feat: add lapack/base/dpoequ

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

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+ <!--
+
+@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.
+
+-->
+
+# dpoequ
+
+> Compute row and column scalings intended to equilibrate a symmetric positive definite matrix `A`.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dpoequ = require( '@stdlib/lapack/base/dpoequ' );
+```
+
+#### dpoequ( order, N, A, LDA, S, scond, amax )
+
+Computes row and column scalings intended to equilibrate a symmetric positive definite matrix `A`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 2.0, 4.0 ] );
+var S = new Float64Array( 2 );
+var scond = new Float64Array( 1 );
+var amax = new Float64Array( 1 );
+
+var out = dpoequ( 'row-major', 2, A, 2, S, scond, amax );
+// returns 0
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **N**: order of matrix.
+-   **A**: input symmetric positive definite [`Float64Array`][mdn-float64array].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **S**: [`Float64Array`][mdn-float64array] containing scale factors.
+-   **scond**: [`Float64Array`][mdn-float64array] containing the ratio of the smallest to the largest scale factors.
+-   **amax**: [`Float64Array`][mdn-float64array] containing the absolute value of the largest matrix element.
+
+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, 2.0, 4.0 ] );
+var S0 = new Float64Array( [ 0.0, 0.0, 0.0 ] );
+var scond0 = new Float64Array( [ 0.0, 0.0 ] );
+var amax0 = new Float64Array( [ 0.0, 0.0 ] );
+
+// Create offset views...
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var S1 = new Float64Array( S0.buffer, S0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var scond1 = new Float64Array( scond0.buffer, scond0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var amax1 = new Float64Array( amax0.buffer, amax0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var out = dpoequ( 'row-major', 2, A1, 2, S1, scond1, amax1 );
+// returns 0
+```
+
+#### dpoequ.ndarray( N, A, sa1, sa2, oa, S, ss, os, sc, osc, am, oam )
+
+Computes row and column scalings intended to equilibrate a symmetric positive definite matrix `A` using alternative semantic indexing.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 2.0, 4.0 ] );
+var S = new Float64Array( 2 );
+var scond = new Float64Array( 1 );
+var amax = new Float64Array( 1 );
+
+var out = dpoequ.ndarray( 2, A, 2, 1, 0, S, 1, 0, scond, 0, amax, 0 );
+// returns 0
+```
+
+The function has the following parameters:
+
+-   **N**: order of matrix.
+-   **A**: input symmetric positive definite [`Float64Array`][mdn-float64array].
+-   **sa1**: stride of the first dimension of `A`.
+-   **sa2**: stride of the second dimension of `A`.
+-   **oa**: starting index for `A`.
+-   **S**: [`Float64Array`][mdn-float64array] containing scale factors.
+-   **ss**: stride length of `S`.
+-   **os**: starting index for `S`.
+-   **sc**: [`Float64Array`][mdn-float64array] containing the ratio of the smallest to the largest scale factors.
+-   **osc**: starting index for `sc`.
+-   **am**: [`Float64Array`][mdn-float64array] containing the absolute value of the largest matrix element.
+-   **oam**: starting index for `am`.
+
+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, 2.0, 4.0 ] );
+var S = new Float64Array( 2 );
+var scond = new Float64Array( 1 );
+var amax = new Float64Array( 1 );
+
+var out = dpoequ.ndarray( 2, A, 2, 1, 1, S, 1, 0, scond, 0, amax, 0 );
+// returns 0
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions return a status code indicating success or failure. A status code indicates the following conditions:
+
+    -   `0`: factorization was successful.
+    -   `<0`: the k-th argument had an illegal value, where `-k` equals the status code value.
+    -   `0 < k < N`: the k-th argument had a non-positive value.
+
+-   `dpoequ()` corresponds to the [LAPACK][lapack] routine [`dpoequ`][lapack-dpoequ].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dpoequ = require( '@stdlib/lapack/base/dpoequ' );
+
+var A = new Float64Array( [ 1.0, 2.0, 2.0, 4.0 ] );
+var S = new Float64Array( 2 );
+var scond = new Float64Array( 1 );
+var amax = new Float64Array( 1 );
+
+var out = dpoequ( 'row-major', 2, A, 2, S, scond, amax );
+console.log( out );
+console.log( scond );
+console.log( amax );
+console.log( S );
+```
+
+</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-dpoequ]: https://www.netlib.org/lapack/explore-html/db/d48/group__poequ_ga64054a216849b768d3b922deba351e50.html#ga64054a216849b768d3b922deba351e50
+
+[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/dpoequ/benchmark/benchmark.js

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+/**
+* @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 pkg = require( './../package.json' ).name;
+var dpoequ = require( './../lib/dpoequ.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 scond = uniform( 1, 1.0, 100.0, options );
+	var amax = uniform( 1, 1.0, 100.0, options );
+	var A = uniform( len, 1.0, 100.0, options );
+	var S = uniform( 2, 1.0, 100.0, options );
+
+	return benchmark;
+
+	function benchmark( b ) {
+		var d;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			d = dpoequ( 'row-major', len, A, len, S, scond, amax);
+			if ( isnan( d ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( d ) ) {
+			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+':order=row-major,len='+len, f );
+	}
+}
+
+main();