Routine xi2delta

From vector form to matrix form.

This routine converts a block-diagonal operator $\Delta$ from vector form to matrix form.

delta=xi2delta(xi,blk)

Vector form of $\Delta=diag\left(\Delta_1,...,\Delta_N\right)$.

blk

Matrix defining the structure of $\Delta$. Its first 2 columns must be defined as follows for all $i=1,...,N$:

blk(i,1:2)=[-ni 0] $\Rightarrow$ $\Delta_i=\delta_iI_{n_i}$ with $\delta_i$ real,
blk(i,1:2)=[ni 0] $\Rightarrow$ $\Delta_i=\delta_iI_{n_i}$ with $\delta_i$ complex,
blk(i,1:2)=[ni mi] $\Rightarrow$ $\Delta_i$ is a full $n_i\times m_i$ complex block.

delta

Matrix form of $\Delta$.

blk=[-3 0;2 0;2 3]; 
xi1=(1:15)'; 
delta=xi2delta(xi1,blk) 
xi2=delta2xi(delta,blk)