/*
 * 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 junit.framework.Test;
import junit.framework.TestCase;
import junit.framework.TestSuite;

import org.apache.commons.math.linear.DecompositionSolver;
import org.apache.commons.math.linear.InvalidMatrixException;
import org.apache.commons.math.linear.LUDecompositionImpl;
import org.apache.commons.math.linear.MatrixUtils;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.linear.ArrayRealVector;

public class LUSolverTest extends TestCase {
	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

	public LUSolverTest(String name) {
		super(name);
	}

	public static Test suite() {
		TestSuite suite = new TestSuite(LUSolverTest.class);
		suite.setName("LUSolver Tests");
		return suite;
	}

	/** test threshold impact */
	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 } });
		assertFalse(new LUDecompositionImpl(matrix, 1.0e-5).getSolver().isNonSingular());
		assertTrue(new LUDecompositionImpl(matrix, 1.0e-10).getSolver().isNonSingular());
	}

	/** test singular */
	public void testSingular() {
		DecompositionSolver solver = new LUDecompositionImpl(MatrixUtils.createRealMatrix(testData)).getSolver();
		assertTrue(solver.isNonSingular());
		solver = new LUDecompositionImpl(MatrixUtils.createRealMatrix(singular)).getSolver();
		assertFalse(solver.isNonSingular());
		solver = new LUDecompositionImpl(MatrixUtils.createRealMatrix(bigSingular)).getSolver();
		assertFalse(solver.isNonSingular());
	}

	/** test solve dimension errors */
	public void testSolveDimensionErrors() {
		DecompositionSolver solver = new LUDecompositionImpl(MatrixUtils.createRealMatrix(testData)).getSolver();
		RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
		try {
			solver.solve(b);
			fail("an exception should have been thrown");
		} catch (IllegalArgumentException iae) {
			// expected behavior
		} catch (Exception e) {
			fail("wrong exception caught");
		}
		try {
			solver.solve(b.getColumn(0));
			fail("an exception should have been thrown");
		} catch (IllegalArgumentException iae) {
			// expected behavior
		} catch (Exception e) {
			fail("wrong exception caught");
		}
		try {
			solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
			fail("an exception should have been thrown");
		} catch (IllegalArgumentException iae) {
			// expected behavior
		} catch (Exception e) {
			fail("wrong exception caught");
		}
	}

	/** test solve singularity errors */
	public void testSolveSingularityErrors() {
		DecompositionSolver solver = new LUDecompositionImpl(MatrixUtils.createRealMatrix(singular)).getSolver();
		RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
		try {
			solver.solve(b);
			fail("an exception should have been thrown");
		} catch (InvalidMatrixException ime) {
			// expected behavior
		} catch (Exception e) {
			fail("wrong exception caught");
		}
		try {
			solver.solve(b.getColumn(0));
			fail("an exception should have been thrown");
		} catch (InvalidMatrixException ime) {
			// expected behavior
		} catch (Exception e) {
			fail("wrong exception caught");
		}
		try {
			solver.solve(b.getColumnVector(0));
			fail("an exception should have been thrown");
		} catch (InvalidMatrixException ime) {
			// expected behavior
		} catch (Exception e) {
			fail("wrong exception caught");
		}
		try {
			solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
			fail("an exception should have been thrown");
		} catch (InvalidMatrixException ime) {
			// expected behavior
		} catch (Exception e) {
			fail("wrong exception caught");
		}
	}

	/** test solve */
	public void testSolve() {
		DecompositionSolver solver = new LUDecompositionImpl(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
		assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 1.0e-13);

		// using double[]
		for (int i = 0; i < b.getColumnDimension(); ++i) {
			assertEquals(0,
					new ArrayRealVector(solver.solve(b.getColumn(i))).subtract(xRef.getColumnVector(i)).getNorm(),
					1.0e-13);
		}

		// using ArrayRealVector
		for (int i = 0; i < b.getColumnDimension(); ++i) {
			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));
			assertEquals(0, solver.solve(v).subtract(xRef.getColumnVector(i)).getNorm(), 1.0e-13);
		}

	}

	/** test determinant */
	public void testDeterminant() {
		assertEquals(-1, getDeterminant(MatrixUtils.createRealMatrix(testData)), 1.0e-15);
		assertEquals(-10, getDeterminant(MatrixUtils.createRealMatrix(luData)), 1.0e-14);
		assertEquals(0, getDeterminant(MatrixUtils.createRealMatrix(singular)), 1.0e-17);
		assertEquals(0, getDeterminant(MatrixUtils.createRealMatrix(bigSingular)), 1.0e-10);
	}

	private double getDeterminant(RealMatrix m) {
		return new LUDecompositionImpl(m).getDeterminant();
	}

}
