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Posted to commits@commons.apache.org by er...@apache.org on 2012/10/30 01:29:06 UTC
svn commit: r1403590 - in /commons/proper/math/trunk/src: changes/changes.xml
main/java/org/apache/commons/math3/linear/EigenDecomposition.java
test/java/org/apache/commons/math3/linear/EigenDecompositionTest.java
Author: erans
Date: Tue Oct 30 00:29:06 2012
New Revision: 1403590
URL: http://svn.apache.org/viewvc?rev=1403590&view=rev
Log:
MATH-883
Added "getSquareRoot()" method. Implementation only supports symmetric,
diagonalizable matrices.
Modified:
commons/proper/math/trunk/src/changes/changes.xml
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/linear/EigenDecomposition.java
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/linear/EigenDecompositionTest.java
Modified: commons/proper/math/trunk/src/changes/changes.xml
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/changes/changes.xml?rev=1403590&r1=1403589&r2=1403590&view=diff
==============================================================================
--- commons/proper/math/trunk/src/changes/changes.xml (original)
+++ commons/proper/math/trunk/src/changes/changes.xml Tue Oct 30 00:29:06 2012
@@ -52,6 +52,10 @@ If the output is not quite correct, chec
<body>
<release version="3.1" date="TBD" description="
">
+ <action dev="erans" type="add" issue="MATH-883">
+ New "getSquareRoot" method in class "EigenDecomposition" (package
+ "o.a.c.m.linear").
+ </action>
<action dev="erans" type="update" issue="MATH-884">
Added "isSymmetric" and "checkSymmetric" in "MatrixUtils" (package
"o.a.c.m.linear").
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math3/linear/EigenDecomposition.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/linear/EigenDecomposition.java?rev=1403590&r1=1403589&r2=1403590&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math3/linear/EigenDecomposition.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math3/linear/EigenDecomposition.java Tue Oct 30 00:29:06 2012
@@ -100,6 +100,8 @@ public class EigenDecomposition {
private RealMatrix cachedD;
/** Cached value of Vt. */
private RealMatrix cachedVt;
+ /** Whether the matrix is symmetric. */
+ private final boolean isSymmetric;
/**
* Calculates the eigen decomposition of the given real matrix.
@@ -113,7 +115,8 @@ public class EigenDecomposition {
*/
public EigenDecomposition(final RealMatrix matrix)
throws MathArithmeticException {
- if (isSymmetric(matrix, false)) {
+ isSymmetric = isSymmetric(matrix, false);
+ if (isSymmetric) {
transformToTridiagonal(matrix);
findEigenVectors(transformer.getQ().getData());
} else {
@@ -149,6 +152,7 @@ public class EigenDecomposition {
* @throws MaxCountExceededException if the algorithm fails to converge.
*/
public EigenDecomposition(final double[] main, final double[] secondary) {
+ isSymmetric = true;
this.main = main.clone();
this.secondary = secondary.clone();
transformer = null;
@@ -386,6 +390,35 @@ public class EigenDecomposition {
}
/**
+ * Computes the square-root of the matrix.
+ * This implementation assumes that the matrix is symmetric and postive
+ * definite.
+ *
+ * @return the square-root of the matrix.
+ * @throws MathUnsupportedOperationException if the matrix is not
+ * symmetric or not positive definite.
+ */
+ public RealMatrix getSquareRoot() {
+ if (!isSymmetric) {
+ throw new MathUnsupportedOperationException();
+ }
+
+ final double[] sqrtEigenValues = new double[realEigenvalues.length];
+ for (int i = 0; i < realEigenvalues.length; i++) {
+ final double eigen = realEigenvalues[i];
+ if (eigen <= 0) {
+ throw new MathUnsupportedOperationException();
+ }
+ sqrtEigenValues[i] = FastMath.sqrt(eigen);
+ }
+ final RealMatrix sqrtEigen = MatrixUtils.createRealDiagonalMatrix(sqrtEigenValues);
+ final RealMatrix v = getV();
+ final RealMatrix vT = getVT();
+
+ return v.multiply(sqrtEigen).multiply(vT);
+ }
+
+ /**
* Gets a solver for finding the A × X = B solution in exact
* linear sense.
* <p>
Modified: commons/proper/math/trunk/src/test/java/org/apache/commons/math3/linear/EigenDecompositionTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/linear/EigenDecompositionTest.java?rev=1403590&r1=1403589&r2=1403590&view=diff
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math3/linear/EigenDecompositionTest.java (original)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math3/linear/EigenDecompositionTest.java Tue Oct 30 00:29:06 2012
@@ -24,6 +24,7 @@ import java.util.Random;
import org.apache.commons.math3.distribution.NormalDistribution;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
+import org.apache.commons.math3.exception.MathUnsupportedOperationException;
import org.junit.After;
import org.junit.Assert;
import org.junit.Before;
@@ -337,6 +338,53 @@ public class EigenDecompositionTest {
}
@Test
+ public void testSquareRoot() {
+ final double[][] data = {
+ { 33, 24, 7 },
+ { 24, 57, 11 },
+ { 7, 11, 9 }
+ };
+
+ final EigenDecomposition dec = new EigenDecomposition(MatrixUtils.createRealMatrix(data));
+ final RealMatrix sqrtM = dec.getSquareRoot();
+
+ // Reconstruct initial matrix.
+ final RealMatrix m = sqrtM.multiply(sqrtM);
+
+ final int dim = data.length;
+ for (int r = 0; r < dim; r++) {
+ for (int c = 0; c < dim; c++) {
+ Assert.assertEquals("m[" + r + "][" + c + "]",
+ data[r][c], m.getEntry(r, c), 1e-13);
+ }
+ }
+ }
+
+ @Test(expected=MathUnsupportedOperationException.class)
+ public void testSquareRootNonSymmetric() {
+ final double[][] data = {
+ { 1, 2, 4 },
+ { 2, 3, 5 },
+ { 11, 5, 9 }
+ };
+
+ final EigenDecomposition dec = new EigenDecomposition(MatrixUtils.createRealMatrix(data));
+ final RealMatrix sqrtM = dec.getSquareRoot();
+ }
+
+ @Test(expected=MathUnsupportedOperationException.class)
+ public void testSquareRootNonPositiveDefinite() {
+ final double[][] data = {
+ { 1, 2, 4 },
+ { 2, 3, 5 },
+ { 4, 5, -9 }
+ };
+
+ final EigenDecomposition dec = new EigenDecomposition(MatrixUtils.createRealMatrix(data));
+ final RealMatrix sqrtM = dec.getSquareRoot();
+ }
+
+ @Test
public void testUnsymmetric() {
// Vandermonde matrix V(x;i,j) = x_i^{n - j} with x = (-1,-2,3,4)
double[][] vData = { { -1.0, 1.0, -1.0, 1.0 },