mdiggory 2003/07/05 11:05:02
Modified: math/src/java/org/apache/commons/math/analysis
RootFinding.java BrentSolver.java
UnivariateRealSolverImpl.java
UnivariateRealSolver.java SecantSolver.java
Added: math/src/java/org/apache/commons/math/analysis
BisectionSolver.java
Log:
PR: http://nagoya.apache.org/bugzilla/show_bug.cgi?id=21313
Submitted by: [EMAIL PROTECTED]
Revision Changes Path
1.2 +18 -51
jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/RootFinding.java
Index: RootFinding.java
===================================================================
RCS file:
/home/cvs/jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/RootFinding.java,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -r1.1 -r1.2
--- RootFinding.java 22 Jun 2003 03:57:53 -0000 1.1
+++ RootFinding.java 5 Jul 2003 18:05:02 -0000 1.2
@@ -53,6 +53,8 @@
*/
package org.apache.commons.math.analysis;
+import org.apache.commons.math.MathException;
+
/**
* Utility class comprised of root finding techniques.
*
@@ -77,14 +79,17 @@
* @param function the function
* @param initial midpoint of the returned range.
* @param lowerBound for numerical safety, a never is less than this value.
- * @param upperBound for numerical safety, b never is greater than this value.
+ * @param upperBound for numerical safety, b never is greater than this
+ * value.
* @return a two element array holding {a, b}.
+ * @throws MathException if a root can not be bracketted.
*/
- public static double[] bracket(UnivariateFunction function,
+ public static double[] bracket(UnivariateRealFunction function,
double initial,
double lowerBound,
- double upperBound) {
- return bracket( function, initial, lowerBound, upperBound,
Integer.MAX_VALUE ) ;
+ double upperBound) throws MathException {
+ return bracket( function, initial, lowerBound, upperBound,
+ Integer.MAX_VALUE ) ;
}
/**
@@ -95,15 +100,18 @@
* @param function the function
* @param initial midpoint of the returned range.
* @param lowerBound for numerical safety, a never is less than this value.
- * @param upperBound for numerical safety, b never is greater than this value.
- * @param maximumIterations to guard against infinite looping, maximum number
of iterations to perform
+ * @param upperBound for numerical safety, b never is greater than this
+ * value.
+ * @param maximumIterations to guard against infinite looping, maximum
+ * number of iterations to perform
* @return a two element array holding {a, b}.
+ * @throws MathException if a root can not be bracketted.
*/
- public static double[] bracket(UnivariateFunction function,
+ public static double[] bracket(UnivariateRealFunction function,
double initial,
double lowerBound,
double upperBound,
- int maximumIterations) {
+ int maximumIterations) throws MathException {
double a = initial;
double b = initial;
double fa;
@@ -113,52 +121,11 @@
do {
a = Math.max(a - 1.0, lowerBound);
b = Math.min(b + 1.0, upperBound);
- fa = function.evaluate(a);
- fb = function.evaluate(b);
+ fa = function.value(a);
+ fb = function.value(b);
numIterations += 1 ;
} while ( (fa * fb > 0.0) && ( numIterations < maximumIterations ) );
return new double[]{a, b};
- }
-
- /**
- * For a function, f, this method returns a root c that lies between a and
- * b, and satisfies f(c) = 0.
- *
- * @param function the function
- * @param a lower (or upper) bound of a root
- * @param b upper (or lower) bound of a root
- * @return a root of f
- */
- public static double bisection(UnivariateFunction function,
- double a,
- double b) {
- double m;
- double fm;
- double fa;
-
- if ( b < a ) {
- double xtemp = a ;
- a = b ;
- b = xtemp ;
- }
-
- fa = function.evaluate(a);
-
- while(Math.abs(a - b) > EPSILON) {
- m = (a + b) * 0.5; // midpoint
- fm = function.evaluate(m);
-
- if(fm * fa > 0.0) {
- // b and m bracket the root.
- a = m;
- fa = fm;
- } else {
- // a and m bracket the root.
- b = m;
- }
- }
-
- return (a + b) * 0.5;
}
}
1.2 +29 -28
jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/BrentSolver.java
Index: BrentSolver.java
===================================================================
RCS file:
/home/cvs/jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/BrentSolver.java,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -r1.1 -r1.2
--- BrentSolver.java 24 Jun 2003 03:01:40 -0000 1.1
+++ BrentSolver.java 5 Jul 2003 18:05:02 -0000 1.2
@@ -64,16 +64,36 @@
* @author pietsch at apache.org
*/
public class BrentSolver extends UnivariateRealSolverImpl {
-
- private UnivariateRealFunction f;
-
+ /**
+ * Construct a solver for the given function.
+ * @param f function to solve.
+ */
public BrentSolver(UnivariateRealFunction f) {
- super(100, 1E-6);
- this.f = f;
+ super(f, 100, 1E-6);
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#solve(double, double)
+ /**
+ * Solve for a zero in the given interval.
+ * @param min the lower bound for the interval.
+ * @param max the upper bound for the interval.
+ * @param initial the start value to use (ignored).
+ * @return the value where the function is zero
+ * @throws MathException if the iteration count was exceeded or the
+ * solver detects convergence problems otherwise.
+ */
+ public double solve(double min, double max, double initial)
+ throws MathException {
+
+ return solve(min, max);
+ }
+
+ /**
+ * Solve for a zero root in the given interval.
+ * @param min the lower bound for the interval.
+ * @param max the upper bound for the interval.
+ * @return the value where the function is zero
+ * @throws MathException if the iteration count was exceeded or the
+ * solver detects convergence problems otherwise.
*/
public double solve(double min, double max) throws MathException {
clearResult();
@@ -116,21 +136,8 @@
setResult(x1, i);
return result;
}
-// System.out.println(
-// " x0="
-// + x0
-// + " y0="
-// + y0
-// + " x1="
-// + x1
-// + " y1="
-// + y1
-// + " x2="
-// + x2+" y2="+y2);
-// System.out.println(" dx="+dx+" delta: "+delta+" olddelta:
"+oldDelta);
if (Math.abs(oldDelta) < tolerance
|| Math.abs(y0) <= Math.abs(y1)) {
-// System.out.println("bisection");
// Force bisection.
delta = 0.5 * dx;
oldDelta = delta;
@@ -140,12 +147,10 @@
double p1;
if (x0 == x2) {
// Linear interpolation.
-// System.out.println("linear");
p = dx * r3;
p1 = 1.0 - r3;
} else {
// Inverse quadratic interpolation.
-// System.out.println("invers quad");
double r1 = y0 / y2;
double r2 = y1 / y2;
p = r3 * (dx * r1 * (r1 - r2) - (x1 - x0) * (r2 - 1.0));
@@ -156,14 +161,11 @@
} else {
p = -p;
}
-// System.out.println(" p="+p+" p1="+p1+" qq: "+(1.5 * dx * p1 -
Math.abs(tolerance * p1)));
-// System.out.println(" p="+p+" q: "+p1+" ad="+Math.abs(0.5 *
oldDelta * p1));
if (2.0 * p >= 1.5 * dx * p1 - Math.abs(tolerance * p1)
|| p >= Math.abs(0.5 * oldDelta * p1)) {
// Inverse quadratic interpolation gives a value
// in the wrong direction, or progress is slow.
// Fall back to bisection.
-// System.out.println("bisection fallback");
delta = 0.5 * dx;
oldDelta = delta;
} else {
@@ -178,9 +180,9 @@
if (Math.abs(delta) > tolerance) {
x1 = x1 + delta;
} else if (dx > 0.0) {
- x1 = x1 + 0.5*tolerance;
+ x1 = x1 + 0.5 * tolerance;
} else if (dx <= 0.0) {
- x1 = x1 - 0.5*tolerance;
+ x1 = x1 - 0.5 * tolerance;
}
y1 = f.value(x1);
if ((y1 > 0) == (y2 > 0)) {
@@ -193,5 +195,4 @@
}
throw new MathException("Maximal iteration number exceeded.");
}
-
}
1.2 +91 -48
jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/UnivariateRealSolverImpl.java
Index: UnivariateRealSolverImpl.java
===================================================================
RCS file:
/home/cvs/jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/UnivariateRealSolverImpl.java,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -r1.1 -r1.2
--- UnivariateRealSolverImpl.java 24 Jun 2003 03:01:40 -0000 1.1
+++ UnivariateRealSolverImpl.java 5 Jul 2003 18:05:02 -0000 1.2
@@ -65,24 +65,57 @@
public abstract class UnivariateRealSolverImpl
implements UnivariateRealSolver {
+ /** Maximum absolute error. */
protected double absoluteAccuracy;
+
+ /** Maximum relative error. */
protected double relativeAccuracy;
+
+ /** Maximum error of function. */
protected double functionValueAccuracy;
+
+ /** Maximum number of iterations. */
protected int maximalIterationCount;
+ /** Default maximum absolute error. */
protected double defaultAbsoluteAccuracy;
+
+ /** Default maximum relative error. */
protected double defaultRelativeAccuracy;
+
+ /** Default maximum error of function. */
protected double defaultFunctionValueAccuracy;
+
+ /** Default maximum number of iterations. */
protected int defaultMaximalIterationCount;
+ /** Indicates where a root has been computed. */
protected boolean resultComputed = false;
+
+ /** The last computed root. */
protected double result;
+
// Mainly for test framework.
+ /** The last iteration count. */
protected int iterationCount;
+ /** The function to solve. */
+ protected UnivariateRealFunction f;
+
+ /**
+ * Construct a solver with given iteration count and accuracy.
+ * @param f the function to solve.
+ * @param defaultAbsoluteAccuracy maximum absolue error.
+ * @param defaultMaximalIterationCount maximum number of iterations.
+ */
protected UnivariateRealSolverImpl(
+ UnivariateRealFunction f,
int defaultMaximalIterationCount,
double defaultAbsoluteAccuracy) {
+
+ super();
+
+ this.f = f;
this.defaultAbsoluteAccuracy = defaultAbsoluteAccuracy;
this.defaultRelativeAccuracy = 1E-14;
this.defaultFunctionValueAccuracy = 1E-15;
@@ -93,48 +126,39 @@
this.maximalIterationCount = defaultMaximalIterationCount;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#solve(double, double)
- */
- public double solve(double min, double max) throws MathException {
- throw new UnsupportedOperationException();
- }
-
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#solve(double, double,
double)
- */
- public double solve(double min, double max, double startValue)
- throws MathException {
- throw new UnsupportedOperationException();
- }
-
- /*
- * Get result of last solver run.
- * @see org.apache.commons.math.UnivariateRealSolver#getResult()
+ /**
+ * Access the last computed root.
+ * @return the last computed root.
+ * @throws MathException if no root has been computed.
*/
public double getResult() throws MathException {
if (resultComputed) {
return result;
} else {
+ // TODO: could this be an IllegalStateException instead?
throw new MathException("No result available");
}
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#getIterationCount()
+ /**
+ * Access the last iteration count.
+ * @return the last iteration count.
+ * @throws MathException if no root has been computed.
+ *
*/
public int getIterationCount() throws MathException {
if (resultComputed) {
return iterationCount;
} else {
+ // TODO: could this be an IllegalStateException instead?
throw new MathException("No result available");
}
}
- /*
+ /**
* Convenience function for implementations.
* @param result the result to set
- * @param iteratinCount the iteration count to set
+ * @param iterationCount the iteration count to set
*/
protected final void setResult(double result, int iterationCount) {
this.result = result;
@@ -142,97 +166,116 @@
this.resultComputed = true;
}
- /*
+ /**
* Convenience function for implementations.
*/
protected final void clearResult() {
this.resultComputed = false;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#setAccuracy(double)
+ /**
+ * Set the absolute accuracy.
+ *
+ * @param accuracy the accuracy.
+ * @throws MathException if the accuracy can't be achieved by the solver or
+ * is otherwise deemed unreasonable.
*/
public void setAbsoluteAccuracy(double accuracy)
throws MathException {
absoluteAccuracy = accuracy;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#getAccuracy()
+ /**
+ * Get the actual absolute accuracy.
+ *
+ * @return the accuracy
*/
public double getAbsoluteAccuracy() {
return absoluteAccuracy;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#resetAbsoluteAccuracy()
+ /**
+ * Reset the absolute accuracy to the default.
*/
public void resetAbsoluteAccuracy() {
absoluteAccuracy = defaultAbsoluteAccuracy;
}
- /* Set maximum iteration count.
- * @see
org.apache.commons.math.UnivariateRealSolver#setMaximalIterationCount(int)
+ /**
+ * Set the upper limit for the number of iterations.
+ *
+ * @param count maximum number of iterations
*/
public void setMaximalIterationCount(int count) {
maximalIterationCount = count;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#getMaximalIterationCount()
+ /**
+ * Get the upper limit for the number of iterations.
+ *
+ * @return the actual upper limit
*/
public int getMaximalIterationCount() {
return maximalIterationCount;
}
- /* (non-Javadoc)
- * @see
org.apache.commons.math.UnivariateRealSolver#resetMaximalIterationCount()
+ /**
+ * Reset the upper limit for the number of iterations to the default.
*/
public void resetMaximalIterationCount() {
maximalIterationCount = defaultMaximalIterationCount;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#setRelativeAccuracy(double)
+ /**
+ * Set the relative accuracy.
+ *
+ * @param accuracy the relative accuracy.
+ * @throws MathException if the accuracy can't be achieved by the solver or
+ * is otherwise deemed unreasonable.
*/
public void setRelativeAccuracy(double accuracy) throws MathException {
relativeAccuracy = accuracy;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#getRelativeAccuracy()
+ /**
+ * Get the actual relative accuracy.
+ * @return the accuracy
*/
public double getRelativeAccuracy() {
return relativeAccuracy;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#resetRelativeAccuracy()
+ /**
+ * Reset the relative accuracy to the default.
*/
public void resetRelativeAccuracy() {
relativeAccuracy = defaultRelativeAccuracy;
}
- /* (non-Javadoc)
- * @see
org.apache.commons.math.UnivariateRealSolver#setFunctionValueAccuracy(double)
+ /**
+ * Set the function value accuracy.
+ *
+ * @param accuracy the accuracy.
+ * @throws MathException if the accuracy can't be achieved by the solver or
+ * is otherwise deemed unreasonable.
*/
public void setFunctionValueAccuracy(double accuracy)
throws MathException {
functionValueAccuracy = accuracy;
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#getFunctionValueAccuracy()
+ /**
+ * Get the actual function value accuracy.
+ * @return the accuracy
*/
public double getFunctionValueAccuracy() {
return functionValueAccuracy;
}
- /* (non-Javadoc)
- * @see
org.apache.commons.math.UnivariateRealSolver#resetFunctionValueAccuracy()
+ /**
+ * Reset the actual function accuracy to the default.
*/
public void resetFunctionValueAccuracy() {
functionValueAccuracy = defaultFunctionValueAccuracy;
}
-
}
1.2 +37 -20
jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/UnivariateRealSolver.java
Index: UnivariateRealSolver.java
===================================================================
RCS file:
/home/cvs/jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/UnivariateRealSolver.java,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -r1.1 -r1.2
--- UnivariateRealSolver.java 24 Jun 2003 03:01:40 -0000 1.1
+++ UnivariateRealSolver.java 5 Jul 2003 18:05:02 -0000 1.2
@@ -66,23 +66,27 @@
/**
* Set the upper limit for the number of iterations.
+ *
* Usually a high iteration count indicates convergence problems. However,
* the "reasonable value" varies widely for different solvers, users are
- * advised to use the default value supplied by the solver.
+ * advised to use the default value supplied by the solver.
+ *
* An exception will be thrown if the number is exceeded.
*
- * @param count
+ * @param count maximum number of iterations
*/
public void setMaximalIterationCount(int count);
/**
* Get the upper limit for the number of iterations.
+ *
* @return the actual upper limit
*/
public int getMaximalIterationCount();
/**
* Reset the upper limit for the number of iterations to the default.
+ *
* The default value is supplied by the solver implementation.
*
* @see #setMaximalIterationCount(int)
@@ -91,41 +95,50 @@
/**
* Set the absolute accuracy.
+ *
* The default is usually choosen so taht roots in the interval
- * -10..-0.1 and +0.1..+10 can be found wit a reasonable accuracy. If the
expected
- * absolute value of your roots is of much smaller magnitude, set this to a
smaller
- * value.
- * Solvers are advised to do a plausibility check with the relative accuracy,
but
- * clients should not rely on this.
+ * -10..-0.1 and +0.1..+10 can be found wit a reasonable accuracy. If the
+ * expected absolute value of your roots is of much smaller magnitude, set
+ * this to a smaller value.
+ *
+ * Solvers are advised to do a plausibility check with the relative
+ * accuracy, but clients should not rely on this.
+ *
* @param accuracy the accuracy.
- * @throws MathException if the accuracy can't be achieved by the solver or is
- * otherwise deemed unreasonable.
+ * @throws MathException if the accuracy can't be achieved by the solver or
+ * is otherwise deemed unreasonable.
*/
public void setAbsoluteAccuracy(double accuracy) throws MathException;
/**
* Get the actual absolute accuracy.
+ *
* @return the accuracy
*/
public double getAbsoluteAccuracy();
/**
* Reset the absolute accuracy to the default.
+ *
* The default value is provided by the solver implementation.
*/
public void resetAbsoluteAccuracy();
/**
* Set the relative accuracy.
- * This is used to stop iterations if the absolute accuracy can't be achieved
- * due to large values or short mantissa length.
- * If this should be the primary criterium for convergence rather then a safety
- * measure, set the absolute accuracy to a ridiculously small value, like
1E-1000.
+ *
+ * This is used to stop iterations if the absolute accuracy can't be
+ * achieved due to large values or short mantissa length.
+ *
+ * If this should be the primary criterium for convergence rather then a
+ * safety measure, set the absolute accuracy to a ridiculously small value,
+ * like 1E-1000.
+ *
* @param accuracy the relative accuracy.
- * @throws MathException if the accuracy can't be achieved by the solver or is
- * otherwise deemed unreasonable.
+ * @throws MathException if the accuracy can't be achieved by the solver or
+ * is otherwise deemed unreasonable.
*/
- public void setRelativeAccuracy(double Accuracy) throws MathException;
+ public void setRelativeAccuracy(double accuracy) throws MathException;
/**
* Get the actual relative accuracy.
@@ -141,14 +154,18 @@
/**
* Set the function value accuracy.
+ *
* This is used to determine whan an evaluated function value or some other
* value which is used as divisor is zero.
- * This is a safety guard and it shouldn't be necesary to change this in
general.
+ *
+ * This is a safety guard and it shouldn't be necesary to change this in
+ * general.
+ *
* @param accuracy the accuracy.
- * @throws MathException if the accuracy can't be achieved by the solver or is
- * otherwise deemed unreasonable.
+ * @throws MathException if the accuracy can't be achieved by the solver or
+ * is otherwise deemed unreasonable.
*/
- public void setFunctionValueAccuracy(double Accuracy) throws MathException;
+ public void setFunctionValueAccuracy(double accuracy) throws MathException;
/**
* Get the actual function value accuracy.
1.2 +31 -13
jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/SecantSolver.java
Index: SecantSolver.java
===================================================================
RCS file:
/home/cvs/jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/SecantSolver.java,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -r1.1 -r1.2
--- SecantSolver.java 24 Jun 2003 03:01:40 -0000 1.1
+++ SecantSolver.java 5 Jul 2003 18:05:02 -0000 1.2
@@ -66,16 +66,36 @@
* @author pietsch at apache.org
*/
public class SecantSolver extends UnivariateRealSolverImpl {
-
- private UnivariateRealFunction f;
-
+ /**
+ * Construct a solver for the given function.
+ * @param f function to solve.
+ */
public SecantSolver(UnivariateRealFunction f) {
- super(100, 1E-6);
- this.f = f;
+ super(f, 100, 1E-6);
}
- /* (non-Javadoc)
- * @see org.apache.commons.math.UnivariateRealSolver#solve(double, double)
+ /**
+ * Solve for a zero in the given interval.
+ * @param min the lower bound for the interval.
+ * @param max the upper bound for the interval.
+ * @param initial the start value to use (ignored).
+ * @return the value where the function is zero
+ * @throws MathException if the iteration count was exceeded or the
+ * solver detects convergence problems otherwise.
+ */
+ public double solve(double min, double max, double initial)
+ throws MathException {
+
+ return solve(min, max);
+ }
+
+ /**
+ * Solve for a zero root in the given interval.
+ * @param min the lower bound for the interval.
+ * @param max the upper bound for the interval.
+ * @return the value where the function is zero
+ * @throws MathException if the iteration count was exceeded or the
+ * solver detects convergence problems otherwise.
*/
public double solve(double min, double max) throws MathException {
clearResult();
@@ -88,7 +108,7 @@
double x1 = max;
double y0 = f.value(x0);
double y1 = f.value(x1);
- if ((y0>0)== (y1>0)) {
+ if ((y0 > 0) == (y1 > 0)) {
throw new MathException("Interval doesn't bracket a zero.");
}
double x2 = x0;
@@ -117,21 +137,19 @@
if (Math.abs(y1) > Math.abs(y0)) {
// Function value increased in last iteration. Force bisection.
delta = 0.5 * oldDelta;
-// System.out.println("Forced Bisection");
} else {
delta = (x0 - x1) / (1 - y0 / y1);
- // System.out.println("delta=" + delta + " olddelta=" + oldDelta);
if (delta / oldDelta > 1) {
- // New approximation falls outside bracket. Fall back to
bisection.
+ // New approximation falls outside bracket.
+ // Fall back to bisection.
delta = 0.5 * oldDelta;
-// System.out.println("Fallback Bisection");
}
}
x0 = x1;
y0 = y1;
x1 = x1 + delta;
y1 = f.value(x1);
- if ((y1>0) == (y2>0)) {
+ if ((y1 > 0) == (y2 > 0)) {
// New bracket is (x0,x1).
x2 = x0;
y2 = y0;
1.1
jakarta-commons-sandbox/math/src/java/org/apache/commons/math/analysis/BisectionSolver.java
Index: BisectionSolver.java
===================================================================
/* ====================================================================
* The Apache Software License, Version 1.1
*
* Copyright (c) 2003 The Apache Software Foundation. All rights
* reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. The end-user documentation included with the redistribution, if
* any, must include the following acknowlegement:
* "This product includes software developed by the
* Apache Software Foundation (http://www.apache.org/)."
* Alternately, this acknowlegement may appear in the software itself,
* if and wherever such third-party acknowlegements normally appear.
*
* 4. The names "The Jakarta Project", "Commons", and "Apache Software
* Foundation" must not be used to endorse or promote products derived
* from this software without prior written permission. For written
* permission, please contact [EMAIL PROTECTED]
*
* 5. Products derived from this software may not be called "Apache"
* nor may "Apache" appear in their names without prior written
* permission of the Apache Software Foundation.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
* ====================================================================
*
* This software consists of voluntary contributions made by many
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*/
package org.apache.commons.math.analysis;
import org.apache.commons.math.MathException;
/**
* Provide the bisection algorithm for solving for zeros of real univariate
* functions. It will only search for one zero in the given interval. The
* function is supposed to be continuous but not necessarily smooth.
*
* @author Brent Worden
*/
public class BisectionSolver extends UnivariateRealSolverImpl {
/**
* Construct a solver for the given function.
* @param f function to solve.
*/
public BisectionSolver(UnivariateRealFunction f) {
super(f, 100, 1E-6);
}
/**
* Solve for a zero in the given interval.
* @param min the lower bound for the interval.
* @param max the upper bound for the interval.
* @param initial the start value to use (ignored).
* @return the value where the function is zero
* @throws MathException if the iteration count was exceeded or the
* solver detects convergence problems otherwise.
*/
public double solve(double min, double max, double initial)
throws MathException {
return solve(min, max);
}
/**
* Solve for a zero root in the given interval.
* @param min the lower bound for the interval.
* @param max the upper bound for the interval.
* @return the value where the function is zero
* @throws MathException if the iteration count was exceeded or the
* solver detects convergence problems otherwise.
*/
public double solve(double min, double max) throws MathException {
clearResult();
double m;
double fm;
double fmin;
int i = 0;
while (i < maximalIterationCount) {
m = midpoint(min, max);
fmin = f.value(min);
fm = f.value(m);
if (fm * fmin > 0.0) {
// max and m bracket the root.
min = m;
fmin = fm;
} else {
// min and m bracket the root.
max = m;
}
if (Math.abs(max - min) <= absoluteAccuracy) {
m = midpoint(min, max);
setResult(m, i);
return m;
}
++i;
}
throw new MathException("Maximal iteration number exceeded");
}
/**
* Compute the midpoint of two values.
* @param a first value.
* @param b second value.
* @return the midpoint.
*/
public static double midpoint(double a, double b) {
return (a + b) * .5;
}
}
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