feat: add lapack/base/dlaev2

lib/node_modules/@stdlib/lapack/base/dlaev2/README.md

@@ -0,0 +1,235 @@
+<!--
+
+@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.
+
+-->
+
+# dlaev2
+
+> Compute the eigendecomposition of a 2x2 symmetric matrix.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dlaev2 = require( '@stdlib/lapack/base/dlaev2' );
+```
+
+#### dlaev2( A, B, C, out, ev )
+
+Computes the eigendecomposition of a 2x2 symmetric matrix.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var ev = new Float64Array( 2 );
+var out = new Float64Array( 2 );
+out = dlaev2( 2.0, 3.0, 4.0, out, ev );
+// out => <Float64Array>[ ~6.162, ~-0.162 ]
+// ev => <Float64Array>[ ~0.585, ~0.811 ]
+```
+
+The function has the following parameters:
+
+-   **A**: the (0,0) element of a 2x2 symmetric matrix.
+-   **B**: the (0,1) and the conjugate of (1,0) element of a 2x2 symmetric matrix.
+-   **C**: the (1,1) element of a 2x2 symmetric matrix.
+-   **out**: output [`Float64Array`][mdn-float64array] containing the eigenvalues of larger and smaller absolute values respectively.
+-   **ev**: output [`Float64Array`][mdn-float64array] containing `CS1` and `SN1` which is unit right eigenvector for `RT1` giving the decomposition.
+
+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( [ 1.0, 2.0, 3.0 ] );
+var ev0 = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+// Create offset views...
+var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var ev1 = new Float64Array( ev0.buffer, ev0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlaev2( 2.0, 3.0, 4.0, out1, ev1 );
+// out0 => <Float64Array>[ 1.0, ~6.162, ~-0.162 ]
+// ev0 => <Float64Array>[ 1.0, ~0.585, ~0.811 ]
+```
+
+#### dlaev2.ndarray( A, B, C, out, sout, oout, ev, sev, oev )
+
+Computes the eigendecomposition of a 2x2 symmetric matrix using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var ev = new Float64Array( 2 );
+var out = new Float64Array( 2 );
+out = dlaev2.ndarray( 2.0, 3.0, 4.0, out, 1, 0, ev, 1, 0 );
+// out => <Float64Array>[ ~6.162, ~-0.162 ]
+// ev => <Float64Array>[ ~0.585, ~0.811 ]
+```
+
+The function has the following additional parameters:
+
+-   **sout**: stride length for `out`.
+-   **oout**: starting index of `out`.
+-   **sev**: stride length for `ev`.
+-   **oev**: starting index of `ev`.
+
+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 ev = new Float64Array( [ 999.9, 0.0, 999.9, 0.0 ] );
+var out = new Float64Array( [ 0.0, 999.9, 0.0 ] );
+out = dlaev2.ndarray( 2.0, 3.0, 4.0, out, -2, 2, ev, 2, 1 );
+// out => <Float64Array>[ ~-0.162, 999.9, ~6.162 ]
+// ev => <Float64Array>[ 999.9, ~0.585, 999.9, ~0.811 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlaev2()` corresponds to the [LAPACK][lapack] routine [`dlaev2`][lapack-dlaev2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dlaev2 = require( '@stdlib/lapack/base/dlaev2' );
+
+var ev = new Float64Array( 2 );
+var out = new Float64Array( 2 );
+out = dlaev2( 2.0, 3.0, 4.0, out, ev );
+console.log( 'out: ', out );
+console.log( 'ev: ', ev );
+```
+
+</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-dlaev2]: https://www.netlib.org/lapack/explore-html/db/d54/group__laev2_gacd10150d9e7ed9fc85ba274c3dcc9849.html#gacd10150d9e7ed9fc85ba274c3dcc9849
+
+[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/dlaev2/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 randu = require( '@stdlib/random/base/randu' );
+var Float64Array = require( '@stdlib/array/float64' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var dlaev2 = require( './../lib/dlaev2.js' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var out;
+	var ev;
+	var A;
+	var B;
+	var C;
+	var i;
+
+	out = new Float64Array( 2 );
+	ev = new Float64Array( 2 );
+	A = ( randu()*1000.0 ) - 500.0;
+	B = ( randu()*1000.0 ) - 500.0;
+	C = ( randu()*1000.0 ) - 500.0;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		out = dlaev2( A, B, C, out, ev );
+		A = out[ i%out.length ];
+		B = out[ i%out.length ];
+		C = ev[ i%ev.length ];
+		if ( isnan( out[ i%out.length ] || isnan( ev[ i%ev.length ] ) ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( out[ i%out.length ] || isnan( ev[ i%ev.length ] ) ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/lapack/base/dlaev2/benchmark/benchmark.ndarray.js

@@ -0,0 +1,63 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 randu = require( '@stdlib/random/base/randu' );
+var Float64Array = require( '@stdlib/array/float64' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var dlaev2 = require( './../lib/ndarray.js' );
+
+
+// MAIN //
+
+bench( pkg+':ndarray', function benchmark( b ) {
+	var out;
+	var ev;
+	var A;
+	var B;
+	var C;
+	var i;
+
+	out = new Float64Array( 2 );
+	ev = new Float64Array( 2 );
+	A = ( randu()*1000.0 ) - 500.0;
+	B = ( randu()*1000.0 ) - 500.0;
+	C = ( randu()*1000.0 ) - 500.0;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		out = dlaev2( A, B, C, out, 1, 0, ev, 1, 0 );
+		A = out[ i%out.length ];
+		B = out[ i%out.length ];
+		C = ev[ i%ev.length ];
+		if ( isnan( out[ i%out.length ] || isnan( ev[ i%ev.length ] ) ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( out[ i%out.length ] || isnan( ev[ i%ev.length ] ) ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});