/**
* Computes the most dominant eigen vector of A using an inverted shifted matrix. The inverted
* shifted matrix is defined as <b>B = (A - αI)<sup>-1</sup></b> and can converge faster if
* α is chosen wisely.
*
* @param A An invertible square matrix matrix.
* @param alpha Shifting factor.
* @return If it converged or not.
*/
public boolean computeShiftInvert(DenseMatrix64F A, double alpha) {
initPower(A);
LinearSolver solver = LinearSolverFactory.linear(A.numCols);
SpecializedOps.addIdentity(A, B, -alpha);
solver.setA(B);
boolean converged = false;
for (int i = 0; i < maxIterations && !converged; i++) {
solver.solve(q0, q1);
double s = NormOps.normPInf(q1);
CommonOps.divide(q1, s, q2);
converged = checkConverged(A);
}
return converged;
}
/**
* Computes the most dominant eigen vector of A using a shifted matrix. The shifted matrix is
* defined as <b>B = A - αI</b> and can converge faster if α is chosen wisely. In
* general it is easier to choose a value for α that will converge faster with the
* shift-invert strategy than this one.
*
* @param A The matrix.
* @param alpha Shifting factor.
* @return If it converged or not.
*/
public boolean computeShiftDirect(DenseMatrix64F A, double alpha) {
SpecializedOps.addIdentity(A, B, -alpha);
return computeDirect(B);
}