stdlib-js
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continued-fraction
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[Continued fraction][continued-fraction] approximation.
bash
npm install @stdlib/math-base-tools-continued-fraction
javascript
var continuedFraction = require( '@stdlib/math-base-tools-continued-fraction' );
#### continuedFraction( generator[, options ] )
Evaluates the continued fraction described by the supplied generator argument. generator can be either a function which returns an array with two elements, the a and b terms of the fraction, or an ES6 [Generator object][es6-generator]. By default, the function computes
javascript
// Continued fraction for (e-1)^(-1):
var gen = generator();
var out = continuedFraction( gen );
// returns ~0.582
function* generator() {
var i = 0;
while ( true ) {
i += 1;
yield [ i, i ];
}
}
Alternatively, one can use a closure to achieve the same goal:
javascript
// Continued fraction for (e-1)^(-1):
var gen = generator();
var out = continuedFraction( gen );
// returns ~0.582
function generator() {
var i = 0;
return gen;
function gen() {
i += 1;
return [ i, i ];
}
}
The function accepts the following options:
- maxIter: integer denoting the maximum number of times the supplied generator object will be called. Default: 1000000.
- tolerance: number primitive specifying the used tolerance to assess convergence. Default: 2.22e-16.
- keep: boolean primitive indicating whether to keep the b0 term in the continued fraction. Default: false.
To evaluate
set the keep option to true.
javascript
var out = continuedFraction( generator(), {
'keep': true
});
// returns ~1.718
function generator() {
var i = 0;
return gen;
function gen() {
i += 1;
return [ i, i ];
}
}
To change the maximum number of iterations, set the maxIter option.
javascript
var out = continuedFraction( generator(), {
'maxIter': 10
});
// returns ~0.582
function generator() {
var i = 0;
return gen;
function gen() {
i += 1;
return [ i, i ];
}
}
The default tolerance of 2.22e-16 to assess convergence can be changed via the tolerance option.
javascript
var out = continuedFraction( generator(), {
'tolerance': 1e-1
});
// returns ~0.579
function generator() {
var i = 0;
return gen;
function gen() {
i += 1;
return [ i, i ];
}
}
javascript
var continuedFraction = require( '@stdlib/math-base-tools-continued-fraction' );
var out;
function* generator() {
while ( true ) {
yield [ 1, 1 ];
}
}
function closure() {
var ones = [ 1, 1 ];
return gen;
function gen() {
return ones;
}
}
out = continuedFraction( generator(), {
'keep': true
});
console.log( 'Golden ratio (generator): %d,', out );
out = continuedFraction( closure(), {
'keep': true
});
console.log( 'Golden ratio (closure): %d', out );
