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Commons Math example source code file (QRSolverTest.java)
The Commons Math QRSolverTest.java source code/* * 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.math.linear; import java.util.Random; import junit.framework.TestCase; public class QRSolverTest extends TestCase { 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 } }; public QRSolverTest(String name) { super(name); } /** test rank */ public void testRank() { DecompositionSolver solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular)).getSolver(); assertTrue(solver.isNonSingular()); solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3Singular)).getSolver(); assertFalse(solver.isNonSingular()); solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x4)).getSolver(); assertTrue(solver.isNonSingular()); solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData4x3)).getSolver(); assertTrue(solver.isNonSingular()); } /** test solve dimension errors */ public void testSolveDimensionErrors() { DecompositionSolver solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular)).getSolver(); RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]); try { solver.solve(b); fail("an exception should have been thrown"); } catch (IllegalArgumentException iae) { // expected behavior } catch (Exception e) { fail("wrong exception caught"); } try { solver.solve(b.getColumn(0)); fail("an exception should have been thrown"); } catch (IllegalArgumentException iae) { // expected behavior } catch (Exception e) { fail("wrong exception caught"); } try { solver.solve(b.getColumnVector(0)); fail("an exception should have been thrown"); } catch (IllegalArgumentException iae) { // expected behavior } catch (Exception e) { fail("wrong exception caught"); } } /** test solve rank errors */ public void testSolveRankErrors() { DecompositionSolver solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3Singular)).getSolver(); RealMatrix b = MatrixUtils.createRealMatrix(new double[3][2]); try { solver.solve(b); fail("an exception should have been thrown"); } catch (InvalidMatrixException iae) { // expected behavior } catch (Exception e) { fail("wrong exception caught"); } try { solver.solve(b.getColumn(0)); fail("an exception should have been thrown"); } catch (InvalidMatrixException iae) { // expected behavior } catch (Exception e) { fail("wrong exception caught"); } try { solver.solve(b.getColumnVector(0)); fail("an exception should have been thrown"); } catch (InvalidMatrixException iae) { // expected behavior } catch (Exception e) { fail("wrong exception caught"); } } /** test solve */ public void testSolve() { QRDecomposition decomposition = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular)); DecompositionSolver solver = decomposition.getSolver(); RealMatrix b = MatrixUtils.createRealMatrix(new double[][] { { -102, 12250 }, { 544, 24500 }, { 167, -36750 } }); RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] { { 1, 2515 }, { 2, 422 }, { -3, 898 } }); // using RealMatrix assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 2.0e-16 * xRef.getNorm()); // using double[] for (int i = 0; i < b.getColumnDimension(); ++i) { final double[] x = solver.solve(b.getColumn(i)); final double error = new ArrayRealVector(x).subtract(xRef.getColumnVector(i)).getNorm(); assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).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(); 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(); assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).getNorm()); } } 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 QRDecompositionImpl(a).getSolver().solve(b); assertEquals(0, x.subtract(xRef).getNorm(), 0.01 * noise * p * q); } 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); RealMatrix x = new QRDecompositionImpl(a).getSolver().solve(b); // too many equations, the system cannot be solved at all assertTrue(x.subtract(xRef).getNorm() / (p * q) > 0.01); // the last unknown should have been set to 0 assertEquals(0.0, x.getSubMatrix(p, q - 1, 0, x.getColumnDimension() - 1).getNorm()); } 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) throws MatrixVisitorException { return 2.0 * r.nextDouble() - 1.0; } }); return m; } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math QRSolverTest.java source code file: |
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