feat: add lapack/base/dlae2

lib/node_modules/@stdlib/lapack/base/dlae2/README.md

@@ -0,0 +1,221 @@
+<!--
+
+@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.
+
+-->
+
+# dlae2
+
+> Compute the eigenvalues of a 2x2 symmetric matrix.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dlae2 = require( '@stdlib/lapack/base/dlae2' );
+```
+
+#### dlae2( A, B, C, Out )
+
+Computes the eigenvalues of a 2x2 symmetric matrix.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var out = new Float64Array( 2 );
+out = dlae2( 2.0, 3.0, 4.0, out );
+// out => <Float64Array>[ 6.16227766016838, -0.1622776601683793 ]
+```
+
+The function has the following parameters:
+
+- **A**: the (0,0) element of matrix.
+- **B**: the (0,1) & (1,0) elements of matrix.
+- **C**: the (1,1) element of matrix.
+- **Out**: output [`Float64Array`][mdn-float64array] containing eigenvalue of larger and smaller absolute value respectively.
+
+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 OUT0 = new Float64Array( [ 0.0, 0.0, 0.0 ] );
+
+// Create offset views...
+var OUT1 = new Float64Array( OUT0.buffer, OUT0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlae2( 2.0, 3.0, 4.0, OUT1 );
+// OUT0 => <Float64Array>[ 0.0, 6.16227766016838, -0.1622776601683793 ]
+```
+
+#### dlae2.ndarray( A, B, C, Out, strideOut, offsetOut )
+
+Computes the eigenvalues of a 2x2 symmetric matrix using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var out = new Float64Array( 2 );
+out = dlae2.ndarray( 2.0, 3.0, 4.0, out, 1, 0 );
+// out => <Float64Array>[ 6.16227766016838, -0.1622776601683793 ]
+```
+
+The function has the following additional parameters:
+
+- **strideOut**: stride length for `Out`.
+- **offsetOut**: starting index of `out`
+
+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 out = new Float64Array( [ 0.0, 0.0, 0.0 ] );
+out = dlae2.ndarray( 2.0, 3.0, 4.0, out, 1, 1 );
+// out => <Float64Array>[ 0.0, 6.16227766016838, -0.1622776601683793 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+- `dlae2()` corresponds to the [LAPACK][lapack] routine [`dlae2`][lapack-dlae2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dlae2 = require( '@stdlib/lapack/base/dlae2' );
+
+var out = new Float64Array( 2 );
+out = dlae2( 2.0, 3.0, 4.0, out );
+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-dlae2]: https://www.netlib.org/lapack/explore-html/d7/dea/group__lae2_ga44e727d32752c2fa22d7deaff099249b.html#ga44e727d32752c2fa22d7deaff099249b
+
+[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/dlae2/benchmark/benchmark.js

@@ -0,0 +1,57 @@
+/**
+* @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 Float64Array = require( '@stdlib/array/float64' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var dlae2 = require( './../lib/dlae2.js' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var out;
+ var A;
+ var B;
+ var C;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ A = ( randu() * 100.0 ) - 50.0;
+ B = ( randu() * 100.0 ) - 50.0;
+ C = ( randu() * 100.0 ) - 50.0;
+ out = new Float64Array( 2 );
+ out = dlae2( A, B, C, out );
+ if ( isnan( out[ i%out.length ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( out[ i%out.length ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});

lib/node_modules/@stdlib/lapack/base/dlae2/benchmark/benchmark.ndarray.js

@@ -0,0 +1,57 @@
+/**
+* @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 Float64Array = require( '@stdlib/array/float64' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var dlae2 = require( './../lib/ndarray.js' );
+
+
+// MAIN //
+
+bench( pkg+':ndarray', function benchmark( b ) {
+ var out;
+ var A;
+ var B;
+ var C;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ A = ( randu() * 100.0 ) - 50.0;
+ B = ( randu() * 100.0 ) - 50.0;
+ C = ( randu() * 100.0 ) - 50.0;
+ out = new Float64Array( 2 );
+ out = dlae2( A, B, C, out, 1, 0 );
+ if ( isnan( out[ i%out.length ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnan( out[ i%out.length ] ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});