/**
* Returns two matrices containing partial derivatives of the complex bus power injections w.r.t
* voltage magnitude and voltage angle respectively (for all buses). If YBUS is a sparse matrix,
* the return values will be also. The following explains the expressions used to form the
* matrices:
*
* <p>S = diag(V) * conj(Ibus) = diag(conj(Ibus)) * V
*
* <p>Partials of V & Ibus w.r.t. voltage magnitudes dV/dVm = diag(V./abs(V)) dI/dVm = Ybus *
* dV/dVm = Ybus * diag(V./abs(V))
*
* <p>Partials of V & Ibus w.r.t. voltage angles dV/dVa = j * diag(V) dI/dVa = Ybus * dV/dVa =
* Ybus * j * diag(V)
*
* <p>Partials of S w.r.t. voltage magnitudes dS/dVm = diag(V) * conj(dI/dVm) + diag(conj(Ibus)) *
* dV/dVm = diag(V) * conj(Ybus * diag(V./abs(V))) + conj(diag(Ibus)) * diag(V./abs(V))
*
* <p>Partials of S w.r.t. voltage angles dS/dVa = diag(V) * conj(dI/dVa) + diag(conj(Ibus)) *
* dV/dVa = diag(V) * conj(Ybus * j * diag(V)) + conj(diag(Ibus)) * j * diag(V) = -j * diag(V) *
* conj(Ybus * diag(V)) + conj(diag(Ibus)) * j * diag(V) = j * diag(V) * conj(diag(Ibus) - Ybus *
* diag(V))
*
* @param Ybus
* @param V
* @return
*/
@SuppressWarnings("static-access")
public static DComplexMatrix2D[] jp_dSbus_dV(DComplexMatrix2D Ybus, DComplexMatrix1D V) {
int n;
int[] ib;
DComplexMatrix1D Ibus, absV, Vnorm;
DComplexMatrix2D[] dSbus_dV;
SparseRCDComplexMatrix2D diagV, diagIbus, diagVnorm, rhs, dS_dVa, conjInorm, dS_dVm, addend;
n = (int) V.size();
ib = Djp_util.irange(n);
Ibus = Ybus.zMult(V, null);
diagV = new SparseRCDComplexMatrix2D(n, n, ib, ib, V.toArray(), false, false);
diagIbus = new SparseRCDComplexMatrix2D(n, n, ib, ib, Ibus.toArray(), false, false);
absV = V.copy().assign(cfunc.abs);
Vnorm = V.copy().assign(absV, cfunc.div);
diagVnorm = new SparseRCDComplexMatrix2D(n, n, ib, ib, Vnorm.toArray(), false, false);
rhs = (SparseRCDComplexMatrix2D) Ybus.zMult(diagV, null);
rhs.assign(diagIbus, cfunc.swapArgs(cfunc.minus)).assign(cfunc.conj);
dS_dVa = (SparseRCDComplexMatrix2D) diagV.zMult(rhs, null);
dS_dVa.assign(cfunc.mult(new double[] {0, 1}));
conjInorm = (SparseRCDComplexMatrix2D) Ybus.zMult(diagVnorm, null);
conjInorm.assign(cfunc.conj);
dS_dVm = (SparseRCDComplexMatrix2D) diagV.zMult(conjInorm, null);
diagIbus.assign(cfunc.conj);
addend = (SparseRCDComplexMatrix2D) diagVnorm.zMult(diagIbus, null);
dS_dVm.assign(addend, cfunc.plus);
dSbus_dV = new DComplexMatrix2D[] {dS_dVm, dS_dVa};
return dSbus_dV;
}
