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# caxpb

> Multiply each element in a single-precision complex floating-point strided array by a scalar constant and add a scalar constant to each result.

<section class="usage">

## Usage

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

#### caxpb( N, alpha, beta, x, strideX )

Multiplies each element in a single-precision complex floating-point strided array by a scalar constant and adds a scalar constant to each result.

```javascript
var Complex64Array = require( '@stdlib/array/complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );

var x = new Complex64Array( [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ] );

var alpha = new Complex64( 2.0, 0.0 );
var beta = new Complex64( 1.0, 0.0 );

caxpb( x.length, alpha, beta, x, 1 );
// x => <Complex64Array>[ -3.0, 2.0, 7.0, -10.0, 9.0, 0.0, -1.0, -6.0 ]
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **alpha**: first scalar constant.
-   **beta**: second scalar constant.
-   **x**: input [`Complex64Array`][@stdlib/array/complex64].
-   **strideX**: stride length.

The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to multiply every other element by `alpha` and add `beta`:

```javascript
var Complex64Array = require( '@stdlib/array/complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );

var x = new Complex64Array( [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ] );

var alpha = new Complex64( 2.0, 0.0 );
var beta = new Complex64( 1.0, 0.0 );

caxpb( 2, alpha, beta, x, 2 );
// x => <Complex64Array>[ -3.0, 2.0, 3.0, -5.0, 9.0, 0.0, -1.0, -3.0 ]
```

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 Complex64 = require( '@stdlib/complex/float32/ctor' );

// Initial array:
var x0 = new Complex64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 ] );

// Create an offset view:
var x1 = new Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

// Define scalar constants:
var alpha = new Complex64( 2.0, 0.0 );
var beta = new Complex64( 1.0, 0.0 );

// Multiply every other element by alpha and add beta starting from the second element:
caxpb( 2, alpha, beta, x1, 2 );
// x0 => <Complex64Array>[ 1.0, -2.0, 7.0, -8.0, 5.0, -6.0, 15.0, -16.0 ]
```

#### caxpb.ndarray( N, alpha, beta, x, strideX, offsetX )

Multiplies each element in a single-precision complex floating-point strided array by a scalar constant and adds a scalar constant to each result using alternative indexing semantics.

```javascript
var Complex64Array = require( '@stdlib/array/complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );

var x = new Complex64Array( [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ] );

var alpha = new Complex64( 2.0, 0.0 );
var beta = new Complex64( 1.0, 0.0 );

caxpb.ndarray( x.length, alpha, beta, x, 1, 0 );
// x => <Complex64Array>[ -3.0, 2.0, 7.0, -10.0, 9.0, 0.0, -1.0, -6.0 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index.

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 access only the last two elements of the strided array:

```javascript
var Complex64Array = require( '@stdlib/array/complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );

var x = new Complex64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

var alpha = new Complex64( 2.0, 0.0 );
var beta = new Complex64( 1.0, 0.0 );

caxpb.ndarray( 2, alpha, beta, x, 1, 1 );
// x => <Complex64Array>[ 1.0, -2.0, 7.0, -8.0, 11.0, -12.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return the strided array unchanged.

</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 Complex64 = require( '@stdlib/complex/float32/ctor' );
var logEach = require( '@stdlib/console/log-each' );
var caxpb = require( '@stdlib/blas/ext/base/caxpb' );

var xbuf = discreteUniform( 20, -100, 100, {
    'dtype': 'float32'
});
var x = new Complex64Array( xbuf.buffer );
var alpha = new Complex64( 2.0, 1.0 );
var beta = new Complex64( 5.0, -3.0 );

caxpb( x.length, alpha, beta, x, 1 );
logEach( '%s', x );
```

</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/caxpb.h"
```

#### stdlib_strided_caxpb( N, alpha, beta, \*X, strideX )

Multiplies each element in a single-precision complex floating-point strided array by a scalar constant and adds a scalar constant to each result.

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

float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
const stdlib_complex64_t alpha = stdlib_complex64( 2.0f, 0.0f );
const stdlib_complex64_t beta = stdlib_complex64( 1.0f, 0.0f );

stdlib_strided_caxpb( 4, alpha, beta, (stdlib_complex64_t *)x, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alpha**: `[in] stdlib_complex64_t` first scalar constant.
-   **beta**: `[in] stdlib_complex64_t` second scalar constant.
-   **X**: `[inout] stdlib_complex64_t*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.

```c
void stdlib_strided_caxpb( const CBLAS_INT N, const stdlib_complex64_t alpha, const stdlib_complex64_t beta, stdlib_complex64_t *X, const CBLAS_INT strideX );
```

#### stdlib_strided_caxpb_ndarray( N, alpha, beta, \*X, strideX, offsetX )

Multiplies each element in a single-precision complex floating-point strided array by a scalar constant and adds a scalar constant to each result using alternative indexing semantics.

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

float x[] = { 1.0f, -2.0f, 3.0f, -4.0f, 5.0f, -6.0f, 7.0f, -8.0f };
const stdlib_complex64_t alpha = stdlib_complex64( 2.0f, 0.0f );
const stdlib_complex64_t beta = stdlib_complex64( 1.0f, 0.0f );

stdlib_strided_caxpb_ndarray( 4, alpha, beta, (stdlib_complex64_t *)x, 1, 0 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **alpha**: `[in] stdlib_complex64_t` first scalar constant.
-   **beta**: `[in] stdlib_complex64_t` second scalar constant.
-   **X**: `[inout] stdlib_complex64_t*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.

```c
void stdlib_strided_caxpb_ndarray( const CBLAS_INT N, const stdlib_complex64_t alpha, const stdlib_complex64_t beta, 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/caxpb.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:
    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 indexed elements:
    const int N = 4;

    // Specify a stride:
    const int strideX = 1;

    // Define scalar constants:
    stdlib_complex64_t alpha = stdlib_complex64( 2.0f, 0.0f );
    stdlib_complex64_t beta = stdlib_complex64( 1.0f, 0.0f );

    // Multiply each element by alpha and add beta:
    stdlib_strided_caxpb( N, alpha, beta, x, strideX );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "x[ %i ] = %f + %fi\n", i, stdlib_complex64_real( x[ i ] ), stdlib_complex64_imag( x[ i ] ) );
    }
}
```

</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">

[@stdlib/array/complex64]: https://www.npmjs.com/package/@stdlib/array-complex64

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

<!-- <related-links> -->

<!-- </related-links> -->

</section>

<!-- /.links -->
