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NAME ZLAHQR - i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI SYNOPSIS SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO ) LOGICAL WANTT, WANTZ INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N COMPLEX*16 H( LDH, * ), W( * ), Z( LDZ, * ) PURPOSE ZLAHQR is an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI. ARGUMENTS WANTT (input) LOGICAL = .TRUE. : the full Schur form T is required; = .FALSE.: only eigenvalues are required. WANTZ (input) LOGICAL = .TRUE. : the matrix of Schur vectors Z is required; = .FALSE.: Schur vectors are not required. N (input) INTEGER The order of the matrix H. N >= 0. ILO (input) INTEGER IHI (input) INTEGER It is assumed that H is already upper triangular in rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1). ZLAHQR works primarily with the Hessenberg submatrix in rows and columns ILO to IHI, but applies transformations to all of H if WANTT is .TRUE.. 1 <= ILO <= max(1,IHI); IHI <= N. H (input/output) COMPLEX*16 array, dimension (LDH,N) On entry, the upper Hessenberg matrix H. On exit, if WANTT is .TRUE., H is upper triangular in rows and columns ILO:IHI, with any 2-by-2 diagonal blocks in standard form. If WANTT is .FALSE., the contents of H are unspecified on exit. LDH (input) INTEGER The leading dimension of the array H. LDH >= max(1,N). W (output) COMPLEX*16 array, dimension (N) The computed eigenvalues ILO to IHI are stored in the corresponding elements of W. If WANTT is .TRUE., the eigenvalues are stored in the same order as on the diagonal of the Schur form returned in H, with W(i) = H(i,i). ILOZ (input) INTEGER IHIZ (input) INTEGER Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. Z (input/output) COMPLEX*16 array, dimension (LDZ,N) If WANTZ is .TRUE., on entry Z must contain the current matrix Z of transformations accumulated by ZHSEQR, and on exit Z has been updated; transforma- tions are applied only to the submatrix Z(ILOZ:IHIZ,ILO:IHI). If WANTZ is .FALSE., Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= max(1,N). INFO (output) INTEGER = 0: successful exit > 0: ZLAHQR failed to compute all the eigenvalues ILO to IHI in a total of 30*(IHI-ILO+1) iterations; if INFO = i, elements i+1:ihi of W contain those eigenvalues which have been successfully computed.