iterContinuedFractionSeq

Usage

var iterContinuedFractionSeq = require( '@stdlib/math/iter/sequences/continued-fraction' );

iterContinuedFractionSeq( x, [options] )

Returns an iterator which generates a list of all continued fraction terms (b_i) which can be obtained given the precision of x.

var it = iterContinuedFractionSeq( 3.245 );
// returns <Object>

var v = it.next().value;
// returns 3

v = it.next().value;
// returns 4

v = it.next().value;
// returns 12

v = it.next().value;
// returns 4

var bool = it.next().done;
// returns true

The returned iterator protocol-compliant object has the following properties:

• next: function which returns an iterator protocol-compliant object containing the next iterated value (if one exists) assigned to a value property and a done property having a boolean value indicating whether the iterator is finished.
• return: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.

The function supports the following options:

• iter: maximum number of iterations. Default: 1e308.

• tol: tolerance at which to terminate further evaluation of the continued fraction. Default: floating-point epsilon.

• returns: specifies the type of result to return. Must be one of the following options:

  • terms: return continued fraction terms.
  • convergents: return continued fraction convergents.
  • *: return both continued fraction terms and their associated convergents as a two-element array: [ <term>, <convergent> ].

  Default: 'terms'.

By default, in theory, the function returns an infinite iterator; however, in practice, due to limited precision, every floating-point number is a rational number, and, thus, every returned iterator will end in a finite number of iterations. To explicitly cap the maximum number of iterations, set the iter option.

var opts = {
    'iter': 2
};
var it = iterContinuedFractionSeq( 3.245, opts );
// returns <Object>

var v = it.next().value;
// returns 3

v = it.next().value;
// returns 4

var bool = it.next().done;
// returns true

The returned iterator terminates once the difference between the input value x and a continued fraction approximation is sufficiently small. The default tolerance is floating-point epsilon (~2.22e-16). Once an update to a continued fraction approximation is less than or equal to this tolerance, the iterator terminates. To adjust the tolerance (e.g., to return a rough approximation of an input value x), set the tol option.

var opts = {
    'tol': 1.0e-7
};
var it = iterContinuedFractionSeq( 3.141592653589793, opts );
// returns <Object>

var v = it.next().value;
// returns 3

v = it.next().value;
// returns 7

v = it.next().value;
// returns 16

var bool = it.next().done;
// returns true

// The returned terms [3; 7, 16] evaluate to 3.1415929203539825

By default, the returned iterator returns continued fraction terms. To return convergents, set the returns option to 'convergents'.

var it = iterContinuedFractionSeq( 3.245, {
    'returns': 'convergents'
});
// returns <Object>

var v = it.next().value;
// returns 3.0

v = it.next().value;
// returns 3.25

v = it.next().value;
// returns ~3.2449

v = it.next().value;
// returns 3.245

var bool = it.next().done;
// returns true

To return both continued fraction terms and their associated convergents, set the returns option to *.

var it = iterContinuedFractionSeq( 3.245, {
    'returns': '*'
});
// returns <Object>

var v = it.next().value;
// returns [ 3, 3.0 ]

v = it.next().value;
// returns [ 4, 3.25 ]

v = it.next().value;
// returns [ 12, ~3.2449 ]

v = it.next().value;
// returns [ 4, 3.245 ]

var bool = it.next().done;
// returns true