Previous: slagts Up: ../lapack-s.html Next: slahrd

NAME SLAHQR - i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI SYNOPSIS SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, INFO ) LOGICAL WANTT, WANTZ INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N REAL H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * ) PURPOSE SLAHQR is an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, 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 quasi-triangular in rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1). SLAHQR 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) REAL array, dimension (LDH,N) On entry, the upper Hessenberg matrix H. On exit, if WANTT is .TRUE., H is upper quasi-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). WR (output) REAL array, dimension (N) WI (output) REAL array, dimension (N) The real and imaginary parts, respectively, of the computed eigenvalues ILO to IHI are stored in the correspond- ing elements of WR and WI. If two eigenvalues are computed as a complex conjugate pair, they are stored in consecutive elements of WR and WI, say the i-th and (i+1)th, with WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the eigenvalues are stored in the same order as on the diagonal of the Schur form returned in H, with WR(i) = H(i,i), and, if H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(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) REAL array, dimension (LDZ,N) If WANTZ is .TRUE., on entry Z must contain the current matrix Z of transformations accumulated by SHSEQR, 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: SLAHQR 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 WR and WI contain those eigenvalues which have been successfully com- puted.