clahqr-f(3)

clahqr.f –

Synopsis

Functions/Subroutines

subroutine clahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO)
CLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.

Function/Subroutine Documentation

subroutine clahqr (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, complex, dimension( ldh, * )H, integerLDH, complex, dimension( * )W, integerILOZ, integerIHIZ, complex, dimension( ldz, * )Z, integerLDZ, integerINFO)

CLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.

Purpose:

 CLAHQR is an auxiliary routine called by CHSEQR to update the
 eigenvalues and Schur decomposition already computed by CHSEQR, by
 dealing with the Hessenberg submatrix in rows and columns ILO to
 IHI.

Parameters:

WANTT

 WANTT is LOGICAL
 = .TRUE. : the full Schur form T is required;
 = .FALSE.: only eigenvalues are required.

WANTZ

 WANTZ is LOGICAL
 = .TRUE. : the matrix of Schur vectors Z is required;
 = .FALSE.: Schur vectors are not required.

 N is INTEGER
 The order of the matrix H. N >= 0.

ILO

 ILO is INTEGER

IHI

 IHI is 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).
 CLAHQR 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 is COMPLEX array, dimension (LDH,N)
 On entry, the upper Hessenberg matrix H.
 On exit, if INFO is zero and if WANTT is .TRUE., then H
 is upper triangular in rows and columns ILO:IHI. If INFO
 is zero and if WANTT is .FALSE., then the contents of H
 are unspecified on exit. The output state of H in case
 INF is positive is below under the description of INFO.

LDH

 LDH is INTEGER
 The leading dimension of the array H. LDH >= max(1,N).

 W is COMPLEX 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

 ILOZ is INTEGER

IHIZ

 IHIZ is INTEGER
 Specify the rows of Z to which transformations must be
 applied if WANTZ is .TRUE..
 1 <= ILOZ <= ILO; IHI <= IHIZ <= N.

 Z is COMPLEX array, dimension (LDZ,N)
 If WANTZ is .TRUE., on entry Z must contain the current
 matrix Z of transformations accumulated by CHSEQR, 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

 LDZ is INTEGER
 The leading dimension of the array Z. LDZ >= max(1,N).

INFO

 INFO is INTEGER
 = 0: successful exit
 .GT. 0: if INFO = i, CLAHQR failed to compute all the
 eigenvalues ILO to IHI in a total of 30 iterations
 per eigenvalue; elements i+1:ihi of W 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.)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

 02-96 Based on modifications by
 David Day, Sandia National Laboratory, USA
 12-04 Further modifications by
 Ralph Byers, University of Kansas, USA
 This is a modified version of CLAHQR from LAPACK version 3.0.
 It is (1) more robust against overflow and underflow and
 (2) adopts the more conservative Ahues & Tisseur stopping
 criterion (LAWN 122, 1997).

Definition at line 195 of file clahqr.f.

Author

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