Java Code Examples for org.apache.commons.math.exception.util.LocalizedFormats#FAILED_BRACKETING
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org.apache.commons.math.exception.util.LocalizedFormats#FAILED_BRACKETING .
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Example 1
| Source File: UnivariateRealSolverUtils.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* This method attempts to find two values a and b satisfying <ul>
* <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li>
* <li> <code> f(a) * f(b) <= 0 </code> </li>
* </ul>
* If f is continuous on <code>[a,b],</code> this means that <code>a</code>
* and <code>b</code> bracket a root of f.
* <p>
* The algorithm starts by setting
* <code>a := initial -1; b := initial +1,</code> examines the value of the
* function at <code>a</code> and <code>b</code> and keeps moving
* the endpoints out by one unit each time through a loop that terminates
* when one of the following happens: <ul>
* <li> <code> f(a) * f(b) <= 0 </code> -- success!</li>
* <li> <code> a = lower </code> and <code> b = upper</code>
* -- ConvergenceException </li>
* <li> <code> maximumIterations</code> iterations elapse
* -- ConvergenceException </li></ul></p>
*
* @param function Function.
* @param initial Initial midpoint of interval being expanded to
* bracket a root.
* @param lowerBound Lower bound (a is never lower than this value).
* @param upperBound Upper bound (b never is greater than this
* value).
* @param maximumIterations Maximum number of iterations to perform
* @return a two element array holding a and b.
* @throws NoBracketingException if the algorithm fails to find a and b
* satisfying the desired conditions.
* @throws IllegalArgumentException if function is null, maximumIterations
* is not positive, or initial is not between lowerBound and upperBound.
*/
public static double[] bracket(UnivariateRealFunction function,
double initial,
double lowerBound, double upperBound,
int maximumIterations) {
if (function == null) {
throw new NullArgumentException(LocalizedFormats.FUNCTION);
}
if (maximumIterations <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.INVALID_MAX_ITERATIONS, maximumIterations);
}
verifySequence(lowerBound, initial, upperBound);
double a = initial;
double b = initial;
double fa;
double fb;
int numIterations = 0;
do {
a = FastMath.max(a - 1.0, lowerBound);
b = FastMath.min(b + 1.0, upperBound);
fa = function.value(a);
fb = function.value(b);
++numIterations;
} while ((fa * fb > 0.0) && (numIterations < maximumIterations) &&
((a > lowerBound) || (b < upperBound)));
if (fa * fb > 0.0) {
throw new NoBracketingException(LocalizedFormats.FAILED_BRACKETING,
a, b, fa, fb,
numIterations, maximumIterations, initial,
lowerBound, upperBound);
}
return new double[] {a, b};
}
Example 2
| Source File: UnivariateRealSolverUtils.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* This method attempts to find two values a and b satisfying <ul>
* <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li>
* <li> <code> f(a) * f(b) <= 0 </code> </li>
* </ul>
* If f is continuous on <code>[a,b],</code> this means that <code>a</code>
* and <code>b</code> bracket a root of f.
* <p>
* The algorithm starts by setting
* <code>a := initial -1; b := initial +1,</code> examines the value of the
* function at <code>a</code> and <code>b</code> and keeps moving
* the endpoints out by one unit each time through a loop that terminates
* when one of the following happens: <ul>
* <li> <code> f(a) * f(b) <= 0 </code> -- success!</li>
* <li> <code> a = lower </code> and <code> b = upper</code>
* -- ConvergenceException </li>
* <li> <code> maximumIterations</code> iterations elapse
* -- ConvergenceException </li></ul></p>
*
* @param function Function.
* @param initial Initial midpoint of interval being expanded to
* bracket a root.
* @param lowerBound Lower bound (a is never lower than this value).
* @param upperBound Upper bound (b never is greater than this
* value).
* @param maximumIterations Maximum number of iterations to perform
* @return a two element array holding a and b.
* @throws NoBracketingException if the algorithm fails to find a and b
* satisfying the desired conditions.
* @throws IllegalArgumentException if function is null, maximumIterations
* is not positive, or initial is not between lowerBound and upperBound.
*/
public static double[] bracket(UnivariateRealFunction function,
double initial,
double lowerBound, double upperBound,
int maximumIterations) {
if (function == null) {
throw new NullArgumentException(LocalizedFormats.FUNCTION);
}
if (maximumIterations <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.INVALID_MAX_ITERATIONS, maximumIterations);
}
verifySequence(lowerBound, initial, upperBound);
double a = initial;
double b = initial;
double fa;
double fb;
int numIterations = 0;
do {
a = FastMath.max(a - 1.0, lowerBound);
b = FastMath.min(b + 1.0, upperBound);
fa = function.value(a);
fb = function.value(b);
++numIterations;
} while ((fa * fb > 0.0) && (numIterations < maximumIterations) &&
((a > lowerBound) || (b < upperBound)));
if (fa * fb > 0.0) {
throw new NoBracketingException(LocalizedFormats.FAILED_BRACKETING,
a, b, fa, fb,
numIterations, maximumIterations, initial,
lowerBound, upperBound);
}
return new double[] {a, b};
}
Example 3
| Source File: UnivariateRealSolverUtils.java From astor with GNU General Public License v2.0 | 5 votes |
|
/**
* This method attempts to find two values a and b satisfying <ul>
* <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li>
* <li> <code> f(a) * f(b) <= 0 </code> </li>
* </ul>
* If f is continuous on <code>[a,b],</code> this means that <code>a</code>
* and <code>b</code> bracket a root of f.
* <p>
* The algorithm starts by setting
* <code>a := initial -1; b := initial +1,</code> examines the value of the
* function at <code>a</code> and <code>b</code> and keeps moving
* the endpoints out by one unit each time through a loop that terminates
* when one of the following happens: <ul>
* <li> <code> f(a) * f(b) <= 0 </code> -- success!</li>
* <li> <code> a = lower </code> and <code> b = upper</code>
* -- ConvergenceException </li>
* <li> <code> maximumIterations</code> iterations elapse
* -- ConvergenceException </li></ul></p>
*
* @param function Function.
* @param initial Initial midpoint of interval being expanded to
* bracket a root.
* @param lowerBound Lower bound (a is never lower than this value).
* @param upperBound Upper bound (b never is greater than this
* value).
* @param maximumIterations Maximum number of iterations to perform
* @return a two element array holding a and b.
* @throws NoBracketingException if the algorithm fails to find a and b
* satisfying the desired conditions.
* @throws IllegalArgumentException if function is null, maximumIterations
* is not positive, or initial is not between lowerBound and upperBound.
*/
public static double[] bracket(UnivariateRealFunction function,
double initial,
double lowerBound, double upperBound,
int maximumIterations) {
if (function == null) {
throw new NullArgumentException(LocalizedFormats.FUNCTION);
}
if (maximumIterations <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.INVALID_MAX_ITERATIONS, maximumIterations);
}
verifySequence(lowerBound, initial, upperBound);
double a = initial;
double b = initial;
double fa;
double fb;
int numIterations = 0;
do {
a = FastMath.max(a - 1.0, lowerBound);
b = FastMath.min(b + 1.0, upperBound);
fa = function.value(a);
fb = function.value(b);
++numIterations;
} while ((fa * fb > 0.0) && (numIterations < maximumIterations) &&
((a > lowerBound) || (b < upperBound)));
if (fa * fb > 0.0) {
throw new NoBracketingException(LocalizedFormats.FAILED_BRACKETING,
a, b, fa, fb,
numIterations, maximumIterations, initial,
lowerBound, upperBound);
}
return new double[] {a, b};
}
Example 4
| Source File: UnivariateRealSolverUtils.java From astor with GNU General Public License v2.0 | 4 votes |
|
/**
* This method attempts to find two values a and b satisfying <ul>
* <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li>
* <li> <code> f(a) * f(b) <= 0 </code> </li>
* </ul>
* If f is continuous on <code>[a,b],</code> this means that <code>a</code>
* and <code>b</code> bracket a root of f.
* <p>
* The algorithm starts by setting
* <code>a := initial -1; b := initial +1,</code> examines the value of the
* function at <code>a</code> and <code>b</code> and keeps moving
* the endpoints out by one unit each time through a loop that terminates
* when one of the following happens: <ul>
* <li> <code> f(a) * f(b) <= 0 </code> -- success!</li>
* <li> <code> a = lower </code> and <code> b = upper</code>
* -- ConvergenceException </li>
* <li> <code> maximumIterations</code> iterations elapse
* -- ConvergenceException </li></ul></p>
*
* @param function the function
* @param initial initial midpoint of interval being expanded to
* bracket a root
* @param lowerBound lower bound (a is never lower than this value)
* @param upperBound upper bound (b never is greater than this
* value)
* @param maximumIterations maximum number of iterations to perform
* @return a two element array holding {a, b}.
* @throws ConvergenceException if the algorithm fails to find a and b
* satisfying the desired conditions
* @throws FunctionEvaluationException if an error occurs evaluating the
* function
* @throws IllegalArgumentException if function is null, maximumIterations
* is not positive, or initial is not between lowerBound and upperBound
*/
public static double[] bracket(UnivariateRealFunction function,
double initial, double lowerBound, double upperBound,
int maximumIterations) throws ConvergenceException,
FunctionEvaluationException {
if (function == null) {
throw new NullArgumentException(LocalizedFormats.FUNCTION);
}
if (maximumIterations <= 0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.INVALID_MAX_ITERATIONS, maximumIterations);
}
if (initial < lowerBound || initial > upperBound || lowerBound >= upperBound) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.INVALID_BRACKETING_PARAMETERS,
lowerBound, initial, upperBound);
}
double a = initial;
double b = initial;
double fa;
double fb;
int numIterations = 0 ;
do {
a = FastMath.max(a - 1.0, lowerBound);
b = FastMath.min(b + 1.0, upperBound);
fa = function.value(a);
fb = function.value(b);
numIterations++ ;
} while ((fa * fb > 0.0) && (numIterations < maximumIterations) &&
((a > lowerBound) || (b < upperBound)));
if (fa * fb > 0.0 ) {
throw new ConvergenceException(
LocalizedFormats.FAILED_BRACKETING,
numIterations, maximumIterations, initial,
lowerBound, upperBound, a, b, fa, fb);
}
return new double[]{a, b};
}
Example 5
| Source File: UnivariateRealSolverUtils.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** Force a root found by a non-bracketing solver to lie on a specified side,
* as if the solver was a bracketing one.
* @param maxEval maximal number of new evaluations of the function
* (evaluations already done for finding the root should have already been subtracted
* from this number)
* @param f function to solve
* @param bracketing bracketing solver to use for shifting the root
* @param baseRoot original root found by a previous non-bracketing solver
* @param min minimal bound of the search interval
* @param max maximal bound of the search interval
* @param allowedSolution the kind of solutions that the root-finding algorithm may
* accept as solutions.
* @return a root approximation, on the specified side of the exact root
*/
public static double forceSide(final int maxEval, final UnivariateRealFunction f,
final BracketedUnivariateRealSolver<UnivariateRealFunction> bracketing,
final double baseRoot, final double min, final double max,
final AllowedSolution allowedSolution) {
if (allowedSolution == AllowedSolution.ANY_SIDE) {
// no further bracketing required
return baseRoot;
}
// find a very small interval bracketing the root
final double step = FastMath.max(bracketing.getAbsoluteAccuracy(),
FastMath.abs(baseRoot * bracketing.getRelativeAccuracy()));
double xLo = FastMath.max(min, baseRoot - step);
double fLo = f.value(xLo);
double xHi = FastMath.min(max, baseRoot + step);
double fHi = f.value(xHi);
int remainingEval = maxEval - 2;
while (remainingEval > 0) {
if ((fLo >= 0 && fHi <= 0) || (fLo <= 0 && fHi >= 0)) {
// compute the root on the selected side
return bracketing.solve(remainingEval, f, xLo, xHi, baseRoot, allowedSolution);
}
// try increasing the interval
boolean changeLo = false;
boolean changeHi = false;
if (fLo < fHi) {
// increasing function
if (fLo >= 0) {
changeLo = true;
} else {
changeHi = true;
}
} else if (fLo > fHi) {
// decreasing function
if (fLo <= 0) {
changeLo = true;
} else {
changeHi = true;
}
} else {
// unknown variation
changeLo = true;
changeHi = true;
}
// update the lower bound
if (changeLo) {
xLo = FastMath.max(min, xLo - step);
fLo = f.value(xLo);
remainingEval--;
}
// update the higher bound
if (changeHi) {
xHi = FastMath.min(max, xHi + step);
fHi = f.value(xHi);
remainingEval--;
}
}
throw new NoBracketingException(LocalizedFormats.FAILED_BRACKETING,
xLo, xHi, fLo, fHi,
maxEval - remainingEval, maxEval, baseRoot,
min, max);
}
Example 6
| Source File: UnivariateRealSolverUtils.java From astor with GNU General Public License v2.0 | 4 votes |
|
/** Force a root found by a non-bracketing solver to lie on a specified side,
* as if the solver was a bracketing one.
* @param maxEval maximal number of new evaluations of the function
* (evaluations already done for finding the root should have already been subtracted
* from this number)
* @param f function to solve
* @param bracketing bracketing solver to use for shifting the root
* @param baseRoot original root found by a previous non-bracketing solver
* @param min minimal bound of the search interval
* @param max maximal bound of the search interval
* @param allowedSolution the kind of solutions that the root-finding algorithm may
* accept as solutions.
* @return a root approximation, on the specified side of the exact root
*/
public static double forceSide(final int maxEval, final UnivariateRealFunction f,
final BracketedUnivariateRealSolver<UnivariateRealFunction> bracketing,
final double baseRoot, final double min, final double max,
final AllowedSolution allowedSolution) {
if (allowedSolution == AllowedSolution.ANY_SIDE) {
// no further bracketing required
return baseRoot;
}
// find a very small interval bracketing the root
final double step = FastMath.max(bracketing.getAbsoluteAccuracy(),
FastMath.abs(baseRoot * bracketing.getRelativeAccuracy()));
double xLo = FastMath.max(min, baseRoot - step);
double fLo = f.value(xLo);
double xHi = FastMath.min(max, baseRoot + step);
double fHi = f.value(xHi);
int remainingEval = maxEval - 2;
while (remainingEval > 0) {
if ((fLo >= 0 && fHi <= 0) || (fLo <= 0 && fHi >= 0)) {
// compute the root on the selected side
return bracketing.solve(remainingEval, f, xLo, xHi, baseRoot, allowedSolution);
}
// try increasing the interval
boolean changeLo = false;
boolean changeHi = false;
if (fLo < fHi) {
// increasing function
if (fLo >= 0) {
changeLo = true;
} else {
changeHi = true;
}
} else if (fLo > fHi) {
// decreasing function
if (fLo <= 0) {
changeLo = true;
} else {
changeHi = true;
}
} else {
// unknown variation
changeLo = true;
changeHi = true;
}
// update the lower bound
if (changeLo) {
xLo = FastMath.max(min, xLo - step);
fLo = f.value(xLo);
remainingEval--;
}
// update the higher bound
if (changeHi) {
xHi = FastMath.min(max, xHi + step);
fHi = f.value(xHi);
remainingEval--;
}
}
throw new NoBracketingException(LocalizedFormats.FAILED_BRACKETING,
xLo, xHi, fLo, fHi,
maxEval - remainingEval, maxEval, baseRoot,
min, max);
}
