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Statistical distributions library (in statu nascendi)
/*
* Class: RootFinder
* Description: Provides methods to solve non-linear equations.
* Environment: Java
* Software: SSJ
* Copyright (C) 2001 Pierre L'Ecuyer and Universite de Montreal
* Organization: DIRO, Universite de Montreal
*
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package math;
import math.function.DoubleUnaryOperator;
/**
* Provides methods to find the root of a non-linear equation.
*/
public final class RootFinder {
private static final boolean DEBUG = false;
/**
* Computes a root {@code x} of the function in {@code f} using the
* Brent-Dekker method. The interval {@code [a, b]} must contain the root
* {@code x}. The calculations are done with an approximate relative
* precision {@code tol}. Returns {@code x} such that {@code f(x) = 0}.
*
* @param a
* left endpoint of initial interval
* @param b
* right endpoint of initial interval
* @param f
* the function which is evaluated
* @param tol
* accuracy goal
* @return the root {@code x} such that {@code f(x) = 0}
*/
public static double brentDekker(double a, double b, DoubleUnaryOperator f, double tol) {
final int MAX_ITER = 150; // Max number of iterations
// special case a > b
if (b < a) {
double tmp = a;
a = b;
b = tmp;
}
if (tol < MathConsts.MIN_TOL) {
tol = MathConsts.MIN_TOL;
}
// initialization
double fa = f.applyAsDouble(a);
if (Math.abs(fa) <= MathConsts.MIN_VAL) {
return a;
}
double fb = f.applyAsDouble(b);
if (Math.abs(fb) <= MathConsts.MIN_VAL) {
return b;
}
double c = a;
double fc = fa;
double e = b - a;
double d = e;
if (Math.abs(fc) < Math.abs(fb)) {
a = b;
b = c;
c = a;
fa = fb;
fb = fc;
fc = fa;
}
int i;
for (i = 0; i < MAX_ITER; i++) {
double tol2 = tol + (4.0 * MathConsts.BIG_INV * Math.abs(b));
double xm = 0.5 * (c - b);
if (DEBUG) {
double err = Math.abs(fa - fb);
System.out.printf("[a, b] = [%g, %g] fa = %g, fb = %g |fa - fb| = %.2g%n", a, b, fa, fb, err);
}
if (Math.abs(fb) <= MathConsts.MIN_VAL) {
return b;
}
if (Math.abs(xm) <= tol2) {
if (Math.abs(b) > MathConsts.MIN_VAL) {
return b;
} else {
return 0.0;
}
}
if ((Math.abs(e) >= tol2) && (Math.abs(fa) > Math.abs(fb))) {
double s;
double p;
double q;
if (a != c) {
// inverse quadratic interpolation
q = fa / fc;
double r = fb / fc;
s = fb / fa;
p = s * (2.0 * xm * q * (q - r) - (b - a) * (r - 1.0));
q = (q - 1.0) * (r - 1.0) * (s - 1.0);
} else {
// linear interpolation
s = fb / fa;
p = 2.0 * xm * s;
q = 1.0 - s;
}
// adjust signs
if (p > 0.0) {
q = -q;
}
p = Math.abs(p);
// is interpolation acceptable?
if (((2.0 * p) >= (3.0 * xm * q - Math.abs(tol2 * q))) || (p >= Math.abs(0.5 * e * q))) {
d = xm;
e = d;
} else {
e = d;
d = p / q;
}
} else {
// bisection necessary
d = xm;
e = d;
}
a = b;
fa = fb;
if (Math.abs(d) > tol2) {
b += d;
} else if (xm < 0.0) {
b -= tol2;
} else {
b += tol2;
}
fb = f.applyAsDouble(b);
if (fb * Math.signum(fc) > 0.0) {
c = a;
fc = fa;
d = e = b - a;
} else {
a = b;
b = c;
c = a;
fa = fb;
fb = fc;
fc = fa;
}
}
if (i >= MAX_ITER) {
System.err.println("WARN: brentDekker root finding does not converge");
}
return b;
}
private RootFinder() {
throw new AssertionError();
}
}