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commit 471d4d60dc21fbccb8c6b4616a00238c245f78f6 Author: Gilles Sadowski <[email protected]> AuthorDate: Mon Oct 28 01:51:42 2019 +0100 MATH-1500 (unit tests). --- .../field/linalg/FieldLUDecompositionTest.java | 195 +++++++++++++-------- 1 file changed, 121 insertions(+), 74 deletions(-) diff --git a/src/test/java/org/apache/commons/math4/field/linalg/FieldLUDecompositionTest.java b/src/test/java/org/apache/commons/math4/field/linalg/FieldLUDecompositionTest.java index b756643..8f08580 100644 --- a/src/test/java/org/apache/commons/math4/field/linalg/FieldLUDecompositionTest.java +++ b/src/test/java/org/apache/commons/math4/field/linalg/FieldLUDecompositionTest.java @@ -17,60 +17,47 @@ package org.apache.commons.math4.field.linalg; -import org.apache.commons.numbers.fraction.Fraction; -import org.apache.commons.numbers.field.FractionField; import org.junit.Test; import org.junit.Assert; -import org.apache.commons.math4.linear.NonSquareMatrixException; +import org.apache.commons.numbers.fraction.Fraction; +import org.apache.commons.numbers.field.FractionField; import org.apache.commons.math4.linear.SingularMatrixException; +import org.apache.commons.math4.exception.DimensionMismatchException; public class FieldLUDecompositionTest { - private final Fraction[][] testData = { - { Fraction.of(1), Fraction.of(2), Fraction.of(3)}, - { Fraction.of(2), Fraction.of(5), Fraction.of(3)}, - { Fraction.of(1), Fraction.of(0), Fraction.of(8)} + private final int[][] testData = { + { 1, 2, 3 }, + { 2, 5, 3 }, + { 1, 0, 8 } + }; + private final int[][] testDataMinus = { + { -1, -2, -3 }, + { -2, -5, -3 }, + { -1, 0, -8 } }; - private final Fraction[][] testDataMinus = { - { Fraction.of(-1), Fraction.of(-2), Fraction.of(-3)}, - { Fraction.of(-2), Fraction.of(-5), Fraction.of(-3)}, - { Fraction.of(-1), Fraction.of(0), Fraction.of(-8)} + private final int[][] luData = { + { 2, 3, 3 }, + { 2, 3, 7 }, + { 6, 6, 8 } }; - private final Fraction[][] luData = { - { Fraction.of(2), Fraction.of(3), Fraction.of(3) }, - { Fraction.of(2), Fraction.of(3), Fraction.of(7) }, - { Fraction.of(6), Fraction.of(6), Fraction.of(8) } + private final int[][] luData2 = { + { 2, 3, 3 }, + { 0, 5, 7 }, + { 6, 9, 8 } }; // singular matrices - private final Fraction[][] singular = { - { Fraction.of(2), Fraction.of(3) }, - { Fraction.of(2), Fraction.of(3) } + private int[][] singular = { + { 2, 3 }, + { 2, 3 } }; - private final Fraction[][] bigSingular = { - { Fraction.of(1), Fraction.of(2), Fraction.of(3), Fraction.of(4) }, - { Fraction.of(2), Fraction.of(5), Fraction.of(3), Fraction.of(4) }, - { Fraction.of(7), Fraction.of(3), Fraction.of(256), Fraction.of(1930) }, - { Fraction.of(3), Fraction.of(7), Fraction.of(6), Fraction.of(8) } + private final int[][] bigSingular = { + { 1, 2, 3, 4 }, + { 2, 5, 3, 4 }, + { 7, 3, 256, 1930 }, + { 3, 7, 6, 8 } }; // 4th row = 1st + 2nd - /** - * @param data Matrix. - * @return a {@link FieldDenseMatrix} instance. - */ - private FieldDenseMatrix<Fraction> create(Fraction[][] data) { - final FieldDenseMatrix<Fraction> m = FieldDenseMatrix.create(FractionField.get(), - data.length, - data[0].length); - for (int i = 0; i < data.length; i++) { - for (int j = 0; j < data.length; j++) { - m.set(i, j, data[i][j]); - } - } - - return m; - } - - /** test dimensions */ @Test public void testDimensions() { FieldDenseMatrix<Fraction> matrix = create(testData); @@ -80,7 +67,6 @@ public class FieldLUDecompositionTest { Assert.assertEquals(testData.length, LU.getP().getRowDimension()); } - /** test PA = LU */ @Test public void testPAEqualLU() { FieldDenseMatrix<Fraction> matrix = create(testData); @@ -105,7 +91,7 @@ public class FieldLUDecompositionTest { Assert.assertEquals(p.multiply(matrix), l.multiply(u)); } - /** test that L is lower triangular with unit diagonal */ + /* L is lower triangular with unit diagonal */ @Test public void testLLowerTriangular() { FieldDenseMatrix<Fraction> matrix = create(testData); @@ -118,7 +104,7 @@ public class FieldLUDecompositionTest { } } - /** test that U is upper triangular */ + /* U is upper triangular */ @Test public void testUUpperTriangular() { FieldDenseMatrix<Fraction> matrix = create(testData); @@ -130,7 +116,7 @@ public class FieldLUDecompositionTest { } } - /** test that P is a permutation matrix */ + /* P is a permutation matrix */ @Test public void testPPermutation() { FieldDenseMatrix<Fraction> matrix = create(testData); @@ -202,20 +188,20 @@ public class FieldLUDecompositionTest { @Test public void testMatricesValues1() { FieldLUDecomposition<Fraction> lu = FieldLUDecomposition.of(create(testData)); - FieldDenseMatrix<Fraction> lRef = create(new Fraction[][] { - { Fraction.of(1), Fraction.of(0), Fraction.of(0) }, - { Fraction.of(2), Fraction.of(1), Fraction.of(0) }, - { Fraction.of(1), Fraction.of(-2), Fraction.of(1) } + FieldDenseMatrix<Fraction> lRef = create(new int[][] { + { 1, 0, 0 }, + { 2, 1, 0 }, + { 1, -2, 1 } }); - FieldDenseMatrix<Fraction> uRef = create(new Fraction[][] { - { Fraction.of(1), Fraction.of(2), Fraction.of(3) }, - { Fraction.of(0), Fraction.of(1), Fraction.of(-3) }, - { Fraction.of(0), Fraction.of(0), Fraction.of(-1) } + FieldDenseMatrix<Fraction> uRef = create(new int[][] { + { 1, 2, 3 }, + { 0, 1, -3 }, + { 0, 0, -1 } }); - FieldDenseMatrix<Fraction> pRef = create(new Fraction[][] { - { Fraction.of(1), Fraction.of(0), Fraction.of(0) }, - { Fraction.of(0), Fraction.of(1), Fraction.of(0) }, - { Fraction.of(0), Fraction.of(0), Fraction.of(1) } + FieldDenseMatrix<Fraction> pRef = create(new int[][] { + { 1, 0, 0 }, + { 0, 1, 0 }, + { 0, 0, 1 } }); int[] pivotRef = { 0, 1, 2 }; @@ -234,34 +220,95 @@ public class FieldLUDecompositionTest { @Test public void testMatricesValues2() { - FieldLUDecomposition<Fraction> lu = FieldLUDecomposition.of(create(luData)); - FieldDenseMatrix<Fraction> lRef = create(new Fraction[][] { - { Fraction.of(1), Fraction.of(0), Fraction.of(0) }, - { Fraction.of(3), Fraction.of(1), Fraction.of(0) }, - { Fraction.of(1), Fraction.of(0), Fraction.of(1) } + final FieldLUDecomposition<Fraction> lu = FieldLUDecomposition.of(create(luData)); + final FieldDenseMatrix<Fraction> lRef = create(new int[][] { + { 1, 0, 0 }, + { 3, 1, 0 }, + { 1, 0, 1 } }); - FieldDenseMatrix<Fraction> uRef = create(new Fraction[][] { - { Fraction.of(2), Fraction.of(3), Fraction.of(3) }, - { Fraction.of(0), Fraction.of(-3), Fraction.of(-1) }, - { Fraction.of(0), Fraction.of(0), Fraction.of(4) } + final FieldDenseMatrix<Fraction> uRef = create(new int[][] { + { 2, 3, 3 }, + { 0, -3, -1 }, + { 0, 0, 4 } }); - FieldDenseMatrix<Fraction> pRef = create(new Fraction[][] { - { Fraction.of(1), Fraction.of(0), Fraction.of(0) }, - { Fraction.of(0), Fraction.of(0), Fraction.of(1) }, - { Fraction.of(0), Fraction.of(1), Fraction.of(0) } + final FieldDenseMatrix<Fraction> pRef = create(new int[][] { + { 1, 0, 0 }, + { 0, 0, 1 }, + { 0, 1, 0 } }); int[] pivotRef = { 0, 2, 1 }; // check values against known references - FieldDenseMatrix<Fraction> l = lu.getL(); + final FieldDenseMatrix<Fraction> l = lu.getL(); Assert.assertEquals(lRef, l); - FieldDenseMatrix<Fraction> u = lu.getU(); + final FieldDenseMatrix<Fraction> u = lu.getU(); Assert.assertEquals(uRef, u); - FieldDenseMatrix<Fraction> p = lu.getP(); + final FieldDenseMatrix<Fraction> p = lu.getP(); Assert.assertEquals(pRef, p); int[] pivot = lu.getPivot(); - for (int i = 0; i < pivotRef.length; ++i) { + for (int i = 0; i < pivotRef.length; i++) { Assert.assertEquals(pivotRef[i], pivot[i]); } } + + @Test(expected=DimensionMismatchException.class) + public void testSolveDimensionErrors() { + FieldLUDecomposition + .of(create(testData)) + .getSolver() + .solve(create(new int[2][2])); + } + + @Test + public void testSolve() { + final FieldDecompositionSolver<Fraction> solver = FieldLUDecomposition + .of(create(testData)) + .getSolver(); + final FieldDenseMatrix<Fraction> b = create(new int[][] { + { 1, 0 }, + { 2, -5 }, + { 3, 1 } + }); + final FieldDenseMatrix<Fraction> xRef = create(new int[][] { + { 19, -71 }, + { -6, 22 }, + { -2, 9 } + }); + + final FieldDenseMatrix<Fraction> x = solver.solve(b); + for (int i = 0; i < x.getRowDimension(); i++){ + for (int j = 0; j < x.getColumnDimension(); j++){ + Assert.assertEquals("(" + i + ", " + j + ")", + xRef.get(i, j), x.get(i, j)); + } + } + } + + @Test + public void testDeterminant() { + Assert.assertEquals(-1, determinant(testData), 1e-15); + Assert.assertEquals(24, determinant(luData), 1e-14); + Assert.assertEquals(-10, determinant(luData2), 1e-14); + Assert.assertEquals(0, determinant(singular), 1e-15); + Assert.assertEquals(0, determinant(bigSingular), 1e-15); + } + + private static double determinant(int[][] data) { + return FieldLUDecomposition.of(create(data)).getDeterminant().doubleValue(); + } + + private static FieldDenseMatrix<Fraction> create(final int[][] data) { + final int numRows = data.length; + final int numCols = data[0].length; + final FieldDenseMatrix<Fraction> m = FieldDenseMatrix + .create(FractionField.get(), numRows, numCols); + + for (int i = 0; i < numRows; i++) { + for (int j = 0; j < numCols; j++) { + m.set(i, j, Fraction.of(data[i][j], 1)); + } + } + + return m; + } }
