Author: luc
Date: Mon Aug 13 14:14:17 2012
New Revision: 1372432
URL: http://svn.apache.org/viewvc?rev=1372432&view=rev
Log:
Added Taylor expansion for DSCompiler.
Modified:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DSCompiler.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructure.java
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.java
Modified:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DSCompiler.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DSCompiler.java?rev=1372432&r1=1372431&r2=1372432&view=diff
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DSCompiler.java
(original)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DSCompiler.java
Mon Aug 13 14:14:17 2012
@@ -1347,15 +1347,25 @@ public class DSCompiler {
}
}
- /** Evaluate Taylor expansion a derivative structure.
+ /** Evaluate Taylor expansion of a derivative structure.
* @param ds array holding the derivative structure
* @param dsOffset offset of the derivative structure in its array
- * @param offsets parameters offsets (dx, dy, ...)
- * @return value of the Taylor expansion at x+dx, y.dy, ...
+ * @param delta parameters offsets (Δx, Δy, ...)
+ * @return value of the Taylor expansion at x + Δx, y + Δy, ...
*/
- public double taylor(final double[] ds, final int dsOffset, final double
... offsets) {
- // TODO
- return Double.NaN;
+ public double taylor(final double[] ds, final int dsOffset, final double
... delta) {
+ double value = 0;
+ for (int i = getSize() - 1; i >= 0; --i) {
+ final int[] orders = getPartialDerivativeOrders(i);
+ double term = ds[dsOffset + i];
+ for (int k = 0; k < orders.length; ++k) {
+ if (orders[k] > 0) {
+ term *= FastMath.pow(delta[k], orders[k]) /
ArithmeticUtils.factorial(orders[k]);
+ }
+ }
+ value += term;
+ }
+ return value;
}
/** Check rules set compatibility.
Modified:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructure.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructure.java?rev=1372432&r1=1372431&r2=1372432&view=diff
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructure.java
(original)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructure.java
Mon Aug 13 14:14:17 2012
@@ -528,11 +528,11 @@ public class DerivativeStructure impleme
}
/** Evaluate Taylor expansion a derivative structure.
- * @param offsets parameters offsets (dx, dy, ...)
- * @return value of the Taylor expansion at x+dx, y.dy, ...
+ * @param delta parameters offsets (Δx, Δy, ...)
+ * @return value of the Taylor expansion at x + Δx, y + Δy, ...
*/
- public double taylor(final double ... offsets) {
- return compiler.taylor(data, 0, offsets);
+ public double taylor(final double ... delta) {
+ return compiler.taylor(data, 0, delta);
}
/**
Modified:
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.java?rev=1372432&r1=1372431&r2=1372432&view=diff
==============================================================================
---
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.java
(original)
+++
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.java
Mon Aug 13 14:14:17 2012
@@ -597,6 +597,48 @@ public class DerivativeStructureTest {
}
@Test
+ public void testTaylorPolynomial() {
+ for (double x = 0; x < 1.2; x += 0.1) {
+ DerivativeStructure dsX = new DerivativeStructure(3, 4, 0, x);
+ for (double y = 0; y < 1.2; y += 0.2) {
+ DerivativeStructure dsY = new DerivativeStructure(3, 4, 1, y);
+ for (double z = 0; z < 1.2; z += 0.2) {
+ DerivativeStructure dsZ = new DerivativeStructure(3, 4, 2,
z);
+ DerivativeStructure f =
dsX.multiply(dsY).add(dsZ).multiply(dsX).multiply(dsY);
+ for (double dx = -0.2; dx < 0.2; dx += 0.2) {
+ for (double dy = -0.2; dy < 0.2; dy += 0.1) {
+ for (double dz = -0.2; dz < 0.2; dz += 0.1) {
+ double ref = (x + dx) * (y + dy) * ((x + dx) *
(y + dy) + (z + dz));
+ Assert.assertEquals(ref, f.taylor(dx, dy, dz),
2.0e-15);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ @Test
+ public void testTaylorAtan2() {
+ double[] expected = new double[] { 0.214, 0.0241, 0.00422, 6.48e-4,
8.04e-5 };
+ double x0 = 0.1;
+ double y0 = -0.3;
+ for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {
+ DerivativeStructure dsX = new DerivativeStructure(2, maxOrder,
0, x0);
+ DerivativeStructure dsY = new DerivativeStructure(2, maxOrder,
1, y0);
+ DerivativeStructure atan2 = DerivativeStructure.atan2(dsY, dsX);
+ double maxError = 0;
+ for (double dx = -0.05; dx < 0.05; dx += 0.001) {
+ for (double dy = -0.05; dy < 0.05; dy += 0.001) {
+ double ref = FastMath.atan2(y0 + dy, x0 + dx);
+ maxError = FastMath.max(maxError, FastMath.abs(ref -
atan2.taylor(dx, dy)));
+ }
+ }
+ Assert.assertEquals(0.0, expected[maxOrder] - maxError, 0.01 *
expected[maxOrder]);
+ }
+ }
+
+ @Test
public void testField() {
for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {
DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0,
1.0);
