Fixed {Field}Complex.atan for real values.

Fixes #351
Hipparchus-Math · Aug 22, 2024 · 1a9b2e5 · 1a9b2e5
1 parent e6a137b
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diff --git a/hipparchus-core/src/changes/changes.xml b/hipparchus-core/src/changes/changes.xml
@@ -50,6 +50,9 @@ If the output is not quite correct, check for invisible trailing spaces!
   </properties>
   <body>
     <release version="4.0" date="TBD" description="TBD">
+      <action dev="luc" type="fix" issue="issues/351">
+        Fixed {Field}Complex.atan for real values.
+      </action>
       <action dev="luc" type="update" issue="issues/349">
         Added getAddendum() to CalculusFieldElement interface.
       </action>

diff --git a/hipparchus-core/src/main/java/org/hipparchus/complex/Complex.java b/hipparchus-core/src/main/java/org/hipparchus/complex/Complex.java
@@ -802,6 +802,9 @@ public Complex atan() {
             final Complex tmp = createComplex((1 + imaginary) / (1 - imaginary), 0.0).log().multiplyPlusI().multiply(0.5);
             return createComplex(FastMath.copySign(tmp.real, real), tmp.imaginary);
 
+        } else if (imaginary == 0.0) {
+            // taking care to preserve the sign of the zero imaginary part
+            return createComplex(FastMath.atan(real), imaginary);
         } else {
             // regular formula
             final Complex n = createComplex(1 + imaginary, -real);

diff --git a/hipparchus-core/src/main/java/org/hipparchus/complex/FieldComplex.java b/hipparchus-core/src/main/java/org/hipparchus/complex/FieldComplex.java
@@ -910,6 +910,9 @@ public FieldComplex<T> atan() {
                                         log().multiplyPlusI().multiply(0.5);
             return createComplex(FastMath.copySign(tmp.real, real), tmp.imaginary);
 
+        } else if (imaginary.isZero()) {
+            // taking care to preserve the sign of the zero imaginary part
+            return createComplex(FastMath.atan(real), imaginary);
         } else {
             // regular formula
             final FieldComplex<T> n = createComplex(one.add(imaginary), real.negate());

diff --git a/hipparchus-core/src/test/java/org/hipparchus/complex/ComplexTest.java b/hipparchus-core/src/test/java/org/hipparchus/complex/ComplexTest.java
@@ -31,6 +31,7 @@
 import org.hipparchus.util.FastMath;
 import org.hipparchus.util.MathUtils;
 import org.hipparchus.util.Precision;
+import org.junit.jupiter.api.Assertions;
 import org.junit.jupiter.api.Test;
 
 import java.util.Arrays;
@@ -860,6 +861,18 @@ void testAtanBranchCuts() {
         assertTrue(FastMath.copySign(1.0, FastMath.atan(new Complex(-0.0, -0.25)).getReal()) < 0.0);
     }
 
+    @Test
+    public void testAtanReal() {
+        final Complex zP = new Complex(0.8734729023516287, 0.0);
+        final Complex aP = new Complex(0.717964439926383,  0.0);
+        Assertions.assertEquals(aP, zP.atan());
+        Assertions.assertEquals(1.0, FastMath.copySign(1.0, zP.atan().getImaginary()), 1.0e-15);
+        final Complex zM = new Complex(0.8734729023516287, -0.0);
+        final Complex aM = new Complex(0.717964439926383,  -0.0);
+        Assertions.assertEquals(aM, zM.atan());
+        Assertions.assertEquals(-1.0, FastMath.copySign(1.0, zM.atan().getImaginary()), 1.0e-15);
+    }
+
     @Test
     @Override
     public void testAtan2() {

diff --git a/hipparchus-core/src/test/java/org/hipparchus/complex/FieldComplexTest.java b/hipparchus-core/src/test/java/org/hipparchus/complex/FieldComplexTest.java
@@ -27,6 +27,7 @@
 import org.hipparchus.util.MathArrays;
 import org.hipparchus.util.MathUtils;
 import org.hipparchus.util.Precision;
+import org.junit.jupiter.api.Assertions;
 import org.junit.jupiter.api.Test;
 
 import java.util.Arrays;
@@ -915,6 +916,18 @@ void testAtanBranchCuts() {
         assertTrue(FastMath.copySign(1.0, FastMath.atan(build(-0.0, -0.25)).getReal()) < 0.0);
     }
 
+    @Test
+    public void testAtanReal() {
+        final FieldComplex<Binary64> zP = build(0.8734729023516287, 0.0);
+        final FieldComplex<Binary64> aP = build(0.717964439926383,  0.0);
+        Assertions.assertEquals(aP, zP.atan());
+        Assertions.assertEquals(1.0, FastMath.copySign(new Binary64(1.0), zP.atan().getImaginary()).getReal(), 1.0e-15);
+        final FieldComplex<Binary64> zM = build(0.8734729023516287, -0.0);
+        final FieldComplex<Binary64> aM = build(0.717964439926383,  -0.0);
+        Assertions.assertEquals(aM, zM.atan());
+        Assertions.assertEquals(-1.0, FastMath.copySign(new Binary64(1.0), zM.atan().getImaginary()).getReal(), 1.0e-15);
+    }
+
     @Test
     @Override
     public void testAtan2() {