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@bjouhier /zeta.js
Last active May 7, 2016

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"use strict";
class Complex {
constructor(a, b) {
this.re = a;
this.im = b;
}
add(c) {
return new Complex(this.re + c.re, this.im + c.im);
}
toString() {
//return this.re + ' + i' + this.im;
return this.abs() + ' e^i' + this.theta();
}
theta() {
return Math.atan(this.im / this.re);
}
abs() {
return Math.sqrt(this.re * this.re + this.im * this.im);
}
}
function zeta(a, b) {
function val(n) {
const na = Math.pow(n, -a);
const logn = Math.log(n);
return new Complex(na * Math.cos(b * logn), -na * Math.sin(b * logn));
}
var z = val(1);
//const max = 10000;
const max = b / 2.25;
for (var i = 2; i < max; i++) {
var nz = val(i);
z = z.add(nz);
//console.log(i + "\tz=" + z.abs() + "\ttheta=" + z.theta() + "\tarc=" + (b * (Math.log(i) - Math.log(i - 1))) + '\tarc2=' + (b/i));
}
return z;
}
function fmt(x) {
var s = '' + Math.round(x * 1000);
return s.substring(0, s.length - 3) + '.' + s.substring(s.length - 3);
}
function findZeros(min, len) {
var lastAbs = 1;
var inc = 1 / 1000;
var up = false;
var results = [];
for (var ii = min; ii < min + len; ii += inc) {
const z = zeta(0.5, ii);
const abs = z.abs();
if (abs < lastAbs && up) {
up = false;
lastAbs = abs;
} else if (abs > lastAbs && !up) {
if (abs < 1 / Math.sqrt(ii)) {
console.log(fmt(ii - inc) + '\t\t' + abs + '\t' + (1 / Math.sqrt(ii)));
results.push(ii - inc);
}
lastAbs = abs;
up = true;
} else {
up = abs > lastAbs;
lastAbs = abs;
}
}
return results;
}
function run(min, len) {
const results = findZeros(min, len);
const zeros = require('./zzeros').filter(x => x >= min && x < min + len);
var i = 0;
var j = 0;
var matches = [];
var bad = 0, missed = 0;
while (i < results.length - 1) {
var delta1 = Math.abs(results[i] - zeros[j]);
var delta2 = Math.abs(results[i] - zeros[j + 1]);
var delta3 = Math.abs(results[i + 1] - zeros[j]);
if (delta1 < delta2 && delta1 < delta3) {
matches.push([results[i], zeros[j]]);
i++;
j++;
} else if (delta2 < delta3) {
console.error(zeros[j] + ': missed');
missed++;
j++;
} else {
console.error(fmt(results[i]) + ': bad');
bad++;
i++;
}
}
console.log();
console.log(bad + " bad results");
console.log(missed + " missed zeros");
const err = a => Math.abs(a[0] - a[1]) / a[1];
matches.sort((a, b) => err(a) - err(b));
const fmtPair = x => fmt(x[0]) + '\t' + x[1] + '\t' + err(x);
console.log("\nbest matches:\n" + matches.slice(0, 20).map(fmtPair).join('\n'))
console.log("\nworst matches:\n" + matches.reverse().slice(0, 20).map(fmtPair).join('\n'))
}
//zeta(0.5, 2002.896408374)
//zeta(0.5, 1001.349482638);
run(0, 2000);
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