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| <div class="subTitle">org.apache.commons.math3.analysis.solvers</div> |
| <h2 title="Class UnivariateSolverUtils" class="title">Class UnivariateSolverUtils</h2> |
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| <pre>public class <span class="strong">UnivariateSolverUtils</span> |
| extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre> |
| <div class="block">Utility routines for <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers"><code>UnivariateSolver</code></a> objects.</div> |
| <dl><dt><span class="strong">Version:</span></dt> |
| <dd>$Id: UnivariateSolverUtils.java 1579346 2014-03-19 18:43:39Z erans $</dd></dl> |
| </li> |
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| <h3>Method Summary</h3> |
| <table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation"> |
| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Method and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double)">bracket</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double initial, |
| double lowerBound, |
| double upperBound)</code> |
| <div class="block">This method simply calls <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, double, double, int)"><code>bracket(function, initial, lowerBound, upperBound, q, r, maximumIterations)</code></a> |
| with <code>q</code> and <code>r</code> set to 1.0 and <code>maximumIterations</code> set to <code>Integer.MAX_VALUE</code>.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, double, double, int)">bracket</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double initial, |
| double lowerBound, |
| double upperBound, |
| double q, |
| double r, |
| int maximumIterations)</code> |
| <div class="block">This method attempts to find two values a and b satisfying |
| <code>lowerBound <= a < initial < b <= upperBound</code> |
| <code>f(a) * f(b) <= 0</code> |
| |
| If <code>f</code> is continuous on <code>[a,b]</code>, this means that <code>a</code> |
| and <code>b</code> bracket a root of <code>f</code>.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, int)">bracket</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double initial, |
| double lowerBound, |
| double upperBound, |
| int maximumIterations)</code> |
| <div class="block">This method simply calls <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, double, double, int)"><code>bracket(function, initial, lowerBound, upperBound, q, r, maximumIterations)</code></a> |
| with <code>q</code> and <code>r</code> set to 1.0.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#forceSide(int, org.apache.commons.math3.analysis.UnivariateFunction, org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver, double, double, double, org.apache.commons.math3.analysis.solvers.AllowedSolution)">forceSide</a></strong>(int maxEval, |
| <a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> f, |
| <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedUnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">BracketedUnivariateSolver</a><<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a>> bracketing, |
| double baseRoot, |
| double min, |
| double max, |
| <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html" title="enum in org.apache.commons.math3.analysis.solvers">AllowedSolution</a> allowedSolution)</code> |
| <div class="block">Force a root found by a non-bracketing solver to lie on a specified side, |
| as if the solver was a bracketing one.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#isBracketing(org.apache.commons.math3.analysis.UnivariateFunction, double, double)">isBracketing</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double lower, |
| double upper)</code> |
| <div class="block">Check whether the interval bounds bracket a root.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#isSequence(double, double, double)">isSequence</a></strong>(double start, |
| double mid, |
| double end)</code> |
| <div class="block">Check whether the arguments form a (strictly) increasing sequence.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#midpoint(double, double)">midpoint</a></strong>(double a, |
| double b)</code> |
| <div class="block">Compute the midpoint of two values.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#solve(org.apache.commons.math3.analysis.UnivariateFunction, double, double)">solve</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double x0, |
| double x1)</code> |
| <div class="block">Convenience method to find a zero of a univariate real function.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#solve(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double)">solve</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double x0, |
| double x1, |
| double absoluteAccuracy)</code> |
| <div class="block">Convenience method to find a zero of a univariate real function.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#verifyBracketing(org.apache.commons.math3.analysis.UnivariateFunction, double, double)">verifyBracketing</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double lower, |
| double upper)</code> |
| <div class="block">Check that the endpoints specify an interval and the end points |
| bracket a root.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#verifyInterval(double, double)">verifyInterval</a></strong>(double lower, |
| double upper)</code> |
| <div class="block">Check that the endpoints specify an interval.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#verifySequence(double, double, double)">verifySequence</a></strong>(double lower, |
| double initial, |
| double upper)</code> |
| <div class="block">Check that <code>lower < initial < upper</code>.</div> |
| </td> |
| </tr> |
| </table> |
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| <h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3> |
| <code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
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| <!-- ============ METHOD DETAIL ========== --> |
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| </a> |
| <h3>Method Detail</h3> |
| <a name="solve(org.apache.commons.math3.analysis.UnivariateFunction, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>solve</h4> |
| <pre>public static double solve(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double x0, |
| double x1) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre> |
| <div class="block">Convenience method to find a zero of a univariate real function. A default |
| solver is used.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - Function.</dd><dd><code>x0</code> - Lower bound for the interval.</dd><dd><code>x1</code> - Upper bound for the interval.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a value where the function is zero.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the function has the same sign at the |
| endpoints.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>function</code> is <code>null</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="solve(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double)"> |
| <!-- --> |
| </a> |
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| <h4>solve</h4> |
| <pre>public static double solve(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double x0, |
| double x1, |
| double absoluteAccuracy) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre> |
| <div class="block">Convenience method to find a zero of a univariate real function. A default |
| solver is used.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - Function.</dd><dd><code>x0</code> - Lower bound for the interval.</dd><dd><code>x1</code> - Upper bound for the interval.</dd><dd><code>absoluteAccuracy</code> - Accuracy to be used by the solver.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a value where the function is zero.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the function has the same sign at the |
| endpoints.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>function</code> is <code>null</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="forceSide(int, org.apache.commons.math3.analysis.UnivariateFunction, org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver, double, double, double, org.apache.commons.math3.analysis.solvers.AllowedSolution)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>forceSide</h4> |
| <pre>public static double forceSide(int maxEval, |
| <a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> f, |
| <a href="../../../../../../org/apache/commons/math3/analysis/solvers/BracketedUnivariateSolver.html" title="interface in org.apache.commons.math3.analysis.solvers">BracketedUnivariateSolver</a><<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a>> bracketing, |
| double baseRoot, |
| double min, |
| double max, |
| <a href="../../../../../../org/apache/commons/math3/analysis/solvers/AllowedSolution.html" title="enum in org.apache.commons.math3.analysis.solvers">AllowedSolution</a> allowedSolution) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre> |
| <div class="block">Force a root found by a non-bracketing solver to lie on a specified side, |
| as if the solver was a bracketing one.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>maxEval</code> - maximal number of new evaluations of the function |
| (evaluations already done for finding the root should have already been subtracted |
| from this number)</dd><dd><code>f</code> - function to solve</dd><dd><code>bracketing</code> - bracketing solver to use for shifting the root</dd><dd><code>baseRoot</code> - original root found by a previous non-bracketing solver</dd><dd><code>min</code> - minimal bound of the search interval</dd><dd><code>max</code> - maximal bound of the search interval</dd><dd><code>allowedSolution</code> - the kind of solutions that the root-finding algorithm may |
| accept as solutions.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a root approximation, on the specified side of the exact root</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the function has the same sign at the |
| endpoints.</dd></dl> |
| </li> |
| </ul> |
| <a name="bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double)"> |
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| </a> |
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| <h4>bracket</h4> |
| <pre>public static double[] bracket(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double initial, |
| double lowerBound, |
| double upperBound) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre> |
| <div class="block">This method simply calls <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, double, double, int)"><code>bracket(function, initial, lowerBound, upperBound, q, r, maximumIterations)</code></a> |
| with <code>q</code> and <code>r</code> set to 1.0 and <code>maximumIterations</code> set to <code>Integer.MAX_VALUE</code>. |
| <strong>Note: </strong> this method can take |
| <code>Integer.MAX_VALUE</code> iterations to throw a |
| <code>ConvergenceException.</code> Unless you are confident that there |
| is a root between <code>lowerBound</code> and <code>upperBound</code> |
| near <code>initial,</code> it is better to use |
| <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, double, double, int)"><code>bracket(function, initial, lowerBound, upperBound, q, r, maximumIterations)</code></a>, |
| explicitly specifying the maximum number of iterations.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - Function.</dd><dd><code>initial</code> - Initial midpoint of interval being expanded to |
| bracket a root.</dd><dd><code>lowerBound</code> - Lower bound (a is never lower than this value)</dd><dd><code>upperBound</code> - Upper bound (b never is greater than this |
| value).</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a two-element array holding a and b.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if a root cannot be bracketted.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>maximumIterations <= 0</code>.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>function</code> is <code>null</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>bracket</h4> |
| <pre>public static double[] bracket(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double initial, |
| double lowerBound, |
| double upperBound, |
| int maximumIterations) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre> |
| <div class="block">This method simply calls <a href="../../../../../../org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.html#bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, double, double, int)"><code>bracket(function, initial, lowerBound, upperBound, q, r, maximumIterations)</code></a> |
| with <code>q</code> and <code>r</code> set to 1.0.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - Function.</dd><dd><code>initial</code> - Initial midpoint of interval being expanded to |
| bracket a root.</dd><dd><code>lowerBound</code> - Lower bound (a is never lower than this value).</dd><dd><code>upperBound</code> - Upper bound (b never is greater than this |
| value).</dd><dd><code>maximumIterations</code> - Maximum number of iterations to perform</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a two element array holding a and b.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the algorithm fails to find a and b |
| satisfying the desired conditions.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>maximumIterations <= 0</code>.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>function</code> is <code>null</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="bracket(org.apache.commons.math3.analysis.UnivariateFunction, double, double, double, double, double, int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>bracket</h4> |
| <pre>public static double[] bracket(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double initial, |
| double lowerBound, |
| double upperBound, |
| double q, |
| double r, |
| int maximumIterations) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre> |
| <div class="block">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 <code>f</code> is continuous on <code>[a,b]</code>, this means that <code>a</code> |
| and <code>b</code> bracket a root of <code>f</code>. |
| <p> |
| The algorithm checks the sign of \( f(l_k) \) and \( f(u_k) \) for increasing |
| values of k, where \( l_k = max(lower, initial - \delta_k) \), |
| \( u_k = min(upper, initial + \delta_k) \), using recurrence |
| \( \delta_{k+1} = r \delta_k + q, \delta_0 = 0\) and starting search with \( k=1 \). |
| The algorithm stops when one of the following happens: <ul> |
| <li> at least one positive and one negative value have been found -- success!</li> |
| <li> both endpoints have reached their respective limites -- NoBracketingException </li> |
| <li> <code>maximumIterations</code> iterations elapse -- NoBracketingException </li></ul></p> |
| <p> |
| If different signs are found at first iteration (<code>k=1</code>), then the returned |
| interval will be \( [a, b] = [l_1, u_1] \). If different signs are found at a later |
| iteration ({code k>1}, then the returned interval will be either |
| \( [a, b] = [l_{k+1}, l_{k}] \) or ( [a, b] = [u_{k}, u_{k+1}] \). A root solver called |
| with these parameters will therefore start with the smallest bracketing interval known |
| at this step. |
| </p> |
| <p> |
| Interval expansion rate is tuned by changing the recurrence parameters <code>r</code> and |
| <code>q</code>. When the multiplicative factor <code>r</code> is set to 1, the sequence is a |
| simple arithmetic sequence with linear increase. When the multiplicative factor <code>r</code> |
| is larger than 1, the sequence has an asymtotically exponential rate. Note than the |
| additive parameter <code>q</code> should never be set to zero, otherwise the interval would |
| degenerate to the single initial point for all values of <code>k</code>. |
| </p> |
| <p> |
| As a rule of thumb, when the location of the root is expected to be approximately known |
| within some error margin, <code>r</code> should be set to 1 and <code>q</code> should be set to the |
| order of magnitude of the error margin. When the location of the root is really a wild guess, |
| then <code>r</code> should be set to a value larger than 1 (typically 2 to double the interval |
| length at each iteration) and <code>q</code> should be set according to half the initial |
| search interval length. |
| </p> |
| <p> |
| As an example, if we consider the trivial function <code>f(x) = 1 - x</code> and use |
| <code>initial = 4</code>, <code>r = 1</code>, <code>q = 2</code>, the algorithm will compute |
| <code>f(4-2) = f(2) = -1</code> and <code>f(4+2) = f(6) = -5</code> for <code>k = 1</code>, then |
| <code>f(4-4) = f(0) = +1</code> and <code>f(4+4) = f(8) = -7</code> for <code>k = 2</code>. Then it will |
| return the interval <code>[0, 2]</code> as the smallest one known to be bracketing the root. |
| As shown by this example, the initial value (here <code>4</code>) may lie outside of the returned |
| bracketing interval. |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - function to check</dd><dd><code>initial</code> - Initial midpoint of interval being expanded to |
| bracket a root.</dd><dd><code>lowerBound</code> - Lower bound (a is never lower than this value).</dd><dd><code>upperBound</code> - Upper bound (b never is greater than this |
| value).</dd><dd><code>q</code> - additive offset used to compute bounds sequence (must be strictly positive)</dd><dd><code>r</code> - multiplicative factor used to compute bounds sequence</dd><dd><code>maximumIterations</code> - Maximum number of iterations to perform</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a two element array holding the bracketing values.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if function cannot be bracketed in the search interval</dd></dl> |
| </li> |
| </ul> |
| <a name="midpoint(double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>midpoint</h4> |
| <pre>public static double midpoint(double a, |
| double b)</pre> |
| <div class="block">Compute the midpoint of two values.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - first value.</dd><dd><code>b</code> - second value.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the midpoint.</dd></dl> |
| </li> |
| </ul> |
| <a name="isBracketing(org.apache.commons.math3.analysis.UnivariateFunction, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>isBracketing</h4> |
| <pre>public static boolean isBracketing(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double lower, |
| double upper) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre> |
| <div class="block">Check whether the interval bounds bracket a root. That is, if the |
| values at the endpoints are not equal to zero, then the function takes |
| opposite signs at the endpoints.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - Function.</dd><dd><code>lower</code> - Lower endpoint.</dd><dd><code>upper</code> - Upper endpoint.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the function values have opposite signs at the |
| given points.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>function</code> is <code>null</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="isSequence(double, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>isSequence</h4> |
| <pre>public static boolean isSequence(double start, |
| double mid, |
| double end)</pre> |
| <div class="block">Check whether the arguments form a (strictly) increasing sequence.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>start</code> - First number.</dd><dd><code>mid</code> - Second number.</dd><dd><code>end</code> - Third number.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the arguments form an increasing sequence.</dd></dl> |
| </li> |
| </ul> |
| <a name="verifyInterval(double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>verifyInterval</h4> |
| <pre>public static void verifyInterval(double lower, |
| double upper) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></pre> |
| <div class="block">Check that the endpoints specify an interval.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>lower</code> - Lower endpoint.</dd><dd><code>upper</code> - Upper endpoint.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>lower >= upper</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="verifySequence(double, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>verifySequence</h4> |
| <pre>public static void verifySequence(double lower, |
| double initial, |
| double upper) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></pre> |
| <div class="block">Check that <code>lower < initial < upper</code>.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>lower</code> - Lower endpoint.</dd><dd><code>initial</code> - Initial value.</dd><dd><code>upper</code> - Upper endpoint.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>lower >= initial</code> or |
| <code>initial >= upper</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="verifyBracketing(org.apache.commons.math3.analysis.UnivariateFunction, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>verifyBracketing</h4> |
| <pre>public static void verifyBracketing(<a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> function, |
| double lower, |
| double upper) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></pre> |
| <div class="block">Check that the endpoints specify an interval and the end points |
| bracket a root.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - Function.</dd><dd><code>lower</code> - Lower endpoint.</dd><dd><code>upper</code> - Upper endpoint.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoBracketingException.html" title="class in org.apache.commons.math3.exception">NoBracketingException</a></code> - if the function has the same sign at the |
| endpoints.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>function</code> is <code>null</code>.</dd></dl> |
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