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[Scalapack] complex pivoted qr factorisation

 ```On 10/20/11 6:01 AM, Sven Hammarling wrote: ``````Dear Jim, Unless I misunderstand (quite likely!), I think that Zlatko and Zvonimir showed a similar example in Figure 1 of LAWN 176 - it certainly has a deep spike. Once ScaLAPACK gets the LAPACK fix it will be interesting to see the result on David's example. Best wishes, Sven. ``````In that figure, the "true" answer is around macheps * norm(A), and R(i,i) drops down way below that. So everything is tiny. I think this is the only way you can get such completely out-of-order R(i,i), when everything is O(macheps*norm(A)) and so possibly totally losing all leading digits. In the example from David Wang below, R(3,3) is O(norm(A)) = O(1), and appears after R(2,2) = O(macheps), which can't be explained by the bug Zlatko and Zvonimir found: R(0,0) -0.707107 + 0i R(1,1) -0.707107 + 0i R(2,2) 8.16273e-17 + 0i R(3,3) -0.243173 + 0i R(4,4) 4.82605e-17 + 0i Jim ```
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