MATH-1500 (unit tests).
This commit is contained in:
Gilles Sadowski
parent
9988a5b3c4
commit
471d4d60dc
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@ -17,60 +17,47 @@
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package org.apache.commons.math4.field.linalg;
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import org.apache.commons.numbers.fraction.Fraction;
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import org.apache.commons.numbers.field.FractionField;
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import org.junit.Test;
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import org.junit.Assert;
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import org.apache.commons.math4.linear.NonSquareMatrixException;
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import org.apache.commons.numbers.fraction.Fraction;
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import org.apache.commons.numbers.field.FractionField;
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import org.apache.commons.math4.linear.SingularMatrixException;
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import org.apache.commons.math4.exception.DimensionMismatchException;
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public class FieldLUDecompositionTest {
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private final Fraction[][] testData = {
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{ Fraction.of(1), Fraction.of(2), Fraction.of(3)},
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{ Fraction.of(2), Fraction.of(5), Fraction.of(3)},
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{ Fraction.of(1), Fraction.of(0), Fraction.of(8)}
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private final int[][] testData = {
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{ 1, 2, 3 },
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{ 2, 5, 3 },
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{ 1, 0, 8 }
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};
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private final Fraction[][] testDataMinus = {
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{ Fraction.of(-1), Fraction.of(-2), Fraction.of(-3)},
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{ Fraction.of(-2), Fraction.of(-5), Fraction.of(-3)},
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{ Fraction.of(-1), Fraction.of(0), Fraction.of(-8)}
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private final int[][] testDataMinus = {
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{ -1, -2, -3 },
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{ -2, -5, -3 },
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{ -1, 0, -8 }
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};
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private final Fraction[][] luData = {
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{ Fraction.of(2), Fraction.of(3), Fraction.of(3) },
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{ Fraction.of(2), Fraction.of(3), Fraction.of(7) },
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{ Fraction.of(6), Fraction.of(6), Fraction.of(8) }
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private final int[][] luData = {
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{ 2, 3, 3 },
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{ 2, 3, 7 },
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{ 6, 6, 8 }
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};
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private final int[][] luData2 = {
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{ 2, 3, 3 },
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{ 0, 5, 7 },
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{ 6, 9, 8 }
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};
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// singular matrices
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private final Fraction[][] singular = {
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{ Fraction.of(2), Fraction.of(3) },
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{ Fraction.of(2), Fraction.of(3) }
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private int[][] singular = {
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{ 2, 3 },
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{ 2, 3 }
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};
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private final Fraction[][] bigSingular = {
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{ Fraction.of(1), Fraction.of(2), Fraction.of(3), Fraction.of(4) },
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{ Fraction.of(2), Fraction.of(5), Fraction.of(3), Fraction.of(4) },
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{ Fraction.of(7), Fraction.of(3), Fraction.of(256), Fraction.of(1930) },
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{ Fraction.of(3), Fraction.of(7), Fraction.of(6), Fraction.of(8) }
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private final int[][] bigSingular = {
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{ 1, 2, 3, 4 },
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{ 2, 5, 3, 4 },
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{ 7, 3, 256, 1930 },
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{ 3, 7, 6, 8 }
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}; // 4th row = 1st + 2nd
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/**
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* @param data Matrix.
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* @return a {@link FieldDenseMatrix} instance.
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*/
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private FieldDenseMatrix<Fraction> create(Fraction[][] data) {
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final FieldDenseMatrix<Fraction> m = FieldDenseMatrix.create(FractionField.get(),
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data.length,
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data[0].length);
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for (int i = 0; i < data.length; i++) {
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for (int j = 0; j < data.length; j++) {
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m.set(i, j, data[i][j]);
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}
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}
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return m;
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}
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/** test dimensions */
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@Test
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public void testDimensions() {
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FieldDenseMatrix<Fraction> matrix = create(testData);
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@ -80,7 +67,6 @@ public class FieldLUDecompositionTest {
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Assert.assertEquals(testData.length, LU.getP().getRowDimension());
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}
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/** test PA = LU */
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@Test
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public void testPAEqualLU() {
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FieldDenseMatrix<Fraction> matrix = create(testData);
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@ -105,7 +91,7 @@ public class FieldLUDecompositionTest {
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Assert.assertEquals(p.multiply(matrix), l.multiply(u));
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}
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/** test that L is lower triangular with unit diagonal */
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/* L is lower triangular with unit diagonal */
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@Test
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public void testLLowerTriangular() {
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FieldDenseMatrix<Fraction> matrix = create(testData);
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@ -118,7 +104,7 @@ public class FieldLUDecompositionTest {
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}
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}
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/** test that U is upper triangular */
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/* U is upper triangular */
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@Test
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public void testUUpperTriangular() {
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FieldDenseMatrix<Fraction> matrix = create(testData);
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@ -130,7 +116,7 @@ public class FieldLUDecompositionTest {
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}
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}
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/** test that P is a permutation matrix */
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/* P is a permutation matrix */
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@Test
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public void testPPermutation() {
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FieldDenseMatrix<Fraction> matrix = create(testData);
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@ -202,20 +188,20 @@ public class FieldLUDecompositionTest {
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@Test
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public void testMatricesValues1() {
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FieldLUDecomposition<Fraction> lu = FieldLUDecomposition.of(create(testData));
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FieldDenseMatrix<Fraction> lRef = create(new Fraction[][] {
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{ Fraction.of(1), Fraction.of(0), Fraction.of(0) },
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{ Fraction.of(2), Fraction.of(1), Fraction.of(0) },
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{ Fraction.of(1), Fraction.of(-2), Fraction.of(1) }
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FieldDenseMatrix<Fraction> lRef = create(new int[][] {
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{ 1, 0, 0 },
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{ 2, 1, 0 },
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{ 1, -2, 1 }
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});
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FieldDenseMatrix<Fraction> uRef = create(new Fraction[][] {
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{ Fraction.of(1), Fraction.of(2), Fraction.of(3) },
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{ Fraction.of(0), Fraction.of(1), Fraction.of(-3) },
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{ Fraction.of(0), Fraction.of(0), Fraction.of(-1) }
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FieldDenseMatrix<Fraction> uRef = create(new int[][] {
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{ 1, 2, 3 },
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{ 0, 1, -3 },
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{ 0, 0, -1 }
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});
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FieldDenseMatrix<Fraction> pRef = create(new Fraction[][] {
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{ Fraction.of(1), Fraction.of(0), Fraction.of(0) },
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{ Fraction.of(0), Fraction.of(1), Fraction.of(0) },
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{ Fraction.of(0), Fraction.of(0), Fraction.of(1) }
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FieldDenseMatrix<Fraction> pRef = create(new int[][] {
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{ 1, 0, 0 },
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{ 0, 1, 0 },
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{ 0, 0, 1 }
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});
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int[] pivotRef = { 0, 1, 2 };
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@ -234,34 +220,95 @@ public class FieldLUDecompositionTest {
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@Test
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public void testMatricesValues2() {
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FieldLUDecomposition<Fraction> lu = FieldLUDecomposition.of(create(luData));
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FieldDenseMatrix<Fraction> lRef = create(new Fraction[][] {
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{ Fraction.of(1), Fraction.of(0), Fraction.of(0) },
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{ Fraction.of(3), Fraction.of(1), Fraction.of(0) },
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{ Fraction.of(1), Fraction.of(0), Fraction.of(1) }
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final FieldLUDecomposition<Fraction> lu = FieldLUDecomposition.of(create(luData));
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final FieldDenseMatrix<Fraction> lRef = create(new int[][] {
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{ 1, 0, 0 },
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{ 3, 1, 0 },
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{ 1, 0, 1 }
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});
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FieldDenseMatrix<Fraction> uRef = create(new Fraction[][] {
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{ Fraction.of(2), Fraction.of(3), Fraction.of(3) },
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{ Fraction.of(0), Fraction.of(-3), Fraction.of(-1) },
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{ Fraction.of(0), Fraction.of(0), Fraction.of(4) }
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final FieldDenseMatrix<Fraction> uRef = create(new int[][] {
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{ 2, 3, 3 },
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{ 0, -3, -1 },
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{ 0, 0, 4 }
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});
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FieldDenseMatrix<Fraction> pRef = create(new Fraction[][] {
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{ Fraction.of(1), Fraction.of(0), Fraction.of(0) },
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{ Fraction.of(0), Fraction.of(0), Fraction.of(1) },
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{ Fraction.of(0), Fraction.of(1), Fraction.of(0) }
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final FieldDenseMatrix<Fraction> pRef = create(new int[][] {
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{ 1, 0, 0 },
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{ 0, 0, 1 },
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{ 0, 1, 0 }
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});
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int[] pivotRef = { 0, 2, 1 };
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// check values against known references
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FieldDenseMatrix<Fraction> l = lu.getL();
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final FieldDenseMatrix<Fraction> l = lu.getL();
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Assert.assertEquals(lRef, l);
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FieldDenseMatrix<Fraction> u = lu.getU();
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final FieldDenseMatrix<Fraction> u = lu.getU();
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Assert.assertEquals(uRef, u);
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FieldDenseMatrix<Fraction> p = lu.getP();
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final FieldDenseMatrix<Fraction> p = lu.getP();
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Assert.assertEquals(pRef, p);
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int[] pivot = lu.getPivot();
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for (int i = 0; i < pivotRef.length; ++i) {
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for (int i = 0; i < pivotRef.length; i++) {
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Assert.assertEquals(pivotRef[i], pivot[i]);
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}
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}
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@Test(expected=DimensionMismatchException.class)
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public void testSolveDimensionErrors() {
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FieldLUDecomposition
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.of(create(testData))
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.getSolver()
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.solve(create(new int[2][2]));
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}
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@Test
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public void testSolve() {
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final FieldDecompositionSolver<Fraction> solver = FieldLUDecomposition
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.of(create(testData))
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.getSolver();
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final FieldDenseMatrix<Fraction> b = create(new int[][] {
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{ 1, 0 },
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{ 2, -5 },
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{ 3, 1 }
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});
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final FieldDenseMatrix<Fraction> xRef = create(new int[][] {
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{ 19, -71 },
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{ -6, 22 },
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{ -2, 9 }
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});
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final FieldDenseMatrix<Fraction> x = solver.solve(b);
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for (int i = 0; i < x.getRowDimension(); i++){
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for (int j = 0; j < x.getColumnDimension(); j++){
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Assert.assertEquals("(" + i + ", " + j + ")",
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xRef.get(i, j), x.get(i, j));
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}
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}
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}
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@Test
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public void testDeterminant() {
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Assert.assertEquals(-1, determinant(testData), 1e-15);
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Assert.assertEquals(24, determinant(luData), 1e-14);
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Assert.assertEquals(-10, determinant(luData2), 1e-14);
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Assert.assertEquals(0, determinant(singular), 1e-15);
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Assert.assertEquals(0, determinant(bigSingular), 1e-15);
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}
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private static double determinant(int[][] data) {
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return FieldLUDecomposition.of(create(data)).getDeterminant().doubleValue();
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}
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private static FieldDenseMatrix<Fraction> create(final int[][] data) {
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final int numRows = data.length;
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final int numCols = data[0].length;
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final FieldDenseMatrix<Fraction> m = FieldDenseMatrix
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.create(FractionField.get(), numRows, numCols);
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for (int i = 0; i < numRows; i++) {
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for (int j = 0; j < numCols; j++) {
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m.set(i, j, Fraction.of(data[i][j], 1));
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}
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}
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return m;
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}
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}
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