import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類

/**

* {@inheritDoc}

*/

@Override

protected double doSolve()

throws TooManyEvaluationsException,

NoBracketingException {

double min = getMin();

double max = getMax();

// [x1, x2] is the bracketing interval in each iteration

// x3 is the midpoint of [x1, x2]

// x is the new root approximation and an endpoint of the new interval

double x1 = min;

double y1 = computeObjectiveValue(x1);

double x2 = max;

double y2 = computeObjectiveValue(x2);

// check for zeros before verifying bracketing

if (y1 == 0) {

return min;

}

if (y2 == 0) {

return max;

}

verifyBracketing(min, max);

final double absoluteAccuracy = getAbsoluteAccuracy();

final double functionValueAccuracy = getFunctionValueAccuracy();

final double relativeAccuracy = getRelativeAccuracy();

double oldx = Double.POSITIVE_INFINITY;

while (true) {

// calculate the new root approximation

final double x3 = 0.5 * (x1 + x2);

final double y3 = computeObjectiveValue(x3);

if (FastMath.abs(y3) <= functionValueAccuracy) {

return x3;

}

final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing

final double correction = (FastMath.signum(y2) * FastMath.signum(y3)) *

(x3 - x1) / FastMath.sqrt(delta);

final double x = x3 - correction; // correction != 0

final double y = computeObjectiveValue(x);

// check for convergence

final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy);

if (FastMath.abs(x - oldx) <= tolerance) {

return x;

}

if (FastMath.abs(y) <= functionValueAccuracy) {

return x;

}

// prepare the new interval for next iteration

// Ridders' method guarantees x1 < x < x2

if (correction > 0.0) { // x1 < x < x3

if (FastMath.signum(y1) + FastMath.signum(y) == 0.0) {

x2 = x;

y2 = y;

} else {

x1 = x;

x2 = x3;

y1 = y;

y2 = y3;

}

} else { // x3 < x < x2

if (FastMath.signum(y2) + FastMath.signum(y) == 0.0) {

x1 = x;

y1 = y;

} else {

x1 = x3;

x2 = x;

y1 = y3;

y2 = y;

}

}

oldx = x;

}

}