npm package: @stdlib/blas-ext-base-csumkbn
Description: Calculate the sum of single-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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# csumkbn

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> Calculate the sum of single-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-csumkbn
```

</section>

<section class="usage">

## Usage

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

#### csumkbn( N, x, strideX )

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

```javascript
var Complex64Array = require( '@stdlib/array-complex64' );

var x = new Complex64Array( [ 1.0, -2.0, 2.0, 3.0 ] );

var v = csumkbn( x.length, x, 1 );
// returns <Complex64>[ 3.0, 1.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Complex64Array`][@stdlib/array/complex64].
-   **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 Complex64Array = require( '@stdlib/array-complex64' );

var x = new Complex64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = csumkbn( 2, x, 2 );
// returns <Complex64>[ -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 Complex64Array = require( '@stdlib/array-complex64' );

var x0 = new Complex64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var v = csumkbn( 2, x1, 2 );
// returns <Complex64>[ 5.0, 2.0 ]
```

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

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

```javascript
var Complex64Array = require( '@stdlib/array-complex64' );

var x = new Complex64Array( [ 1.0, -2.0, 2.0, 3.0 ] );

var v = csumkbn.ndarray( 2, x, 1, 0 );
// returns <Complex64>[ 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 Complex64Array = require( '@stdlib/array-complex64' );

var x = new Complex64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = csumkbn.ndarray( 2, x, 2, 1 );
// returns <Complex64>[ 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 Complex64Array = require( '@stdlib/array-complex64' );
var csumkbn = require( '@stdlib/blas-ext-base-csumkbn' );

var xbuf = discreteUniform( 10, -100, 100, {
    'dtype': 'float32'
});
console.log( xbuf );

var x = new Complex64Array( xbuf );
var v = csumkbn( 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/csumkbn.h"
```

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

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

```c
#include "stdlib/complex/float32/ctor.h"

const stdlib_complex64_t x[] = {
    stdlib_complex64( 1.0f, 2.0f ),
    stdlib_complex64( 3.0f, 4.0f )
};

stdlib_complex64_t v = stdlib_strided_csumkbn( 2, x, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] stdlib_complex64_t*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.

```c
stdlib_complex64_t stdlib_strided_csumkbn( const CBLAS_INT N, const stdlib_complex64_t *X, const CBLAS_INT strideX );
```

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

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

```c
#include "stdlib/complex/float32/ctor.h"

const stdlib_complex64_t x[] = {
    stdlib_complex64( 1.0f, 2.0f ),
    stdlib_complex64( 3.0f, 4.0f )
};

stdlib_complex64_t v = stdlib_strided_csumkbn_ndarray( 2, x, 1, 0 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **X**: `[in] stdlib_complex64_t*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.

```c
stdlib_complex64_t stdlib_strided_csumkbn_ndarray( const CBLAS_INT N, const stdlib_complex64_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/csumkbn.h"
#include "stdlib/complex/float32/ctor.h"
#include "stdlib/complex/float32/real.h"
#include "stdlib/complex/float32/imag.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const stdlib_complex64_t x[] = {
        stdlib_complex64( 1.0f, 2.0f ),
        stdlib_complex64( 3.0f, 4.0f ),
        stdlib_complex64( 5.0f, 6.0f ),
        stdlib_complex64( 7.0f, 8.0f )
    };

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

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

    // Compute the sum:
    stdlib_complex64_t v = stdlib_strided_csumkbn( N, x, strideX );

    // Print the result:
    printf( "sum: %f + %fi\n", stdlib_complex64_real( v ), stdlib_complex64_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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