@Test
public void testNumbers() {
Real a = Real.valueOf(1.2);
Real b = Real.valueOf(1.2);
Real c = Real.valueOf(2.4);
assertEquals(c, a.plus(b));
BigInt i = BigInt.valueOf(10);
BigInt j = BigInt.valueOf(12);
assertEquals(Real.valueOf(11.2), a.plus(i));
assertEquals(j, i.times(a));
}
@Test
public void matrixRemove() {
VectorSpace<Vector<Real>, Real> space = provider.getVectorSpaceOver(RealField.getInstance(), 3);
Matrix<Real> M = space.matrix(3, 3, Real.valueOf(1, 1, 2, 1, 2, 1, 2, 1, 1));
M = M.remove(0, 0);
assertEquals(2, M.rowsCount());
assertEquals(2, M.columnsCount());
System.out.println(M);
assertEquals(Real.valueOf(2), M.get(0, 0));
assertEquals(Real.valueOf(1), M.get(1, 0));
assertEquals(Real.valueOf(1), M.get(0, 1));
assertEquals(Real.valueOf(1), M.get(1, 1));
}
@Test(expected = ArithmeticException.class)
public void matrixInversNotExists() {
VectorSpace<Vector<Real>, Real> space = provider.getVectorSpaceOver(RealField.getInstance(), 3);
Matrix<Real> X =
space.matrix(
3,
3,
Real.valueOf(
1, 3, 3, 1, 3, 3, // two equal rows => zero determinant
1, 3, 4));
X.inverse();
}
@Test
public void matrix() {
VectorSpace<Vector<Real>, Real> space = provider.getVectorSpaceOver(RealField.getInstance(), 3);
// Vector<Real> v1 = space.vector(1,1,2);
// Vector<Real> v2 = space.vector(1,2,1);
// Vector<Real> v3 = space.vector(2,1,1);
Matrix<Real> M = space.matrix(3, 3, Real.valueOf(1, 1, 2, 1, 2, 1, 2, 1, 1));
Vector<Real> v4 = space.vector(2, 2, 4);
// Vector<Real> v5 = space.vector(2,4,2);
// Vector<Real> v6 = space.vector(4,2,2);
Matrix<Real> N = space.matrix(3, 3, Real.valueOf(2, 2, 4, 2, 4, 2, 4, 2, 2));
// determinant
Real det = M.determinant();
assertEquals(Real.valueOf(-4), det);
assertEquals(Real.valueOf(4), M.trace());
// transpose
assertEquals(M, M.transpose());
// multiplication
assertEquals(N, M.times(Real.valueOf(2.0)));
// addition
assertEquals(N, M.plus(M));
// vector x matrix
Vector<Real> v7 = space.vector(12, 10, 10);
assertEquals(v7, M.rightTimes(v4));
// Matrix equality
Matrix<Real> P = space.matrix(3, 3, Real.valueOf(1, 1, 2, 1, 2, 1, 2, 1, 1));
assertEquals(M, P);
// Matrix multiplication
Matrix<Real> Q = space.matrix(3, 3, Real.valueOf(12, 10, 10, 10, 12, 10, 10, 10, 12));
assertEquals(Q, M.times(N));
// Adjoint
Matrix<Real> A = space.matrix(3, 3, Real.valueOf(1, 1, -3, 1, -3, 1, -3, 1, 1));
assertEquals(A, M.adjoint());
// Identity Multiplication
Matrix<Real> I = space.identity(3);
assertEquals(I, I.times(I));
assertEquals(I.getRow(1), I.getColumn(1));
Matrix<Real> X = space.matrix(3, 3, Real.valueOf(1, 3, 3, 1, 4, 3, 1, 3, 4));
// Identity relation M = M.I and M = I.M
assertEquals(X, X.times(I));
assertEquals(X, I.times(X));
Matrix<Real> XInv = space.matrix(3, 3, Real.valueOf(7, -3, -3, -1, 1, 0, -1, 0, 1));
// inverse
assertEquals(XInv, X.inverse());
// Invertion relation I = M.M^-1
assertEquals(I, X.times(X.inverse()));
// transpose of the transpose is it self
assertTrue(M == M.transpose().transpose());
}
@Test
public void matrixLU() {
VectorSpace<Vector<Real>, Real> space = provider.getVectorSpaceOver(RealField.getInstance(), 3);
// http://en.wikipedia.org/wiki/LU_decomposition
Matrix<Real> A =
space.matrix(
2,
2,
Real.valueOf(
4, 3,
6, 3));
Matrix<Real> U = space.matrix(2, 2, Real.valueOf(4, 3, 0, -1.5));
Matrix<Real> L = space.matrix(2, 2, Real.valueOf(1, 0, 1.5, 1));
LuDecomposition<Real> lud = LuDecomposition.decompose(A);
assertEquals("Incorrect 2x2 L", L, lud.getL());
assertEquals("Incorrect 2x2 U", U, lud.getU());
assertEquals(A, L.times(U));
assertEquals(A, lud.getL().times(lud.getU()));
A = space.matrix(3, 3, Real.valueOf(6, -2, 0, 9, -1, 1, 3, 7, 5));
U =
space.matrix(
3,
3,
new Real[] {
Real.valueOf(6), Real.valueOf(-2), Real.valueOf(0),
Real.valueOf(0), Real.valueOf(2), Real.valueOf(1),
Real.valueOf(0), Real.valueOf(0), Real.valueOf(1)
});
L =
space.matrix(
3,
3,
new Real[] {
Real.valueOf(1), Real.valueOf(0), Real.valueOf(0),
Real.valueOf(3, 2), Real.valueOf(1), Real.valueOf(0),
Real.valueOf(1, 2), Real.valueOf(4), Real.valueOf(1)
});
assertEquals("wrong test data", A, L.times(U));
lud = LuDecomposition.decompose(A);
assertEquals("Incorrect decomposition product", A, lud.getL().times(lud.getU()));
assertEquals("Incorrect 3x3 L", L, lud.getL());
assertEquals("Incorrect 3x3 U", U, lud.getU());
Matrix<Real> N = space.matrix(3, 3, Real.valueOf(1, 1, 2, 1, 2, 1, 2, 1, 1));
lud = LuDecomposition.decompose(N);
assertEquals(N, lud.getL().times(lud.getU()));
}