feat: add lapack/base/dlaqge

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

@@ -0,0 +1,264 @@
+<!--
+
+@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.
+
+-->
+
+# dlaqge
+
+> Equilibrate a general `M` by `N` matrix `A` using the row and scaling factors in vectors `R` and `C`.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dlaqge = require( '@stdlib/lapack/base/dlaqge' );
+```
+
+#### dlaqge( order, M, N, A, LDA, R, C, rowcnd, colcnd, amax )
+
+Equilibrates a general `M` by `N` matrix `A` using the row and scaling factors in vectors `R` and `C`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var R = new Float64Array( [ 1.0, 11.0 ] );
+var C = new Float64Array( [ 1.0, 11.0 ] );
+
+var out = dlaqge( 'row-major', 2, 2, A, 2, R, C, 1.0/11.0, 1.0/11.0, 4.0 );
+// out => 'B'
+// A => <Float64Array>[ 1.0, 22.0, 33.0, 484.0 ]
+```
+
+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`).
+-   **R**: row scale factors.
+-   **C**: column scale factors.
+-   **rowcnd**: ratio of the smallest to the largest row scale factor.
+-   **colcnd**: ratio of the smallest to the largest column scale factor.
+-   **amax**: absolute value of the largest matrix entry.
+
+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 arrays...
+var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
+var R0 = new Float64Array( [ 0.0, 1.0, 11.0 ] );
+var C0 = new Float64Array( [ 0.0, 1.0, 11.0 ] );
+
+// Create offset views...
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var R1 = new Float64Array( R0.buffer, R0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var C1 = new Float64Array( C0.buffer, C0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var out = dlaqge( 'row-major', 2, 2, A1, 2, R1, C1, 1.0/11.0, 1.0/11.0, 4.0 );
+// A0 => <Float64Array>[ 0.0, 1.0, 22.0, 33.0, 484.0 ]
+```
+
+#### dlaqge.ndarray( M, N, A, sa1, sa2, oa, R, sr, or, C, sc, oc, rc, cc, ax )
+
+Equilibrates a general `M` by `N` matrix `A` using the row and scaling factors in vectors `R` and `C` using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var R = new Float64Array( [ 1.0, 11.0 ] );
+var C = new Float64Array( [ 1.0, 11.0 ] );
+
+var out = dlaqge.ndarray( 2, 2, A, 2, 1, 0, R, 1, 0, C, 1, 0, 1.0/11.0, 1.0/11.0, 4.0 ); // eslint-disable-line max-len
+// out => 'B'
+// A => <Float64Array>[ 1.0, 22.0, 33.0, 484.0 ]
+```
+
+The function has the following parameters:
+
+-   **M**: number of rows in `A`.
+-   **N**: number of columns in `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **sa1**: stride of the first dimension of `A`.
+-   **sa2**: stride of the second dimension of `A`.
+-   **oa**: starting index for `A`.
+-   **R**: row scale factors.
+-   **sr**: stride length for `R`.
+-   **or**: starting index of `R`.
+-   **C**: row scale factors.
+-   **sc**: stride length for `C`.
+-   **oc**: starting index of `C`.
+-   **rc**: ratio of the smallest to the largest row scale factor.
+-   **cc**: ratio of the smallest to the largest column scale factor.
+
+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 A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+var R = new Float64Array( [ 0.0, 1.0, 11.0 ] );
+var C = new Float64Array( [ 0.0, 0.0, 1.0, 11.0 ] );
+
+var out = dlaqge.ndarray( 2, 2, A, 2, 1, 1, R, 1, 1, C, 1, 2, 1.0/11.0, 1.0/11.0, 4.0 ); // eslint-disable-line max-len
+// out => 'B'
+// A => <Float64Array>[ 0.0, 1.0, 22.0, 33.0, 484.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlaqge()` corresponds to the [LAPACK][lapack] routine [`dlaqge`][lapack-dlaqge].
+-   The output of function specifies form of equilibration that was done.
+-   'N' signifies No equilibration
+-   'R' signifies `A` has been premultiplied by `diag(R)` i.e. Row Equilibration
+-   'C' signifies `A` has been premultiplied by `diag(C)` i.e. Column Equilibration
+-   'B' signifies `A` has been replaced by `diag(R) * A * diag(C)` i.e. both row and column equilibration 
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dlaqge = require( '@stdlib/lapack/base/dlaqge' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var R = new Float64Array( [ 1.0, 11.0 ] );
+var C = new Float64Array( [ 1.0, 11.0 ] );
+
+var out = dlaqge( 'row-major', 2, 2, A, 2, R, C, 1.0/11.0, 1.0/11.0, 4.0 );
+console.log( out );
+console.log( A );
+```
+
+</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-dlaqge]: https://www.netlib.org/lapack/explore-html/d3/d21/group__laqge_gad474e329dbefb47f6baeca18ce09e249.html#gad474e329dbefb47f6baeca18ce09e249
+
+[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/dlaqge/benchmark/benchmark.js

@@ -0,0 +1,116 @@
+/**
+* @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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pkg = require( './../package.json' ).name;
+var dlaqge = require( './../lib/dlaqge.js' );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - number of elements along each dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var opts;
+	var A;
+	var M;
+	var R;
+	var C;
+
+	opts = {
+		'dtype': 'float64'
+	};
+	M = floor( N / 2 );
+
+	R = uniform( N, -10.0, 10.0, opts );
+	C = uniform( N, -10.0, 10.0, opts );
+
+	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 = uniform( M*N, -10.0, 10.0, opts );
+			z = dlaqge( 'row-major', M, N, A, N, R, C, 1.0/11.0, 1.0/11.0, 10.0 );
+			if ( isnan( z ) ) {
+				b.fail( 'should not return NaN' );
+			}
+			if ( isnan( A[ i%A.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		if ( isnan( A[ i%A.length ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var min;
+	var max;
+	var N;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+		f = createBenchmark( N );
+		bench( pkg+':order=row-major,size='+(N*N), f );
+	}
+}
+
+main();