【发布时间】：2015-07-28 17:14:29
【问题描述】：
我的 Java 类中有一个项目，但遇到了问题。 该项目基本上是在屏幕上标记坐标，用它们制作一个（复杂的）多项式，然后使用牛顿法使用随机猜测求解多项式，并在屏幕上绘制猜测的路径。 我对任何绘图、标记等都没有问题。 但由于某种原因，我的牛顿法算法随机漏了根。有时它没有击中它们，有时它错过了一两个。我已经改变了几个小时的东西，但我真的想不出一个解决方案。 当一个根丢失时，通常我在数组中得到的值要么收敛到无穷大或负无穷大（非常高的数字） 任何帮助将不胜感激。
> // Polynomial evaluation method.
public Complex evalPoly(Complex complexArray[], Complex guess) {
Complex result = new Complex(0, 0);
for (int i = 0; i < complexArray.length; i++) {
result = result.gaussMult(guess).addComplex(complexArray[complexArray.length - i - 1]);
}
return result;
}
> // Polynomial differentation method.
public Complex[] diff(Complex[] comp) {
Complex[] result = new Complex[comp.length - 1];
for (int j = 0; j < result.length; j++) {
result[j] = new Complex(0, 0);
}
for (int i = 0; i < result.length - 1; i++) {
result[i].real = comp[i + 1].real * (i + 1);
result[i].imaginary = comp[i + 1].imaginary * (i + 1);
}
return result;
}
> // Method which eliminates some of the things that I don't want to go into the array
public boolean rootCheck2(Complex[] comps, Complex comp) {
double accLim = 0.01;
if (comp.real == Double.NaN)
return false;
if (comp.real == Double.NEGATIVE_INFINITY || comp.real == Double.POSITIVE_INFINITY)
return false;
if (comp.imaginary == Double.NaN)
return false;
if (comp.imaginary == Double.NEGATIVE_INFINITY || comp.imaginary == Double.POSITIVE_INFINITY)
return false;
for (int i = 0; i < comps.length; i++) {
if (Math.abs(comp.real - comps[i].real) < accLim && Math.abs(comp.imaginary - comps[i].imaginary) < accLim)
return false;
}
return true;
}
> // Method which finds (or attempts) to find all of the roots
public Complex[] addUnique2(Complex[] poly, Bitmap bitmapx, Paint paint, Canvas canvasx) {
Complex[] rootsC = new Complex[poly.length - 1];
int iterCount = 0;
int iteLim = 20000;
for (int i = 0; i < rootsC.length; i++) {
rootsC[i] = new Complex(0, 0);
}
while (iterCount < iteLim && MainActivity.a < rootsC.length) {
double guess = -492 + 984 * rand.nextDouble();
double guess2 = -718 + 1436 * rand.nextDouble();
if (rootCheck2(rootsC, findRoot2(poly, new Complex(guess, guess2), bitmapx, paint, canvasx))) {
rootsC[MainActivity.a] = findRoot2(poly, new Complex(guess, guess2), bitmapx, paint, canvasx);
MainActivity.a = MainActivity.a + 1;
}
iterCount = iterCount + 1;
}
return rootsC;
}
> // Method which finds a single root of the complex polynomial.
public Complex findRoot2(Complex[] comp, Complex guess, Bitmap bitmapx, Paint paint, Canvas canvasx) {
int iterCount = 0;
double accLim = 0.001;
int itLim = 20000;
Complex[] diffedComplex = diff(comp);
while (Math.abs(evalPoly(comp, guess).real) >= accLim && Math.abs(evalPoly(comp, guess).imaginary) >= accLim) {
if (iterCount >= itLim) {
return new Complex(Double.NaN, Double.NaN);
}
if (evalPoly(diffedComplex, guess).real == 0 || evalPoly(diffedComplex, guess).imaginary == 0) {
return new Complex(Double.NaN, Double.NaN);
}
iterCount = iterCount + 1;
guess.real = guess.subtractComplex(evalPoly(comp, guess).divideComplex(evalPoly(diffedComplex, guess))).real;
guess.imaginary = guess.subtractComplex(evalPoly(comp, guess).divideComplex(evalPoly(diffedComplex, guess))).imaginary;
drawCircles((float) guess.real, (float) guess.imaginary, paint, canvasx, bitmapx);
}
return guess;
}
> // Drawing method
void drawCircles(float x, float y, Paint paint, Canvas canvasx, Bitmap bitmapx) {
canvasx.drawCircle(x + 492, shiftBackY(y), 5, paint);
coordPlane.setAdjustViewBounds(false);
coordPlane.setImageBitmap(bitmapx);
}
}
【问题讨论】：
-
应该注意
== Double.NaN总是假的。您应该使用Double.isNan(double)来查看值是否为 NaN。 -
所以它是在随机猜测，而你错过了根源？这并不奇怪。你在 x 处暗中试探。牛顿法的工作原理是查看一个产生正 y 的 x 和另一个产生负 y 的 x，然后对差进行二等分。
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@rajah9 这就是我们被教导的方式。同样的方法对正态多项式没有问题。随机猜测总是最终会收敛到一个根。我很难理解你所说的第二部分的意思，一个例子将不胜感激。
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@Obicere 注意，谢谢！
-
@rajah9：这就是二分法。虽然它像推土机一样坚固，但如果条件适用，它也一样慢。牛顿是法拉利，处理起来可能更精致，但速度也快了很多。 -- 此外，二分法并不容易应用于复平面上的函数。
标签： java newtons-method