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feat: add blas/base/zdotu
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‎lib/node_modules/@stdlib/blas/base/zdotu/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# zdotu
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> Calculate the dot product of two double-precision complex floating-point vectors.
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<section class="intro">
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The [dot product][dot-product] (or scalar product) is defined as
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<!-- <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."> -->
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```math
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\mathbf{zx}\cdot\mathbf{zy} = \sum_{i=0}^{N-1} zx_i zy_i = zx_0 zy_0 + zx_1 zy_1 + \ldots + zx_{N-1} zy_{N-1}
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```
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<!-- <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">
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<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.">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var zdotu = require( '@stdlib/blas/base/zdotu' );
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```
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#### zdotu( N, zx, strideX, zy, strideY )
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Calculates the dot product of vectors `zx` and `zy`.
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var real = require( '@stdlib/complex/float64/real' );
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var imag = require( '@stdlib/complex/float64/imag' );
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var zx = new Complex128Array( [ 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 ] );
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var zy = new Complex128Array( [ 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 ] );
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var z = zdotu( 3, zx, 1, zy, 1 );
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// returns <Complex128>
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var re = real( z );
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// returns -52.0
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var im = imag( z );
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// returns 82.0
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **zx**: input [`Complex128Array`][@stdlib/array/complex128].
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- **strideX**: index increment for `zx`.
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- **zy**: input [`Complex128Array`][@stdlib/array/complex128].
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- **strideY**: index increment for `zy`.
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The `N` and strides parameters determine which elements in the strided arrays are accessed at runtime. For example, to calculate the dot product of every other value in `zx` and the first `N` elements of `zy` in reverse order,
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var real = require( '@stdlib/complex/float64/real' );
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var imag = require( '@stdlib/complex/float64/imag' );
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var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
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var zy = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
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var z = zdotu( 2, zx, 2, zy, -1 );
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// returns <Complex128>
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var re = real( z );
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// returns -2.0
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var im = imag( z );
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// returns 14.0
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var real = require( '@stdlib/complex/float64/real' );
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var imag = require( '@stdlib/complex/float64/imag' );
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// Initial arrays...
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var zx0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var zy0 = new Complex128Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
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// Create offset views...
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var zx1 = new Complex128Array( zx0.buffer, zx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var zy1 = new Complex128Array( zy0.buffer, zy0.BYTES_PER_ELEMENT*2 ); // start at 3th element
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var z = zdotu( 1, zx1, 1, zy1, 1 );
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// returns <Complex128>
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var re = real( z );
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// returns -15.0
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var im = imag( z );
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// returns 80.0
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```
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#### zdotu.ndarray( N, zx, strideX, offsetX, zy, strideY, offsetY )
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Calculates the dot product of `zx` and `zy` using alternative indexing semantics.
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var real = require( '@stdlib/complex/float64/real' );
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var imag = require( '@stdlib/complex/float64/imag' );
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var zx = new Complex128Array( [ 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 ] );
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var zy = new Complex128Array( [ 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 ] );
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var z = zdotu.ndarray( zx.length, zx, 1, 0, zy, 1, 0 );
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// returns <Complex128>
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var re = real( z );
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// returns -52.0
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var im = imag( z );
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// returns 82.0
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```
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The function has the following additional parameters:
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- **offsetX**: starting index for `zx`.
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- **offsetY**: starting index for `zy`.
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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 value in `zx` starting from the second value with the last 2 elements in `zy` in reverse order
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```javascript
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var Complex128Array = require( '@stdlib/array/complex128' );
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var real = require( '@stdlib/complex/float64/real' );
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var imag = require( '@stdlib/complex/float64/imag' );
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var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
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var zy = new Complex128Array( [ 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0 ] ); // eslint-disable-line max-len
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var z = zdotu.ndarray( 2, zx, 2, 1, zy, -1, zy.length-1 );
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// returns <Complex128>
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var re = real( z );
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// returns -40.0
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var im = imag( z );
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// returns 310.0
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- If `N <= 0`, both functions return `0.0 + 0.0i`.
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- `zdotu()` corresponds to the [BLAS][blas] level 1 function [`zdotu`][zdotu].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
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var Complex128 = require( '@stdlib/complex/float64/ctor' );
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var filledarrayBy = require( '@stdlib/array/filled-by' );
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var zdotu = require( '@stdlib/blas/base/zdotu' );
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function rand() {
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return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
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}
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var zx = filledarrayBy( 10, 'complex128', rand );
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console.log( zx.toString() );
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var zy = filledarrayBy( 10, 'complex128', rand );
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console.log( zy.toString() );
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var out = zdotu.ndarray( zx.length, zx, 1, 0, zy, -1, zy.length-1 );
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console.log( out.toString() );
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[dot-product]: https://en.wikipedia.org/wiki/Dot_product
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[blas]: http://www.netlib.org/blas
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[zdotu]: https://www.netlib.org/lapack/explore-html/d1/dcc/group__dot_ga6b0b69474b384d45fc4c7b1f7ec5959f.html#ga6b0b69474b384d45fc4c7b1f7ec5959f
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[@stdlib/array/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var Complex128Array = require( '@stdlib/array/complex128' );
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var pkg = require( './../package.json' ).name;
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var zdotu = require( './../lib/zdotu.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float64'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var zx;
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var zy;
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zx = new Complex128Array( uniform( len*2, -100.0, 100.0, options ) );
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zy = new Complex128Array( uniform( len*2, -100.0, 100.0, options ) );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var d;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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d = zdotu( zx.length, zx, 1, zy, 1 );
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if ( isnan( d ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( d ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 5; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

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