```
F08RNF Example Program Results

Unitary matrix X
1                 2                 3                 4
1  (-0.0130,-0.3260) (-0.1404,-0.2617) ( 0.2518,-0.7979) (-0.0510,-0.2175)
2  ( 0.4276,-0.6258) ( 0.0863,-0.0382) (-0.3219, 0.1611) ( 0.1198, 0.1632)
3  (-0.3260, 0.1643) ( 0.3816,-0.1822) ( 0.1323,-0.0146) (-0.5067, 0.1861)
4  ( 0.1591,-0.0052) (-0.2821, 0.1973) ( 0.2160, 0.1881) (-0.4016, 0.2679)
5  (-0.1721,-0.0130) (-0.5094,-0.5032) ( 0.0365, 0.2032) ( 0.1927, 0.1557)
6  (-0.2634,-0.2477) (-0.1086, 0.2847) ( 0.1091,-0.1271) (-0.0882, 0.5617)

5                 6
1  (-0.0459, 0.0001) (-0.0528,-0.2249)
2  (-0.0803,-0.4361) (-0.0381,-0.2191)
3  ( 0.0597,-0.5897) (-0.1385,-0.0909)
4  (-0.0464, 0.3086) (-0.3735,-0.5515)
5  ( 0.5784,-0.1244) (-0.0188,-0.0557)
6  ( 0.0158, 0.0471) ( 0.6501, 0.0049)

Theta Component of CS factorization of X:

Theta
1
1   0.1973
2   0.5387

Components of CS factorization of X:

Theta
1
1   0.1973
2   0.5387

Recombined matrix X = U * Sigma_p * V^H
1                 2                 3                 4
1  (-0.0130,-0.3260) (-0.1404,-0.2617) ( 0.2518,-0.7979) (-0.0510,-0.2175)
2  ( 0.4276,-0.6258) ( 0.0863,-0.0382) (-0.3219, 0.1611) ( 0.1198, 0.1632)
3  (-0.3260, 0.1643) ( 0.3816,-0.1822) ( 0.1323,-0.0146) (-0.5067, 0.1861)
4  ( 0.1591,-0.0052) (-0.2821, 0.1973) ( 0.2160, 0.1881) (-0.4016, 0.2679)
5  (-0.1721,-0.0131) (-0.5094,-0.5032) ( 0.0365, 0.2032) ( 0.1927, 0.1557)
6  (-0.2634,-0.2477) (-0.1086, 0.2847) ( 0.1091,-0.1271) (-0.0882, 0.5617)

5                 6
1  (-0.0459, 0.0001) (-0.0528,-0.2249)
2  (-0.0803,-0.4361) (-0.0381,-0.2191)
3  ( 0.0597,-0.5897) (-0.1385,-0.0909)
4  (-0.0464, 0.3086) (-0.3735,-0.5515)
5  ( 0.5784,-0.1244) (-0.0188,-0.0557)
6  ( 0.0158, 0.0471) ( 0.6501, 0.0049)
```