/*
* Copyright (C) 2003-2006 Bjørn-Ove Heimsund
*
* This file is part of MTJ.
*
* This library 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 2.1 of the License, or (at your
* option) any later version.
*
* This library 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 this library; if not, write to the Free Software Foundation,
* Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
package no.uib.cipr.matrix;
import org.junit.After;
import org.junit.Before;
import org.junit.Test;
import static org.junit.Assert.*;
/**
* Tests a matrix
*/
public abstract class MatrixTestAbstract {
/**
* Matrix to test
*/
protected Matrix A;
/**
* Jagged array version of A
*/
protected double[][] Ad;
/**
* Matrix of the same size as A, dense and non-dense
*/
protected Matrix Bdense, B;
/**
* Contents of B
*/
protected double[][] Bd;
/**
* Non-dense vectors with size equal the number of rows in A
*/
protected Vector xR, yR;
/**
* Non-dense vectors with size equal the number of columns in A
*/
protected Vector xC, yC;
/**
* Dense vectors with size equal the number of rows in A
*/
protected Vector xDenseR, yDenseR;
/**
* Dense vectors with size equal the number of columns in A
*/
protected Vector xDenseC, yDenseC;
/**
* Contents of the vectors
*/
protected double[] xdR, ydR, xdC, ydC;
/**
* Tolerance for floating-point comparisons
*/
protected double tol = 1e-4;
/**
* Maximum matrix size, to avoid too slow tests
*/
protected int max = 100;
@Before
public void setUp() throws Exception {
createPrimary();
createAuxillerary();
}
protected abstract void createPrimary() throws Exception;
@After
public void tearDown() throws Exception {
A = B = Bdense = null;
Ad = Bd = null;
xC = xDenseC = xDenseR = xR = yC = yDenseC = yDenseR = yR = null;
xdC = xdR = ydC = ydR = null;
}
/**
* Called after setUp() to create additional datastructures
*/
protected void createAuxillerary() {
Bdense = Matrices.random(A.numRows(), A.numColumns());
B = Matrices.synchronizedMatrix(Bdense.copy());
Bd = Matrices.getArray(B);
xDenseC = Matrices.random(A.numColumns());
yDenseC = Matrices.random(A.numColumns());
xDenseR = Matrices.random(A.numRows());
yDenseR = Matrices.random(A.numRows());
xC = Matrices.synchronizedVector(xDenseC);
yC = Matrices.synchronizedVector(yDenseC);
xR = Matrices.synchronizedVector(xDenseR);
yR = Matrices.synchronizedVector(yDenseR);
xdC = Matrices.getArray(xC);
ydC = Matrices.getArray(yC);
xdR = Matrices.getArray(xR);
ydR = Matrices.getArray(yR);
}
@Test
public void testMatrixRank2Dense() {
if (A.isSquare()) {
int n = Utilities.getInt(1, max);
Matrix B = Matrices.random(A.numRows(), n), C = Matrices.random(
A.numRows(), n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
A = A.rank2(alpha, B, C);
rank2(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
}
@Test
public void testMatrixRank2() {
if (A.isSquare()) {
int n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(A.numRows(),
n)), C = Matrices.synchronizedMatrix(Matrices.random(
A.numRows(), n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
A = A.rank2(alpha, B, C);
rank2(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
}
@Test
public void testMatrixTransRank2Dense() {
if (A.isSquare()) {
int n = Utilities.getInt(1, max);
Matrix B = Matrices.random(n, A.numColumns()), C = Matrices.random(
n, A.numColumns());
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
A = A.transRank2(alpha, B, C);
transRank2(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
}
@Test
public void testMatrixTransRank2() {
if (A.isSquare()) {
int n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(n,
A.numColumns())), C = Matrices.synchronizedMatrix(Matrices
.random(n, A.numColumns()));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
A = A.transRank2(alpha, B, C);
transRank2(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
}
@Test
public void testMatrixRank1Dense() {
if (A.isSquare()) {
Matrix C = Matrices.random(A.numRows(), A.numColumns());
double[][] Cd = Matrices.getArray(C);
double alpha = Math.random();
A = A.rank1(alpha, C);
rank1(Ad, alpha, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Cd, C);
}
}
@Test
public void testMatrixRank1() {
if (A.isSquare()) {
Matrix C = Matrices.synchronizedMatrix(Matrices.random(A.numRows(),
A.numColumns()));
double[][] Cd = Matrices.getArray(C);
double alpha = Math.random();
A = A.rank1(alpha, C);
rank1(Ad, alpha, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Cd, C);
}
}
@Test
public void testMatrixTransRank1Dense() {
if (A.isSquare()) {
Matrix C = Matrices.random(A.numRows(), A.numColumns());
double[][] Cd = Matrices.getArray(C);
double alpha = Math.random();
A = A.transRank1(alpha, C);
transRank1(Ad, alpha, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Cd, C);
}
}
@Test
public void testMatrixTransRank1() {
if (A.isSquare()) {
Matrix C = Matrices.synchronizedMatrix(Matrices.random(A.numRows(),
A.numColumns()));
double[][] Cd = Matrices.getArray(C);
double alpha = Math.random();
A = A.transRank1(alpha, C);
transRank1(Ad, alpha, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Cd, C);
}
}
@Test
public void testMatrixMultDense() {
int m = A.numRows(), k = A.numColumns(), n = Utilities.getInt(1, max);
Matrix B = Matrices.random(k, n), C = Matrices.random(m, n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.mult(alpha, B, C);
Cd = mult(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixMult() {
int m = A.numRows(), k = A.numColumns(), n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(k, n)), C = Matrices
.synchronizedMatrix(Matrices.random(m, n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.mult(alpha, B, C);
Cd = mult(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransAmultDense() {
int m = A.numColumns(), k = A.numRows(), n = Utilities.getInt(1, max);
Matrix B = Matrices.random(k, n), C = Matrices.random(m, n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transAmult(alpha, B, C);
Cd = transAmult(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransAmult() {
int m = A.numColumns(), k = A.numRows(), n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(k, n)), C = Matrices
.synchronizedMatrix(Matrices.random(m, n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transAmult(alpha, B, C);
Cd = transAmult(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransABmultDense() {
int m = A.numColumns(), k = A.numRows(), n = Utilities.getInt(1, max);
Matrix B = Matrices.random(n, k), C = Matrices.random(m, n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transABmult(alpha, B, C);
Cd = transABmult(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransABmult() {
int m = A.numColumns(), k = A.numRows(), n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(n, k)), C = Matrices
.synchronizedMatrix(Matrices.random(m, n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transABmult(alpha, B, C);
Cd = transABmult(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransBmultDense() {
int m = A.numRows(), k = A.numColumns(), n = Utilities.getInt(1, max);
Matrix B = Matrices.random(n, k), C = Matrices.random(m, n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transBmult(alpha, B, C);
Cd = transBmult(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransBmult() {
int m = A.numRows(), k = A.numColumns(), n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(n, k)), C = Matrices
.synchronizedMatrix(Matrices.random(m, n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transBmult(alpha, B, C);
Cd = transBmult(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixMultAddDense() {
int m = A.numRows(), k = A.numColumns(), n = Utilities.getInt(1, max);
Matrix B = Matrices.random(k, n), C = Matrices.random(m, n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.multAdd(alpha, B, C);
Cd = multAdd(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixMultAdd() {
int m = A.numRows(), k = A.numColumns(), n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(k, n)), C = Matrices
.synchronizedMatrix(Matrices.random(m, n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.multAdd(alpha, B, C);
Cd = multAdd(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransAmultAddDense() {
int m = A.numColumns(), k = A.numRows(), n = Utilities.getInt(1, max);
Matrix B = Matrices.random(k, n), C = Matrices.random(m, n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transAmultAdd(alpha, B, C);
Cd = transAmultAdd(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransAmultAdd() {
int m = A.numColumns(), k = A.numRows(), n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(k, n)), C = Matrices
.synchronizedMatrix(Matrices.random(m, n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transAmultAdd(alpha, B, C);
Cd = transAmultAdd(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransABmultAddDense() {
int m = A.numColumns(), k = A.numRows(), n = Utilities.getInt(1, max);
Matrix B = Matrices.random(n, k), C = Matrices.random(m, n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transABmultAdd(alpha, B, C);
Cd = transABmultAdd(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransABmultAdd() {
int m = A.numColumns(), k = A.numRows(), n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(n, k)), C = Matrices
.synchronizedMatrix(Matrices.random(m, n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transABmultAdd(alpha, B, C);
Cd = transABmultAdd(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransBmultAddDense() {
int m = A.numRows(), k = A.numColumns(), n = Utilities.getInt(1, max);
Matrix B = Matrices.random(n, k), C = Matrices.random(m, n);
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transBmultAdd(alpha, B, C);
Cd = transBmultAdd(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
@Test
public void testMatrixTransBmultAdd() {
int m = A.numRows(), k = A.numColumns(), n = Utilities.getInt(1, max);
Matrix B = Matrices.synchronizedMatrix(Matrices.random(n, k)), C = Matrices
.synchronizedMatrix(Matrices.random(m, n));
double[][] Bd = Matrices.getArray(B), Cd = Matrices.getArray(C);
double alpha = Math.random();
C = A.transBmultAdd(alpha, B, C);
Cd = transBmultAdd(Ad, alpha, Bd, Cd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
assertMatrixEquals(Cd, C);
}
protected double[][] rank2(double[][] Ad, double alpha, double[][] Bd,
double[][] Cd) {
return transBmultAdd(Bd, alpha, Cd, transBmultAdd(Cd, alpha, Bd, Ad));
}
protected double[][] transRank2(double[][] Ad, double alpha, double[][] Bd,
double[][] Cd) {
return transAmultAdd(Bd, alpha, Cd, transAmultAdd(Cd, alpha, Bd, Ad));
}
protected double[][] rank1(double[][] Ad, double alpha, double[][] Cd) {
return transBmultAdd(Cd, alpha, Cd, Ad);
}
protected double[][] transRank1(double[][] Ad, double alpha, double[][] Cd) {
return transAmultAdd(Cd, alpha, Cd, Ad);
}
@Test
public void testVectorRank2Dense() {
if (A.isSquare()) {
double alpha = Math.random();
assertMatrixEquals(rank2(alpha, xdR, ydR),
A.rank2(alpha, xDenseR, yDenseR));
}
}
@Test
public void testVectorRank2() {
if (A.isSquare()) {
double alpha = Math.random();
assertMatrixEquals(rank2(alpha, xdR, ydR), A.rank2(alpha, xR, yR));
}
}
@Test
public void testVectorRank1Dense() {
if (A.isSquare()) {
double alpha = Math.random();
assertMatrixEquals(rank1(alpha, xdR, ydR),
A.rank1(alpha, xDenseR, yDenseR));
}
}
@Test
public void testVectorRank1() {
if (A.isSquare()) {
double alpha = Math.random();
assertMatrixEquals(rank1(alpha, xdR, ydR), A.rank1(alpha, xR, yR));
}
}
protected double[][] rank2(double alpha, double[] xd, double[] yd) {
rank1(alpha, xd, yd);
rank1(alpha, yd, xd);
return Ad;
}
protected double[][] rank1(double alpha, double[] xd, double[] yd) {
for (int i = 0; i < xd.length; ++i)
for (int j = 0; j < yd.length; ++j)
Ad[i][j] += alpha * xd[i] * yd[j];
return Ad;
}
@Test
public void testVectorTransMultAddDense() {
double alpha = Math.random();
assertVectorEquals(transMultAdd(alpha, xdR, ydC),
A.transMultAdd(alpha, xDenseR, yDenseC));
assertMatrixEquals(Ad, A);
assertVectorEquals(xdR, xDenseR);
assertVectorEquals(ydC, yDenseC);
}
@Test
public void testVectorTransMultAdd() {
double alpha = Math.random();
assertVectorEquals(transMultAdd(alpha, xdR, ydC),
A.transMultAdd(alpha, xR, yC));
assertMatrixEquals(Ad, A);
assertVectorEquals(xdR, xR);
assertVectorEquals(ydC, yC);
}
protected double[] transMultAdd(double alpha, double[] xd, double[] yd) {
int rows = Ad.length, cols = 0;
if (rows > 0)
cols = Ad[0].length;
for (int j = 0; j < cols; ++j) {
double dot = 0;
for (int i = 0; i < rows; ++i)
dot += Ad[i][j] * xd[i];
yd[j] += alpha * dot;
}
return yd;
}
@Test
public void testVectorMultDense() {
double alpha = Math.random();
assertVectorEquals(mult(alpha, xdC, ydR),
A.mult(alpha, xDenseC, yDenseR));
assertMatrixEquals(Ad, A);
assertVectorEquals(xdC, xDenseC);
assertVectorEquals(ydR, yDenseR);
}
@Test
public void testVectorMult() {
double alpha = Math.random();
assertVectorEquals(mult(alpha, xdC, ydR), A.mult(alpha, xC, yR));
assertMatrixEquals(Ad, A);
assertVectorEquals(xdC, xC);
assertVectorEquals(ydR, yR);
}
protected double[] mult(double alpha, double[] xd, double[] yd) {
for (int i = 0; i < Ad.length; ++i) {
double dot = 0;
for (int j = 0; j < Ad[i].length; ++j)
dot += Ad[i][j] * xd[j];
yd[i] = alpha * dot;
}
return yd;
}
@Test
public void testVectorMultAddDense() {
double alpha = Math.random();
assertVectorEquals(multAdd(Ad, alpha, xdC, ydR),
A.multAdd(alpha, xDenseC, yDenseR));
assertMatrixEquals(Ad, A);
assertVectorEquals(xdC, xDenseC);
assertVectorEquals(ydR, yDenseR);
}
@Test
public void testVectorMultAdd() {
double alpha = Math.random();
assertVectorEquals(multAdd(Ad, alpha, xdC, ydR),
A.multAdd(alpha, xC, yR));
assertMatrixEquals(Ad, A);
assertVectorEquals(xdC, xC);
assertVectorEquals(ydR, yR);
}
protected double[] multAdd(double[][] Ad, double alpha, double[] xd,
double[] yd) {
for (int i = 0; i < Ad.length; ++i) {
double dot = 0;
for (int j = 0; j < Ad[i].length; ++j)
dot += Ad[i][j] * xd[j];
yd[i] += alpha * dot;
}
return yd;
}
protected double[][] mult(double[][] Ad, double alpha, double[][] Bd,
double[][] Cd) {
int m = Cd.length, n = 0, k = Bd.length;
if (k > 0)
n = Bd[0].length;
Utilities.zero(Cd);
for (int j = 0; j < n; ++j)
for (int l = 0; l < k; ++l)
for (int i = 0; i < m; ++i)
Cd[i][j] += alpha * Ad[i][l] * Bd[l][j];
return Cd;
}
protected double[][] transAmult(double[][] Ad, double alpha, double[][] Bd,
double[][] Cd) {
int m = Cd.length, n = 0, k = Bd.length;
if (k > 0)
n = Bd[0].length;
for (int j = 0; j < n; ++j)
for (int i = 0; i < m; ++i) {
double temp = 0;
for (int l = 0; l < k; ++l)
temp += Ad[l][i] * Bd[l][j];
Cd[i][j] = alpha * temp;
}
return Cd;
}
protected double[][] transBmult(double[][] Ad, double alpha, double[][] Bd,
double[][] Cd) {
int m = Cd.length, n = Bd.length, k = 0;
if (n > 0)
k = Bd[0].length;
Utilities.zero(Cd);
for (int j = 0; j < n; ++j) {
for (int l = 0; l < k; ++l)
for (int i = 0; i < m; ++i)
Cd[i][j] += alpha * Ad[i][l] * Bd[j][l];
}
return Cd;
}
protected double[][] transABmult(double[][] Ad, double alpha,
double[][] Bd, double[][] Cd) {
int m = Cd.length, n = Bd.length, k = 0;
if (n > 0)
k = Bd[0].length;
for (int j = 0; j < n; ++j)
for (int i = 0; i < m; ++i) {
double temp = 0;
for (int l = 0; l < k; ++l)
temp += Ad[l][i] * Bd[j][l];
Cd[i][j] = alpha * temp;
}
return Cd;
}
protected double[][] multAdd(double[][] Ad, double alpha, double[][] Bd,
double[][] Cd) {
int m = Cd.length, n = 0, k = Bd.length;
if (k > 0)
n = Bd[0].length;
for (int j = 0; j < n; ++j)
for (int l = 0; l < k; ++l)
for (int i = 0; i < m; ++i)
Cd[i][j] += alpha * Ad[i][l] * Bd[l][j];
return Cd;
}
protected double[][] transAmultAdd(double[][] Ad, double alpha,
double[][] Bd, double[][] Cd) {
int m = Cd.length, n = 0, k = Bd.length;
if (k > 0)
n = Bd[0].length;
for (int j = 0; j < n; ++j)
for (int i = 0; i < m; ++i) {
double temp = 0;
for (int l = 0; l < k; ++l)
temp += Ad[l][i] * Bd[l][j];
Cd[i][j] += alpha * temp;
}
return Cd;
}
protected double[][] transBmultAdd(double[][] Ad, double alpha,
double[][] Bd, double[][] Cd) {
int m = Cd.length, n = Bd.length, k = 0;
if (n > 0)
k = Bd[0].length;
for (int j = 0; j < n; ++j)
for (int l = 0; l < k; ++l)
for (int i = 0; i < m; ++i)
Cd[i][j] += alpha * Ad[i][l] * Bd[j][l];
return Cd;
}
protected double[][] transABmultAdd(double[][] Ad, double alpha,
double[][] Bd, double[][] Cd) {
int m = Cd.length, n = Bd.length, k = 0;
if (n > 0)
k = Bd[0].length;
for (int j = 0; j < n; ++j)
for (int i = 0; i < m; ++i) {
double temp = 0;
for (int l = 0; l < k; ++l)
temp += Ad[l][i] * Bd[j][l];
Cd[i][j] += alpha * temp;
}
return Cd;
}
/**
* Tests <code>A = A + alpha*B</code>
*/
@Test
public void testRandomMatrixAdd() {
double alpha = Math.random();
A = A.add(alpha, B);
add(Ad, alpha, Bd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
}
/**
* Tests <code>A = A + B</code>
*/
@Test
public void testMatrixAdd() {
A = A.add(B);
add(Ad, 1, Bd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
}
/**
* Tests <code>A = A + 1*B</code>
*/
@Test
public void testOneMatrixAdd() {
A = A.add(1, B);
add(Ad, 1, Bd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
}
/**
* Tests <code>A = A + 0*B</code>
*/
@Test
public void testZeroMatrixAdd() {
A = A.add(0, B);
add(Ad, 0, Bd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
}
/**
* Tests <code>A = alpha*B</code>
*/
@Test
public void testRandomMatrixSet() {
double alpha = Math.random();
A = A.set(alpha, B);
set(Ad, alpha, Bd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
}
/**
* Tests <code>A = B</code>
*/
@Test
public void testMatrixSet() {
A = A.set(B);
set(Ad, 1, Bd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
}
/**
* Tests <code>A = 1*B</code>
*/
@Test
public void testOneMatrixSet() {
A = A.set(1, B);
set(Ad, 1, Bd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
}
/**
* Tests <code>A = 0*B</code>
*/
@Test
public void testZeroMatrixSet() {
A = A.set(0, B);
set(Ad, 0, Bd);
assertMatrixEquals(Ad, A);
assertMatrixEquals(Bd, B);
}
/**
* Checks transpose
*/
@Test
public void testTranspose() {
Matrix At = Matrices.random(A.numColumns(), A.numRows());
assertMatrixEquals(transpose(), A.transpose(At));
}
protected void set(double[][] A, double alpha, double[][] B) {
for (int i = 0; i < A.length; ++i)
for (int j = 0; j < A[i].length; ++j)
A[i][j] = alpha * B[i][j];
}
protected void add(double[][] A, double alpha, double[][] B) {
for (int i = 0; i < A.length; ++i)
for (int j = 0; j < A[i].length; ++j)
A[i][j] += alpha * B[i][j];
}
protected double[][] transpose() {
if (Ad.length == 0)
return new double[0][0];
double[][] Adt = new double[Ad[0].length][Ad.length];
for (int i = 0; i < Ad.length; ++i)
for (int j = 0; j < Ad[i].length; ++j)
Adt[j][i] = Ad[i][j];
return Adt;
}
/**
* Test of direct matrix solver
*/
@Test
public void testMatrixSolve() {
while (true) {
try {
Matrix B = Matrices.random(A.numRows(), A.numColumns());
Matrix X = Matrices.random(A.numRows(), A.numColumns());
X = A.solve(B, X);
Matrix Y = A.multAdd(X, X.copy().set(-1, B));
assertEquals(0, Y.norm(Matrix.Norm.Frobenius), tol);
assertMatrixEquals(Ad, A);
return;
} catch (MatrixSingularException e) {
Utilities.addDiagonal(A, Ad, 1);
} catch (MatrixNotSPDException e) {
Utilities.addDiagonal(A, Ad, 1);
}
}
}
/**
* Test of direct transpose matrix solver
*/
@Test
public void testTransMatrixSolve() {
while (true) {
try {
Matrix B = Matrices.random(A.numRows(), A.numColumns());
Matrix X = Matrices.random(A.numRows(), A.numColumns());
X = A.transSolve(B, X);
Matrix Y = A.transAmultAdd(X, X.copy().set(-1, B));
assertEquals(0, Y.norm(Matrix.Norm.Frobenius), tol);
assertMatrixEquals(Ad, A);
return;
} catch (MatrixSingularException e) {
Utilities.addDiagonal(A, Ad, 1);
} catch (MatrixNotSPDException e) {
Utilities.addDiagonal(A, Ad, 1);
}
}
}
/**
* Test of direct vector solver
*/
@Test
public void testVectorSolve() {
while (true) {
try {
Vector b = Matrices.random(A.numRows());
Vector x = Matrices.random(A.numRows());
x = A.solve(b, x);
Vector y = A.multAdd(-1, x, x.copy().set(b));
assertEquals(0, y.norm(Vector.Norm.Two), tol);
assertMatrixEquals(Ad, A);
return;
} catch (MatrixSingularException e) {
Utilities.addDiagonal(A, Ad, 1);
} catch (MatrixNotSPDException e) {
Utilities.addDiagonal(A, Ad, 1);
}
}
}
/**
* Test of direct transpose vector solver
*/
@Test
public void testTransVectorSolve() {
while (true) {
try {
Vector b = Matrices.random(A.numRows());
Vector x = Matrices.random(A.numRows());
x = A.transSolve(b, x);
Vector y = A.transMultAdd(-1, x, x.copy().set(b));
assertEquals(0, y.norm(Vector.Norm.Two), tol);
assertMatrixEquals(Ad, A);
return;
} catch (MatrixSingularException e) {
Utilities.addDiagonal(A, Ad, 1);
} catch (MatrixNotSPDException e) {
Utilities.addDiagonal(A, Ad, 1);
}
}
}
/**
* Test additions using iterators
*/
@Test
public void testAdd() {
double alpha = Math.random();
for (MatrixEntry e : A) {
A.add(e.row(), e.column(), alpha);
A.add(e.row(), e.column(), -alpha);
}
assertMatrixEquals(Ad, A);
}
/**
* Checks that copy is deep, not reference
*/
@Test
public void testCopy() {
Matrix Ac = A.copy();
A = A.zero();
assertMatrixEquals(Ad, Ac);
}
/**
* Test iterator get
*/
@Test
public void testIterator() {
double[][] Ac = new double[A.numRows()][A.numColumns()];
for (MatrixEntry e : A)
Ac[e.row()][e.column()] = e.get();
assertMatrixEquals(Ad, Ac);
}
/**
* Test iterator set
*/
@Test
public void testIteratorSet() {
double alpha = Math.random();
for (MatrixEntry e : A)
e.set(e.get() * alpha);
assertMatrixEquals(scale(alpha), A);
}
/**
* Test iterator read and write
*/
@Test
public void testIteratorSetGet() {
double alpha = Math.random();
double[][] Ac = new double[A.numRows()][A.numColumns()];
for (MatrixEntry e : A) {
Ac[e.row()][e.column()] = e.get();
e.set(alpha * e.get());
e.set(e.get() / alpha);
}
assertMatrixEquals(Ad, Ac);
assertMatrixEquals(Ad, A);
}
/**
* Checks zero()
*/
@Test
public void testZero() {
assertMatrixEquals(zero(), A.zero());
}
protected double[][] zero() {
for (int i = 0; i < Ad.length; ++i)
for (int j = 0; j < Ad[i].length; ++j)
Ad[i][j] = 0;
return Ad;
}
/**
* Cardinality computation
*/
@Test
public void testCardinality() {
assertEquals(Matrices.cardinality(A), cardinality());
}
protected int cardinality() {
int nz = 0;
for (int i = 0; i < Ad.length; ++i)
for (int j = 0; j < Ad[i].length; ++j)
if (Ad[i][j] != 0.)
nz++;
return nz;
}
/**
* Checks in-place transpose for square matrices
*/
@Test
public void testTransposeInplace() {
if (A.isSquare())
assertMatrixEquals(transpose(), A.copy().transpose());
}
/**
* Scaling with an arbitrary scalar
*/
@Test
public void testScale() {
double alpha = Math.random();
A = A.scale(alpha);
scale(alpha);
assertMatrixEquals(Ad, A);
}
/**
* Scaling by zero
*/
@Test
public void testZeroScale() {
A = A.scale(0);
scale(0);
assertMatrixEquals(Ad, A);
}
/**
* Scaling by one
*/
@Test
public void testOneScale() {
A = A.scale(1);
scale(1);
assertMatrixEquals(Ad, A);
}
protected double[][] scale(double alpha) {
for (int i = 0; i < Ad.length; ++i)
for (int j = 0; j < Ad[i].length; ++j)
Ad[i][j] *= alpha;
return Ad;
}
/**
* Checks the 1 norm
*/
@Test
public void testOneNorm() {
assertEquals(norm1(Ad), A.norm(Matrix.Norm.One), tol);
assertMatrixEquals(Ad, A);
}
/**
* Checks the Frobenius norm
*/
@Test
public void testFrobeniusNorm() {
assertEquals(normF(Ad), A.norm(Matrix.Norm.Frobenius), tol);
assertMatrixEquals(Ad, A);
}
/**
* Checks the infinity norm
*/
@Test
public void testInfinityNorm() {
assertEquals(normInf(Ad), A.norm(Matrix.Norm.Infinity), tol);
assertMatrixEquals(Ad, A);
}
protected double norm1(double[][] A) {
double max = 0;
for (int i = 0; i < A.length; ++i) {
double rowsum = 0;
for (int j = 0; j < A[i].length; ++j)
rowsum += Math.abs(A[i][j]);
max = Math.max(rowsum, max);
}
return max;
}
protected double normF(double[][] A) {
double norm = 0;
for (int i = 0; i < A.length; ++i)
for (int j = 0; j < A[i].length; ++j)
norm += A[i][j] * A[i][j];
return Math.sqrt(norm);
}
protected double normInf(double[][] A) {
if (A.length == 0)
return 0;
double[] columnSum = new double[A[0].length];
for (int i = 0; i < A.length; ++i)
for (int j = 0; j < A[i].length; ++j)
columnSum[j] += Math.abs(A[i][j]);
double max = 0;
for (double d : columnSum)
max = Math.max(max, d);
return max;
}
/**
* Checks for equality between the matrix and the array
*/
protected void assertMatrixEquals(double[][] Ad, Matrix A) {
assertTrue(A != null);
assertTrue(Ad != null);
assertTrue(A.numRows() == Ad.length);
for (int i = 0; i < A.numRows(); ++i) {
assertTrue(A.numColumns() == Ad[i].length);
for (int j = 0; j < A.numColumns(); ++j)
assertEquals(Ad[i][j], A.get(i, j), 1e-12);
}
}
/**
* Checks for equality between two arrays
*/
protected void assertMatrixEquals(double[][] Ad, double[][] Ac) {
assertTrue(Ac.length == Ad.length);
for (int i = 0; i < A.numRows(); ++i) {
assertTrue(Ac[i].length == Ad[i].length);
for (int j = 0; j < A.numColumns(); ++j)
assertEquals(Ad[i][j], Ac[i][j], 1e-12);
}
}
protected void assertVectorEquals(double[] xd, Vector x) {
assertEquals(xd.length, x.size());
for (int i = 0; i < xd.length; ++i)
assertEquals(xd[i], x.get(i), tol);
}
protected void assertVectorEquals(double[] xd, double[] yd) {
for (int i = 0; i < xd.length; ++i)
assertEquals(xd[i], yd[i], tol);
}
public static void assertMatrixEquals(Matrix expected, Matrix test) {
assertEquals(expected.numRows(), test.numRows());
assertEquals(expected.numColumns(), test.numColumns());
for (int i = 0; i < test.numRows(); i++) {
for (int j = 0; j < test.numColumns(); j++) {
assertEquals(expected.get(i, j), test.get(i, j), 0.0001);
}
}
}
public static void assertVectorEquals(Vector expected, Vector test) {
assertEquals(expected.size(), test.size());
for (int i = 0; i < test.size(); i++) {
assertEquals(expected.get(i), test.get(i), 0.0001);
}
}
public static void assertEqualsOrOpposite(Vector expected, Vector test) {
assertEquals(expected.size(), test.size());
for (int i = 0; i < test.size(); i++) {
double a = expected.get(i);
double b = test.get(i);
assertTrue("abs(" + a + ") != abs(" + b + ")",
Math.abs(a) - Math.abs(b) < 0.0001);
}
}
}