feat: add blas/base/zdotu

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

@@ -0,0 +1,362 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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 single-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 length for `x`.
+-   **y**: input [`Complex128Array`][@stdlib/array/complex128].
+-   **strideY**: stride length 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 -->
+
+<!-- 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
+#include "stdlib/blas/base/zdotu.h"
+```
+
+#### c_zdotu( N, \*X, strideX, \*Y, strideY, \*dot )
+
+Calculates the dot product of two single-precision complex floating-point vectors.
+
+```c
+#include "stdlib/complex/float64/ctor.h"
+
+const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 };
+const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 };
+
+stdlib_complex128_t dot;
+c_zdotu( 3, (void *)x, 1, (void *)y, 1, (void *)&dot );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **X**: `[in] void*` first input array.
+-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
+-   **Y**: `[in] void*` second input array.
+-   **strideY**: `[in] CBLAS_INT` index increment for `Y`.
+-   **dot**: `[out] void*` output variable.
+
+```c
+void c_zdotu( const CBLAS_INT N, const void *X, const CBLAS_INT strideX, const void *Y, const CBLAS_INT strideY, void *dot );
+```
+
+#### c_zdotu_ndarray( N, \*X, strideX, offsetX, \*Y, strideY, offsetY, \*dot )
+
+Calculates the dot product of two single-precision complex floating-point vectors using alternative indexing semantics.
+
+```c
+#include "stdlib/complex/float64/ctor.h"
+
+const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 };
+const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 };
+
+stdlib_complex128_t dot;
+c_zdotu_ndarray( 3, (void *)x, 1, 0, (void *)y, 1, 0, (void *)&dot );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **X**: `[in] void*` first input array.
+-   **strideX**: `[in] CBLAS_INT` index increment for `X`.
+-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
+-   **Y**: `[in] void*` second input array.
+-   **strideY**: `[in] CBLAS_INT` index increment for `Y`.
+-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
+-   **dot**: `[out] void*` output variable.
+
+```c
+void c_zdotu_ndarray( const CBLAS_INT N, const void *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const void *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, void *dot );
+```
+
+</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
+#include "stdlib/blas/base/zdotu.h"
+#include "stdlib/complex/float64/real.h"
+#include "stdlib/complex/float64/imag.h"
+#include "stdlib/complex/float64/ctor.h"
+#include <stdio.h>
+
+int main( void ) {
+    // Create strided arrays:
+    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
+    const double y[] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
+
+    // Specify the number of elements:
+    const int N = 4;
+
+    // Specify strides:
+    const int strideX = 1;
+    const int strideY = 1;
+
+    // Create a complex number to store the result:
+    stdlib_complex128_t z;
+
+    // Compute the dot product:
+    c_zdotu( N, (const void *)x, strideX, (const void *)y, strideY, (void *)&z );
+
+    // Print the result:
+    printf( "dot: %lf + %lfi\n", stdlib_complex128_real( z ), stdlib_complex128_imag( z ) );
+
+    // Compute the dot product:
+    c_zdotu_ndarray( N, (const void *)x, strideX, 0, (const void *)y, strideY, 0, (void *)&z );
+
+    // Print the result:
+    printf( "dot: %lf + %lfi\n", stdlib_complex128_real( z ), stdlib_complex128_imag( z ) );
+}
+```
+
+</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">
+
+[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_ga2cce681b6aed3728b893a555b3bee55c.html#ga2cce681b6aed3728b893a555b3bee55c
+
+[@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 -->