Calculate the sum of single-precision complex floating-point strided array elements using an improved Kahan–Babuška algorithm.
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> Calculate the sum of single-precision complex floating-point strided array elements using an improved Kahan–Babuška algorithm.
``bash`
npm install @stdlib/blas-ext-base-csumkbn
`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
`
The function has the following parameters:
- N: number of indexed elements.
- x: input [Complex64Array][@stdlib/array/complex64].x
- strideX: stride length for .
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
`
Note that indexing is relative to the first index. To introduce an offset, use [typed array][mdn-typed-array] views.
`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
`
#### 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
`
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
`
- If N <= 0, both functions return 0.0 + 0.0i.
`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 );
`
*
`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.[in] stdlib_complex64_t*
- X: input array.[in] CBLAS_INT
- strideX: 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.[in] stdlib_complex64_t*
- X: input array.[in] CBLAS_INT
- strideX: stride length for X.[in] CBLAS_INT
- offsetX: 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 );
`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
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 ) );
}
`
- 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].
*
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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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