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Routine xi2delta

From vector form to matrix form.

Description

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

Synta

delta=xi2delta(xi,blk)

Input arguments

xi 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.

Output argument

delta Matrix form of $\Delta$.

Example

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

See also

delta2xi