Tests for the ScaLAPACK LU routines

The LU test program generates random nonsymmetric test matrices with values in the interval [-1,1], calls the ScaLAPACK routines to factor and solve the system, and computes a solve and/or factorization residual error check to verify that each operation has performed correctly. Condition estimation and iterative refinement routines are included and are optionally tested.

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

• Factor the matrix $A = LU$ using PxGETRF
• Solve the system $A X = B$ using PxGETRS, and compute the ratio
  • SRESID $= \vert\vert AX - B\vert\vert / ( n \vert\vert A\vert\vert \, \vert\vert X\vert\vert \varepsilon )$
• If SRESID $>$ THRESH, then compute the ratio
  • FRESID $= \vert\vert LU - A \vert\vert / ( n \vert\vert A \vert\vert \varepsilon )$

The expert driver (PxGESVX) performs condition estimation and iterative refinement and thus incorporates the following additional test:

• Compute the reciprocal condition number RCOND using PxGECON.
• Use iterative refinement (PxGERFS) to improve the solution, and recompute the ratio
  • SRESID $= \vert\vert AX - B\vert\vert / ( n \vert\vert A\vert\vert \, \vert\vert X\vert\vert \varepsilon )$