// Last vector component imaginary so matrix is triangular
if (FastMath.abs(matrixT[idx][idx - 1]) > FastMath.abs(matrixT[idx - 1][idx])) {
matrixT[idx - 1][idx - 1] = q / matrixT[idx][idx - 1];
matrixT[idx - 1][idx] = -(matrixT[idx][idx] - p) / matrixT[idx][idx - 1];
} else {
final Complex result = cdiv(0.0, -matrixT[idx - 1][idx],
matrixT[idx - 1][idx - 1] - p, q);
matrixT[idx - 1][idx - 1] = result.getReal();
matrixT[idx - 1][idx] = result.getImaginary();
}
matrixT[idx][idx - 1] = 0.0;
matrixT[idx][idx] = 1.0;
for (int i = idx - 2; i >= 0; i--) {
double ra = 0.0;
double sa = 0.0;
for (int j = l; j <= idx; j++) {
ra += matrixT[i][j] * matrixT[j][idx - 1];
sa += matrixT[i][j] * matrixT[j][idx];
}
double w = matrixT[i][i] - p;
if (Precision.compareTo(imagEigenvalues[i], 0.0, EPSILON) < 0) {
z = w;
r = ra;
s = sa;
} else {
l = i;
if (Precision.equals(imagEigenvalues[i], 0.0)) {
final Complex c = cdiv(-ra, -sa, w, q);
matrixT[i][idx - 1] = c.getReal();
matrixT[i][idx] = c.getImaginary();
} else {
// Solve complex equations
double x = matrixT[i][i + 1];
double y = matrixT[i + 1][i];
double vr = (realEigenvalues[i] - p) * (realEigenvalues[i] - p) +
imagEigenvalues[i] * imagEigenvalues[i] - q * q;
final double vi = (realEigenvalues[i] - p) * 2.0 * q;
if (Precision.equals(vr, 0.0) && Precision.equals(vi, 0.0)) {
vr = Precision.EPSILON * norm *
(FastMath.abs(w) + FastMath.abs(q) + FastMath.abs(x) +
FastMath.abs(y) + FastMath.abs(z));
}
final Complex c = cdiv(x * r - z * ra + q * sa,
x * s - z * sa - q * ra, vr, vi);
matrixT[i][idx - 1] = c.getReal();
matrixT[i][idx] = c.getImaginary();
if (FastMath.abs(x) > (FastMath.abs(z) + FastMath.abs(q))) {
matrixT[i + 1][idx - 1] = (-ra - w * matrixT[i][idx - 1] +
q * matrixT[i][idx]) / x;
matrixT[i + 1][idx] = (-sa - w * matrixT[i][idx] -
q * matrixT[i][idx - 1]) / x;
} else {
final Complex c2 = cdiv(-r - y * matrixT[i][idx - 1],
-s - y * matrixT[i][idx], z, q);
matrixT[i + 1][idx - 1] = c2.getReal();
matrixT[i + 1][idx] = c2.getImaginary();
}
}
// Overflow control
double t = FastMath.max(FastMath.abs(matrixT[i][idx - 1]),