Tests for the ScaLAPACK QR, RQ, LQ, QL, QP, and TZ routines

The QR test program generates random nonsymmetric test matrices with values in the interval [-1,1], calls the ScaLAPACK routines to factor the system, and computes a factorization residual error check to verify that each operation has performed correctly.

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

• Compute the QR factorization using PxGEQRF, and generate the orthogonal matrix $Q$ from the Householder vectors
• Compute the ratio
  • FRESID $= \vert\vert QR - A \vert\vert / ( n \vert\vert A \vert\vert \varepsilon )$

The testing of the RQ, LQ, QL, and QP routines proceeds in a similar fashion. Simply replace all occurrences of QR in the previous discussion with RQ, LQ, QL, or QP respectively. For TZ, the factorization routine is called PxTZRZF.