Tests for the ScaLAPACK TRD routines

The TRD test program generates random symmetric test matrices with values in the interval [-1,1], calls the ScaLAPACK routines to reduce the test matrix to symmetric tridiagonal 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 symmetric matrix $A$ to symmetric tridiagonal form $T$ using PxSYTRD
  • $Q^{T} \ast A \ast Q = T$.
• and compute the ratio
  • FRESID $= \vert\vert Q \ast T \ast Q^{T} - A \vert\vert / ( n \vert\vert A \vert\vert \varepsilon )$