Performs the orthogonal/unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
subroutineaccepts as input an upper Hessenberg matrix
Hand performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output
His overwritten by a new Hessenberg matrix that is a perturbation of an orthogonal similarity transformation of
H. It is to be hoped that the final version of
Hhas many zero subdiagonal entries.
- (global )LOGICALIf.TRUE., then the Hessenberg matrixHis fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the callingsubroutine).If.FALSE., then only enough ofHis updated to preserve the eigenvalues.
- (global )LOGICALIf.TRUE., then the orthogonal matrixZis updated so that the orthogonal Schur factor may be computed (in cooperation with the callingsubroutine).If.FALSE., thenzis not referenced.
- (global )INTEGERThe order of the matrixHand (ifwantzis), the order of the orthogonal matrix.TRUE.Z.
- (global )INTEGERIt is assumed that eitherktop= 1 orH(ktop,ktop-1)=0.kbotandktoptogether determine an isolated block along the diagonal of the Hessenberg matrix.
- (global )INTEGERIt is assumed without a check that eitherkbot=norH(kbot+1,kbot)=0.kbotandktoptogether determine an isolated block along the diagonal of the Hessenberg matrix.
- (global )INTEGERDeflation window size. 1≤nw≤(kbot-ktop+1).
- REALforpslaqr3DOUBLE PRECISIONforpdlaqr3(local ) array of size(lld_h,(LOCcn))The initialn-by-nsection ofHstores the Hessenberg matrix undergoing aggressive early deflation.
- (global and local)array of sizeINTEGERdlen_.The array descriptor for the distributed matrixH.
- (global )INTEGERSpecify the rows of the matrixZto which transformations must be applied if