[MATH-1204] backport to 3.5 branch.

src/changes/changes.xml

@@ -54,6 +54,10 @@ If the output is not quite correct, check for invisible trailing spaces!
     </release>
 
     <release version="3.5" date="2015-01-11" description="">
+      <action dev="evanward" type="fix" issue="MATH-1204">
+        "UnivariateSolverUtils#bracket(...)" sometimes failed to bracket
+        if a reached the lower bound.
+      </action>
       <action dev="sebb" type="add" issue="MATH-1198">
         Simplified "FastMath#exp(double)" in order to avoid a potential
         Java 1.5 JIT bug when calling with negative infinity as argument.

src/main/java/org/apache/commons/math3/analysis/solvers/UnivariateSolverUtils.java

@@ -243,7 +243,7 @@ public class UnivariateSolverUtils {
      * \( \delta_{k+1} = r \delta_k + q, \delta_0 = 0\) 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> both endpoints have reached their respective limits -- NoBracketingException </li>
      * <li> {@code maximumIterations} iterations elapse -- NoBracketingException </li></ul></p>
      * <p>
      * If different signs are found at first iteration ({@code k=1}), then the returned
@@ -257,7 +257,7 @@ public class UnivariateSolverUtils {
      * Interval expansion rate is tuned by changing the recurrence parameters {@code r} and
      * {@code q}. When the multiplicative factor {@code r} is set to 1, the sequence is a
      * simple arithmetic sequence with linear increase. When the multiplicative factor {@code r}
-     * is larger than 1, the sequence has an asymtotically exponential rate. Note than the
+     * is larger than 1, the sequence has an asymptotically exponential rate. Note than the
      * additive parameter {@code q} should never be set to zero, otherwise the interval would
      * degenerate to the single initial point for all values of {@code k}.
      * </p>
@@ -314,7 +314,7 @@ public class UnivariateSolverUtils {
         double delta = 0;
 
         for (int numIterations = 0;
-             (numIterations < maximumIterations) && (a > lowerBound || b > upperBound);
+             (numIterations < maximumIterations) && (a > lowerBound || b < upperBound);
              ++numIterations) {
 
             final double previousA  = a;

src/test/java/org/apache/commons/math3/analysis/solvers/UnivariateSolverUtilsTest.java

@@ -175,6 +175,14 @@ public class UnivariateSolverUtilsTest {
         UnivariateSolverUtils.bracket(sin, 1.5, 0, 2.0, 0);
     }
 
+    /** check the search continues when a = lowerBound and b < upperBound. */
+    @Test
+    public void testBracketLoopConditionForB() {
+        double[] result = UnivariateSolverUtils.bracket(sin, -0.9, -1, 1, 0.1, 1, 100);
+        Assert.assertTrue(result[0] <= 0);
+        Assert.assertTrue(result[1] >= 0);
+    }
+
     @Test
     public void testMisc() {
         UnivariateFunction f = new QuinticFunction();