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Commons Math example source code file (BiDiagonalTransformerTest.java)
The Commons Math BiDiagonalTransformerTest.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 org.apache.commons.math.linear.BiDiagonalTransformer; import org.apache.commons.math.linear.MatrixUtils; import org.apache.commons.math.linear.RealMatrix; import org.junit.Assert; import org.junit.Test; public class BiDiagonalTransformerTest { private double[][] testSquare = { { 24.0 / 25.0, 43.0 / 25.0 }, { 57.0 / 25.0, 24.0 / 25.0 } }; private double[][] testNonSquare = { { -540.0 / 625.0, 963.0 / 625.0, -216.0 / 625.0 }, { -1730.0 / 625.0, -744.0 / 625.0, 1008.0 / 625.0 }, { -720.0 / 625.0, 1284.0 / 625.0, -288.0 / 625.0 }, { -360.0 / 625.0, 192.0 / 625.0, 1756.0 / 625.0 }, }; @Test public void testDimensions() { checkdimensions(MatrixUtils.createRealMatrix(testSquare)); checkdimensions(MatrixUtils.createRealMatrix(testNonSquare)); checkdimensions(MatrixUtils.createRealMatrix(testNonSquare).transpose()); } private void checkdimensions(RealMatrix matrix) { final int m = matrix.getRowDimension(); final int n = matrix.getColumnDimension(); BiDiagonalTransformer transformer = new BiDiagonalTransformer(matrix); Assert.assertEquals(m, transformer.getU().getRowDimension()); Assert.assertEquals(m, transformer.getU().getColumnDimension()); Assert.assertEquals(m, transformer.getB().getRowDimension()); Assert.assertEquals(n, transformer.getB().getColumnDimension()); Assert.assertEquals(n, transformer.getV().getRowDimension()); Assert.assertEquals(n, transformer.getV().getColumnDimension()); } @Test public void testAEqualUSVt() { checkAEqualUSVt(MatrixUtils.createRealMatrix(testSquare)); checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare)); checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare).transpose()); } private void checkAEqualUSVt(RealMatrix matrix) { BiDiagonalTransformer transformer = new BiDiagonalTransformer(matrix); RealMatrix u = transformer.getU(); RealMatrix b = transformer.getB(); RealMatrix v = transformer.getV(); double norm = u.multiply(b).multiply(v.transpose()).subtract(matrix).getNorm(); Assert.assertEquals(0, norm, 1.0e-14); } @Test public void testUOrthogonal() { checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getU()); checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getU()); checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getU()); } @Test public void testVOrthogonal() { checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getV()); checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getV()); checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getV()); } private void checkOrthogonal(RealMatrix m) { RealMatrix mTm = m.transpose().multiply(m); RealMatrix id = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension()); Assert.assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-14); } @Test public void testBBiDiagonal() { checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getB()); checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getB()); checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getB()); } private void checkBiDiagonal(RealMatrix m) { final int rows = m.getRowDimension(); final int cols = m.getColumnDimension(); for (int i = 0; i < rows; ++i) { for (int j = 0; j < cols; ++j) { if (rows < cols) { if ((i < j) || (i > j + 1)) { Assert.assertEquals(0, m.getEntry(i, j), 1.0e-16); } } else { if ((i < j - 1) || (i > j)) { Assert.assertEquals(0, m.getEntry(i, j), 1.0e-16); } } } } } @Test public void testSingularMatrix() { BiDiagonalTransformer transformer = new BiDiagonalTransformer(MatrixUtils.createRealMatrix(new double[][] { { 1.0, 2.0, 3.0 }, { 2.0, 3.0, 4.0 }, { 3.0, 5.0, 7.0 } })); final double s3 = Math.sqrt(3.0); final double s14 = Math.sqrt(14.0); final double s1553 = Math.sqrt(1553.0); RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] { { -1.0 / s14, 5.0 / (s3 * s14), 1.0 / s3 }, { -2.0 / s14, -4.0 / (s3 * s14), 1.0 / s3 }, { -3.0 / s14, 1.0 / (s3 * s14), -1.0 / s3 } }); RealMatrix bRef = MatrixUtils.createRealMatrix(new double[][] { { -s14, s1553 / s14, 0.0 }, { 0.0, -87 * s3 / (s14 * s1553), -s3 * s14 / s1553 }, { 0.0, 0.0, 0.0 } }); RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] { { 1.0, 0.0, 0.0 }, { 0.0, -23 / s1553, 32 / s1553 }, { 0.0, -32 / s1553, -23 / s1553 } }); // check values against known references RealMatrix u = transformer.getU(); Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-14); RealMatrix b = transformer.getB(); Assert.assertEquals(0, b.subtract(bRef).getNorm(), 1.0e-14); RealMatrix v = transformer.getV(); Assert.assertEquals(0, v.subtract(vRef).getNorm(), 1.0e-14); // check the same cached instance is returned the second time Assert.assertTrue(u == transformer.getU()); Assert.assertTrue(b == transformer.getB()); Assert.assertTrue(v == transformer.getV()); } @Test public void testMatricesValues() { BiDiagonalTransformer transformer = new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)); final double s17 = Math.sqrt(17.0); RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] { { -8 / (5 * s17), 19 / (5 * s17) }, { -19 / (5 * s17), -8 / (5 * s17) } }); RealMatrix bRef = MatrixUtils.createRealMatrix(new double[][] { { -3 * s17 / 5, 32 * s17 / 85 }, { 0.0, -5 * s17 / 17 } }); RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] { { 1.0, 0.0 }, { 0.0, -1.0 } }); // check values against known references RealMatrix u = transformer.getU(); Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-14); RealMatrix b = transformer.getB(); Assert.assertEquals(0, b.subtract(bRef).getNorm(), 1.0e-14); RealMatrix v = transformer.getV(); Assert.assertEquals(0, v.subtract(vRef).getNorm(), 1.0e-14); // check the same cached instance is returned the second time Assert.assertTrue(u == transformer.getU()); Assert.assertTrue(b == transformer.getB()); Assert.assertTrue(v == transformer.getV()); } @Test public void testUpperOrLower() { Assert.assertTrue(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).isUpperBiDiagonal()); Assert.assertTrue(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).isUpperBiDiagonal()); Assert.assertFalse(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).isUpperBiDiagonal()); } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math BiDiagonalTransformerTest.java source code file: |
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