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.

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] )

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 );