/*
* Copyright (c) 2009-2012, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* EJML is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation, either version 3
* of the License, or (at your option) any later version.
*
* EJML is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with EJML. If not, see <http://www.gnu.org/licenses/>.
*/
package org.ejml.ops;
import org.ejml.alg.dense.mult.VectorVectorMult;
import org.ejml.data.Complex64F;
import org.ejml.data.DenseMatrix64F;
import org.ejml.data.UtilTestMatrix;
import org.ejml.factory.DecompositionFactory;
import org.ejml.factory.EigenDecomposition;
import org.ejml.factory.SingularValueDecomposition;
import org.junit.Test;
import java.util.Arrays;
import java.util.Random;
import static org.junit.Assert.*;
/**
* @author Peter Abeles
*/
public class TestRandomMatrices {
Random rand = new Random(48757);
/**
* Checks to see if all the vectors are orthogonal and of unit length.
*/
@Test
public void createSpan() {
// test with combinations of vectors and numbers
for( int dimension = 3; dimension <= 5; dimension++ ) {
for( int numVectors = 1; numVectors <= dimension; numVectors++ ) {
DenseMatrix64F span[] = RandomMatrices.createSpan(dimension,numVectors,rand);
assertEquals(numVectors,span.length);
for( int i = 0; i < span.length; i++ ) {
DenseMatrix64F a = span[i];
assertEquals(1,NormOps.fastNormF(a),1e-8);
for( int j = i+1; j < span.length; j++ ) {
double dot = VectorVectorMult.innerProd(a,span[j]);
assertEquals(0,dot,1e-8);
}
}
}
}
}
@Test
public void createInSpan() {
DenseMatrix64F span[] = RandomMatrices.createSpan(5,5,rand);
DenseMatrix64F A = RandomMatrices.createInSpan(span,-1,1,rand);
// reconstructed matrix
DenseMatrix64F R = new DenseMatrix64F(A.numRows,A.numCols);
DenseMatrix64F tmp = new DenseMatrix64F(A.numRows,A.numCols);
// project the matrix into the span and recreate the original matrix
for( int i = 0; i < 5; i++ ) {
double val = VectorVectorMult.innerProd(span[i],A);
assertTrue( Math.abs(val) > 1e-10 );
CommonOps.scale(val,span[i],tmp);
CommonOps.add(R,tmp,R);
}
double error = SpecializedOps.diffNormF(A,R);
assertEquals( error , 0 , 1e-8 );
}
@Test
public void createOrthogonal() {
for( int numRows = 3; numRows <= 5; numRows++ ) {
for( int numCols = 1; numCols <= numRows; numCols++ ) {
DenseMatrix64F Q = RandomMatrices.createOrthogonal(numRows,numCols,rand);
assertEquals(Q.numRows,numRows);
assertEquals(Q.numCols,numCols);
assertTrue(CommonOps.elementSum(Q) != 0);
assertTrue(MatrixFeatures.isOrthogonal(Q,1e-8));
}
}
}
@Test
public void createDiagonal_square() {
DenseMatrix64F A = RandomMatrices.createDiagonal(5,1,10,rand);
assertTrue(CommonOps.elementSum(A) > 5 );
for( int i = 0; i < A.numRows; i++ ) {
for( int j = 0; j < A.numCols; j++ ) {
double v = A.get(i,j);
if( i == j ) {
assertTrue(v >= 1 || v <= 10);
} else {
assertTrue(v == 0);
}
}
}
}
@Test
public void createDiagonal_general() {
testDiagonal(5,3);
testDiagonal(3,5);
testDiagonal(3,3);
}
public void testDiagonal( int numRows , int numCols ) {
DenseMatrix64F A = RandomMatrices.createDiagonal(numRows,numCols,1,10,rand);
assertEquals(A.getNumRows(),numRows);
assertEquals(A.getNumCols(),numCols);
assertTrue(CommonOps.elementSum(A) > 5 );
for( int i = 0; i < A.numRows; i++ ) {
for( int j = 0; j < A.numCols; j++ ) {
double v = A.get(i,j);
if( i == j ) {
assertTrue(v >= 1 || v <= 10);
} else {
assertTrue(v == 0);
}
}
}
}
@Test
public void createSingularValues() {
// check case when sv is more than or equal to the matrix dimension
double sv[] = new double[]{8.2,6.2,4.1,2};
for( int numRows = 1; numRows <= 4; numRows++ ) {
for( int numCols = 1; numCols <= 4; numCols++ ) {
DenseMatrix64F A = RandomMatrices.createSingularValues(numRows,numCols, rand, sv);
SingularValueDecomposition<DenseMatrix64F> svd =
DecompositionFactory.svd(A.numRows,A.numCols,true,true,false);
assertTrue(svd.decompose(A));
int o = Math.min(numRows,numCols);
UtilTestMatrix.checkSameElements(1e-8,o,sv,svd.getSingularValues());
}
}
// see if it fills in zeros when it is smaller than the dimension
DenseMatrix64F A = RandomMatrices.createSingularValues(5,5, rand, sv);
SingularValueDecomposition<DenseMatrix64F> svd =
DecompositionFactory.svd(A.numRows,A.numCols,true,true,false);
assertTrue(svd.decompose(A));
UtilTestMatrix.checkSameElements(1e-8,sv.length,sv,svd.getSingularValues());
assertEquals(0,svd.getSingularValues()[4],1e-8);
}
@Test
public void createEigenvaluesSymm() {
DenseMatrix64F A = RandomMatrices.createEigenvaluesSymm(5,rand,1,2,3,4,5);
// this should be symmetric
assertTrue(MatrixFeatures.isSymmetric(A,1e-10));
// decompose the matrix and extract its eigenvalues
EigenDecomposition<DenseMatrix64F> eig = DecompositionFactory.eig(A.numRows,true);
assertTrue(eig.decompose(A));
double ev[] = new double[5];
for( int i = 0; i < 5; i++ ) {
Complex64F e = eig.getEigenvalue(i);
assertTrue(e.isReal());
ev[i] = e.real;
}
// need to sort the eigenvalues so that I know where they are in the array
Arrays.sort(ev);
// see if they are what I expected them to be
for( int i = 0; i < ev.length; i++ ) {
assertEquals(i+1.0,ev[i],1e-8);
}
}
@Test
public void addRandom() {
DenseMatrix64F A = new DenseMatrix64F(3,4);
CommonOps.fill(A, -2.0);
RandomMatrices.addRandom(A,1,2,rand);
for( int i = 0; i < A.getNumElements(); i++ ) {
assertTrue(A.get(i) >= -1 && A.get(i) <= 0 );
}
}
@Test
public void createRandom() {
DenseMatrix64F A = RandomMatrices.createRandom(5,4,rand);
checkRandom1(A);
}
@Test
public void createRandom_min_max() {
DenseMatrix64F A = RandomMatrices.createRandom(30,20,-1,1,rand);
checkRandomRange(A);
}
@Test
public void setRandom() {
DenseMatrix64F A = new DenseMatrix64F(5,4);
RandomMatrices.setRandom(A,rand);
checkRandom1(A);
}
private void checkRandom1(DenseMatrix64F a) {
assertEquals(5, a.numRows);
assertEquals(4, a.numCols);
double total = 0;
for( int i = 0; i < a.numRows; i++ ) {
for( int j = 0; j < a.numCols; j++ ) {
double val = a.get(i,j);
assertTrue( val >= 0);
assertTrue( val <= 1);
total += val;
}
}
assertTrue(total>0);
}
@Test
public void setRandom_min_max() {
DenseMatrix64F A = new DenseMatrix64F(30,20);
RandomMatrices.setRandom(A,-1,1,rand);
checkRandomRange(A);
}
private void checkRandomRange(DenseMatrix64F a) {
assertEquals(30, a.numRows);
assertEquals(20, a.numCols);
int numNeg = 0;
int numPos = 0;
for( int i = 0; i < a.numRows; i++ ) {
for( int j = 0; j < a.numCols; j++ ) {
double val = a.get(i,j);
if( val < 0 )
numNeg++;
else
numPos++;
if( Math.abs(val) > 1 )
fail("Out of range");
}
}
assertTrue(numNeg>0);
assertTrue(numPos>0);
}
@Test
public void createSymmPosDef() {
for( int i = 0; i < 10; i++ ) {
DenseMatrix64F A = RandomMatrices.createSymmPosDef(6+i,rand);
assertTrue(MatrixFeatures.isPositiveDefinite(A));
}
}
@Test
public void createSymmetric() {
DenseMatrix64F A = RandomMatrices.createSymmetric(10,-1,1,rand);
assertTrue(MatrixFeatures.isSymmetric(A,1e-8));
// see if it has the expected range of elements
double min = CommonOps.elementMin(A);
double max = CommonOps.elementMax(A);
assertTrue(min < 0 && min >= -1);
assertTrue(max > 0 && max <= 1);
}
@Test
public void createUpperTriangle() {
for( int hess = 0; hess < 3; hess++ ) {
DenseMatrix64F A = RandomMatrices.createUpperTriangle(10,hess,-1,1,rand);
assertTrue(MatrixFeatures.isUpperTriangle(A,hess,1e-8));
// quick sanity check to make sure it could be proper
assertTrue(A.get(hess,0) != 0 );
// see if it has the expected range of elements
double min = CommonOps.elementMin(A);
double max = CommonOps.elementMax(A);
assertTrue(min < 0 && min >= -1);
assertTrue(max > 0 && max <= 1);
}
}
}