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Notice revision #20110804
- (global )If, then the Hessenberg matrixwanttis non-zeroAis fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the callingfunction).If, then only enough ofwanttequals zeroAis updated to preserve the eigenvalues.
- (global )If, then the orthogonal matrixwantzis non-zeroZis updated so that the orthogonal Schur factor may be computed (in cooperation with the callingfunction).If, thenwantzequals zerozis not referenced.
- (global )The order of the matrixAand (ifwantzisnon-zero) the order of the orthogonal matrixZ.
- (global )It is assumed without a check that eitherkbot=norA(kbot+1,kbot)=0.kbotandktoptogether determine an isolated block along the diagonal of the Hessenberg matrix. However,A(ktop,ktop-1)=0 is not essentially necessary ifwanttisnon-zero.
- (global )Deflation window size. 1≤nw≤(kbot-ktop+1). Normallynw≥3 ifp?laqr2is called byp?laqr1.
- (local ) array of sizelld_a*(LOCcn)The initialn-by-nsection ofastores the Hessenberg matrix undergoing aggressive early deflation.
- (global and local) array of sizedlen_.The array descriptor for the distributed matrixA.
- (global )Specify the rows ofthe matrixto which transformations must be applied ifZwantzisnon-zero. 1≤iloz≤ihiz≤n.
- Array of sizelld_z*(LOCcn)Ifwantzisnon-zero, then on output, the orthogonal similarity transformation mentioned above has been accumulated intothe matrix(Ziloz:ihiz,kbot:ktop), stored infrom the right.z,Ifwantziszero, thenzis unreferenced.
- (global and local) array of sizedlen_.The array descriptor for the distributed matrixZ.
- (local workspace) array of size.ldt*nw
- (local )The leading dimension of the arrayt.ldt≥nw.
- (local workspace) array of size.ldv*nw
- (local )The leading dimension of the arrayv.ldv≥nw.
- (local workspace) array of sizekbot.
- (local workspace) array of sizelwork.
- (local )work(lwork) is a local array andlworkis assumed big enough so thatlwork≥nw*nw.
- On outputahas been transformed by an orthogonal similarity transformation, perturbed, and returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries.
- (global )The number of unconverged (that is, approximate) eigenvalues returned insrandsithat may be used as shifts by the callingfunction.
- (global )The number of converged eigenvalues uncovered by thisfunction.
- (global ) array of sizekbotOn output, the real and imaginary parts of approximate eigenvalues that may be used for shifts are stored in, respectively.sr[kbot-nd-ns] throughsr[kbot-nd-1] andsi[kbot-nd-ns] throughsi[kbot-nd-1]On processor #0, the real and imaginary parts of converged eigenvalues are stored in, respectively. On other processors, these entries are set to zero.sr[kbot-nd] throughsr[kbot-1] andsi[kbot-nd] throughsi[kbot-1]