/**
* Copyright Nos_lkSsvOhB ( http://wonderfl.net/user/Nos_lkSsvOhB )
* MIT License ( http://www.opensource.org/licenses/mit-license.php )
* Downloaded from: http://wonderfl.net/c/z3iF
*/
package {
import flash.display.Sprite;
import flash.events.*;
import com.bit101.components.*;
//前にもあった気がしたんで、参考に作ってみました。
public class RootFinder extends Sprite {
public var EPS : Number = Math.pow(10,-38); //1e-16;
private static var MAX : Number = 1e6;
private var _text : Text;
private var _label : Text;
private var _rootsRe : Text;
private var _rootsAll : Text;
private static var _trace : Text;
private var _solve : PushButton;
public function RootFinder() {
_text = new Text(this, 30, 60, "");
_text.width = 400;
_text.height = 20;
_text.textField.restrict = "-0-9 +\.";
_text.textField.addEventListener(Event.CHANGE, onTextChange);
_text.text = "1 -6 11 -6";
_label = new Text(this, 30, 100, "");
_label.editable = false;
_label.width = 400;
_label.height = 40;
var lr : Label = new Label(this, 30, 230, "real roots");
_rootsRe = new Text(this, 90, 230, "");
_rootsRe.editable = false;
_rootsRe.width = 340;
_rootsRe.height = 70;
var la : Label = new Label(this, 30, 160, "all roots");
_rootsAll = new Text(this, 90, 160, "");
_rootsAll.editable = false;
_rootsAll.width = 340;
_rootsAll.height = 70;
onTextChange(null);
_solve = new PushButton(this, 130, 300, "Solve it!", onSolve);
_solve.width = 200;
_solve.height = 100;
_trace = new Text(this, 30, 400, "");
_trace.width = 400;
_trace.height = 56;
// _trace.text = String(MAX);
}
private function onTextChange(e : Event = null) : void
{
var a : Array = _text.text.split(" ");
var text : String = "";
var first : Boolean = true;
for(var i : uint = 0;i < a.length;i++){
var deg : int = a.length - 1 - i;
a[i] = parseFloat(a[i]);
if(isNaN(a[i]) || a[i] == 0)continue;
if(first){
first = false;
}else{
if(a[i] >= 0)text += "+";
}
if(deg == 0){
text += a[i];
}else if(deg == 1){
text += (a[i] == 1 ? "" : (a[i] == -1 ? "-" : a[i])) + "x";
}else{
text += (a[i] == 1 ? "" : (a[i] == -1 ? "-" : a[i])) + "x^" + deg;
}
}
_label.text = text + " = 0";
}
private function onSolve(e : MouseEvent) : void
{
var c : Array = []
for each(var el : String in _text.text.split(" ")){
var num : Number = parseFloat(el);
c.push(isNaN(num) ? 0 : num);
}
RootFinder._trace.text = "";
// real roots
var retre : Array = findRoots(c, EPS, true);
retre.sort(Array.NUMERIC);
_rootsRe.text = "x = " + (retre.length ? retre.join(",") : "None!");
// all roots
var retall : Array = findRoots(c, EPS, false);
retall.sortOn(["re", "im"], Array.NUMERIC);
var strs : Array = [];
for each(var rt : Object in retall){
strs.push(
(rt.re||"") + (rt.im ? ((rt.im>=0 && rt.re!=0?"+":"") + rt.im + "i") : "")
);
}
_rootsAll.text = "x = " + (retall.length ? strs.join(",") : "None!");
}
private static function findRoots(a : Array, eps : Number, realOnly : Boolean) : Array
{
cutHead(a);
var p : Number = a.length >= 1 ? 2/a[0] : 0;
var q : Number = a.length >= 2 ? 2/a[0] : 0;
var ret : Array = [];
for(var j : uint = 0;j < MAX;j++){
// while(true){
var n : uint = a.length;
if(n == 3){
var sqa : Number = a[1] * a[1] - 4 * a[0] * a[2];
if(realOnly){
if(sqa >= 0){
ret.push((-a[1]+Math.sqrt(sqa))/(2*a[0]), (-a[1]-Math.sqrt(sqa))/(2*a[0]));
}
}else{
if(sqa >= 0){
ret.push({re:(-a[1]+Math.sqrt(sqa))/(2*a[0])}, {re:(-a[1]-Math.sqrt(sqa))/(2*a[0])});
}else{
ret.push(
{re:-a[1]/(2*a[0]), im:Math.sqrt(-sqa)/(2*a[0])},
{re:-a[1]/(2*a[0]), im:-Math.sqrt(-sqa)/(2*a[0])}
);
}
}
break;
}else if(n == 2){
if(realOnly){
ret.push(-a[1]/a[0]);
}else{
ret.push({re:-a[1]/a[0]});
}
break;
}else if(n <= 1){
break;
}
var b : Array = [];
var c : Array = [];
for(var i : uint = 0;i < n;i++){
b.push(a[i] - p*(b[i-1]||0) - q*(b[i-2]||0));
c.push(b[i] - p*(c[i-1]||0) - q*(c[i-2]||0));
}
var D : Number = c[n-3]*c[n-3]-c[n-4]*(c[n-2]-b[n-2]);
var dp : Number = (b[n-2]*c[n-3]-b[n-1]*c[n-4])/D;
var dq : Number = (b[n-1]*c[n-3]-b[n-2]*(c[n-2]-b[n-2]))/D;
if(Math.abs(dp) < eps && Math.abs(dq) < eps){
// x^2+px+q=0
RootFinder._trace.text+="n=" + n + " dp=" + dp + " dq=" + dq + "\n" + "p=" + p + " q=" + q + "\n";
var sq : Number = p * p - 4 * q;
if(realOnly){
if(sq >= 0){
ret.push((-p+Math.sqrt(sq))/2, (-p-Math.sqrt(sq))/2);
}
}else{
if(sq >= 0){
ret.push({re:(-p+Math.sqrt(sq))/2}, {re:(-p-Math.sqrt(sq))/2});
}else{
ret.push(
{re:-p/2, im:Math.sqrt(-sq)/2},
{re:-p/2, im:-Math.sqrt(-sq)/2}
);
}
}
a = b.slice(0, n - 2);
// break;
}else{
p += dp;
q += dq;
}
if(j==MAX){
RootFinder._trace.text+="Not converged.Change initial value of p,q, and retry.\n";
break;
}
}
return ret;
}
private static function cutHead(a : Array) : Array
{
while(a.length > 0 && a[0] == 0)a.shift();
return a;
}
}
/* public class Global
{
// public static var _trace : Text;
public static var tex : String;
}
*/
}
