/**
* Only eigenvalues of a symmetric real matrix are computed.
*
* @param A a symmetric real matrix
* @return a 1D {@code double} array containing the eigenvalues in decreasing order (absolute
* value)
*/
public static double[] computeEigenvalues(Matrix A) {
SparseMatrix S = (SparseMatrix) decompose(A, false)[1];
int m = S.getRowDimension();
int n = S.getColumnDimension();
int len = m >= n ? n : m;
double[] s = ArrayOperator.allocateVector(len, 0);
for (int i = 0; i < len; i++) {
s[i] = S.getEntry(i, i);
}
return s;
}
/**
* Build the diagonal matrix containing all eigenvalues.
*
* @param s eigenvalues
* @param m number of rows
* @param n number of columns
* @return a diagonal matrix containing all eigenvalues
*/
private static Matrix buildD(double[] s, int m, int n) {
TreeMap<Pair<Integer, Integer>, Double> map = new TreeMap<Pair<Integer, Integer>, Double>();
for (int i = 0; i < m; i++) {
if (i < n) map.put(Pair.of(i, i), s[i]);
}
return SparseMatrix.createSparseMatrix(map, m, n);
}
/**
* Unpack Q and T from the result of tridiagonalization.
*
* @param A tridiagonalization result
* @param a diagonal
* @param b superdiagonal
* @param computeV if V is to be computed
* @return a {@code Matrix} array [Q, T]
*/
private static Matrix[] unpack(Matrix A, double[] a, double[] b, boolean computeV) {
Matrix[] QT = new Matrix[3];
int m = A.getRowDimension();
int n = A.getColumnDimension();
DenseMatrix Q = null;
if (computeV) {
Q = new DenseMatrix(m, m, 0);
double[][] QData = Q.getData();
double s = 0;
double[] y = null;
for (int i = 0; i < m; i++) {
// Compute U^T * e_i
y = QData[i];
y[i] = 1;
for (int j = 0; j < n - 2; j++) {
s = 0;
for (int k = j + 1; k < m; k++) {
s += A.getEntry(k, j) * y[k];
}
for (int k = j + 1; k < m; k++) {
y[k] -= A.getEntry(k, j) * s;
}
}
}
/*fprintf("Q:\n");
disp(Q);*/
}
TreeMap<Pair<Integer, Integer>, Double> map = new TreeMap<Pair<Integer, Integer>, Double>();
for (int i = 0; i < m; i++) {
if (i < n) map.put(Pair.of(i, i), a[i]);
if (i < n - 1) {
map.put(Pair.of(i, i + 1), b[i]);
map.put(Pair.of(i + 1, i), b[i]);
}
}
Matrix T = SparseMatrix.createSparseMatrix(map, m, n);
/*fprintf("T:\n");
printMatrix(T);
T = new SparseMatrix(m, n);
for (int i = 0; i < m; i++) {
if (i < n)
T.setEntry(i, i, a[i]);
if (i < n - 1) {
T.setEntry(i, i + 1, b[i]);
T.setEntry(i + 1, i, b[i]);
}
}*/
if (computeV) {
/*fprintf("T:\n");
printMatrix(T);*/
/*fprintf("A:\n");
printMatrix(A);
fprintf("Q'Q:\n");
disp(Q.transpose().mtimes(Q));*/
/*fprintf("QTQ':\n");
disp(Q.mtimes(T).mtimes(Q.transpose()));*/
}
QT[0] = Q;
QT[1] = T;
return QT;
}