feat: add blas/base/zdotu

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

@@ -0,0 +1,218 @@
+<!--
+
+@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.
+
+-->
+
+# zdotu
+
+> Calculate the dot product of two double-precision complex floating-point vectors.
+
+<section class="intro">
+
+The [dot product][dot-product] (or scalar product) is defined as
+
+<!-- <equation class="equation" label="eq:dot_product" align="center" raw="\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}" alt="Dot product definition."> -->
+
+```math
+\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}" data-equation="eq:dot_product">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@929657146427564b61e3e6bdda76949ebe2ce923/lib/node_modules/@stdlib/blas/base/ddot/docs/img/equation_dot_product.svg" alt="Dot product definition.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var zdotu = require( '@stdlib/blas/base/zdotu' );
+```
+
+#### zdotu( N, x, strideX, y, strideY )
+
+Calculates the dot product of vectors `x` and `y`.
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+
+var x = new Complex128Array( [ 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 ] );
+var y = new Complex128Array( [ 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 ] );
+
+var z = zdotu( 3, x, 1, y, 1 );
+// returns <Complex128>[ -52.0, 82.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **x**: input [`Complex128Array`][@stdlib/array/complex128].
+-   **strideX**: stride kength for `x`.
+-   **y**: input [`Complex128Array`][@stdlib/array/complex128].
+-   **strideY**: stride kength for `y`.
+
+The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to calculate the dot product of every other element in `x` and the first `N` elements of `y` in reverse order,
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+
+var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
+var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
+
+var z = zdotu( 2, x, 2, y, -1 );
+// returns <Complex128>[ -2.0, 14.0 ]
+```
+
+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' );
+
+// Initial arrays...
+var x0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var y0 = new Complex128Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+
+// Create offset views...
+var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var y1 = new Complex128Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element
+
+var z = zdotu( 1, x1, 1, y1, 1 );
+// returns <Complex128>[ -15.0, 80.0 ]
+```
+
+#### zdotu.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )
+
+Calculates the dot product of `x` and `y` using alternative indexing semantics.
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+
+var x = new Complex128Array( [ 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 ] );
+var y = new Complex128Array( [ 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 ] );
+
+var z = zdotu.ndarray( x.length, x, 1, 0, y, 1, 0 );
+// returns <Complex128>[ -52.0, 82.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `x`.
+-   **offsetY**: starting index for `y`.
+
+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, to calculate the dot product of every other element in `x` starting from the second element with the last 2 elements in `y` in reverse order
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Complex128Array = require( '@stdlib/array/complex128' );
+
+var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
+var y = new Complex128Array( [ 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0 ] );
+
+var z = zdotu.ndarray( 2, x, 2, 1, y, -1, y.length-1 );
+// returns <Complex128>[ -40.0, 310.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0`, both functions return `0.0 + 0.0i`.
+-   `zdotu()` corresponds to the [BLAS][blas] level 1 function [`zdotu`][zdotu].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
+var Complex128 = require( '@stdlib/complex/float64/ctor' );
+var filledarrayBy = require( '@stdlib/array/filled-by' );
+var zdotu = require( '@stdlib/blas/base/zdotu' );
+
+function rand() {
+    return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
+}
+
+var x = filledarrayBy( 10, 'complex128', rand );
+console.log( x.toString() );
+
+var y = filledarrayBy( 10, 'complex128', rand );
+console.log( y.toString() );
+
+// Compute the dot product:
+var out = zdotu( x.length, x, 1, y, -1 );
+console.log( out.toString() );
+
+// Compute the dot product using alternative indexing semantics:
+out = zdotu.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
+console.log( out.toString() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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">
+
+[dot-product]: https://en.wikipedia.org/wiki/Dot_product
+
+[blas]: http://www.netlib.org/blas
+
+[zdotu]: https://www.netlib.org/lapack/explore-html/d1/dcc/group__dot_ga6b0b69474b384d45fc4c7b1f7ec5959f.html#ga6b0b69474b384d45fc4c7b1f7ec5959f
+
+[@stdlib/array/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

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

@@ -0,0 +1,109 @@
+/**
+* @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 real = require( '@stdlib/complex/float64/real' );
+var imag = require( '@stdlib/complex/float64/imag' );
+var pkg = require( './../package.json' ).name;
+var zdotu = require( './../lib/zdotu.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var x;
+	var y;
+
+	x = new Complex128Array( uniform( N*2, -100.0, 100.0, options ) );
+	y = new Complex128Array( uniform( N*2, -100.0, 100.0, options ) );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var d;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			d = zdotu( x.length, x, 1, y, 1 );
+			if ( isnan( real( d ) ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( imag( d ) ) ) {
+			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 = 5; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		N = pow( 10, i );
+		f = createBenchmark( N );
+		bench( pkg+':size='+N, f );
+	}
+}
+
+main();