1CLAHQR(1) LAPACK auxiliary routine (version 3.2) CLAHQR(1)
2
6 CLAHQR - CLAHQR i an auxiliary routine called by CHSEQR to update the
7 eigenvalues and Schur decomposition already computed by CHSEQR, by
8 dealing with the Hessenberg submatrix in rows and columns ILO to IHI
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11 SUBROUTINE CLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z,
12 LDZ, INFO )
13 INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
15 LOGICAL WANTT, WANTZ
17 COMPLEX H( LDH, * ), W( * ), Z( LDZ, * )
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21 CLAHQR is an auxiliary routine called by CHSEQR to update the
22 eigenvalues and Schur decomposition already computed by CHSEQR, by
23 dealing with the Hessenberg submatrix in rows and columns ILO to
24 IHI.
25
27 WANTT (input) LOGICAL
28 = .TRUE. : the full Schur form T is required;
29 = .FALSE.: only eigenvalues are required.
30 WANTZ (input) LOGICAL
32 = .TRUE. : the matrix of Schur vectors Z is required;
33 = .FALSE.: Schur vectors are not required.
34 N (input) INTEGER
36 The order of the matrix H. N >= 0.
37 ILO (input) INTEGER
39 IHI (input) INTEGER It is assumed that H is already upper
40 triangular in rows and columns IHI+1:N, and that H(ILO,ILO-1) =
41 0 (unless ILO = 1). CLAHQR works primarily with the Hessenberg
42 submatrix in rows and columns ILO to IHI, but applies transfor‐
43 mations to all of H if WANTT is .TRUE.. 1 <= ILO <=
44 max(1,IHI); IHI <= N.
45 H (input/output) COMPLEX array, dimension (LDH,N)
47 On entry, the upper Hessenberg matrix H. On exit, if INFO is
48 zero and if WANTT is .TRUE., then H is upper triangular in rows
49 and columns ILO:IHI. If INFO is zero and if WANTT is .FALSE.,
50 then the contents of H are unspecified on exit. The output
51 state of H in case INF is positive is below under the descrip‐
52 tion of INFO.
53 LDH (input) INTEGER
55 The leading dimension of the array H. LDH >= max(1,N).
56 W (output) COMPLEX array, dimension (N)
58 The computed eigenvalues ILO to IHI are stored in the corre‐
59 sponding elements of W. If WANTT is .TRUE., the eigenvalues are
60 stored in the same order as on the diagonal of the Schur form
61 returned in H, with W(i) = H(i,i).
62 ILOZ (input) INTEGER
64 IHIZ (input) INTEGER Specify the rows of Z to which trans‐
65 formations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <=
66 ILO; IHI <= IHIZ <= N.
67 Z (input/output) COMPLEX array, dimension (LDZ,N)
69 If WANTZ is .TRUE., on entry Z must contain the current matrix
70 Z of transformations accumulated by CHSEQR, and on exit Z has
71 been updated; transformations are applied only to the submatrix
72 Z(ILOZ:IHIZ,ILO:IHI). If WANTZ is .FALSE., Z is not refer‐
73 enced.
74 LDZ (input) INTEGER
76 The leading dimension of the array Z. LDZ >= max(1,N).
77 INFO (output) INTEGER
79 = 0: successful exit
80 eigenvalues ILO to IHI in a total of 30 iterations per eigen‐
81 value; elements i+1:ihi of W contain those eigenvalues which
82 have been successfully computed. If INFO .GT. 0 and WANTT is
83 .FALSE., then on exit, the remaining unconverged eigenvalues
84 are the eigenvalues of the upper Hessenberg matrix rows and
85 columns ILO thorugh INFO of the final, output value of H. If
86 INFO .GT. 0 and WANTT is .TRUE., then on exit (*) (ini‐
87 tial value of H)*U = U*(final value of H) where U is an
88 orthognal matrix. The final value of H is upper Hessenberg
89 and triangular in rows and columns INFO+1 through IHI. If INFO
90 .GT. 0 and WANTZ is .TRUE., then on exit (final value of Z) =
91 (initial value of Z)*U where U is the orthogonal matrix in (*)
92 (regardless of the value of WANTT.)
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95 02-96 Based on modifications by
96 David Day, Sandia National Laboratory, USA
97 12-04 Further modifications by
98 Ralph Byers, University of Kansas, USA
99 This is a modified version of CLAHQR from LAPACK version 3.0.
100 It is (1) more robust against overflow and underflow and
101 (2) adopts the more conservative Ahues & Tisseur stopping
102 criterion (LAWN 122, 1997).
103 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 CLAHQR(1)