/*
 * 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 java.math.BigDecimal;

/**
 * Test cases for the {@link BigMatrixImpl} class.
 *
 * @version $Revision$ $Date$
 */
@Deprecated
public final class BigMatrixImplTest extends TestCase {

	// Test data for String constructors
	protected String[][] testDataString = { { "1", "2", "3" }, { "2", "5", "3" }, { "1", "0", "8" } };

	// 3 x 3 identity matrix
	protected double[][] id = { { 1d, 0d, 0d }, { 0d, 1d, 0d }, { 0d, 0d, 1d } };

	// Test data for group operations
	protected double[][] testData = { { 1d, 2d, 3d }, { 2d, 5d, 3d }, { 1d, 0d, 8d } };
	protected double[][] testDataLU = { { 2d, 5d, 3d }, { .5d, -2.5d, 6.5d }, { 0.5d, 0.2d, .2d } };
	protected double[][] testDataPlus2 = { { 3d, 4d, 5d }, { 4d, 7d, 5d }, { 3d, 2d, 10d } };
	protected double[][] testDataMinus = { { -1d, -2d, -3d }, { -2d, -5d, -3d }, { -1d, 0d, -8d } };
	protected double[] testDataRow1 = { 1d, 2d, 3d };
	protected double[] testDataCol3 = { 3d, 3d, 8d };
	protected double[][] testDataInv = { { -40d, 16d, 9d }, { 13d, -5d, -3d }, { 5d, -2d, -1d } };
	protected double[] preMultTest = { 8, 12, 33 };
	protected double[][] testData2 = { { 1d, 2d, 3d }, { 2d, 5d, 3d } };
	protected double[][] testData2T = { { 1d, 2d }, { 2d, 5d }, { 3d, 3d } };
	protected double[][] testDataPlusInv = { { -39d, 18d, 12d }, { 15d, 0d, 0d }, { 6d, -2d, 7d } };

	// lu decomposition tests
	protected double[][] luData = { { 2d, 3d, 3d }, { 0d, 5d, 7d }, { 6d, 9d, 8d } };
	protected double[][] luDataLUDecomposition = { { 6d, 9d, 8d }, { 0d, 5d, 7d },
			{ 0.33333333333333, 0d, 0.33333333333333 } };

	// singular matrices
	protected double[][] singular = { { 2d, 3d }, { 2d, 3d } };
	protected double[][] bigSingular = { { 1d, 2d, 3d, 4d }, { 2d, 5d, 3d, 4d }, { 7d, 3d, 256d, 1930d },
			{ 3d, 7d, 6d, 8d } }; // 4th row = 1st + 2nd
	protected double[][] detData = { { 1d, 2d, 3d }, { 4d, 5d, 6d }, { 7d, 8d, 10d } };
	protected double[][] detData2 = { { 1d, 3d }, { 2d, 4d } };

	// vectors
	protected double[] testVector = { 1, 2, 3 };
	protected double[] testVector2 = { 1, 2, 3, 4 };

	// submatrix accessor tests
	protected double[][] subTestData = { { 1, 2, 3, 4 }, { 1.5, 2.5, 3.5, 4.5 }, { 2, 4, 6, 8 }, { 4, 5, 6, 7 } };
	// array selections
	protected double[][] subRows02Cols13 = { { 2, 4 }, { 4, 8 } };
	protected double[][] subRows03Cols12 = { { 2, 3 }, { 5, 6 } };
	protected double[][] subRows03Cols123 = { { 2, 3, 4 }, { 5, 6, 7 } };
	// effective permutations
	protected double[][] subRows20Cols123 = { { 4, 6, 8 }, { 2, 3, 4 } };
	protected double[][] subRows31Cols31 = { { 7, 5 }, { 4.5, 2.5 } };
	// contiguous ranges
	protected double[][] subRows01Cols23 = { { 3, 4 }, { 3.5, 4.5 } };
	protected double[][] subRows23Cols00 = { { 2 }, { 4 } };
	protected double[][] subRows00Cols33 = { { 4 } };
	// row matrices
	protected double[][] subRow0 = { { 1, 2, 3, 4 } };
	protected double[][] subRow3 = { { 4, 5, 6, 7 } };
	// column matrices
	protected double[][] subColumn1 = { { 2 }, { 2.5 }, { 4 }, { 5 } };
	protected double[][] subColumn3 = { { 4 }, { 4.5 }, { 8 }, { 7 } };

	// tolerances
	protected double entryTolerance = 10E-16;
	protected double normTolerance = 10E-14;

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

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

	public static final double[] asDouble(BigDecimal[] data) {
		double d[] = new double[data.length];
		for (int i = 0; i < d.length; i++) {
			d[i] = data[i].doubleValue();
		}
		return d;
	}

	public static final double[][] asDouble(BigDecimal[][] data) {
		double d[][] = new double[data.length][data[0].length];
		for (int i = 0; i < d.length; i++) {
			for (int j = 0; j < d[i].length; j++)
				d[i][j] = data[i][j].doubleValue();
		}
		return d;
	}

	public static final BigDecimal[] asBigDecimal(double[] data) {
		BigDecimal d[] = new BigDecimal[data.length];
		for (int i = 0; i < d.length; i++) {
			d[i] = new BigDecimal(data[i]);
		}
		return d;
	}

	public static final BigDecimal[][] asBigDecimal(double[][] data) {
		BigDecimal d[][] = new BigDecimal[data.length][data[0].length];
		for (int i = 0; i < d.length; i++) {
			for (int j = 0; j < data[i].length; j++) {
				d[i][j] = new BigDecimal(data[i][j]);
			}
		}
		return d;
	}

	/** test dimensions */
	public void testDimensions() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrixImpl m2 = new BigMatrixImpl(testData2);
		assertEquals("testData row dimension", 3, m.getRowDimension());
		assertEquals("testData column dimension", 3, m.getColumnDimension());
		assertTrue("testData is square", m.isSquare());
		assertEquals("testData2 row dimension", m2.getRowDimension(), 2);
		assertEquals("testData2 column dimension", m2.getColumnDimension(), 3);
		assertTrue("testData2 is not square", !m2.isSquare());
	}

	/** test copy functions */
	public void testCopyFunctions() {
		BigMatrixImpl m1 = new BigMatrixImpl(testData);
		BigMatrixImpl m2 = new BigMatrixImpl(m1.getData());
		assertEquals(m2, m1);
		BigMatrixImpl m3 = new BigMatrixImpl(testData);
		BigMatrixImpl m4 = new BigMatrixImpl(m3.getData(), false);
		assertEquals(m4, m3);
	}

	/** test constructors */
	public void testConstructors() {
		BigMatrix m1 = new BigMatrixImpl(testData);
		BigMatrix m2 = new BigMatrixImpl(testDataString);
		BigMatrix m3 = new BigMatrixImpl(asBigDecimal(testData));
		BigMatrix m4 = new BigMatrixImpl(asBigDecimal(testData), true);
		BigMatrix m5 = new BigMatrixImpl(asBigDecimal(testData), false);
		assertClose("double, string", m1, m2, Double.MIN_VALUE);
		assertClose("double, BigDecimal", m1, m3, Double.MIN_VALUE);
		assertClose("string, BigDecimal", m2, m3, Double.MIN_VALUE);
		assertClose("double, BigDecimal/true", m1, m4, Double.MIN_VALUE);
		assertClose("double, BigDecimal/false", m1, m5, Double.MIN_VALUE);
		try {
			new BigMatrixImpl(new String[][] { { "0", "hello", "1" } });
			fail("Expecting NumberFormatException");
		} catch (NumberFormatException ex) {
			// expected
		}
		try {
			new BigMatrixImpl(new String[][] {});
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// expected
		}
		try {
			new BigMatrixImpl(new String[][] { {}, {} });
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// expected
		}
		try {
			new BigMatrixImpl(new String[][] { { "a", "b" }, { "c" } });
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// expected
		}

		try {
			new BigMatrixImpl(0, 1);
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// expected
		}
		try {
			new BigMatrixImpl(1, 0);
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// expected
		}
	}

	/** test add */
	public void testAdd() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrixImpl mInv = new BigMatrixImpl(testDataInv);
		BigMatrix mPlusMInv = m.add(mInv);
		double[][] sumEntries = asDouble(mPlusMInv.getData());
		for (int row = 0; row < m.getRowDimension(); row++) {
			for (int col = 0; col < m.getColumnDimension(); col++) {
				assertEquals("sum entry entry", testDataPlusInv[row][col], sumEntries[row][col], entryTolerance);
			}
		}
	}

	/** test add failure */
	public void testAddFail() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrixImpl m2 = new BigMatrixImpl(testData2);
		try {
			m.add(m2);
			fail("IllegalArgumentException expected");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
	}

	/** test norm */
	public void testNorm() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrixImpl m2 = new BigMatrixImpl(testData2);
		assertEquals("testData norm", 14d, m.getNorm().doubleValue(), entryTolerance);
		assertEquals("testData2 norm", 7d, m2.getNorm().doubleValue(), entryTolerance);
	}

	/** test m-n = m + -n */
	public void testPlusMinus() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrixImpl m2 = new BigMatrixImpl(testDataInv);
		assertClose("m-n = m + -n", m.subtract(m2), m2.scalarMultiply(new BigDecimal(-1d)).add(m), entryTolerance);
		try {
			m.subtract(new BigMatrixImpl(testData2));
			fail("Expecting illegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
	}

	/** test multiply */
	public void testMultiply() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrixImpl mInv = new BigMatrixImpl(testDataInv);
		BigMatrixImpl identity = new BigMatrixImpl(id);
		BigMatrixImpl m2 = new BigMatrixImpl(testData2);
		assertClose("inverse multiply", m.multiply(mInv), identity, entryTolerance);
		assertClose("inverse multiply", mInv.multiply(m), identity, entryTolerance);
		assertClose("identity multiply", m.multiply(identity), m, entryTolerance);
		assertClose("identity multiply", identity.multiply(mInv), mInv, entryTolerance);
		assertClose("identity multiply", m2.multiply(identity), m2, entryTolerance);
		try {
			m.multiply(new BigMatrixImpl(bigSingular));
			fail("Expecting illegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
	}

	// Additional Test for BigMatrixImplTest.testMultiply

	private double[][] d3 = new double[][] { { 1, 2, 3, 4 }, { 5, 6, 7, 8 } };
	private double[][] d4 = new double[][] { { 1 }, { 2 }, { 3 }, { 4 } };
	private double[][] d5 = new double[][] { { 30 }, { 70 } };

	public void testMultiply2() {
		BigMatrix m3 = new BigMatrixImpl(d3);
		BigMatrix m4 = new BigMatrixImpl(d4);
		BigMatrix m5 = new BigMatrixImpl(d5);
		assertClose("m3*m4=m5", m3.multiply(m4), m5, entryTolerance);
	}

	/** test isSingular */
	public void testIsSingular() {
		BigMatrixImpl m = new BigMatrixImpl(singular);
		assertTrue("singular", m.isSingular());
		m = new BigMatrixImpl(bigSingular);
		assertTrue("big singular", m.isSingular());
		m = new BigMatrixImpl(id);
		assertTrue("identity nonsingular", !m.isSingular());
		m = new BigMatrixImpl(testData);
		assertTrue("testData nonsingular", !m.isSingular());
	}

	/** test inverse */
	public void testInverse() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrix mInv = new BigMatrixImpl(testDataInv);
		assertClose("inverse", mInv, m.inverse(), normTolerance);
		assertClose("inverse^2", m, m.inverse().inverse(), 10E-12);

		// Not square
		m = new BigMatrixImpl(testData2);
		try {
			m.inverse();
			fail("Expecting InvalidMatrixException");
		} catch (InvalidMatrixException ex) {
			// expected
		}

		// Singular
		m = new BigMatrixImpl(singular);
		try {
			m.inverse();
			fail("Expecting InvalidMatrixException");
		} catch (InvalidMatrixException ex) {
			// expected
		}
	}

	/** test solve */
	public void testSolve() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrix mInv = new BigMatrixImpl(testDataInv);
		// being a bit slothful here -- actually testing that X = A^-1 * B
		assertClose("inverse-operate", asDouble(mInv.operate(asBigDecimal(testVector))),
				asDouble(m.solve(asBigDecimal(testVector))), normTolerance);
		try {
			asDouble(m.solve(asBigDecimal(testVector2)));
			fail("expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
		BigMatrix bs = new BigMatrixImpl(bigSingular);
		try {
			bs.solve(bs);
			fail("Expecting InvalidMatrixException");
		} catch (InvalidMatrixException ex) {
			// ignored
		}
		try {
			m.solve(bs);
			fail("Expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
		try {
			new BigMatrixImpl(testData2).solve(bs);
			fail("Expecting illegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
		try {
			(new BigMatrixImpl(testData2)).luDecompose();
			fail("Expecting InvalidMatrixException");
		} catch (InvalidMatrixException ex) {
			// ignored
		}
	}

	/** test determinant */
	public void testDeterminant() {
		BigMatrix m = new BigMatrixImpl(bigSingular);
		assertEquals("singular determinant", 0, m.getDeterminant().doubleValue(), 0);
		m = new BigMatrixImpl(detData);
		assertEquals("nonsingular test", -3d, m.getDeterminant().doubleValue(), normTolerance);

		// Examples verified against R (version 1.8.1, Red Hat Linux 9)
		m = new BigMatrixImpl(detData2);
		assertEquals("nonsingular R test 1", -2d, m.getDeterminant().doubleValue(), normTolerance);
		m = new BigMatrixImpl(testData);
		assertEquals("nonsingular  R test 2", -1d, m.getDeterminant().doubleValue(), normTolerance);

		try {
			double d = new BigMatrixImpl(testData2).getDeterminant().doubleValue();
			fail("Expecting InvalidMatrixException, got " + d);
		} catch (InvalidMatrixException ex) {
			// ignored
		}
	}

	/** test trace */
	public void testTrace() {
		BigMatrix m = new BigMatrixImpl(id);
		assertEquals("identity trace", 3d, m.getTrace().doubleValue(), entryTolerance);
		m = new BigMatrixImpl(testData2);
		try {
			double t = m.getTrace().doubleValue();
			fail("Expecting NonSquareMatrixException, got " + t);
		} catch (NonSquareMatrixException ex) {
			// ignored
		}
	}

	/** test sclarAdd */
	public void testScalarAdd() {
		BigMatrix m = new BigMatrixImpl(testData);
		assertClose("scalar add", new BigMatrixImpl(testDataPlus2), m.scalarAdd(new BigDecimal(2d)), entryTolerance);
	}

	/** test operate */
	public void testOperate() {
		BigMatrix m = new BigMatrixImpl(id);
		double[] x = asDouble(m.operate(asBigDecimal(testVector)));
		assertClose("identity operate", testVector, x, entryTolerance);
		m = new BigMatrixImpl(bigSingular);
		try {
			asDouble(m.operate(asBigDecimal(testVector)));
			fail("Expecting illegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
	}

	/** test issue MATH-209 */
	public void testMath209() {
		BigMatrix a = new BigMatrixImpl(new BigDecimal[][] { { new BigDecimal(1), new BigDecimal(2) },
				{ new BigDecimal(3), new BigDecimal(4) }, { new BigDecimal(5), new BigDecimal(6) } }, false);
		BigDecimal[] b = a.operate(new BigDecimal[] { new BigDecimal(1), new BigDecimal(1) });
		assertEquals(a.getRowDimension(), b.length);
		assertEquals(3.0, b[0].doubleValue(), 1.0e-12);
		assertEquals(7.0, b[1].doubleValue(), 1.0e-12);
		assertEquals(11.0, b[2].doubleValue(), 1.0e-12);
	}

	/** test transpose */
	public void testTranspose() {
		BigMatrix m = new BigMatrixImpl(testData);
		assertClose("inverse-transpose", m.inverse().transpose(), m.transpose().inverse(), normTolerance);
		m = new BigMatrixImpl(testData2);
		BigMatrix mt = new BigMatrixImpl(testData2T);
		assertClose("transpose", mt, m.transpose(), normTolerance);
	}

	/** test preMultiply by vector */
	public void testPremultiplyVector() {
		BigMatrix m = new BigMatrixImpl(testData);
		assertClose("premultiply", asDouble(m.preMultiply(asBigDecimal(testVector))), preMultTest, normTolerance);
		m = new BigMatrixImpl(bigSingular);
		try {
			m.preMultiply(asBigDecimal(testVector));
			fail("expecting IllegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
	}

	public void testPremultiply() {
		BigMatrix m3 = new BigMatrixImpl(d3);
		BigMatrix m4 = new BigMatrixImpl(d4);
		BigMatrix m5 = new BigMatrixImpl(d5);
		assertClose("m3*m4=m5", m4.preMultiply(m3), m5, entryTolerance);

		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrixImpl mInv = new BigMatrixImpl(testDataInv);
		BigMatrixImpl identity = new BigMatrixImpl(id);
		new BigMatrixImpl(testData2);
		assertClose("inverse multiply", m.preMultiply(mInv), identity, entryTolerance);
		assertClose("inverse multiply", mInv.preMultiply(m), identity, entryTolerance);
		assertClose("identity multiply", m.preMultiply(identity), m, entryTolerance);
		assertClose("identity multiply", identity.preMultiply(mInv), mInv, entryTolerance);
		try {
			m.preMultiply(new BigMatrixImpl(bigSingular));
			fail("Expecting illegalArgumentException");
		} catch (IllegalArgumentException ex) {
			// ignored
		}
	}

	public void testGetVectors() {
		BigMatrix m = new BigMatrixImpl(testData);
		assertClose("get row", m.getRowAsDoubleArray(0), testDataRow1, entryTolerance);
		assertClose("get col", m.getColumnAsDoubleArray(2), testDataCol3, entryTolerance);
		try {
			m.getRowAsDoubleArray(10);
			fail("expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// ignored
		}
		try {
			m.getColumnAsDoubleArray(-1);
			fail("expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// ignored
		}
	}

	public void testLUDecomposition() throws Exception {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrix lu = m.getLUMatrix();
		assertClose("LU decomposition", lu, new BigMatrixImpl(testDataLU), normTolerance);
		verifyDecomposition(m, lu);
		m = new BigMatrixImpl(luData);
		lu = m.getLUMatrix();
		assertClose("LU decomposition", lu, new BigMatrixImpl(luDataLUDecomposition), normTolerance);
		verifyDecomposition(m, lu);
		m = new BigMatrixImpl(testDataMinus);
		lu = m.getLUMatrix();
		verifyDecomposition(m, lu);
		m = new BigMatrixImpl(id);
		lu = m.getLUMatrix();
		verifyDecomposition(m, lu);
		try {
			m = new BigMatrixImpl(bigSingular); // singular
			lu = m.getLUMatrix();
			fail("Expecting InvalidMatrixException");
		} catch (InvalidMatrixException ex) {
			// expected
		}
		try {
			m = new BigMatrixImpl(testData2); // not square
			lu = m.getLUMatrix();
			fail("Expecting InvalidMatrixException");
		} catch (InvalidMatrixException ex) {
			// expected
		}
	}

	/**
	 * test submatrix accessors
	 */
	public void testSubMatrix() {
		BigMatrix m = new BigMatrixImpl(subTestData);
		BigMatrix mRows23Cols00 = new BigMatrixImpl(subRows23Cols00);
		BigMatrix mRows00Cols33 = new BigMatrixImpl(subRows00Cols33);
		BigMatrix mRows01Cols23 = new BigMatrixImpl(subRows01Cols23);
		BigMatrix mRows02Cols13 = new BigMatrixImpl(subRows02Cols13);
		BigMatrix mRows03Cols12 = new BigMatrixImpl(subRows03Cols12);
		BigMatrix mRows03Cols123 = new BigMatrixImpl(subRows03Cols123);
		BigMatrix mRows20Cols123 = new BigMatrixImpl(subRows20Cols123);
		BigMatrix mRows31Cols31 = new BigMatrixImpl(subRows31Cols31);
		assertEquals("Rows23Cols00", mRows23Cols00, m.getSubMatrix(2, 3, 0, 0));
		assertEquals("Rows00Cols33", mRows00Cols33, m.getSubMatrix(0, 0, 3, 3));
		assertEquals("Rows01Cols23", mRows01Cols23, m.getSubMatrix(0, 1, 2, 3));
		assertEquals("Rows02Cols13", mRows02Cols13, m.getSubMatrix(new int[] { 0, 2 }, new int[] { 1, 3 }));
		assertEquals("Rows03Cols12", mRows03Cols12, m.getSubMatrix(new int[] { 0, 3 }, new int[] { 1, 2 }));
		assertEquals("Rows03Cols123", mRows03Cols123, m.getSubMatrix(new int[] { 0, 3 }, new int[] { 1, 2, 3 }));
		assertEquals("Rows20Cols123", mRows20Cols123, m.getSubMatrix(new int[] { 2, 0 }, new int[] { 1, 2, 3 }));
		assertEquals("Rows31Cols31", mRows31Cols31, m.getSubMatrix(new int[] { 3, 1 }, new int[] { 3, 1 }));
		assertEquals("Rows31Cols31", mRows31Cols31, m.getSubMatrix(new int[] { 3, 1 }, new int[] { 3, 1 }));

		try {
			m.getSubMatrix(1, 0, 2, 4);
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
		try {
			m.getSubMatrix(-1, 1, 2, 2);
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
		try {
			m.getSubMatrix(1, 0, 2, 2);
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
		try {
			m.getSubMatrix(1, 0, 2, 4);
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
		try {
			m.getSubMatrix(new int[] {}, new int[] { 0 });
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
		try {
			m.getSubMatrix(new int[] { 0 }, new int[] { 4 });
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
	}

	public void testGetColumnMatrix() {
		BigMatrix m = new BigMatrixImpl(subTestData);
		BigMatrix mColumn1 = new BigMatrixImpl(subColumn1);
		BigMatrix mColumn3 = new BigMatrixImpl(subColumn3);
		assertEquals("Column1", mColumn1, m.getColumnMatrix(1));
		assertEquals("Column3", mColumn3, m.getColumnMatrix(3));
		try {
			m.getColumnMatrix(-1);
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
		try {
			m.getColumnMatrix(4);
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
	}

	public void testGetRowMatrix() {
		BigMatrix m = new BigMatrixImpl(subTestData);
		BigMatrix mRow0 = new BigMatrixImpl(subRow0);
		BigMatrix mRow3 = new BigMatrixImpl(subRow3);
		assertEquals("Row0", mRow0, m.getRowMatrix(0));
		assertEquals("Row3", mRow3, m.getRowMatrix(3));
		try {
			m.getRowMatrix(-1);
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
		try {
			m.getRowMatrix(4);
			fail("Expecting MatrixIndexException");
		} catch (MatrixIndexException ex) {
			// expected
		}
	}

	public void testEqualsAndHashCode() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		BigMatrixImpl m1 = (BigMatrixImpl) m.copy();
		BigMatrixImpl mt = (BigMatrixImpl) m.transpose();
		assertTrue(m.hashCode() != mt.hashCode());
		assertEquals(m.hashCode(), m1.hashCode());
		assertEquals(m, m);
		assertEquals(m, m1);
		assertFalse(m.equals(null));
		assertFalse(m.equals(mt));
		assertFalse(m.equals(new BigMatrixImpl(bigSingular)));
		// Different scales make BigDecimals, so matrices unequal
		m = new BigMatrixImpl(new String[][] { { "2.0" } });
		m1 = new BigMatrixImpl(new String[][] { { "2.00" } });
		assertTrue(m.hashCode() != m1.hashCode());
		assertFalse(m.equals(m1));
	}

	public void testToString() {
		BigMatrixImpl m = new BigMatrixImpl(testData);
		assertEquals("BigMatrixImpl{{1,2,3},{2,5,3},{1,0,8}}", m.toString());
		m = new BigMatrixImpl();
		assertEquals("BigMatrixImpl{}", m.toString());
	}

	public void testSetSubMatrix() throws Exception {
		BigDecimal[][] detData3 = MatrixUtils.createBigMatrix(detData2).getData();
		BigMatrixImpl m = new BigMatrixImpl(testData);
		m.setSubMatrix(detData3, 1, 1);
		BigMatrix expected = MatrixUtils
				.createBigMatrix(new double[][] { { 1.0, 2.0, 3.0 }, { 2.0, 1.0, 3.0 }, { 1.0, 2.0, 4.0 } });
		assertEquals(expected, m);

		m.setSubMatrix(detData3, 0, 0);
		expected = MatrixUtils
				.createBigMatrix(new double[][] { { 1.0, 3.0, 3.0 }, { 2.0, 4.0, 3.0 }, { 1.0, 2.0, 4.0 } });
		assertEquals(expected, m);

		BigDecimal[][] testDataPlus3 = MatrixUtils.createBigMatrix(testDataPlus2).getData();
		m.setSubMatrix(testDataPlus3, 0, 0);
		expected = MatrixUtils
				.createBigMatrix(new double[][] { { 3.0, 4.0, 5.0 }, { 4.0, 7.0, 5.0 }, { 3.0, 2.0, 10.0 } });
		assertEquals(expected, m);

		// javadoc example
		BigMatrixImpl matrix = (BigMatrixImpl) MatrixUtils
				.createBigMatrix(new double[][] { { 1, 2, 3, 4 }, { 5, 6, 7, 8 }, { 9, 0, 1, 2 } });
		matrix.setSubMatrix(new BigDecimal[][] { { new BigDecimal(3), new BigDecimal(4) },
				{ new BigDecimal(5), new BigDecimal(6) } }, 1, 1);
		expected = MatrixUtils.createBigMatrix(
				new BigDecimal[][] { { new BigDecimal(1), new BigDecimal(2), new BigDecimal(3), new BigDecimal(4) },
						{ new BigDecimal(5), new BigDecimal(3), new BigDecimal(4), new BigDecimal(8) },
						{ new BigDecimal(9), new BigDecimal(5), new BigDecimal(6), new BigDecimal(2) } });
		assertEquals(expected, matrix);

		// dimension overflow
		try {
			m.setSubMatrix(matrix.getData(), 1, 1);
			fail("expecting MatrixIndexException");
		} catch (MatrixIndexException e) {
			// expected
		}

		// null
		try {
			m.setSubMatrix(null, 1, 1);
			fail("expecting NullPointerException");
		} catch (NullPointerException e) {
			// expected
		}

		// ragged
		try {
			m.setSubMatrix(new BigDecimal[][] { { new BigDecimal(1) }, { new BigDecimal(2), new BigDecimal(3) } }, 0,
					0);
			fail("expecting IllegalArgumentException");
		} catch (IllegalArgumentException e) {
			// expected
		}

		// empty
		try {
			m.setSubMatrix(new BigDecimal[][] { {} }, 0, 0);
			fail("expecting IllegalArgumentException");
		} catch (IllegalArgumentException e) {
			// expected
		}

	}

	// --------------- -----------------Protected methods

	/** verifies that two matrices are close (1-norm) */
	protected void assertClose(String msg, BigMatrix m, BigMatrix n, double tolerance) {
		assertTrue(msg, m.subtract(n).getNorm().doubleValue() < tolerance);
	}

	/** verifies that two vectors are close (sup norm) */
	protected void assertClose(String msg, double[] m, double[] n, double tolerance) {
		if (m.length != n.length) {
			fail("vectors not same length");
		}
		for (int i = 0; i < m.length; i++) {
			assertEquals(msg + " " + i + " elements differ", m[i], n[i], tolerance);
		}
	}

	/** extracts the l and u matrices from compact lu representation */
	protected void splitLU(BigMatrix lu, BigDecimal[][] lowerData, BigDecimal[][] upperData)
			throws InvalidMatrixException {
		if (!lu.isSquare() || lowerData.length != lowerData[0].length || upperData.length != upperData[0].length
				|| lowerData.length != upperData.length || lowerData.length != lu.getRowDimension()) {
			throw new InvalidMatrixException("incorrect dimensions");
		}
		int n = lu.getRowDimension();
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				if (j < i) {
					lowerData[i][j] = lu.getEntry(i, j);
					upperData[i][j] = new BigDecimal(0);
				} else if (i == j) {
					lowerData[i][j] = new BigDecimal(1);
					upperData[i][j] = lu.getEntry(i, j);
				} else {
					lowerData[i][j] = new BigDecimal(0);
					upperData[i][j] = lu.getEntry(i, j);
				}
			}
		}
	}

	/**
	 * Returns the result of applying the given row permutation to the matrix
	 */
	protected BigMatrix permuteRows(BigMatrix matrix, int[] permutation) {
		if (!matrix.isSquare() || matrix.getRowDimension() != permutation.length) {
			throw new IllegalArgumentException("dimension mismatch");
		}
		int n = matrix.getRowDimension();
		int m = matrix.getColumnDimension();
		BigDecimal out[][] = new BigDecimal[m][n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				out[i][j] = matrix.getEntry(permutation[i], j);
			}
		}
		return new BigMatrixImpl(out);
	}

	/**
	 * Extracts l and u matrices from lu and verifies that matrix = l times u
	 * modulo permutation
	 */
	protected void verifyDecomposition(BigMatrix matrix, BigMatrix lu) throws Exception {
		int n = matrix.getRowDimension();
		BigDecimal[][] lowerData = new BigDecimal[n][n];
		BigDecimal[][] upperData = new BigDecimal[n][n];
		splitLU(lu, lowerData, upperData);
		BigMatrix lower = new BigMatrixImpl(lowerData);
		BigMatrix upper = new BigMatrixImpl(upperData);
		int[] permutation = ((BigMatrixImpl) matrix).getPermutation();
		BigMatrix permuted = permuteRows(matrix, permutation);
		assertClose("lu decomposition does not work", permuted, lower.multiply(upper), normTolerance);
	}

	// /** Useful for debugging */
	// private void dumpMatrix(BigMatrix m) {
	// for (int i = 0; i < m.getRowDimension(); i++) {
	// String os = "";
	// for (int j = 0; j < m.getColumnDimension(); j++) {
	// os += m.getEntry(i, j) + " ";
	// }
	// System.out.println(os);
	// }
	// }

}
