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MATH-883 

Added "getSquareRoot()" method. Implementation only supports symmetric,
diagonalizable matrices.


git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1403590 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Gilles Sadowski 2012-10-30 00:29:06 +00:00
parent 4d12f0ca68
commit 06c63da6c7
3 changed files with 86 additions and 1 deletions
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4
src/changes/changes.xml
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@ -52,6 +52,10 @@ If the output is not quite correct, check for invisible trailing spaces!
<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").

35
src/main/java/org/apache/commons/math3/linear/EigenDecomposition.java
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@ -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;
@ -385,6 +389,35 @@ public class EigenDecomposition {
return determinant;
}
/**
* 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 &times; X = B solution in exact
* linear sense.

48
src/test/java/org/apache/commons/math3/linear/EigenDecompositionTest.java
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@ -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;
@ -336,6 +337,53 @@ public class EigenDecompositionTest {
Assert.assertEquals(0, norm, 6.0e-13);
}
@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)