base/dlacn2' );
+
+var V = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var ISGN = new Int32Array( [ 1, 1, 1, 1 ] );
+var EST = new Float64Array( [ 0.0 ] );
+var KASE = new Int32Array( [ 1.0 ] );
+var ISAVE = new Int32Array( [ 1, 0, 0 ] );
+
+ISGN = dlacn2( 4, V, X, ISGN, EST, KASE, ISAVE );
+console.log( ISGN );
+```
+
+</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-dlacn2]: https://www.netlib.org/lapack/explore-html/d6/d2d/group__lacn2_gabc1e7463e250c9e43596bfcbfa83c1de.html#gabc1e7463e250c9e43596bfcbfa83c1de
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-int32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Int32Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/lapack/base/dlacn2/benchmark/benchmark.js

@@ -0,0 +1,104 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 uniform = require( '@stdlib/random/array/uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var pkg = require( './../package.json' ).name;
+var dlacn2 = require( './../lib/dlacn2.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var ISAVE = new Int32Array( [ 1, 0, 0, 0, 0 ] );
+	var ISGN = new Int32Array( [ 1, 1, 1, 1 ] );
+	var KASE = new Int32Array( [ 0 ] );
+	var EST = new Float64Array( [ 0.0 ] );
+	var V = uniform( len, 1.0, 100.0, options );
+	var X = uniform( len, 1.0, 100.0, options );
+
+	return benchmark;
+
+	function benchmark( b ) {
+		var z;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			z = dlacn2( len, V, X, ISGN, EST, KASE, ISAVE );
+			if ( isnan( z[ i%z.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z[ i%z.length ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':isave=1,len='+len, f );
+	}
+}
+
+main();