@Test
public void testLU() {
// we are testing that PA = LU
AMatrix a = Matrixx.create(new double[][] {{4, 3}, {6, 3}});
AMatrix[] ms = SimpleLUP.decomposeLUP(a);
AMatrix lu = ms[0].innerProduct(ms[1]);
assertEquals(ms[2].innerProduct(a), lu);
// assertEquals(Matrixx.create(new double[][] {{1,0},{1.5,1}}),lu[0]);
// assertEquals(Matrixx.create(new double[][] {{4,3},{0,-1.5}}),lu[1]);
a = Matrixx.createRandomSquareMatrix(4);
ms = SimpleLUP.decomposeLUP(a);
lu = ms[0].innerProduct(ms[1]);
assertTrue(ms[2].innerProduct(a).epsilonEquals(lu));
a = PermutationMatrix.create(0, 2, 1, 3);
ms = SimpleLUP.decomposeLUP(a);
lu = ms[0].innerProduct(ms[1]);
assertTrue(ms[2].innerProduct(a).epsilonEquals(lu));
assertEquals(IdentityMatrix.create(4), ms[0]);
assertEquals(IdentityMatrix.create(4), ms[1]);
assertEquals(a, ms[2].inverse());
}
@Test
public void testCholesky() {
AMatrix m =
Matrixx.create(Vector.of(4, 12, -16), Vector.of(12, 37, -43), Vector.of(-16, -43, 98));
Matrix L = Cholesky.decompose(m);
assertEquals((Matrixx.create(Vector.of(2, 0, 0), Vector.of(6, 1, 0), Vector.of(-8, 5, 3))), L);
}
@Test
public void testSVD() {
AMatrix a = Matrixx.createRandomMatrix(5, 3);
AMatrix[] ms = ThinSVD.decompose(a);
AMatrix u = ms[0];
AMatrix s = ms[1];
AMatrix v = ms[2];
// we are testing that A = USV*
AMatrix usvt = u.innerProduct(s.innerProduct(v.getTranspose()));
// assertEquals(a,usvt);
assertTrue(usvt.epsilonEquals(a));
assertTrue(v.isOrthogonal());
assertTrue(s.isRectangularDiagonal());
assertTrue(u.hasOrthonormalColumns());
}
@Test
public void testQR() {
AMatrix a = Matrixx.createRandomMatrix(5, 4);
AMatrix[] ms = QR.decompose(a);
AMatrix q = ms[0];
AMatrix r = ms[1];
// we are testing that A = QR
assertTrue(q.innerProduct(r).epsilonEquals(a));
// check properties of Q - should be orthogonal
assertTrue(q.hasOrthonormalColumns());
// assertTrue(q.isSquare()); // TODO: should be square??
// check properties of R - should be upper triangular
assertTrue(r.isUpperTriangular());
}