| /* |
| * 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.exception.MathIllegalArgumentException; |
| |
| import org.junit.Test; |
| import org.junit.Assert; |
| |
| public class LUSolverTest { |
| private double[][] testData = { |
| { 1.0, 2.0, 3.0}, |
| { 2.0, 5.0, 3.0}, |
| { 1.0, 0.0, 8.0} |
| }; |
| private double[][] luData = { |
| { 2.0, 3.0, 3.0 }, |
| { 0.0, 5.0, 7.0 }, |
| { 6.0, 9.0, 8.0 } |
| }; |
| |
| // singular matrices |
| private double[][] singular = { |
| { 2.0, 3.0 }, |
| { 2.0, 3.0 } |
| }; |
| private double[][] bigSingular = { |
| { 1.0, 2.0, 3.0, 4.0 }, |
| { 2.0, 5.0, 3.0, 4.0 }, |
| { 7.0, 3.0, 256.0, 1930.0 }, |
| { 3.0, 7.0, 6.0, 8.0 } |
| }; // 4th row = 1st + 2nd |
| |
| /** test threshold impact */ |
| @Test |
| public void testThreshold() { |
| final RealMatrix matrix = MatrixUtils.createRealMatrix(new double[][] { |
| { 1.0, 2.0, 3.0}, |
| { 2.0, 5.0, 3.0}, |
| { 4.000001, 9.0, 9.0} |
| }); |
| Assert.assertFalse(new LUDecomposition(matrix, 1.0e-5).getSolver().isNonSingular()); |
| Assert.assertTrue(new LUDecomposition(matrix, 1.0e-10).getSolver().isNonSingular()); |
| } |
| |
| /** test singular */ |
| @Test |
| public void testSingular() { |
| DecompositionSolver solver = |
| new LUDecomposition(MatrixUtils.createRealMatrix(testData)).getSolver(); |
| Assert.assertTrue(solver.isNonSingular()); |
| solver = new LUDecomposition(MatrixUtils.createRealMatrix(singular)).getSolver(); |
| Assert.assertFalse(solver.isNonSingular()); |
| solver = new LUDecomposition(MatrixUtils.createRealMatrix(bigSingular)).getSolver(); |
| Assert.assertFalse(solver.isNonSingular()); |
| } |
| |
| /** test solve dimension errors */ |
| @Test |
| public void testSolveDimensionErrors() { |
| DecompositionSolver solver = |
| new LUDecomposition(MatrixUtils.createRealMatrix(testData)).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 |
| } |
| try { |
| solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0))); |
| Assert.fail("an exception should have been thrown"); |
| } catch (MathIllegalArgumentException iae) { |
| // expected behavior |
| } |
| } |
| |
| /** test solve singularity errors */ |
| @Test |
| public void testSolveSingularityErrors() { |
| DecompositionSolver solver = |
| new LUDecomposition(MatrixUtils.createRealMatrix(singular)).getSolver(); |
| RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]); |
| try { |
| solver.solve(b); |
| Assert.fail("an exception should have been thrown"); |
| } catch (SingularMatrixException ime) { |
| // expected behavior |
| } |
| try { |
| solver.solve(b.getColumnVector(0)); |
| Assert.fail("an exception should have been thrown"); |
| } catch (SingularMatrixException ime) { |
| // expected behavior |
| } |
| try { |
| solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0))); |
| Assert.fail("an exception should have been thrown"); |
| } catch (SingularMatrixException ime) { |
| // expected behavior |
| } |
| } |
| |
| /** test solve */ |
| @Test |
| public void testSolve() { |
| DecompositionSolver solver = |
| new LUDecomposition(MatrixUtils.createRealMatrix(testData)).getSolver(); |
| RealMatrix b = MatrixUtils.createRealMatrix(new double[][] { |
| { 1, 0 }, { 2, -5 }, { 3, 1 } |
| }); |
| RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] { |
| { 19, -71 }, { -6, 22 }, { -2, 9 } |
| }); |
| |
| // using RealMatrix |
| Assert.assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 1.0e-13); |
| |
| // using ArrayRealVector |
| for (int i = 0; i < b.getColumnDimension(); ++i) { |
| Assert.assertEquals(0, |
| solver.solve(b.getColumnVector(i)).subtract(xRef.getColumnVector(i)).getNorm(), |
| 1.0e-13); |
| } |
| |
| // using RealVector with an alternate implementation |
| for (int i = 0; i < b.getColumnDimension(); ++i) { |
| ArrayRealVectorTest.RealVectorTestImpl v = |
| new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(i)); |
| Assert.assertEquals(0, |
| solver.solve(v).subtract(xRef.getColumnVector(i)).getNorm(), |
| 1.0e-13); |
| } |
| } |
| |
| /** test determinant */ |
| @Test |
| public void testDeterminant() { |
| Assert.assertEquals( -1, getDeterminant(MatrixUtils.createRealMatrix(testData)), 1.0e-15); |
| Assert.assertEquals(-10, getDeterminant(MatrixUtils.createRealMatrix(luData)), 1.0e-14); |
| Assert.assertEquals( 0, getDeterminant(MatrixUtils.createRealMatrix(singular)), 1.0e-17); |
| Assert.assertEquals( 0, getDeterminant(MatrixUtils.createRealMatrix(bigSingular)), 1.0e-10); |
| } |
| |
| private double getDeterminant(RealMatrix m) { |
| return new LUDecomposition(m).getDeterminant(); |
| } |
| } |