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).
p?laqr2accepts as input an upper Hessenberg matrix
Aand performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output
Ais overwritten by a new Hessenberg matrix that is a perturbation of an orthogonal similarity transformation of
A. It is to be hoped that the final version of
Ahas many zero subdiagonal entries.
routinehandles small deflation windows which is affordable by one processor. Normally, it is called by
p?laqr1. All the inputs are assumed to be valid without checking.
Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.
Notice revision #20110804
This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.
- (global )LOGICALIf.TRUE., then the Hessenberg matrixAis fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the callingsubroutine).If.FALSE., then only enough ofAis 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 matrixAand (ifwantzis) the order of the orthogonal matrix.TRUE.Z.
- (global )INTEGERIt 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 ifwanttis..TRUE.
- (global )INTEGERDeflation window size. 1≤nw≤(kbot-ktop+1). Normallynw≥3 ifp?laqr2is called byp?laqr1.
- REALforpslaqr2DOUBLE PRECISIONforpdlaqr2(local ) array of size(lld_a,(LOCcn))The initialn-by-nsection ofa