1ZLAHQR(1) LAPACK auxiliary routine (version 3.1) ZLAHQR(1)
2
6 ZLAHQR - i an auxiliary routine called by CHSEQR to update the eigen‐
7 values and Schur decomposition already computed by CHSEQR, by dealing
8 with the Hessenberg submatrix in rows and columns ILO to IHI
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11 SUBROUTINE ZLAHQR( 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*16 H( LDH, * ), W( * ), Z( LDZ, * )
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21 ZLAHQR 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
28 WANTT (input) LOGICAL
29 = .TRUE. : the full Schur form T is required;
30 = .FALSE.: only eigenvalues are required.
31 WANTZ (input) LOGICAL
33 = .TRUE. : the matrix of Schur vectors Z is required;
34 = .FALSE.: Schur vectors are not required.
35 N (input) INTEGER
37 The order of the matrix H. N >= 0.
38 ILO (input) INTEGER
40 IHI (input) INTEGER It is assumed that H is already upper
41 triangular in rows and columns IHI+1:N, and that H(ILO,ILO-1) =
42 0 (unless ILO = 1). ZLAHQR works primarily with the Hessenberg
43 submatrix in rows and columns ILO to IHI, but applies transfor‐
44 mations to all of H if WANTT is .TRUE.. 1 <= ILO <=
45 max(1,IHI); IHI <= N.
46 H (input/output) COMPLEX*16 array, dimension (LDH,N)
48 On entry, the upper Hessenberg matrix H. On exit, if INFO is
49 zero and if WANTT is .TRUE., then H is upper triangular in rows
50 and columns ILO:IHI. If INFO is zero and if WANTT is .FALSE.,
51 then the contents of H are unspecified on exit. The output
52 state of H in case INF is positive is below under the descrip‐
53 tion of INFO.
54 LDH (input) INTEGER
56 The leading dimension of the array H. LDH >= max(1,N).
57 W (output) COMPLEX*16 array, dimension (N)
59 The computed eigenvalues ILO to IHI are stored in the corre‐
60 sponding elements of W. If WANTT is .TRUE., the eigenvalues are
61 stored in the same order as on the diagonal of the Schur form
62 returned in H, with W(i) = H(i,i).
63 ILOZ (input) INTEGER
65 IHIZ (input) INTEGER Specify the rows of Z to which trans‐
66 formations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <=
67 ILO; IHI <= IHIZ <= N.
68 Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
70 If WANTZ is .TRUE., on entry Z must contain the current matrix
71 Z of transformations accumulated by CHSEQR, and on exit Z has
72 been updated; transformations are applied only to the submatrix
73 Z(ILOZ:IHIZ,ILO:IHI). If WANTZ is .FALSE., Z is not refer‐
74 enced.
75 LDZ (input) INTEGER
77 The leading dimension of the array Z. LDZ >= max(1,N).
78 INFO (output) INTEGER
80 = 0: successful exit
81 eigenvalues ILO to IHI in a total of 30 iterations per eigen‐
82 value; elements i+1:ihi of W contain those eigenvalues which
83 have been successfully computed.
84 If INFO .GT. 0 and WANTT is .FALSE., then on exit, the remain‐
86 ing unconverged eigenvalues are the eigenvalues of the upper
87 Hessenberg matrix rows and columns ILO thorugh INFO of the
88 final, output value of H.
89 If INFO .GT. 0 and WANTT is .TRUE., then on exit (*)
91 (initial value of H)*U = U*(final value of H) where U is an
92 orthognal matrix. The final value of H is upper Hessenberg
93 and triangular in rows and columns INFO+1 through IHI.
94 If INFO .GT. 0 and WANTZ is .TRUE., then on exit (final value
96 of Z) = (initial value of Z)*U where U is the orthogonal
97 matrix in (*) (regardless of the value of WANTT.)
98
100 02-96 Based on modifications by
101 David Day, Sandia National Laboratory, USA
102 12-04 Further modifications by
104 Ralph Byers, University of Kansas, USA
105 This is a modified version of ZLAHQR from LAPACK version 3.0.
107 It is (1) more robust against overflow and underflow and
108 (2) adopts the more conservative Ahues & Tisseur stopping
109 criterion (LAWN 122, 1997).
110 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006 ZLAHQR(1)