time-to-botec/squiggle/node_modules/@stdlib/math/base/special/kernel-betainc/README.md

Kernel Betainc

Incomplete beta function and its first derivative.

Usage

var kernelBetainc = require( '@stdlib/math/base/special/kernel-betainc' );

kernelBetainc( x, a, b, regularized, upper )

Evaluates the incomplete beta function and its first derivative for parameters x, a > 0 and b > 0. The regularized and upper boolean parameters are used to specify whether to evaluate the regularized or non-regularized and the upper or lower incomplete beta functions, respectively.

var out = kernelBetainc( 0.8, 1.0, 0.3, false, false );
// returns [ ~1.277, ~0.926 ]

out = kernelBetainc( 0.2, 1.0, 2.0, true, false );
// returns [ 0.36, 1.6 ]

out = kernelBetainc( 0.2, 1.0, 2.0, true, true );
// returns [ 0.64, 1.6 ]

If provided NaN for x, a, or b, the function returns [ NaN, NaN ].

var out = kernelBetainc( NaN, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]

out = kernelBetainc( 0.8, NaN, 1.0, true, true );
// returns [ NaN, NaN ]

out = kernelBetainc( 0.8, 1.0, NaN, true, true );
// returns [ NaN, NaN ]

If x is outside the interval [0,1], the function returns [ NaN, NaN ].

var out = kernelBetainc( 1.5, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]

out = kernelBetainc( -0.5, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]

If a or b is negative, the function returns [ NaN, NaN ].

var out = kernelBetainc( 0.5, -2.0, 2.0, true, true );
// returns [ NaN, NaN ]

out = kernelBetainc( 0.5, 2.0, -2.0, true, true );
// returns [ NaN, NaN ]

kernelBetainc.assign( x, a, b, regularized, upper, out, stride, offset )

Evaluates the incomplete beta function and its first derivative for parameters x, a > 0 and b > 0 and assigns results to a provided output array.

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

var out = new Float64Array( 2 );
var v = kernelBetainc.assign( 0.2, 1.0, 2.0, true, true, out, 1, 0 );
// returns <Float64Array>[ 0.64, 1.6 ]

var bool = ( v === out );
// returns true

The offset parameter specifies the index of the first output array element, and the stride parameter specifies the stride length between consecutive output array elements.

Examples

var randu = require( '@stdlib/random/base/randu' );
var kernelBetainc = require( '@stdlib/math/base/special/kernel-betainc' );

var out;
var i;
var x;
var a;
var b;

out = [ 0.0, 0.0 ];
for ( i = 0; i < 100; i++ ) {
    x = randu();
    a = randu() * 10.0;
    b = randu() * 10.0;
    kernelBetainc( x, a, b, true, false, out, 1, 0 );
    console.log( 'x: %d, \t a: %d, \t b: %d, \t f(x,a,b): %d, \t f^1(x,a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), out[ 0 ].toFixed( 4 ), out[ 1 ].toFixed( 4 ) );
}