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Problem with quadratic solution - couldn't find it today

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Martin Thoma 2013-12-13 23:35:07 +01:00
parent f241ed6bf5
commit 76ec8c9cab
3 changed files with 34 additions and 13 deletions
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40
documents/math-minimal-distance-to-cubic-function/quadratic-min-visualization/quadratic-vis.js
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@ -168,19 +168,37 @@ function findMin(p) {
var b = parseFloat(document.getElementById("b").value);
var c1 = parseFloat(document.getElementById("c").value);
var currentMinX = p.x;
for (var i=0; i < 10; i++) {
// Funktionswert
var fx = -2.0*p.x+2.0*currentMinX-2.0*p.y*getDValue(currentMinX) +gedSquaredValueD(currentMinX);
var fxd = 2.0 -2.0*p.y*getDDValue(currentMinX)+gedSquaredValueDD(currentMinX);
if (Math.abs(fxd) < 0.0001) {
return currentMinX;
}
/* old iterative solution that had problems near the center*/
var lastx = -10000;
var x = p.x;
var i = 0;
while (Math.abs(lastx-x) > 1 && i < 100) {
// first derivate of the square of the distance function
var fx = -2.0*p.x+2.0*x-2.0*p.y*getDValue(x) +2*getValue(x)*getDValue(x);
var fxd = 2.0 -2.0*p.y*getDDValue(x)+2*(getDValue(x)*getDValue(x) + getValue(x)*getDDValue(x));
if (fxd == 0) {
console.log("wow!");
return x;
}
// x_{n+1} = x_n - f(x_n)/f'(x_n) wenn x gesucht, sodass f(x) = 0 gilt
currentMinX -= fx / fxd;
lastx = x;
x -= fx / fxd;
i++;
}
return currentMinX;
// New direct solution
/*var xs = -b / (2*a);
var w = p.y + b*b/(4*a)-c1;
var z = p.x + b / (2*a);
var alpha = (1-2*a*w)/(2*a*a);
var beta = -z/(2*a*a);
var t = Math.pow(Math.pow(3*(4*Math.pow(alpha,3) +27* Math.pow(beta,2)),1/2) - 9*beta, 1/3);
var currentMinX = t / (Math.pow(18, 1/3)) - Math.pow(2/3*alpha, 1/3) / t;
*/
return x;
}
function getDist(p, minX) {
@ -244,7 +262,7 @@ canvas.addEventListener('mousemove',
var x = r(mouseCoords.x, true).toFixed(3);
var y = r(mouseCoords.y, false).toFixed(3);
context.fillText("(" + x + ", " + y + ")", mouseCoords.x + 5, mouseCoords.y - 5);
var minX = findMin({"x":x, "y":y});
var minX = findMin({"x": mouseCoords.x, "y": mouseCoords.y});
var minY = getValue(minX);
context.beginPath();
context.moveTo(c(minX, true), c(minY, false), false);