npm package: @stdlib/blas-ext-base-zsumkbn
Description: Calculate the sum of double-precision complex floating-point strided array elements using an improved Kahan–Babuška algorithm.
Author: The Stdlib Authors
Latest version: 0.1.1

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# zsumkbn

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> Calculate the sum of double-precision complex floating-point strided array elements using an improved Kahan–Babuška algorithm.

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/blas-ext-base-zsumkbn
```

</section>

<section class="usage">

## Usage

```javascript
var zsumkbn = require( '@stdlib/blas-ext-base-zsumkbn' );
```

#### zsumkbn( N, x, strideX )

Computes the sum of double-precision complex floating-point strided array elements using an improved Kahan–Babuška algorithm.

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 1.0, -2.0, 2.0, 3.0 ] );

var v = zsumkbn( x.length, x, 1 );
// returns <Complex128>[ 3.0, 1.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Complex128Array`][@stdlib/array/complex128].
-   **strideX**: stride length for `x`.

The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the sum of every other element:

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = zsumkbn( 2, x, 2 );
// returns <Complex128>[ -1.0, 5.0 ]
```

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 x0 = new Complex128Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var v = zsumkbn( 2, x1, 2 );
// returns <Complex128>[ 5.0, 2.0 ]
```

#### zsumkbn.ndarray( N, x, strideX, offsetX )

Computes the sum of double-precision complex floating-point strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 1.0, -2.0, 2.0, 3.0 ] );

var v = zsumkbn.ndarray( 2, x, 1, 0 );
// returns <Complex128>[ 3.0, 1.0 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.

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 calculate the sum of every other element starting from the second element:

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );

var x = new Complex128Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = zsumkbn.ndarray( 2, x, 2, 1 );
// returns <Complex128>[ 5.0, 2.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `0.0 + 0.0i`.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Complex128Array = require( '@stdlib/array-complex128' );
var zsumkbn = require( '@stdlib/blas-ext-base-zsumkbn' );

var xbuf = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
console.log( xbuf );

var x = new Complex128Array( xbuf );
var v = zsumkbn( x.length, x, 1 );
console.log( v );
```

</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/ext/base/zsumkbn.h"
```

#### stdlib_strided_zsumkbn( N, \*X, strideX )

Computes the sum of double-precision complex floating-point strided array elements using an improved Kahan–Babuška algorithm.

```c
#include "stdlib/complex/float64/ctor.h"

const stdlib_complex128_t x[] = {
    stdlib_complex128( 1.0, 2.0 ),
    stdlib_complex128( 3.0, 4.0 )
};

stdlib_complex128_t v = stdlib_strided_zsumkbn( 2, x, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] stdlib_complex128_t*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.

```c
stdlib_complex128_t stdlib_strided_zsumkbn( const CBLAS_INT N, const stdlib_complex128_t *X, const CBLAS_INT strideX );
```

#### stdlib_strided_zsumkbn_ndarray( N, \*X, strideX, offsetX )

Computes the sum of double-precision complex floating-point strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.

```c
#include "stdlib/complex/float64/ctor.h"

const stdlib_complex128_t x[] = {
    stdlib_complex128( 1.0, 2.0 ),
    stdlib_complex128( 3.0, 4.0 )
};

stdlib_complex128_t v = stdlib_strided_zsumkbn_ndarray( 2, x, 1, 0 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] stdlib_complex128_t*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.

```c
stdlib_complex128_t stdlib_strided_zsumkbn_ndarray( const CBLAS_INT N, const stdlib_complex128_t *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );
```

</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/ext/base/zsumkbn.h"
#include "stdlib/complex/float64/ctor.h"
#include "stdlib/complex/float64/real.h"
#include "stdlib/complex/float64/imag.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const stdlib_complex128_t x[] = {
        stdlib_complex128( 1.0, 2.0 ),
        stdlib_complex128( 3.0, 4.0 ),
        stdlib_complex128( 5.0, 6.0 ),
        stdlib_complex128( 7.0, 8.0 )
    };

    // Specify the number of elements:
    const int N = 4;

    // Specify the stride length:
    const int strideX = 1;

    // Compute the sum:
    stdlib_complex128_t v = stdlib_strided_zsumkbn( N, x, strideX );

    // Print the result:
    printf( "sum: %lf + %lfi\n", stdlib_complex128_real( v ), stdlib_complex128_imag( v ) );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<section class="references">

## References

-   Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106][@neumaier:1974a].

</section>

<!-- /.references -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106

</section>

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