bessel/test.js

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/* vim: set ts=2: */
var X;
if(typeof require !== 'undefined') {
assert = require('assert');
describe('source',function(){
it('should load',function(){X=require('./');});
it('all bessel functions', function() {
assert.equal(typeof X.besseli, 'function');
assert.equal(typeof X.besselj, 'function');
assert.equal(typeof X.besselk, 'function');
assert.equal(typeof X.bessely, 'function');
});
});
} else { X = BESSEL; }
function approx(a, b, t) { return Math.abs((a - b) / (Math.abs(a) + Math.abs(b))) <= t; }
function chk(func, x, n, v, F, t) {
var V = func(x,n);
if(!approx(V, v, t) && v != V && !(isNaN(v) && isNaN(V))) throw new Error(F + "(" + x + "," + n + ") = " + V + " !~ " + v);
}
var funcs = ['besseli', 'besselj', 'besselk', 'bessely'];
var tests = {
'besseli': [
[1.5, 1, 0.981666],
[1.9, 2, 0.603272435],
[2.5, 1, 2.516716242]
],
'besselj': [
[1.5, 1, 0.557936508],
[1.9, 2, 0.329925829],
[2.5, 1, 0.497094103]
],
'besselk': [
[1.5, 1, 0.277388],
[1.9, 2, 0.296909301],
[2.5, 1, 0.073890816]
],
'bessely': [
[1.5, 1, -0.412308627],
[1.9, 2, -0.669878674],
[2.5, 1, 0.14591814]
] };
describe('correctness', function() {
funcs.forEach(function(F) { it(F, function() {
tests[F].forEach(function(t) { chk(X[F], t[0], t[1], t[2], F, 1e-6); });
});});
if(typeof require != 'undefined') {
var fs = require('fs');
it('excel', function() {
var xl = fs.readFileSync("test_files/excel.tsv", 'ascii').split("\n").map(function(l) { return l.split("\t");});
xl.forEach(function(l) { if(l.length < 6) return;
var x=Number(l[0]), n=Number(l[1]);
var i=Number(l[2]), j=Number(l[3]), k=Number(l[4]), y=Number(l[5]);
chk(X.besseli, x, n, i, 'besseli', 1e-4);
chk(X.besselj, x, n, j, 'besselj', 1e-4);
chk(X.besselk, x, n, k, 'besselk', 1e-4);
chk(X.bessely, x, n, y, 'bessely', 1e-4);
});
});
it('mma', function() {
var mma = fs.readFileSync("test_files/mma.tsv", 'ascii').split("\n").map(function(l) { return l.split("\t");});
mma.forEach(function(l) { if(l.length < 6) return;
var x=Number(l[0]), n=Number(l[1]);
var i=Number(l[2]), j=Number(l[3]), k=Number(l[4]), y=Number(l[5]);
chk(X.besseli, x, n, i, 'besseli', 1e-5);
chk(X.besselj, x, n, j, 'besselj', 1e-5);
chk(X.besselk, x, n, k, 'besselk', 1e-5);
chk(X.bessely, x, n, y, 'bessely', 1e-5);
});
});
}
});
var rand = [
0.3946086812775882, 3.946086812775882, 39.46086812775882,
0.03119419917289612, 0.3119419917289612, 3.119419917289612,
0.18311903629136062, 1.8311903629136062, 18.311903629136062,
0.5317681126599452, 5.317681126599452, 53.17681126599452,
0.37724541457032235, 3.7724541457032235, 37.724541457032235,
0.8287802926845655, 8.287802926845655, 82.87802926845655,
0.7197724866379658, 7.197724866379658, 71.97724866379658
];
describe('properties', function() {
var t = 1e-4;
it('limiting behavior', function() {
chk(X.besselj, 0, 0, 1, 'besselj', 1e-6);
chk(X.besseli, 0, 0, 1, 'besseli', 1e-6);
chk(X.besselk, 0, 0, Infinity, 'besselk', 1e-6);
chk(X.bessely, 0, 0, -Infinity, 'bessely', 1e-6);
for(var i = 1; i < 20; ++i) {
chk(X.besselj, 0, i, 0, 'besselj', 1e-6);
chk(X.besseli, 0, i, 0, 'besseli', 1e-6);
}
});
it('besselj', function() {
var F = "BESSELJ", f = X.besselj;
rand.forEach(function(r) {
for(var n = 0; n < 20; ++n) {
var pp = f( r, n), pn = f( r, -n), np = f(-r, n), nn = f(-r, -n);
if((n%2)) {
/* besselj odd if n is odd */
if(!approx(np, -pp, t)) throw new Error(F + " np[" + np + "] != -pp[" + (-pp) + "] (" + r + "," + n + ")");
if(!approx(nn, -pn, t)) throw new Error(F + " nn[" + nn + "] != -pn[" + (-pn) + "] (" + r + "," + n + ")");
/* asymmetric in n */
if(!approx(pn, -pp, t)) throw new Error(F + " pn[" + pn + "] != -pp[" + (-pp) + "] (" + r + "," + n + ")");
if(!approx(nn, -np, t)) throw new Error(F + " nn[" + nn + "] != -pn[" + (-pn) + "] (" + r + "," + n + ")");
} else {
/* besselj even if n is even */
if(!approx(np, pp, t)) throw new Error(F + " np[" + np + "] != pp[" + (pp) + "] (" + r + "," + n + ")");
if(!approx(nn, pn, t)) throw new Error(F + " nn[" + nn + "] != pn[" + (pn) + "] (" + r + "," + n + ")");
/* symmetric in n */
if(!approx(pn, pp, t)) throw new Error(F + " pn[" + pn + "] != pp[" + (pp) + "] (" + r + "," + n + ")");
if(!approx(nn, np, t)) throw new Error(F + " nn[" + nn + "] != pn[" + (pn) + "] (" + r + "," + n + ")");
}
}
});
});
});