Added derivatives evaluation for field Hermite interpolator.

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1449822 13f79535-47bb-0310-9956-ffa450edef68

Author: Luc Maisonobe

src/main/java/org/apache/commons/math3/analysis/interpolation/FieldHermiteInterpolator.java

@@ -149,4 +149,49 @@ public T[] value(T x) throws NoDataException {
 
     }
 
+    /** Interpolate value and first derivatives at a specified abscissa.
+     * @param x interpolation abscissa
+     * @param order maximum derivation order
+     * @return interpolated value and derivatives (value in row 0,
+     * 1<sup>st</sup> derivative in row 1, ... n<sup>th</sup> derivative in row n)
+     * @exception NoDataException if sample is empty
+     */
+    public T[][] derivatives(T x, int order) throws NoDataException {
+
+        // safety check
+        if (abscissae.isEmpty()) {
+            throw new NoDataException(LocalizedFormats.EMPTY_INTERPOLATION_SAMPLE);
+        }
+
+        final T zero = x.getField().getZero();
+        final T one  = x.getField().getOne();
+        final T[] tj = MathArrays.buildArray(x.getField(), order + 1);
+        tj[0] = zero;
+        for (int i = 0; i < order; ++i) {
+            tj[i + 1] = tj[i].add(one);
+        }
+
+        final T[][] derivatives =
+                MathArrays.buildArray(x.getField(), order + 1, topDiagonal.get(0).length);
+        final T[] valueCoeff = MathArrays.buildArray(x.getField(), order + 1);
+        valueCoeff[0] = x.getField().getOne();
+        for (int i = 0; i < topDiagonal.size(); ++i) {
+            T[] dividedDifference = topDiagonal.get(i);
+            final T deltaX = x.subtract(abscissae.get(i));
+            for (int j = order; j >= 0; --j) {
+                for (int k = 0; k < derivatives[j].length; ++k) {
+                    derivatives[j][k] =
+                            derivatives[j][k].add(dividedDifference[k].multiply(valueCoeff[j]));
+                }
+                valueCoeff[j] = valueCoeff[j].multiply(deltaX);
+                if (j > 0) {
+                    valueCoeff[j] = valueCoeff[j].add(tj[j].multiply(valueCoeff[j - 1]));
+                }
+            }
+        }
+
+        return derivatives;
+
+    }
+
 }

src/test/java/org/apache/commons/math3/analysis/interpolation/FieldHermiteInterpolatorTest.java

@@ -36,6 +36,9 @@ public void testZero() {
         for (int x = -10; x < 10; x++) {
             BigFraction y = interpolator.value(new BigFraction(x))[0];
             Assert.assertEquals(BigFraction.ZERO, y);
+            BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(x), 1);
+            Assert.assertEquals(BigFraction.ZERO, derivatives[0][0]);
+            Assert.assertEquals(BigFraction.ZERO, derivatives[1][0]);
         }
     }
 
@@ -48,6 +51,11 @@ public void testQuadratic() {
         for (double x = -10; x < 10; x += 1.0) {
             BigFraction y = interpolator.value(new BigFraction(x))[0];
             Assert.assertEquals((x - 1) * (x - 2), y.doubleValue(), 1.0e-15);
+            BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(x), 3);
+            Assert.assertEquals((x - 1) * (x - 2), derivatives[0][0].doubleValue(), 1.0e-15);
+            Assert.assertEquals(2 * x - 3, derivatives[1][0].doubleValue(), 1.0e-15);
+            Assert.assertEquals(2, derivatives[2][0].doubleValue(), 1.0e-15);
+            Assert.assertEquals(0, derivatives[3][0].doubleValue(), 1.0e-15);
         }
     }
 
@@ -57,9 +65,27 @@ public void testMixedDerivatives() {
         interpolator.addSamplePoint(new BigFraction(0), new BigFraction[] { new BigFraction(1) }, new BigFraction[] { new BigFraction(2) });
         interpolator.addSamplePoint(new BigFraction(1), new BigFraction[] { new BigFraction(4) });
         interpolator.addSamplePoint(new BigFraction(2), new BigFraction[] { new BigFraction(5) }, new BigFraction[] { new BigFraction(2) });
-        Assert.assertEquals(new BigFraction(1), interpolator.value(new BigFraction(0))[0]);
-        Assert.assertEquals(new BigFraction(4), interpolator.value(new BigFraction(1))[0]);
-        Assert.assertEquals(new BigFraction(5), interpolator.value(new BigFraction(2))[0]);
+        BigFraction[][] derivatives = interpolator.derivatives(new BigFraction(0), 5);
+        Assert.assertEquals(new BigFraction(  1), derivatives[0][0]);
+        Assert.assertEquals(new BigFraction(  2), derivatives[1][0]);
+        Assert.assertEquals(new BigFraction(  8), derivatives[2][0]);
+        Assert.assertEquals(new BigFraction(-24), derivatives[3][0]);
+        Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
+        Assert.assertEquals(new BigFraction(  0), derivatives[5][0]);
+        derivatives = interpolator.derivatives(new BigFraction(1), 5);
+        Assert.assertEquals(new BigFraction(  4), derivatives[0][0]);
+        Assert.assertEquals(new BigFraction(  2), derivatives[1][0]);
+        Assert.assertEquals(new BigFraction( -4), derivatives[2][0]);
+        Assert.assertEquals(new BigFraction(  0), derivatives[3][0]);
+        Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
+        Assert.assertEquals(new BigFraction(  0), derivatives[5][0]);
+        derivatives = interpolator.derivatives(new BigFraction(2), 5);
+        Assert.assertEquals(new BigFraction(  5), derivatives[0][0]);
+        Assert.assertEquals(new BigFraction(  2), derivatives[1][0]);
+        Assert.assertEquals(new BigFraction(  8), derivatives[2][0]);
+        Assert.assertEquals(new BigFraction( 24), derivatives[3][0]);
+        Assert.assertEquals(new BigFraction( 24), derivatives[4][0]);
+        Assert.assertEquals(new BigFraction(  0), derivatives[5][0]);
     }
 
     @Test
@@ -230,10 +256,15 @@ private PolynomialFunction randomPolynomial(int degree, Random random) {
     }
 
     @Test(expected=NoDataException.class)
-    public void testEmptySample() {
+    public void testEmptySampleValue() {
         new FieldHermiteInterpolator<BigFraction>().value(BigFraction.ZERO);
     }
 
+    @Test(expected=NoDataException.class)
+    public void testEmptySampleDerivative() {
+        new FieldHermiteInterpolator<BigFraction>().derivatives(BigFraction.ZERO, 1);
+    }
+
     @Test(expected=IllegalArgumentException.class)
     public void testDuplicatedAbscissa() {
         FieldHermiteInterpolator<BigFraction> interpolator = new FieldHermiteInterpolator<BigFraction>();