slahqr (l)  Linux Manuals
slahqr: 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
NAME
SLAHQR  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 IHISYNOPSIS
 SUBROUTINE SLAHQR(
 WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, INFO )
 INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
 LOGICAL WANTT, WANTZ
 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 quasitriangular in rows and columns IHI+1:N, and that H(ILO,ILO1) = 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 INFO is zero and if WANTT is .TRUE., H is upper quasitriangular in rows and columns ILO:IHI, with any 2by2 diagonal blocks in standard form. If INFO is zero and WANTT is .FALSE., the contents of H are unspecified on exit. The output state of H if INFO is nonzero is given below under the description of INFO.
 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 corresponding 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 ith 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 2by2 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; transformations 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
eigenvalues ILO to IHI in a total of 30 iterations per eigenvalue; elements i+1:ihi of WR and WI contain those eigenvalues which have been successfully computed. If INFO .GT. 0 and WANTT is .FALSE., then on exit, the remaining unconverged eigenvalues are the eigenvalues of the upper Hessenberg matrix rows and columns ILO thorugh INFO of the final, output value of H. If INFO .GT. 0 and WANTT is .TRUE., then on exit (*) (initial value of H)*U = U*(final value of H) where U is an orthognal matrix. The final value of H is upper Hessenberg and triangular in rows and columns INFO+1 through IHI. If INFO .GT. 0 and WANTZ is .TRUE., then on exit (final value of Z) = (initial value of Z)*U where U is the orthogonal matrix in (*) (regardless of the value of WANTT.)
FURTHER DETAILS
0296 Based on modifications by
David Day, Sandia National Laboratory, USA
1204 Further modifications by
Ralph Byers, University of Kansas, USA
This is a modified version of SLAHQR from LAPACK version 3.0.
It is
(2)
criterion