/**
* Compute the eigenvalue of square matrix.
*
* @param matrix Input matrix A.
* @return A pair of column vectors A and B s.t. each row of A + Bi is a eigenvalue of the
* underlying matrix
* @throws UnsupportedOperationException if unable to compute
*/
public Pair compute(Matrix matrix) {
Throw.when()
.isNull(() -> matrix, () -> "No input matrix.")
.isFalse(
() -> matrix.getRowCount() == matrix.getColCount(),
() -> "Input matrix is not square.");
switch (matrix.getRowCount()) {
case 0:
return Pair.EMPTY;
case 1:
return Pair.of(Matrices.scalar(matrix.get(0, 0)), Matrices.zeros(1));
case 2:
return DoubleShift.of(matrix, 0).eig();
default:
break;
}
return this.findEig(this.qrImpl.compute(new DefaultMatrix(matrix), null, false));
}
/**
* Find eigen-values of a square matrix in Schur form.
*
* @param schur Input matrix in Schur form
* @return A pair of column vectors A and B s.t. each row of A + Bi is a eigenvalue of the
* underlying matrix
*/
protected Pair findEig(Matrix schur) {
int n = schur.getRowCount() - 1;
int k = 0;
double[] re = new double[schur.getRowCount()];
double[] im = new double[schur.getRowCount()];
while (k < n) {
if (Math.abs(schur.get(k + 1, k)) < QRStep.EPSILON) {
re[k] = schur.get(k, k);
k++;
} else {
Pair eig = DoubleShift.of(schur, k).eig();
re[k] = eig.getLeft().get(0, 0);
re[k + 1] = eig.getLeft().get(1, 0);
im[k] = eig.getRight().get(0, 0);
im[k + 1] = eig.getRight().get(1, 0);
k += 2;
}
}
if (k < schur.getRowCount()) {
re[k] = schur.get(k, k);
}
return Pair.of(new ColumnVector(re), new ColumnVector(im));
}