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From l..@apache.org
Subject svn commit: r1372414 - in /commons/proper/math/trunk/src: main/java/org/apache/commons/math3/analysis/differentiation/DSCompiler.java test/java/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.java
Date Mon, 13 Aug 2012 13:06:26 GMT
Author: luc
Date: Mon Aug 13 13:06:26 2012
New Revision: 1372414

URL: http://svn.apache.org/viewvc?rev=1372414&view=rev
Log:
Added support for atan2 in DSCompiler.

Modified:
    commons/proper/math/trunk/src/main/java/org/apache/commons/math3/analysis/differentiation/DSCompiler.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=1372414&r1=1372413&r2=1372414&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 13:06:26 2012
@@ -1286,14 +1286,36 @@ public class DSCompiler {
                       final double[] x, final int xOffset,
                       final double[] result, final int resultOffset) {
 
-        final double y0 = y[yOffset];
-        final double x0 = x[xOffset];
-        result[resultOffset] = FastMath.atan2(y0, x0);
-        if (order > 0) {
-            for (int i = 1; i <= order; ++i) {
-                // TODO compute higher order derivatives
-                result[resultOffset + i] = Double.NaN;
+        // compute r = sqrt(x^2+y^2)
+        double[] tmp1 = new double[getSize()];
+        multiply(x, xOffset, x, xOffset, tmp1, 0);      // x^2
+        double[] tmp2 = new double[getSize()];
+        multiply(y, yOffset, y, yOffset, tmp2, 0);      // y^2
+        add(tmp1, 0, tmp2, 0, tmp2, 0);                 // x^2 + y^2
+        rootN(tmp2, 0, 2, tmp1, 0);                     // r = sqrt(x^2 + y^2)
+
+        if (x[xOffset] >= 0) {
+
+            // compute atan2(y, x) = 2 atan(y / (r + x))
+            add(tmp1, 0, x, xOffset, tmp2, 0);          // r + x
+            divide(y, yOffset, tmp2, 0, tmp1, 0);       // y /(r + x)
+            atan(tmp1, 0, tmp2, 0);                     // atan(y / (r + x))
+            for (int i = 0; i < tmp2.length; ++i) {
+                result[resultOffset + i] = 2 * tmp2[i]; // 2 * atan(y / (r + x))
             }
+
+        } else {
+
+            // compute atan2(y, x) = +/- pi - 2 atan(y / (r - x))
+            subtract(tmp1, 0, x, xOffset, tmp2, 0);     // r - x
+            divide(y, yOffset, tmp2, 0, tmp1, 0);       // y /(r - x)
+            atan(tmp1, 0, tmp2, 0);                     // atan(y / (r - x))
+            result[resultOffset] =
+                    ((tmp2[0] <= 0) ? -FastMath.PI : FastMath.PI) - 2 * tmp2[0]; // +/-pi
- 2 * atan(y / (r - x))
+            for (int i = 1; i < tmp2.length; ++i) {
+                result[resultOffset + i] = -2 * tmp2[i]; // +/-pi - 2 * atan(y / (r - x))
+            }
+
         }
 
     }

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=1372414&r1=1372413&r2=1372414&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 13:06:26 2012
@@ -543,6 +543,32 @@ public class DerivativeStructureTest {
     }
 
     @Test
+    public void testAtan2() {
+        double[] epsilon = new double[] { 5.0e-16, 3.0e-15, 2.0e-14, 1.0e-12, 8.0e-11 };
+        for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {
+            for (double x = -1.7; x < 2; x += 0.2) {
+                DerivativeStructure dsX = new DerivativeStructure(2, maxOrder, 0, x);
+                for (double y = -1.7; y < 2; y += 0.2) {
+                    DerivativeStructure dsY = new DerivativeStructure(2, maxOrder, 1, y);
+                    DerivativeStructure atan2 = DerivativeStructure.atan2(dsY, dsX);
+                    DerivativeStructure ref = dsY.divide(dsX).atan();
+                    if (x < 0) {
+                        ref = (y < 0) ? ref.subtract(FastMath.PI) : ref.add(FastMath.PI);
+                    }
+                    DerivativeStructure zero = atan2.subtract(ref);
+                    for (int n = 0; n <= maxOrder; ++n) {
+                        for (int m = 0; m <= maxOrder; ++m) {
+                            if (n + m <= maxOrder) {
+                                Assert.assertEquals(0, zero.getPartialDerivative(n, m), epsilon[n
+ m]);
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    @Test
     public void testCompositionOneVariableY() {
         double epsilon = 1.0e-13;
         for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {



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