ZGGLSE Example

To solve the linear equality constrained least squares problem

$\displaystyle \min_{{x}}^{}$$\displaystyle \left\Vert\vphantom{ c - A x }\right.$c - Ax$\displaystyle \left.\vphantom{ c - A x }\right\Vert _{{2}}^{}$  subject to  Bx = d

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)$

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)$c = $\displaystyle \left(\vphantom{
\begin{array}{r}
-2.54 + 0.09 i \\
1.65 - 2...
...
1.82 + 3.30 i \\
-6.41 + 3.77 i \\
2.07 + 0.66 i
\end{array} }\right.$$\displaystyle \begin{array}{r}
-2.54 + 0.09 i \\
1.65 - 2.26 i \\
-2.11 - 3.96 i \\
1.82 + 3.30 i \\
-6.41 + 3.77 i \\
2.07 + 0.66 i
\end{array}$$\displaystyle \left.\vphantom{
\begin{array}{r}
-2.54 + 0.09 i \\
1.65 - 2...
...
1.82 + 3.30 i \\
-6.41 + 3.77 i \\
2.07 + 0.66 i
\end{array} }\right)$ and  d = $\displaystyle \left(\vphantom{
\begin{array}{r}
0 \\
0
\end{array} }\right.$$\displaystyle \begin{array}{r}
0 \\
0
\end{array}$$\displaystyle \left.\vphantom{
\begin{array}{r}
0 \\
0
\end{array} }\right)$.

The constraints Bx = d correspond to x1 = x3 and x2 = x4.

Example program
Example data
Example results