feat: add blas/base/zher

lib/node_modules/@stdlib/blas/base/zher/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# zher
+
+> Perform the hermitian rank 1 operation `A = α*x*x**H + A`, where `α` is a real scalar, `x` is an `N` element vector and `A` is an `N` by `N` hermitian matrix.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var zher = require( '@stdlib/blas/base/zher' );
+```
+
+#### zher( order, uplo, N, α, x, strideX, A, LDA )
+
+Performs the hermitian rank 1 operation `A = α*x*x**H + A`, where `α` is a real scalar, `x` is an `N` element vector and `A` is an `N` by `N` hermitian matrix.
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+
+var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
+
+zher( 'row-major', 'lower', x.length, 2.0, x, 1, A, 2 );
+// A => <Complex128Array>[ 11.0, 0.0, 0.0, 0.0, 24.0, -1.0, 54.0, 0.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **uplo**: specifies whether the upper or lower triangular part of the matrix `A` is supplied.
+-   **N**: specifies the order of the matrix `A`.
+-   **α**: scalar constant.
+-   **x**: input vector [`Complex128Array`][@stdlib/array/complex128].
+-   **strideX**: index increment for `x`.
+-   **A**: input matrix stored in linear memory as [`Complex128Array`][@stdlib/array/complex128].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+
+The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to iterate over the elements of `x` in reverse order,
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+
+var x = new Complex128Array( [ 3.0, 4.0, 1.0, 2.0 ] );
+var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
+
+zher( 'row-major', 'lower', x.length, 2.0, x, -1, A, 2 );
+// A => <Complex128Array>[ 11.0, 0.0, 0.0, 0.0, 24.0, -1.0, 54.0, 0.0 ]
+```
+
+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 Complex128Array = require( '@stdlib/array/complex128' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+
+// Initial array:
+var x0 = new Complex128Array( [ 0.0, 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+
+// Define a input matrix:
+var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
+
+// Create an offset view:
+var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+zher( 'row-major', 'lower', x1.length, 2.0, x1, 1, A, 2 );
+// A => <Complex128Array>[ 11.0, 0.0, 0.0, 0.0, 24.0, -1.0, 54.0, 0.0 ]
+```
+
+#### zher.ndarray( uplo, N, α, x, strideX, offsetX, A, strideA1, strideA2, offsetA )
+
+Performs the hermitian rank 1 operation `A = α*x*x**H + A`, where `α` is a real scalar, `x` is an `N` element vector and `A` is an `N` by `N` hermitian matrix using alternative indexing semantics.
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+
+var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
+
+zher.ndarray( 'lower', x.length, 2.0, x, 1, 0, A, 2, 1, 0 );
+// A => <Complex128Array>[ 11.0, 0.0, 0.0, 0.0, 24.0, -1.0, 54.0, 0.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **strideA1**: stride of the first dimension of `A`.
+-   **strideA2**: stride of the second dimension of `A`.
+-   **offsetX**: starting index for `x`.
+-   **offsetA**: starting index for `A`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to scale every other value in the input strided array starting from the second element,
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+
+var x = new Complex128Array( [ 3.0, 4.0, 1.0, 2.0 ] );
+var A = new Complex128Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
+
+zher.ndarray( 'lower', x.length, 2.0, x, -1, 1, A, 2, 1, 0 );
+// A => <Complex128Array>[ 11.0, 0.0, 0.0, 0.0, 24.0, -1.0, 54.0, 0.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N = 0` or `α = 0.0`, both functions return `x` unchanged.
+-   `zher()` corresponds to the [BLAS][blas] level 2 function [`zher`][zher].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var filledarrayBy = require( '@stdlib/array/filled-by' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+var logEach = require( '@stdlib/console/log-each' );
+var zher = require( '@stdlib/blas/base/zher' );
+
+function rand() {
+    return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
+}
+
+var x = filledarrayBy( 3, 'complex128', rand );
+console.log( x.get( 0 ).toString() );
+
+var A = filledarrayBy( 9, 'complex128', rand );
+console.log( A.get( 0 ).toString() );
+
+zher( 'row-major', 'upper', 3, 1.0, x, 1, A, 3 );
+
+// Print the results:
+logEach( '(%s)', A );
+
+zher.ndarray( 'upper', 3, 1.0, x, 1, 0, A, 3, 1, 0 );
+
+// Print the results:
+logEach( '(%s)', 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">
+
+[blas]: http://www.netlib.org/blas
+
+[zher]: https://www.netlib.org/lapack/explore-html/dc/d82/group__her_gae92bde9f7f6f83c0edaa96f4f2bb2bc3.html
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/base/zher/benchmark/benchmark.js

@@ -0,0 +1,111 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 Complex128Array = require( '@stdlib/array/complex128' );
+var pkg = require( './../package.json' ).name;
+var zher = require( './../lib/zher.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 xbuf;
+	var Abuf;
+	var x;
+	var A;
+
+	xbuf = uniform( len*2, -100.0, 100.0, options );
+	x = new Complex128Array( xbuf.buffer );
+	Abuf = uniform( (len*len)*2, -100.0, 100.0, options );
+	A = new Complex128Array( Abuf.buffer );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			zher( 'row-major', 'lower', len, 2.0, x, 1, A, len );
+			if ( isnan( Abuf[ i%(len*2) ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( Abuf[ i%(len*2) ] ) ) {
+			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 = 4; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':len='+len, f );
+	}
+}
+
+main();