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bessely0By

Compute the Bessel function of the second kind of order zero for each element retrieved from an input strided array via a callback function.

Installation

npm install @stdlib/math-strided-special-bessely0-by

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var bessely0By = require( '@stdlib/math-strided-special-bessely0-by' );

bessely0By( N, x, strideX, y, strideY, clbk[, thisArg] )

Computes the Bessel function of the second kind of order zero for each element retrieved from an input strided array x via a callback function and assigns each result to an element in an output strided array y.

function accessor( v ) {
    return v;
}

var x = [ 0.0, 1.0, 0.1, 0.25, 0.5 ];
var y = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];

bessely0By( x.length, x, 1, y, 1, accessor );
// y => [ -Infinity, ~0.088, ~-1.534, ~-0.932, ~-0.445 ]

The function accepts the following arguments:

• N: number of indexed elements.
• x: input Array, typed array, or an array-like object (excluding strings and functions).
• strideX: index increment for x.
• y: output Array, typed array, or an array-like object (excluding strings and functions).
• strideY: index increment for y.
• clbk: callback function.
• thisArg: execution context (optional).

The invoked callback function is provided six arguments:

• value: input array element.
• idx: iteration index (zero-based).
• xi: input array strided index (offsetX + idx*strideX).
• yi: output array strided index (offsetY + idx*strideY).
• x: input array/collection.
• y: output array/collection.

To set the callback execution context, provide a thisArg.

function accessor( v ) {
    this.count += 1;
    return v;
}

var context = {
    'count': 0
};

var x = [ 0.0, 1.0, 0.1, 0.25, 0.5 ];
var y = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];

bessely0By( x.length, x, 1, y, 1, accessor, context );
// y => [ -Infinity, ~0.088, ~-1.534, ~-0.932, ~-0.445 ]

var cnt = context.count;
// returns 5

The N and stride parameters determine which elements in x and y are accessed at runtime. For example, to index every other value in x and to index the first N elements of y in reverse order,

function accessor( v ) {
    return v;
}

var x = [ 0.0, 1.0, 0.1, 0.25, 0.5, 0.67 ];
var y = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

bessely0By( 3, x, 2, y, -1, accessor );
// y => [ ~-0.445, ~-1.534, -Infinity, 0.0, 0.0, 0.0 ]

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float64Array = require( '@stdlib/array-float64' );

function accessor( v ) {
    return v;
}

// Initial arrays...
var x0 = new Float64Array( [ 0.0, 1.0, 0.1, 0.25, 0.5, 0.67 ] );
var y0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

bessely0By( 3, x1, -2, y1, 1, accessor );
// y0 => <Float64Array>[ 0.0, 0.0, 0.0, ~-0.224, ~-0.932, ~0.088 ]

bessely0By.ndarray( N, x, strideX, offsetX, y, strideY, offsetY, clbk[, thisArg] )

Computes the Bessel function of the second kind of order zero for each element retrieved from an input strided array x via a callback function and assigns each result to an element in an output strided array y using alternative indexing semantics.

function accessor( v ) {
    return v;
}

var x = [ 0.0, 1.0, 0.1, 0.25, 0.5 ];
var y = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];

bessely0By.ndarray( x.length, x, 1, 0, y, 1, 0, accessor );
// y => [ -Infinity, ~0.088, ~-1.534, ~-0.932, ~-0.445 ]

The function accepts the following additional arguments:

• offsetX: starting index for x.
• offsetY: starting index for y.

While typed array views mandate a view offset based on the underlying buffer, the offsetX and offsetY parameters support indexing semantics based on starting indices. For example, to index every other value in x starting from the second value and to index the last N elements in y,

function accessor( v ) {
    return v;
}

var x = [ 0.0, 1.0, 0.1, 0.25, 0.5, 0.67 ];
var y = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

bessely0By.ndarray( 3, x, 2, 1, y, -1, y.length-1, accessor );
// y => [ 0.0, 0.0, 0.0, ~-0.224, ~-0.932, ~0.088 ]

Notes

• If a provided callback function does not return any value (or equivalently, explicitly returns undefined), the value is ignored.

  function accessor() {
      // No-op...
  }
  
  var x = [ 0.0, 1.0, 0.1, 0.25, 0.5 ];
  var y = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
  
  bessely0By( x.length, x, 1, y, 1, accessor );
  // y => [ 0.0, 0.0, 0.0, 0.0, 0.0 ]

Examples

var uniform = require( '@stdlib/random-base-uniform' ).factory;
var filledarray = require( '@stdlib/array-filled' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var bessely0By = require( '@stdlib/math-strided-special-bessely0-by' );

function accessor( v, i ) {
    if ( (i%3) === 0 ) {
        // Simulate a "missing" value...
        return;
    }
    return v;
}

var x = filledarrayBy( 10, 'generic', uniform( 0.0, 10.0 ) );
console.log( x );

var y = filledarray( null, 10, 'generic' );
console.log( y );

bessely0By.ndarray( x.length, x, 1, 0, y, -1, y.length-1, accessor );
console.log( y );

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.