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Tests for the ScaLAPACK EVC routines

The PCTREVC/PZTREVC test program performs a right and left eigenvector calculation of a triangular matrix followed by a residual checks of the calculated eigenvectors.

The following tests will be performed on P_TREVC. The basic test is:

$\displaystyle r_1$ $\textstyle =$ $\displaystyle \frac{\left\Vert H Z - Z D \right\Vert}
{n \, ulp \, \left\Vert T \right\Vert}$  

using the 1-norm. It also tests the normalization of $Z$.
$\displaystyle r_2$ $\textstyle =$ $\displaystyle \frac{max_j \left\Vert m-norm( Z(j) ) - 1 \right\Vert)}
{n \, ulp }$  

where $H$ is the upper Hessenberg matrix, $n$ is the order of the matrix, $Z(j)$ is the j-th eigenvector, and m-norm is the max-norm of a vector, and $ulp$ represents PxLAMCH( ICTXT, 'P' ). The max-norm of a complex n-vector $x$ in this case is the maximum of $\left\Vert re(x(i))\right\Vert$ + $\left\Vert im(x(i)) \right\Vert$ over $i = 1, \ldots, n$.


Susan Blackford 2001-08-12