incrprod

Compute a product incrementally.

The product is defined as

Usage

var incrprod = require( '@stdlib/stats/incr/prod' );

incrprod()

Returns an accumulator function which incrementally computes a product.

var accumulator = incrprod();

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated product. If not provided an input value x, the accumulator function returns the current product.

var accumulator = incrprod();

var prod = accumulator( 2.0 );
// returns 2.0

prod = accumulator( 1.0 );
// returns 2.0

prod = accumulator( 3.0 );
// returns 6.0

prod = accumulator();
// returns 6.0

Under certain conditions, overflow may be transient.

// Large values:
var x = 5.0e+300;
var y = 1.0e+300;

// Tiny value:
var z = 2.0e-302;

// Initialize an accumulator:
var accumulator = incrprod();

var prod = accumulator( x );
// returns 5.0e+300

// Transient overflow:
prod = accumulator( y );
// returns Infinity

// Recover a finite result:
prod = accumulator( z );
// returns 1.0e+299

Similarly, under certain conditions, underflow may be transient.

// Tiny values:
var x = 4.0e-302;
var y = 9.0e-303;

// Large value:
var z = 2.0e+300;

// Initialize an accumulator:
var accumulator = incrprod();

var prod = accumulator( x );
// returns 4.0e-302

// Transient underflow:
prod = accumulator( y );
// returns 0.0

// Recover a non-zero result:
prod = accumulator( z );
// returns 7.2e-304

Notes

Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for all future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
For long running accumulations or accumulations of either large or small numbers, care should be taken to prevent overflow and underflow. Note, however, that overflow/underflow may be transient, as the accumulator does not use a double-precision floating-point number to store an accumulated product. Instead, the accumulator splits an accumulated product into a normalized fraction and exponent and updates each component separately. Doing so guards against a loss in precision.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrprod = require( '@stdlib/stats/incr/prod' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrprod();

// For each simulated value, update the product...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );