add test for expm()

Author: stefan-zobel

.gitignore

@@ -4,5 +4,5 @@
 .settings/
 /doc/
 /target/
-/src/test/java/
+/src/tests/java/
 /upload/

pom.xml

@@ -36,6 +36,12 @@
             <version>1.1.0</version>
             <scope>compile</scope>
         </dependency>
+        <dependency>
+            <groupId>junit</groupId>
+            <artifactId>junit</artifactId>
+            <version>4.13.2</version>
+            <scope>test</scope>
+        </dependency>
     </dependencies>
 
     <properties>

src/test/java/net/jamu/matrix/ExpmTest.java

@@ -0,0 +1,183 @@
+/*
+ * Copyright 2020, 2025 Stefan Zobel
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package net.jamu.matrix;
+
+import static org.junit.Assert.assertTrue;
+import org.junit.Test;
+
+/**
+ * Tests for Expm
+ */
+public final class ExpmTest {
+
+    @Test
+    public void testComplex() {
+        ComplexMatrixD C = Matrices.createComplexD(2, 2);
+        C.set(0, 0, 1.0, 0.0);
+        C.set(1, 0, 2.0, 0.0);
+        C.set(0, 1, -1.0, 0.0);
+        C.set(1, 1, 3.0, 0.0);
+        // C = i * C
+        C = C.scaleInplace(0.0, 1.0);
+        // C = e^C
+        C = C.expm();
+
+        // expected
+        // reference: scipy.linalg.expm()
+        ComplexMatrixD expm = Matrices.createComplexD(2, 2);
+        expm.set(0, 0, 4.2645929667E-01, 1.8921755097E+00);
+        expm.set(1, 0, -2.1372148428E+00, -9.7811251808E-01);
+        expm.set(0, 1, 1.0686074214E+00, 4.8905625904E-01);
+        expm.set(1, 1, -1.7107555461E+00, 9.1406299158E-01);
+        assertTrue(Matrices.approxEqual(expm, C));
+    }
+
+    @Test
+    public void testComplexZero() {
+        ComplexMatrixD zeros = Matrices.createComplexD(3, 3);
+        ComplexMatrixD identity = Matrices.identityComplexD(3);
+        assertTrue(Matrices.approxEqual(identity, zeros.expm()));
+    }
+
+    @Test
+    public void testRealZero() {
+        MatrixD zeros = Matrices.createD(3, 3);
+        MatrixD identity = Matrices.identityD(3);
+        assertTrue(Matrices.approxEqual(identity, zeros.expm()));
+    }
+
+    @Test
+    public void testRealMatlab() {
+        // https://www.mathworks.com/help/matlab/ref/expm.html
+        MatrixD A = Matrices.createD(3, 3);
+        A.set(0, 0, 1);
+        A.set(0, 1, 1);
+        A.set(0, 2, 0);
+        A.set(1, 0, 0);
+        A.set(1, 1, 0);
+        A.set(1, 2, 2);
+        A.set(2, 0, 0);
+        A.set(2, 1, 0);
+        A.set(2, 2, -1);
+        MatrixD eA = A.expm();
+
+        MatrixD expm = Matrices.createD(3, 3);
+        expm.set(0, 0, 2.7183);
+        expm.set(0, 1, 1.7183);
+        expm.set(0, 2, 1.0862);
+        expm.set(1, 0, 0.0);
+        expm.set(1, 1, 1.0);
+        expm.set(1, 2, 1.2642);
+        expm.set(2, 0, 0.0);
+        expm.set(2, 1, 0.0);
+        expm.set(2, 2, 0.3679);
+        assertTrue(Matrices.approxEqual(expm, eA, 1.0e-4));
+    }
+
+    @Test
+    public void testRealJuliaA1() {
+        // A1: https://gist.github.com/sdewaele/2c176cb634280cf8a23c5970739cea0e
+        MatrixD A1 = Matrices.createD(3, 3);
+        A1.set(0, 0, 4);
+        A1.set(0, 1, 2);
+        A1.set(0, 2, 0);
+        A1.set(1, 0, 1);
+        A1.set(1, 1, 4);
+        A1.set(1, 2, 1);
+        A1.set(2, 0, 1);
+        A1.set(2, 1, 1);
+        A1.set(2, 2, 4);
+        A1 = A1.transpose();
+        MatrixD eA1 = A1.expm();
+
+        MatrixD expm = Matrices.createD(3, 3);
+        expm.set(0, 0, 147.866622446369);
+        expm.set(0, 1, 127.781085523181);
+        expm.set(0, 2, 127.781085523182);
+        expm.set(1, 0, 183.765138646367);
+        expm.set(1, 1, 183.765138646366);
+        expm.set(1, 2, 163.679601723179);
+        expm.set(2, 0, 71.797032399996);
+        expm.set(2, 1, 91.8825693231832);
+        expm.set(2, 2, 111.968106246371);
+        assertTrue(Matrices.approxEqual(expm, eA1));
+    }
+
+    @Test
+    public void testRealJuliaA3() {
+        // A3: https://gist.github.com/sdewaele/2c176cb634280cf8a23c5970739cea0e
+        MatrixD A3 = Matrices.createD(3, 3);
+        A3.set(0, 0, -131);
+        A3.set(0, 1, 19);
+        A3.set(0, 2, 18);
+        A3.set(1, 0, -390);
+        A3.set(1, 1, 56);
+        A3.set(1, 2, 54);
+        A3.set(2, 0, -387);
+        A3.set(2, 1, 57);
+        A3.set(2, 2, 52);
+        A3 = A3.transpose();
+        MatrixD eA3 = A3.expm();
+        
+        MatrixD expm = Matrices.createD(3, 3);
+        expm.set(0, 0, -1.50964415879218);
+        expm.set(0, 1, -5.6325707998812);
+        expm.set(0, 2, -4.934938326092);
+        expm.set(1, 0, 0.367879439109187);
+        expm.set(1, 1, 1.47151775849686);
+        expm.set(1, 2, 1.10363831732856);
+        expm.set(2, 0, 0.135335281175235);
+        expm.set(2, 1, 0.406005843524598);
+        expm.set(2, 2, 0.541341126763207);
+        assertTrue(Matrices.approxEqual(expm, eA3));
+    }
+
+    @Test
+    public void testRealJuliaA4() {
+        // A4: https://gist.github.com/sdewaele/2c176cb634280cf8a23c5970739cea0e
+        MatrixD A4 = Matrices.createD(2, 2);
+        A4.set(0, 0, 0.25);
+        A4.set(0, 1, 0.25);
+        A4.set(1, 0, 0);
+        A4.set(1, 1, 0);
+        MatrixD eA4 = A4.expm();
+
+        MatrixD expm = Matrices.createD(2, 2);
+        expm.set(0, 0, 1.2840254166877416);
+        expm.set(0, 1, 0.2840254166877415);
+        expm.set(1, 0, 0.0);
+        expm.set(1, 1, 1.0);
+        assertTrue(Matrices.approxEqual(expm, eA4));
+    }
+
+    @Test
+    public void testRealJuliaA5() {
+        // A5: https://gist.github.com/sdewaele/2c176cb634280cf8a23c5970739cea0e
+        MatrixD A5 = Matrices.createD(2, 2);
+        A5.set(0, 0, 0);
+        A5.set(0, 1, 0.02);
+        A5.set(1, 0, 0);
+        A5.set(1, 1, 0);
+        MatrixD eA5 = A5.expm();
+
+        MatrixD expm = Matrices.createD(2, 2);
+        expm.set(0, 0, 1.0);
+        expm.set(0, 1, 0.02);
+        expm.set(1, 0, 0.0);
+        expm.set(1, 1, 1.0);
+        assertTrue(Matrices.approxEqual(expm, eA5));
+    }
+}