ZGGSVD Example

To find the generalized singular value decomposition

A = U $\displaystyle \Sigma_{1}^{}$ $\displaystyle \left(\vphantom{ \begin{array}{cc} 0 & R \end{array} }\right.$ $\displaystyle \begin{array}{cc} 0 & R \end{array}$ $\displaystyle \left.\vphantom{ \begin{array}{cc} 0 & R \end{array} }\right)$ Q^H, B = V $\displaystyle \Sigma_{2}^{}$ $\displaystyle \left(\vphantom{ \begin{array}{cc} 0 & R \end{array} }\right.$ $\displaystyle \begin{array}{cc} 0 & R \end{array}$ $\displaystyle \left.\vphantom{ \begin{array}{cc} 0 & R \end{array} }\right)$ Q^H,

where

A = $\displaystyle \left(\vphantom{ \begin{array}{rrrr} 0.96 - 0.81 i & -0.03 + 0.... ...- 0.28 i & 0.20 - 0.12 i & -0.07 + 1.23 i & 0.26 + 0.26 i \end{array} }\right.$ $\displaystyle \begin{array}{rrrr} 0.96 - 0.81 i & -0.03 + 0.96 i & -0.91 + 2.0... ... 1.08 - 0.28 i & 0.20 - 0.12 i & -0.07 + 1.23 i & 0.26 + 0.26 i \end{array}$ $\displaystyle \left.\vphantom{ \begin{array}{rrrr} 0.96 - 0.81 i & -0.03 + 0.... ...- 0.28 i & 0.20 - 0.12 i & -0.07 + 1.23 i & 0.26 + 0.26 i \end{array} }\right)$

and

B = $\displaystyle \left(\vphantom{ \begin{array}{rrrr} 1 & 0 & -1 & 0 \\ 0 & 1 & 0 & -1 \end{array} }\right.$ $\displaystyle \begin{array}{rrrr} 1 & 0 & -1 & 0 \\ 0 & 1 & 0 & -1 \end{array}$ $\displaystyle \left.\vphantom{ \begin{array}{rrrr} 1 & 0 & -1 & 0 \\ 0 & 1 & 0 & -1 \end{array} }\right)$ ,

together with estimates for the condition number of R and the error bound for the computed generalized singular values.

The example program assumes that m $\ge$ n, and would need slight modification if this is not the case.

Example program
Example data
Example results