Example (from Program LA_GELSY_EXAMPLE)

The results below are computed with $\epsilon = 1.19209 \times 10^{-7}$.

$$A = \left( \begin{array}{rrrr} 0 & 9 & -6 & 3 \\ -3 & 0 ... ...0 & 2 & 2 \\ -4 & 1 & 2 \\ 1 & -2 & 6 \end{array} \right)$$

A, B, JPVT and RCOND on entry:

$$\begin{array}{c} {\bf A} \\ \begin{array}{\vert rrrr\vert... ...vert} \hline 0 & 0 & 1 & 0 \\ \hline \end{array} \end{array}$$

The call:
CALL LA_GELSY( A, B, RANK, JPVT, 1.0E-5_wp ) ^6.1

B, RANK and JPVT on exit:

$$\hspace{-1.00 cm} \begin{array}{c} {\bf B} \\ \begin{array... ...; 2.20431 & \;\;\; 5.33678 \\ \hline \end{array} \end{array}$$

$$\begin{array}{c} {\bf RANK} \\ \begin{array}{\vert c\vert}... ...vert} \hline 3 & 2 & 1 & 4 \\ \hline \end{array} \end{array}$$

The rank of matrix $A$ is 2.

The solution matrix is:

$$X = \left( \begin{array}{lll} \;\;\; 4.20045 \times 10^{-1} ... ...mes 10^{-1} & -5.91214 \times 10^{-3} \\ \end{array} \right).$$