Tests for the ScaLAPACK HRD routines

The HRD test program generates random nonsymmetric test matrices with values in the interval [-1,1], calls the ScaLAPACK routines to reduce the test matrix to upper Hessenberg form, and computes a reduction residual error check to verify that each operation has performed correctly.

Specifically, each test matrix is subjected to the following tests:

• Reduce the matrix $A$ to upper Hessenberg form $H$ using PxGEHRD
  • $Q^{T} \ast A \ast Q = H$.
• and compute the ratio
  • FRESID $= \vert\vert Q \ast H \ast Q^{T} - A \vert\vert / ( n \vert\vert A \vert\vert \varepsilon )$