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Added BELOW_SIDE and ABOVE_SIDE in the possible allowed solutions for bracketing solvers. 

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1142244 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe 2011-07-02 16:27:03 +00:00
parent 5c185f118b
commit fac2e96a31
4 changed files with 82 additions and 19 deletions
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36
src/main/java/org/apache/commons/math/analysis/solvers/AllowedSolutions.java
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@ -18,9 +18,10 @@
package org.apache.commons.math.analysis.solvers;
/** The kinds of solutions that a {@link UnivariateRealSolver (univariate real)
* root-finding algorithm} may accept as solutions. This basically controls
* whether or not under-approximations and over-approximations are allowed.
/** The kinds of solutions that a {@link BracketedUnivariateRealSolver
* (bracketed univariate real) root-finding algorithm} may accept as solutions.
* This basically controls whether or not under-approximations and
* over-approximations are allowed.
*
* <p>If all solutions are accepted ({@link #EITHER_SIDE}), then the solution
* that the root-finding algorithm returns for a given root may be equal to the
@ -30,8 +31,8 @@ package org.apache.commons.math.analysis.solvers;
* tolerances. In certain cases however, in particular for
* {@link org.apache.commons.math.ode.events.EventHandler state events} of
* {@link org.apache.commons.math.ode.ODEIntegrator ODE solvers}, it
* may be necessary to guarantee that a solution is returned that does not
* under-approximate the solution.</p>
* may be necessary to guarantee that a solution is returned that lies on a
* specific side the solution.</p>
*
* @see BracketedUnivariateRealSolver
* @since 3.0
@ -40,23 +41,36 @@ package org.apache.commons.math.analysis.solvers;
public enum AllowedSolutions {
/** There are no additional side restriction on the solutions for
* root-finding. That is, both under-approximations and over-approximations
* are allowed. So, if a function f(x) has a root at x = y, then the
* root-finding result s may be smaller than y, equal to y, or greater
* than y.
* are allowed. So, if a function f(x) has a root at x = x0, then the
* root-finding result s may be smaller than x0, equal to x0, or greater
* than x0.
*/
EITHER_SIDE,
/** Only solutions that are less than or equal to the actual root are
* acceptable as solutions for root-finding. In other words,
* over-approximations are not allowed. So, if a function f(x) has a root
* at x = y, then the root-finding result s must satisfy s &lt;= y.
* at x = x0, then the root-finding result s must satisfy s &lt;= x0.
*/
LEFT_SIDE,
/** Only solutions that are greater than or equal to the actual root are
* acceptable as solutions for root-finding. In other words,
* under-approximations are not allowed. So, if a function f(x) has a root
* at x = y, then the root-finding result s must satisfy s &gt;= y.
* at x = x0, then the root-finding result s must satisfy s &gt;= x0.
*/
RIGHT_SIDE;
RIGHT_SIDE,
/** Only solutions for which values are less than or equal to zero are
* acceptable as solutions for root-finding. So, if a function f(x) has
* a root at x = x0, then the root-finding result s must satisfy f(s) &lt;= 0.
*/
BELOW_SIDE,
/** Only solutions for which values are greater than or equal to zero are
* acceptable as solutions for root-finding. So, if a function f(x) has
* a root at x = x0, then the root-finding result s must satisfy f(s) &gt;= 0.
*/
ABOVE_SIDE;
}

24
src/main/java/org/apache/commons/math/analysis/solvers/BaseSecantSolver.java
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@ -101,10 +101,6 @@ public abstract class BaseSecantSolver extends AbstractUnivariateRealSolver {
final double atol = getAbsoluteAccuracy();
final double rtol = getRelativeAccuracy();
// Variables to hold new bounds.
double x;
double fx;
// Keep track of inverted intervals, meaning that the left bound is
// larger than the right bound. Not used for the original Secant
// method.
@ -113,8 +109,8 @@ public abstract class BaseSecantSolver extends AbstractUnivariateRealSolver {
// Keep finding better approximations.
while (true) {
// Calculate the next approximation.
x = x1 - ((f1 * (x1 - x0)) / (f1 - f0));
fx = computeObjectiveValue(x);
final double x = x1 - ((f1 * (x1 - x0)) / (f1 - f0));
final double fx = computeObjectiveValue(x);
// If the new approximation is the exact root, return it. Since
// this is not an under-approximation or an over-approximation,
@ -151,7 +147,7 @@ public abstract class BaseSecantSolver extends AbstractUnivariateRealSolver {
}
// If the function value of the last approximation is too small,
// given the function value accuracy, then we can't get close to
// given the function value accuracy, then we can't get closer to
// the root than we already are.
if (FastMath.abs(f1) <= ftol) {
switch (allowedSolutions) {
@ -167,6 +163,16 @@ public abstract class BaseSecantSolver extends AbstractUnivariateRealSolver {
return x1;
}
break;
case BELOW_SIDE:
if (f1 <= 0) {
return x1;
}
break;
case ABOVE_SIDE:
if (f1 >= 0) {
return x1;
}
break;
default:
throw new MathInternalError();
}
@ -183,6 +189,10 @@ public abstract class BaseSecantSolver extends AbstractUnivariateRealSolver {
return inverted ? x1 : x0;
case RIGHT_SIDE:
return inverted ? x0 : x1;
case BELOW_SIDE:
return (f1 <= 0) ? x1 : x0;
case ABOVE_SIDE:
return (f1 >= 0) ? x1 : x0;
default:
throw new MathInternalError();
}

3
src/site/xdoc/changes.xml
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@ -59,7 +59,8 @@ The <action> type attribute can be add,update,fix,remove.
</action>
<action dev="eran" type="add" issue="MATH-599" due-to="Dennis Hendriks">
Modified "SecantSolver" to comply with the original algorithm. Added several
secant-based solvers.
secant-based solvers. Added a way to select the side of the root with bracketing
solvers.
</action>
<action dev="luc" type="fix" issue="MATH-600">
Fixed javadoc for ODEIntegrator interface

38
src/test/java/org/apache/commons/math/analysis/solvers/BaseSecantSolverAbstractTest.java
View File

@ -195,4 +195,42 @@ public abstract class BaseSecantSolverAbstractTest {
right += 0.3;
}
}
@Test
public void testSolutionBelowSide() {
UnivariateRealFunction f = new SinFunction();
UnivariateRealSolver solver = getSolver();
if (!(solver instanceof BracketedUnivariateRealSolver)) return;
((BracketedUnivariateRealSolver)solver).setAllowedSolutions(AllowedSolutions.BELOW_SIDE);
double left = -1.5;
double right = 0.05;
for(int i = 0; i < 10; i++) {
// Test whether the allowed solutions are taken into account.
double solution = solver.solve(100, f, left, right);
Assert.assertTrue(f.value(solution) <= 0.0);
// Prepare for next test.
left -= 0.1;
right += 0.3;
}
}
@Test
public void testSolutionAboveSide() {
UnivariateRealFunction f = new SinFunction();
UnivariateRealSolver solver = getSolver();
if (!(solver instanceof BracketedUnivariateRealSolver)) return;
((BracketedUnivariateRealSolver)solver).setAllowedSolutions(AllowedSolutions.ABOVE_SIDE);
double left = -1.5;
double right = 0.05;
for(int i = 0; i < 10; i++) {
// Test whether the allowed solutions are taken into account.
double solution = solver.solve(100, f, left, right);
Assert.assertTrue(f.value(solution) >= 0.0);
// Prepare for next test.
left -= 0.1;
right += 0.3;
}
}
}