added missing files from previous patches (JIRA:MATH-161 and JIRA:MATH-162)

git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@496489 13f79535-47bb-0310-9956-ffa450edef68

src/mantissa/src/org/spaceroots/mantissa/algebra/CoefficientsGenerator.java

@@ -0,0 +1,141 @@
+package org.spaceroots.mantissa.algebra;
+
+import java.util.ArrayList;
+
+public abstract class CoefficientsGenerator {
+
+  /** Build a generator with coefficients for two polynomials.
+   * <p>The first polynomial must be a degree 0 polynomial
+   * P<sub>0</sub>(X)=a<sub>0,0</sub> and the second polynomial
+   * must be a degree 1 polynomial P<sub>1</sub>(X)=a<sub>0,1</sub>
+   * +a<sub>1,1</sub>X</p>
+   * @param a00 constant term for the degree 0 polynomial
+   * @param a01 constant term for the degree 1 polynomial
+   * @param a11 X term for the degree 1 polynomial
+   */
+  protected CoefficientsGenerator(RationalNumber a00,
+                                  RationalNumber a01, RationalNumber a11) {
+    l = new ArrayList();
+    l.add(a00);
+    l.add(a01);
+    l.add(a11);
+    maxDegree = 1;
+  }
+
+  /** Set the recurrence coefficients.
+   * @param b2k b<sub>2,k</sub> coefficient (b<sub>2,k</sub> = a<sub>2,k</sub> / a<sub>1,k</sub>)
+   * @param b3k b<sub>3,k</sub> coefficient (b<sub>3,k</sub> = a<sub>3,k</sub> / a<sub>1,k</sub>)
+   * @param b4k b<sub>4,k</sub> coefficient (b<sub>4,k</sub> = a<sub>4,k</sub> / a<sub>1,k</sub>)
+   */
+  protected void setRecurrenceCoefficients(RationalNumber b2k,
+                                           RationalNumber b3k,
+                                           RationalNumber b4k) {
+    this.b2k = b2k;
+    this.b3k = b3k;
+    this.b4k = b4k;
+  }
+
+  /** Set the recurrence coefficients.
+   * The recurrence relation is
+   *  <pre>a<sub>1,k</sub> O<sub>k+1</sub>(X) =(a<sub>2,k</sub> + a<sub>3,k</sub> X) O<sub>k</sub>(X) - a<sub>4,k</sub> O<sub>k-1</sub>(X)</pre>
+   * the method must call {@link #setRecurrenceCoefficients(RationalNumber,
+   * RationalNumber, RationalNumber)} to provide the coefficients
+   * @param k index of the current step
+   */
+  protected abstract void setRecurrenceCoefficients(int k);
+
+  /** Compute all the polynomial coefficients up to a given degree.
+   * @param degree maximal degree
+   */
+  private void computeUpToDegree(int degree) {
+
+    int startK = (maxDegree - 1) * maxDegree / 2;
+    for (int k = maxDegree; k < degree; ++k) {
+
+      // start indices of two previous polynomials Ok(X) and Ok-1(X)
+      int startKm1 = startK;
+      startK += k;
+
+      // a1k Ok+1(X) = (a2k + a3k X) Ok(X) - a4k Ok-1(X)
+      // we use bik = aik/a1k
+      setRecurrenceCoefficients(k);
+
+      RationalNumber ckPrev = null;
+      RationalNumber ck     = (RationalNumber) l.get(startK);
+      RationalNumber ckm1   = (RationalNumber) l.get(startKm1);
+
+      // degree 0 coefficient
+      l.add(ck.multiply(b2k).subtract(ckm1.multiply(b4k)));
+
+      // degree 1 to degree k-1 coefficients
+      for (int i = 1; i < k; ++i) {
+        ckPrev = ck;
+        ck     = (RationalNumber) l.get(startK + i);
+        ckm1   = (RationalNumber) l.get(startKm1 + i);
+        l.add(ck.multiply(b2k).add(ckPrev.multiply(b3k)).subtract(ckm1.multiply(b4k)));
+      }
+
+      // degree k coefficient
+      ckPrev = ck;
+      ck     = (RationalNumber) l.get(startK + k);
+      l.add(ck.multiply(b2k).add(ckPrev.multiply(b3k)));
+
+      // degree k+1 coefficient
+      l.add(ck.multiply(b3k));
+
+    }
+
+    maxDegree = degree;
+
+  }
+
+  /** Get the coefficients array for a given degree.
+   * @param degree degree of the polynomial
+   * @return coefficients array
+   */
+  public RationalNumber[] getCoefficients(int degree) {
+
+    synchronized (this) {
+      if (degree > maxDegree) {
+        computeUpToDegree(degree);
+      }
+    }
+
+    // coefficient  for polynomial 0 is  l [0]
+    // coefficients for polynomial 1 are l [1] ... l [2] (degrees 0 ... 1)
+    // coefficients for polynomial 2 are l [3] ... l [5] (degrees 0 ... 2)
+    // coefficients for polynomial 3 are l [6] ... l [9] (degrees 0 ... 3)
+    // coefficients for polynomial 4 are l[10] ... l[14] (degrees 0 ... 4)
+    // coefficients for polynomial 5 are l[15] ... l[20] (degrees 0 ... 5)
+    // coefficients for polynomial 6 are l[21] ... l[27] (degrees 0 ... 6)
+    // ...
+    int start = degree * (degree + 1) / 2;
+
+    RationalNumber[] a = new RationalNumber[degree + 1];
+    for (int i = 0; i <= degree; ++i) {
+      a[i] = (RationalNumber) l.get(start + i);
+    }
+
+    return a;
+
+  }
+  
+  /** List holding the coefficients of the polynomials computed so far. */
+  private ArrayList l;
+
+  /** Maximal degree of the polynomials computed so far. */
+  private int maxDegree;
+
+  /** b<sub>2,k</sub> coefficient to initialize
+   * (b<sub>2,k</sub> = a<sub>2,k</sub> / a<sub>1,k</sub>). */
+  private RationalNumber b2k;
+
+  /** b<sub>3,k</sub> coefficient to initialize
+   * (b<sub>3,k</sub> = a<sub>3,k</sub> / a<sub>1,k</sub>). */
+  private RationalNumber b3k;
+
+  /** b<sub>4,k</sub> coefficient to initialize
+   * (b<sub>4,k</sub> = a<sub>4,k</sub> / a<sub>1,k</sub>). */
+  private RationalNumber b4k;
+
+}

src/mantissa/tests-src/org/spaceroots/mantissa/ode/StepProblem.java

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+package org.spaceroots.mantissa.ode;
+
+
+public class StepProblem
+  implements FirstOrderDifferentialEquations, SwitchingFunction {
+
+  public StepProblem(double rateBefore, double rateAfter,
+                     double switchTime) {
+    this.rateAfter  = rateAfter;
+    this.switchTime = switchTime;
+    setRate(rateBefore);
+  }
+
+  public void computeDerivatives(double t, double[] y, double[] yDot) {
+    yDot[0] = rate;
+  }
+
+  public int getDimension() {
+    return 1;
+  }
+
+  public void setRate(double rate) {
+    this.rate = rate;
+  }
+
+  public int eventOccurred(double t, double[] y) {
+    setRate(rateAfter);
+    return RESET_DERIVATIVES;
+  }
+
+  public double g(double t, double[] y) {
+    return t - switchTime;
+  }
+
+  public void resetState(double t, double[] y) {
+  }
+
+  private double rate;
+  private double rateAfter;
+  private double switchTime;
+
+  private static final long serialVersionUID = 7590601995477504318L;
+
+}