time-to-botec/squiggle/node_modules/@stdlib/stats/incr/mprod/README.md

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() );