Example (from Program LA_GBSVX_EXAMPLE)

The results below are computed with $\epsilon = 1.19209 \times 10^{-7}$.
$A$ and $B$ are the same as in Example $2$ for LA_GBSV, except that the first column of $A$ is multiplied by $10^{-6}$.
Arrays ${\bf AB}$ and ${\bf B}$ on entry:

$$\hspace{-1.00 cm} \begin{array}{c} {\bf AB} \\ \begin{array... ...& 56 \\ 13 & 26 \\ 4 & 8 \\ \hline \end{array} \end{array}$$

Elements marked $\ast$ are not referenced by the routine.

The call:

   CALL LA_GBSVX( AB, B, X, 2, FACT='E', TRANS='T',  EQUED=EQUED, & 


R=R, C=C, FERR=FERR, BERR=BERR )  

X, EQUED, R, C, FERR and BERR on exit:

$$\begin{array}{c} {\bf X} \\ \begin{array}{\vert rr\vert} \h... ...\ \hline \end{array} \end{array} \ \ {\bf EQUED} = \mbox{'C'}$$

$$\begin{array}{c} {\bf C} \\ \begin{array}{\vert rrrrrr\vert... ...1.00000 & 1.00000 & 2.33333\\ \hline \end{array} \end{array}$$

$$\begin{array}{c} {\bf FERR} \\ \begin{array}{\vert rr\vert}... ...{-8} & 1.70299 \times 10^{-8}\\ \hline \end{array} \end{array}$$

The solution of the system $A^T X = B$ is:

$$X = \left( \begin{array}{rr} 1.00000 & 2.00000 \\ 1.0000... ....00000 & 2.00000 \\ 1.00000 & 2.00000 \end{array} \right) .$$

The columns of matrix $A$ were equilibrated by multiplication from the right with the matrix

$$C = \left( \begin{array}{cccccc} 1.40000 \times 10^{6} & 0 &... ...00000 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2.33333 \end{array} \right).$$

The forward and backward errors of the two solution vectors are:

$$\left( \begin{array}{cc} 2.87146 \times 10^{-4} & 2.87146 ... ...9 \times 10^{-8} & 1.70299 \times 10^{-8} \end{array} \right).$$