Tests for the ScaLAPACK GSEP routines

Finding the eigenvalues and eigenvectors of symmetric matrices A and B, where B is also positive definite, follows the same stages as the symmetric eigenvalue problem except that the problem is first reduced from generalized to standard form using PxSYGST/PxHEGST.

To check these calculations, the following test ratios are computed:

$$r_1 = \frac{ \left\Vert A \, Z - B \, Z \, D \right\Vert} { \left\Vert A\right\Vert\, \left\Vert Z \right\Vert\, n \, ulp}$$

$$\mbox{calling PxSYGVX/PxHEGVX with ITYPE=1 and UPLO='U'}$$

$$r_2 = \frac{ \left\Vert A \, Z - B \, Z \, D \right\Vert} { \left\Vert A\right\Vert\, \left\Vert Z \right\Vert\, n \, ulp}$$

$$\mbox{calling PxSYGVX/PxHEGVX with ITYPE=1 and UPLO='L'}$$

$$r_5 = \frac{ \left\Vert A \, Z - B \, Z \, D \right\Vert} { \left\Vert A\right\Vert\, \left\Vert Z \right\Vert\, n \, ulp}$$

$$\mbox{calling PxSYGVX/PxHEEVX with ITYPE=2 and UPLO='U'}$$

$$r_8 = \frac{ \left\Vert A \, B \, Z - Z \, D \right\Vert} { \left\Vert A\right\Vert\, \left\Vert Z \right\Vert\, n \, ulp}$$

$$\mbox{calling PxSYGVX/PxHEEVX with ITYPE=2 and UPLO='L'}$$

$$r_{10} = \frac{ \left\Vert A \, B \, Z - Z \, D \right\Vert} { \left\Vert A\right\Vert\, \left\Vert Z \right\Vert\, n \, ulp}$$

$$\mbox{calling PxSYGVX/PxHEEVX with ITYPE=3 and UPLO='U'}$$

$$r_{12} = \frac{ \left\Vert B \, A \, Z - Z \, D \right\Vert} { \left\Vert A\right\Vert\, \left\Vert Z \right\Vert\, n \, ulp}$$

$$\mbox{calling PxSYGVX/PxHEEVX with ITYPE=3 and UPLO='L'}$$

$$r_{14} = \frac{ \left\Vert B \, A \, Z - Z \, D \right\Vert} { \left\Vert A\right\Vert\, \left\Vert Z \right\Vert\, n \, ulp}$$