incrmprod

Compute a moving product incrementally.

For a window of size W, the moving product is defined as

Usage

var incrmprod = require( '@stdlib/stats/incr/mprod' );

incrmprod( window )

Returns an accumulator function which incrementally computes a moving product. The window parameter defines the number of values over which to compute the moving product.

var accumulator = incrmprod( 3 );

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 = incrmprod( 3 );

var p = accumulator();
// returns null

// Fill the window...
p = accumulator( 2.0 ); // [2.0]
// returns 2.0

p = accumulator( 1.0 ); // [2.0, 1.0]
// returns 2.0

p = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns 6.0

// Window begins sliding...
p = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns -21.0

p = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns 105.0

p = accumulator();
// returns 105.0

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 = incrmprod( 3 );

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

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

// Recover a finite result:
p = 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 = incrmprod( 3 );

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

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

// Recover a non-zero result:
p = 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 at least W-1 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.
As W values are needed to fill the window buffer, the first W-1 returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
For large accumulation windows 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 incrmprod = require( '@stdlib/stats/incr/mprod' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrmprod( 5 );

// For each simulated datum, update the moving product...
for ( i = 0; i < 100; i++ ) {
    v = ( randu()*10.0 ) - 5.0;
    accumulator( v );
}
console.log( accumulator() );