@Override
protected Rotation<ComplexNumber>[] rotations(
final PhysicalStore<ComplexNumber> aStore,
final int aLowInd,
final int aHighInd,
final Rotation<ComplexNumber>[] retVal) {
final ComplexNumber a00 = aStore.get(aLowInd, aLowInd);
final ComplexNumber a01 = aStore.get(aLowInd, aHighInd);
final ComplexNumber a10 = aStore.get(aHighInd, aLowInd);
final ComplexNumber a11 = aStore.get(aHighInd, aHighInd);
final ComplexNumber x = a00.add(a11);
final ComplexNumber y = a10.subtract(a01);
ComplexNumber t; // tan, cot or something temporary
// Symmetrise - Givens
final ComplexNumber cg; // cos Givens
final ComplexNumber sg; // sin Givens
if (ComplexNumber.isSmall(PrimitiveMath.ONE, y)) {
cg = x.signum();
sg = ComplexNumber.ZERO;
} else if (ComplexNumber.isSmall(PrimitiveMath.ONE, x)) {
sg = y.signum();
cg = ComplexNumber.ZERO;
} else if (y.compareTo(x) == 1) {
t = x.divide(y); // cot
sg = y.signum().divide(ComplexFunction.SQRT1PX2.invoke(t));
cg = sg.multiply(t);
} else {
t = y.divide(x); // tan
cg = x.signum().divide(ComplexFunction.SQRT1PX2.invoke(t));
sg = cg.multiply(t);
}
final ComplexNumber b00 = cg.multiply(a00).add(sg.multiply(a10));
final ComplexNumber b11 = cg.multiply(a11).subtract(sg.multiply(a01));
final ComplexNumber b2 =
cg.multiply(a01.add(a10)).add(sg.multiply(a11.subtract(a00))); // b01 + b10
t = b11.subtract(b00).divide(b2);
t = t.signum().divide(ComplexFunction.SQRT1PX2.invoke(t).add(t.norm()));
// Annihilate - Jacobi
final ComplexNumber cj = ComplexFunction.SQRT1PX2.invoke(t).invert(); // Cos Jacobi
final ComplexNumber sj = cj.multiply(t); // Sin Jacobi
retVal[1] = new Rotation.Complex(aLowInd, aHighInd, cj, sj); // Jacobi
retVal[0] =
new Rotation.Complex(
aLowInd,
aHighInd,
cj.multiply(cg).add(sj.multiply(sg)),
cj.multiply(sg).subtract(sj.multiply(cg))); // Givens - Jacobi
return retVal;
}
