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Added rank revealing QR decomposition. 

Patch applied after conversion to current status and slight adaptations.

JIRA: MATH-630

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1455627 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe 2013-03-12 17:08:52 +00:00
parent 62f86d9580
commit e1f1860894
6 changed files with 735 additions and 56 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
src/changes/changes.xml
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@ -55,6 +55,9 @@ This is a minor release: It combines bug fixes and new features.
Changes to existing features were made in a backwards-compatible
way such as to allow drop-in replacement of the v3.1[.1] JAR file.
">
<action dev="luc" type="fix" issue="MATH-630" due-to="Christopher Nix" >
Added rank revealing QR decomposition.
</action>
<action dev="luc" type="fix" issue="MATH-570" due-to="Arne Plöse" >
ArrayFieldVector can now be constructed from any FieldVector.
</action>

120
src/main/java/org/apache/commons/math3/linear/QRDecomposition.java
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@ -100,71 +100,83 @@ public class QRDecomposition {
cachedR = null;
cachedH = null;
/*
* The QR decomposition of a matrix A is calculated using Householder
* reflectors by repeating the following operations to each minor
* A(minor,minor) of A:
*/
for (int minor = 0; minor < FastMath.min(m, n); minor++) {
decompose(qrt);
final double[] qrtMinor = qrt[minor];
}
/** Decompose matrix.
* @param qrt transposed matrix
*/
protected void decompose(double[][] qrt) {
for (int minor = 0; minor < FastMath.min(qrt.length, qrt[0].length); minor++) {
performHouseholderReflection(minor, qrt);
}
}
/** Perform Householder reflection for a minor A(minor, minor) of A.
* @param minor minor index
* @param qrt transposed matrix
*/
protected void performHouseholderReflection(int minor, double[][] qrt) {
final double[] qrtMinor = qrt[minor];
/*
* Let x be the first column of the minor, and a^2 = |x|^2.
* x will be in the positions qr[minor][minor] through qr[m][minor].
* The first column of the transformed minor will be (a,0,0,..)'
* The sign of a is chosen to be opposite to the sign of the first
* component of x. Let's find a:
*/
double xNormSqr = 0;
for (int row = minor; row < qrtMinor.length; row++) {
final double c = qrtMinor[row];
xNormSqr += c * c;
}
final double a = (qrtMinor[minor] > 0) ? -FastMath.sqrt(xNormSqr) : FastMath.sqrt(xNormSqr);
rDiag[minor] = a;
if (a != 0.0) {
/*
* Let x be the first column of the minor, and a^2 = |x|^2.
* x will be in the positions qr[minor][minor] through qr[m][minor].
* The first column of the transformed minor will be (a,0,0,..)'
* The sign of a is chosen to be opposite to the sign of the first
* component of x. Let's find a:
* Calculate the normalized reflection vector v and transform
* the first column. We know the norm of v beforehand: v = x-ae
* so |v|^2 = <x-ae,x-ae> = <x,x>-2a<x,e>+a^2<e,e> =
* a^2+a^2-2a<x,e> = 2a*(a - <x,e>).
* Here <x, e> is now qr[minor][minor].
* v = x-ae is stored in the column at qr:
*/
double xNormSqr = 0;
for (int row = minor; row < m; row++) {
final double c = qrtMinor[row];
xNormSqr += c * c;
}
final double a = (qrtMinor[minor] > 0) ? -FastMath.sqrt(xNormSqr) : FastMath.sqrt(xNormSqr);
rDiag[minor] = a;
qrtMinor[minor] -= a; // now |v|^2 = -2a*(qr[minor][minor])
if (a != 0.0) {
/*
* Transform the rest of the columns of the minor:
* They will be transformed by the matrix H = I-2vv'/|v|^2.
* If x is a column vector of the minor, then
* Hx = (I-2vv'/|v|^2)x = x-2vv'x/|v|^2 = x - 2<x,v>/|v|^2 v.
* Therefore the transformation is easily calculated by
* subtracting the column vector (2<x,v>/|v|^2)v from x.
*
* Let 2<x,v>/|v|^2 = alpha. From above we have
* |v|^2 = -2a*(qr[minor][minor]), so
* alpha = -<x,v>/(a*qr[minor][minor])
*/
for (int col = minor+1; col < qrt.length; col++) {
final double[] qrtCol = qrt[col];
double alpha = 0;
for (int row = minor; row < qrtCol.length; row++) {
alpha -= qrtCol[row] * qrtMinor[row];
}
alpha /= a * qrtMinor[minor];
/*
* Calculate the normalized reflection vector v and transform
* the first column. We know the norm of v beforehand: v = x-ae
* so |v|^2 = <x-ae,x-ae> = <x,x>-2a<x,e>+a^2<e,e> =
* a^2+a^2-2a<x,e> = 2a*(a - <x,e>).
* Here <x, e> is now qr[minor][minor].
* v = x-ae is stored in the column at qr:
*/
qrtMinor[minor] -= a; // now |v|^2 = -2a*(qr[minor][minor])
/*
* Transform the rest of the columns of the minor:
* They will be transformed by the matrix H = I-2vv'/|v|^2.
* If x is a column vector of the minor, then
* Hx = (I-2vv'/|v|^2)x = x-2vv'x/|v|^2 = x - 2<x,v>/|v|^2 v.
* Therefore the transformation is easily calculated by
* subtracting the column vector (2<x,v>/|v|^2)v from x.
*
* Let 2<x,v>/|v|^2 = alpha. From above we have
* |v|^2 = -2a*(qr[minor][minor]), so
* alpha = -<x,v>/(a*qr[minor][minor])
*/
for (int col = minor+1; col < n; col++) {
final double[] qrtCol = qrt[col];
double alpha = 0;
for (int row = minor; row < m; row++) {
alpha -= qrtCol[row] * qrtMinor[row];
}
alpha /= a * qrtMinor[minor];
// Subtract the column vector alpha*v from x.
for (int row = minor; row < m; row++) {
qrtCol[row] -= alpha * qrtMinor[row];
}
// Subtract the column vector alpha*v from x.
for (int row = minor; row < qrtCol.length; row++) {
qrtCol[row] -= alpha * qrtMinor[row];
}
}
}
}
/**
* Returns the matrix R of the decomposition.
* <p>R is an upper-triangular matrix</p>

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src/main/java/org/apache/commons/math3/linear/RRQRDecomposition.java Normal file
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@ -0,0 +1,230 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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 org.apache.commons.math3.linear;
import org.apache.commons.math3.util.FastMath;
/**
* Calculates the rank-revealing QR-decomposition of a matrix, with column pivoting.
* <p>The rank-revealing QR-decomposition of a matrix A consists of three matrices Q,
* R and P such that AP=QR. Q is orthogonal (Q<sup>T</sup>Q = I), and R is upper triangular.
* If A is m&times;n, Q is m&times;m and R is m&times;n and P is n&times;n.</p>
* <p>QR decomposition with column pivoting produces a rank-revealing QR
* decomposition and the {@link #getRank(double)} method may be used to return the rank of the
* input matrix A.</p>
* <p>This class compute the decomposition using Householder reflectors.</p>
* <p>For efficiency purposes, the decomposition in packed form is transposed.
* This allows inner loop to iterate inside rows, which is much more cache-efficient
* in Java.</p>
* <p>This class is based on the class with similar name from the
* <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
* following changes:</p>
* <ul>
* <li>a {@link #getQT() getQT} method has been added,</li>
* <li>the {@code solve} and {@code isFullRank} methods have been replaced
* by a {@link #getSolver() getSolver} method and the equivalent methods
* provided by the returned {@link DecompositionSolver}.</li>
* </ul>
*
* @see <a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a>
* @see <a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a>
*
* @version $Id$
* @since 3.2
*/
public class RRQRDecomposition extends QRDecomposition {
/** An array to record the column pivoting for later creation of P. */
private int[] p;
/** Cached value of P. */
private RealMatrix cachedP;
/**
* Calculates the QR-decomposition of the given matrix.
* The singularity threshold defaults to zero.
*
* @param matrix The matrix to decompose.
*
* @see #QRDecomposition(RealMatrix,double)
*/
public RRQRDecomposition(RealMatrix matrix) {
this(matrix, 0d);
}
/**
* Calculates the QR-decomposition of the given matrix.
*
* @param matrix The matrix to decompose.
* @param threshold Singularity threshold.
*/
public RRQRDecomposition(RealMatrix matrix, double threshold) {
super(matrix, threshold);
}
/** Decompose matrix.
* @param qrt transposed matrix
*/
protected void decompose(double[][] qrt) {
p = new int[qrt.length];
for (int i = 0; i < p.length; i++) {
p[i] = i;
}
super.decompose(qrt);
}
/** Perform Householder reflection for a minor A(minor, minor) of A.
* @param minor minor index
* @param qrt transposed matrix
*/
protected void performHouseholderReflection(int minor, double[][] qrt) {
double l2NormSquaredMax = 0;
// Find the unreduced column with the greatest L2-Norm
int l2NormSquaredMaxIndex = minor;
for (int i = minor; i < qrt.length; i++) {
double l2NormSquared = 0;
for (int j = 0; j < qrt[i].length; j++) {
l2NormSquared += qrt[i][j] * qrt[i][j];
}
if (l2NormSquared > l2NormSquaredMax) {
l2NormSquaredMax = l2NormSquared;
l2NormSquaredMaxIndex = i;
}
}
// swap the current column with that with the greated L2-Norm and record in p
if (l2NormSquaredMaxIndex != minor) {
double[] tmp1 = qrt[minor];
qrt[minor] = qrt[l2NormSquaredMaxIndex];
qrt[l2NormSquaredMaxIndex] = tmp1;
int tmp2 = p[minor];
p[minor] = p[l2NormSquaredMaxIndex];
p[l2NormSquaredMaxIndex] = tmp2;
}
super.performHouseholderReflection(minor, qrt);
}
/**
* Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.
*
* If no pivoting is used in this decomposition then P is equal to the identity matrix.
*
* @return a permutation matrix.
*/
public RealMatrix getP() {
if (cachedP == null) {
int n = p.length;
cachedP = MatrixUtils.createRealMatrix(n,n);
for (int i = 0; i < n; i++) {
cachedP.setEntry(p[i], i, 1);
}
}
return cachedP ;
}
/**
* Return the effective numerical matrix rank.
* <p>The effective numerical rank is the number of non-negligible
* singular values.</p>
* <p>This implementation looks at Frobenius norms of the sequence of
* bottom right submatrices. When a large fall in norm is seen,
* the rank is returned. The drop is computed as:</p>
* <pre>
* (thisNorm/lastNorm) * rNorm < dropThreshold
* </pre>
* <p>
* where thisNorm is the Frobenius norm of the current submatrix,
* lastNorm is the Frobenius norm of the previous submatrix,
* rNorm is is the Frobenius norm of the complete matrix
* </p>
*
* @param dropThreshold threshold triggering rank computation
* @return effective numerical matrix rank
*/
public int getRank(final double dropThreshold) {
RealMatrix r = getR();
int rows = r.getRowDimension();
int columns = r.getColumnDimension();
int rank = 1;
double lastNorm = r.getFrobeniusNorm();
double rNorm = lastNorm;
while (rank < FastMath.min(rows, columns)) {
double thisNorm = r.getSubMatrix(rank, rows - 1, rank, columns - 1).getFrobeniusNorm();
if (thisNorm == 0 || (thisNorm / lastNorm) * rNorm < dropThreshold) {
break;
}
lastNorm = thisNorm;
rank++;
}
return rank;
}
/**
* Get a solver for finding the A &times; X = B solution in least square sense.
* @return a solver
*/
public DecompositionSolver getSolver() {
return new Solver(super.getSolver(), this.getP());
}
/** Specialized solver. */
private static class Solver implements DecompositionSolver {
/** Upper level solver. */
private final DecompositionSolver upper;
/** A permutation matrix for the pivots used in the QR decomposition */
private RealMatrix p;
/**
* Build a solver from decomposed matrix.
*
* @param upper upper level solver.
* @param p permutation matrix
*/
private Solver(final DecompositionSolver upper, final RealMatrix p) {
this.upper = upper;
this.p = p;
}
/** {@inheritDoc} */
public boolean isNonSingular() {
return upper.isNonSingular();
}
/** {@inheritDoc} */
public RealVector solve(RealVector b) {
return p.operate(upper.solve(b));
}
/** {@inheritDoc} */
public RealMatrix solve(RealMatrix b) {
return p.multiply(upper.solve(b));
}
/** {@inheritDoc} */
public RealMatrix getInverse() {
return solve(MatrixUtils.createRealIdentityMatrix(p.getRowDimension()));
}
}
}

3
src/test/java/org/apache/commons/math3/linear/QRDecompositionTest.java
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@ -245,8 +245,7 @@ public class QRDecompositionTest {
public void testNonInvertible() {
QRDecomposition qr =
new QRDecomposition(MatrixUtils.createRealMatrix(testData3x3Singular));
final RealMatrix inv = qr.getSolver().getInverse();
qr.getSolver().getInverse();
}
private RealMatrix createTestMatrix(final Random r, final int rows, final int columns) {

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@ -0,0 +1,233 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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 org.apache.commons.math3.linear;
import java.util.Random;
import org.junit.Assert;
import org.junit.Test;
public class RRQRDecompositionTest {
private double[][] testData3x3NonSingular = {
{ 12, -51, 4 },
{ 6, 167, -68 },
{ -4, 24, -41 }, };
private double[][] testData3x3Singular = {
{ 1, 4, 7, },
{ 2, 5, 8, },
{ 3, 6, 9, }, };
private double[][] testData3x4 = {
{ 12, -51, 4, 1 },
{ 6, 167, -68, 2 },
{ -4, 24, -41, 3 }, };
private double[][] testData4x3 = {
{ 12, -51, 4, },
{ 6, 167, -68, },
{ -4, 24, -41, },
{ -5, 34, 7, }, };
private static final double entryTolerance = 10e-16;
private static final double normTolerance = 10e-14;
/** test dimensions */
@Test
public void testDimensions() {
checkDimension(MatrixUtils.createRealMatrix(testData3x3NonSingular));
checkDimension(MatrixUtils.createRealMatrix(testData4x3));
checkDimension(MatrixUtils.createRealMatrix(testData3x4));
Random r = new Random(643895747384642l);
int p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
int q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
checkDimension(createTestMatrix(r, p, q));
checkDimension(createTestMatrix(r, q, p));
}
private void checkDimension(RealMatrix m) {
int rows = m.getRowDimension();
int columns = m.getColumnDimension();
RRQRDecomposition qr = new RRQRDecomposition(m);
Assert.assertEquals(rows, qr.getQ().getRowDimension());
Assert.assertEquals(rows, qr.getQ().getColumnDimension());
Assert.assertEquals(rows, qr.getR().getRowDimension());
Assert.assertEquals(columns, qr.getR().getColumnDimension());
}
/** test AP = QR */
@Test
public void testAPEqualQR() {
checkAPEqualQR(MatrixUtils.createRealMatrix(testData3x3NonSingular));
checkAPEqualQR(MatrixUtils.createRealMatrix(testData3x3Singular));
checkAPEqualQR(MatrixUtils.createRealMatrix(testData3x4));
checkAPEqualQR(MatrixUtils.createRealMatrix(testData4x3));
Random r = new Random(643895747384642l);
int p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
int q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
checkAPEqualQR(createTestMatrix(r, p, q));
checkAPEqualQR(createTestMatrix(r, q, p));
}
private void checkAPEqualQR(RealMatrix m) {
RRQRDecomposition rrqr = new RRQRDecomposition(m);
double norm = rrqr.getQ().multiply(rrqr.getR()).subtract(m.multiply(rrqr.getP())).getNorm();
Assert.assertEquals(0, norm, normTolerance);
}
/** test the orthogonality of Q */
@Test
public void testQOrthogonal() {
checkQOrthogonal(MatrixUtils.createRealMatrix(testData3x3NonSingular));
checkQOrthogonal(MatrixUtils.createRealMatrix(testData3x3Singular));
checkQOrthogonal(MatrixUtils.createRealMatrix(testData3x4));
checkQOrthogonal(MatrixUtils.createRealMatrix(testData4x3));
Random r = new Random(643895747384642l);
int p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
int q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
checkQOrthogonal(createTestMatrix(r, p, q));
checkQOrthogonal(createTestMatrix(r, q, p));
}
private void checkQOrthogonal(RealMatrix m) {
RRQRDecomposition qr = new RRQRDecomposition(m);
RealMatrix eye = MatrixUtils.createRealIdentityMatrix(m.getRowDimension());
double norm = qr.getQT().multiply(qr.getQ()).subtract(eye).getNorm();
Assert.assertEquals(0, norm, normTolerance);
}
/** test that R is upper triangular */
@Test
public void testRUpperTriangular() {
RealMatrix matrix = MatrixUtils.createRealMatrix(testData3x3NonSingular);
checkUpperTriangular(new RRQRDecomposition(matrix).getR());
matrix = MatrixUtils.createRealMatrix(testData3x3Singular);
checkUpperTriangular(new RRQRDecomposition(matrix).getR());
matrix = MatrixUtils.createRealMatrix(testData3x4);
checkUpperTriangular(new RRQRDecomposition(matrix).getR());
matrix = MatrixUtils.createRealMatrix(testData4x3);
checkUpperTriangular(new RRQRDecomposition(matrix).getR());
Random r = new Random(643895747384642l);
int p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
int q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
matrix = createTestMatrix(r, p, q);
checkUpperTriangular(new RRQRDecomposition(matrix).getR());
matrix = createTestMatrix(r, p, q);
checkUpperTriangular(new RRQRDecomposition(matrix).getR());
}
private void checkUpperTriangular(RealMatrix m) {
m.walkInOptimizedOrder(new DefaultRealMatrixPreservingVisitor() {
@Override
public void visit(int row, int column, double value) {
if (column < row) {
Assert.assertEquals(0.0, value, entryTolerance);
}
}
});
}
/** test that H is trapezoidal */
@Test
public void testHTrapezoidal() {
RealMatrix matrix = MatrixUtils.createRealMatrix(testData3x3NonSingular);
checkTrapezoidal(new RRQRDecomposition(matrix).getH());
matrix = MatrixUtils.createRealMatrix(testData3x3Singular);
checkTrapezoidal(new RRQRDecomposition(matrix).getH());
matrix = MatrixUtils.createRealMatrix(testData3x4);
checkTrapezoidal(new RRQRDecomposition(matrix).getH());
matrix = MatrixUtils.createRealMatrix(testData4x3);
checkTrapezoidal(new RRQRDecomposition(matrix).getH());
Random r = new Random(643895747384642l);
int p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
int q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
matrix = createTestMatrix(r, p, q);
checkTrapezoidal(new RRQRDecomposition(matrix).getH());
matrix = createTestMatrix(r, p, q);
checkTrapezoidal(new RRQRDecomposition(matrix).getH());
}
private void checkTrapezoidal(RealMatrix m) {
m.walkInOptimizedOrder(new DefaultRealMatrixPreservingVisitor() {
@Override
public void visit(int row, int column, double value) {
if (column > row) {
Assert.assertEquals(0.0, value, entryTolerance);
}
}
});
}
@Test(expected=SingularMatrixException.class)
public void testNonInvertible() {
RRQRDecomposition qr =
new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3Singular), 3.0e-16);
qr.getSolver().getInverse();
}
private RealMatrix createTestMatrix(final Random r, final int rows, final int columns) {
RealMatrix m = MatrixUtils.createRealMatrix(rows, columns);
m.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor(){
@Override
public double visit(int row, int column, double value) {
return 2.0 * r.nextDouble() - 1.0;
}
});
return m;
}
/** test the rank is returned correctly */
@Test
public void testRank() {
double[][] d = { { 1, 1, 1 }, { 0, 0, 0 }, { 1, 2, 3 } };
RealMatrix m = new Array2DRowRealMatrix(d);
RRQRDecomposition qr = new RRQRDecomposition(m);
Assert.assertEquals(2, qr.getRank(1.0e-16));
}
}

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@ -0,0 +1,202 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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 org.apache.commons.math3.linear;
import java.util.Random;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.junit.Test;
import org.junit.Assert;
public class RRQRSolverTest {
double[][] testData3x3NonSingular = {
{ 12, -51, 4 },
{ 6, 167, -68 },
{ -4, 24, -41 }
};
double[][] testData3x3Singular = {
{ 1, 2, 2 },
{ 2, 4, 6 },
{ 4, 8, 12 }
};
double[][] testData3x4 = {
{ 12, -51, 4, 1 },
{ 6, 167, -68, 2 },
{ -4, 24, -41, 3 }
};
double[][] testData4x3 = {
{ 12, -51, 4 },
{ 6, 167, -68 },
{ -4, 24, -41 },
{ -5, 34, 7 }
};
/** test rank */
@Test
public void testRank() {
DecompositionSolver solver =
new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3NonSingular), 1.0e-16).getSolver();
Assert.assertTrue(solver.isNonSingular());
solver = new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3Singular), 1.0e-16).getSolver();
Assert.assertFalse(solver.isNonSingular());
solver = new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x4), 1.0e-16).getSolver();
Assert.assertTrue(solver.isNonSingular());
solver = new RRQRDecomposition(MatrixUtils.createRealMatrix(testData4x3), 1.0e-16).getSolver();
Assert.assertTrue(solver.isNonSingular());
}
/** test solve dimension errors */
@Test
public void testSolveDimensionErrors() {
DecompositionSolver solver =
new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3NonSingular)).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
try {
solver.solve(b);
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException iae) {
// expected behavior
}
try {
solver.solve(b.getColumnVector(0));
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException iae) {
// expected behavior
}
}
/** test solve rank errors */
@Test
public void testSolveRankErrors() {
DecompositionSolver solver =
new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3Singular), 1.0e-16).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[3][2]);
try {
solver.solve(b);
Assert.fail("an exception should have been thrown");
} catch (SingularMatrixException iae) {
// expected behavior
}
try {
solver.solve(b.getColumnVector(0));
Assert.fail("an exception should have been thrown");
} catch (SingularMatrixException iae) {
// expected behavior
}
}
/** test solve */
@Test
public void testSolve() {
RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
{ -102, 12250 }, { 544, 24500 }, { 167, -36750 }
});
RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
{ 1, 2515 }, { 2, 422 }, { -3, 898 }
});
RRQRDecomposition decomposition = new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3NonSingular));
DecompositionSolver solver = decomposition.getSolver();
// using RealMatrix
Assert.assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 3.0e-16 * xRef.getNorm());
// using ArrayRealVector
for (int i = 0; i < b.getColumnDimension(); ++i) {
final RealVector x = solver.solve(b.getColumnVector(i));
final double error = x.subtract(xRef.getColumnVector(i)).getNorm();
Assert.assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).getNorm());
}
// using RealVector with an alternate implementation
for (int i = 0; i < b.getColumnDimension(); ++i) {
ArrayRealVectorTest.RealVectorTestImpl v =
new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(i));
final RealVector x = solver.solve(v);
final double error = x.subtract(xRef.getColumnVector(i)).getNorm();
Assert.assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).getNorm());
}
}
@Test
public void testOverdetermined() {
final Random r = new Random(5559252868205245l);
int p = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
int q = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
RealMatrix a = createTestMatrix(r, p, q);
RealMatrix xRef = createTestMatrix(r, q, BlockRealMatrix.BLOCK_SIZE + 3);
// build a perturbed system: A.X + noise = B
RealMatrix b = a.multiply(xRef);
final double noise = 0.001;
b.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor() {
@Override
public double visit(int row, int column, double value) {
return value * (1.0 + noise * (2 * r.nextDouble() - 1));
}
});
// despite perturbation, the least square solution should be pretty good
RealMatrix x = new RRQRDecomposition(a).getSolver().solve(b);
Assert.assertEquals(0, x.subtract(xRef).getNorm(), 0.01 * noise * p * q);
}
@Test
public void testUnderdetermined() {
final Random r = new Random(42185006424567123l);
int p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
int q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
RealMatrix a = createTestMatrix(r, p, q);
RealMatrix xRef = createTestMatrix(r, q, BlockRealMatrix.BLOCK_SIZE + 3);
RealMatrix b = a.multiply(xRef);
RRQRDecomposition rrqrd = new RRQRDecomposition(a);
RealMatrix x = rrqrd.getSolver().solve(b);
// too many equations, the system cannot be solved at all
Assert.assertTrue(x.subtract(xRef).getNorm() / (p * q) > 0.01);
// the last permuted unknown should have been set to 0
RealMatrix permuted = rrqrd.getP().transpose().multiply(x);
Assert.assertEquals(0.0, permuted.getSubMatrix(p, q - 1, 0, permuted.getColumnDimension() - 1).getNorm(), 0);
}
private RealMatrix createTestMatrix(final Random r, final int rows, final int columns) {
RealMatrix m = MatrixUtils.createRealMatrix(rows, columns);
m.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor() {
@Override
public double visit(int row, int column, double value) {
return 2.0 * r.nextDouble() - 1.0;
}
});
return m;
}
}