fJfac – IQClab

The function $[M,J]=fJfac(P,dimQ)$ factorizes the symmetric matrix

$\left(\begin{array}{cc}Q&S\\S^T&R\end{array}\right),$

where $Q\succ0$ and $R-S^TQ^{-1}S\prec0$ as

$P=M^TJM=\left(\bullet\right)^T\left(\begin{array}{cc}I_{n_Q}&0\\0&-I_{n_R}\end{array}\right) \left(\begin{array}{cc}M_{11}& M_{12} \\0&M_{22}\end{array}\right).$

Here $n_Q$ and $n_R$ denote the dimension of $Q$ and $R$ respectively.