| /* |
| * 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.math4.linear; |
| |
| import org.apache.commons.math4.exception.MathIllegalArgumentException; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| public class SingularValueSolverTest { |
| |
| private double[][] testSquare = { |
| { 24.0 / 25.0, 43.0 / 25.0 }, |
| { 57.0 / 25.0, 24.0 / 25.0 } |
| }; |
| 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 |
| |
| private static final double normTolerance = 10e-14; |
| |
| /** test solve dimension errors */ |
| @Test |
| public void testSolveDimensionErrors() { |
| DecompositionSolver solver = |
| new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)).getSolver(); |
| RealMatrix b = MatrixUtils.createRealMatrix(new double[3][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 least square solve */ |
| @Test |
| public void testLeastSquareSolve() { |
| RealMatrix m = |
| MatrixUtils.createRealMatrix(new double[][] { |
| { 1.0, 0.0 }, |
| { 0.0, 0.0 } |
| }); |
| DecompositionSolver solver = new SingularValueDecomposition(m).getSolver(); |
| RealMatrix b = MatrixUtils.createRealMatrix(new double[][] { |
| { 11, 12 }, { 21, 22 } |
| }); |
| RealMatrix xMatrix = solver.solve(b); |
| Assert.assertEquals(11, xMatrix.getEntry(0, 0), 1.0e-15); |
| Assert.assertEquals(12, xMatrix.getEntry(0, 1), 1.0e-15); |
| Assert.assertEquals(0, xMatrix.getEntry(1, 0), 1.0e-15); |
| Assert.assertEquals(0, xMatrix.getEntry(1, 1), 1.0e-15); |
| RealVector xColVec = solver.solve(b.getColumnVector(0)); |
| Assert.assertEquals(11, xColVec.getEntry(0), 1.0e-15); |
| Assert.assertEquals(0, xColVec.getEntry(1), 1.0e-15); |
| RealVector xColOtherVec = solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0))); |
| Assert.assertEquals(11, xColOtherVec.getEntry(0), 1.0e-15); |
| Assert.assertEquals(0, xColOtherVec.getEntry(1), 1.0e-15); |
| } |
| |
| /** test solve */ |
| @Test |
| public void testSolve() { |
| DecompositionSolver solver = |
| new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)).getSolver(); |
| RealMatrix b = MatrixUtils.createRealMatrix(new double[][] { |
| { 1, 2, 3 }, { 0, -5, 1 } |
| }); |
| RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] { |
| { -8.0 / 25.0, -263.0 / 75.0, -29.0 / 75.0 }, |
| { 19.0 / 25.0, 78.0 / 25.0, 49.0 / 25.0 } |
| }); |
| |
| // using RealMatrix |
| Assert.assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), normTolerance); |
| |
| // 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 condition number */ |
| @Test |
| public void testConditionNumber() { |
| SingularValueDecomposition svd = |
| new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)); |
| // replace 1.0e-15 with 1.5e-15 |
| Assert.assertEquals(3.0, svd.getConditionNumber(), 1.5e-15); |
| } |
| |
| @Test |
| public void testMath320B() { |
| RealMatrix rm = new Array2DRowRealMatrix(new double[][] { |
| { 1.0, 2.0 }, { 1.0, 2.0 } |
| }); |
| SingularValueDecomposition svd = |
| new SingularValueDecomposition(rm); |
| RealMatrix recomposed = svd.getU().multiply(svd.getS()).multiply(svd.getVT()); |
| Assert.assertEquals(0.0, recomposed.subtract(rm).getNorm(), 2.0e-15); |
| } |
| |
| @Test |
| public void testSingular() { |
| SingularValueDecomposition svd = |
| new SingularValueDecomposition(MatrixUtils.createRealMatrix(bigSingular)); |
| RealMatrix pseudoInverse = svd.getSolver().getInverse(); |
| RealMatrix expected = new Array2DRowRealMatrix(new double[][] { |
| {-0.0355022687,0.0512742236,-0.0001045523,0.0157719549}, |
| {-0.3214992438,0.3162419255,0.0000348508,-0.0052573183}, |
| {0.5437098346,-0.4107754586,-0.0008256918,0.132934376}, |
| {-0.0714905202,0.053808742,0.0006279816,-0.0176817782} |
| }); |
| Assert.assertEquals(0, expected.subtract(pseudoInverse).getNorm(), 1.0e-9); |
| } |
| |
| } |