LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
zget36.f
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1 *> \brief \b ZGET36
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE ZGET36( RMAX, LMAX, NINFO, KNT, NIN )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER KNT, LMAX, NIN, NINFO
15 * DOUBLE PRECISION RMAX
16 * ..
17 *
18 *
19 *> \par Purpose:
20 * =============
21 *>
22 *> \verbatim
23 *>
24 *> ZGET36 tests ZTREXC, a routine for reordering diagonal entries of a
25 *> matrix in complex Schur form. Thus, ZLAEXC computes a unitary matrix
26 *> Q such that
27 *>
28 *> Q' * T1 * Q = T2
29 *>
30 *> and where one of the diagonal blocks of T1 (the one at row IFST) has
31 *> been moved to position ILST.
32 *>
33 *> The test code verifies that the residual Q'*T1*Q-T2 is small, that T2
34 *> is in Schur form, and that the final position of the IFST block is
35 *> ILST.
36 *>
37 *> The test matrices are read from a file with logical unit number NIN.
38 *> \endverbatim
39 *
40 * Arguments:
41 * ==========
42 *
43 *> \param[out] RMAX
44 *> \verbatim
45 *> RMAX is DOUBLE PRECISION
46 *> Value of the largest test ratio.
47 *> \endverbatim
48 *>
49 *> \param[out] LMAX
50 *> \verbatim
51 *> LMAX is INTEGER
52 *> Example number where largest test ratio achieved.
53 *> \endverbatim
54 *>
55 *> \param[out] NINFO
56 *> \verbatim
57 *> NINFO is INTEGER
58 *> Number of examples where INFO is nonzero.
59 *> \endverbatim
60 *>
61 *> \param[out] KNT
62 *> \verbatim
63 *> KNT is INTEGER
64 *> Total number of examples tested.
65 *> \endverbatim
66 *>
67 *> \param[in] NIN
68 *> \verbatim
69 *> NIN is INTEGER
70 *> Input logical unit number.
71 *> \endverbatim
72 *
73 * Authors:
74 * ========
75 *
76 *> \author Univ. of Tennessee
77 *> \author Univ. of California Berkeley
78 *> \author Univ. of Colorado Denver
79 *> \author NAG Ltd.
80 *
81 *> \date December 2016
82 *
83 *> \ingroup complex16_eig
84 *
85 * =====================================================================
86  SUBROUTINE zget36( RMAX, LMAX, NINFO, KNT, NIN )
87 *
88 * -- LAPACK test routine (version 3.7.0) --
89 * -- LAPACK is a software package provided by Univ. of Tennessee, --
90 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
91 * December 2016
92 *
93 * .. Scalar Arguments ..
94  INTEGER KNT, LMAX, NIN, NINFO
95  DOUBLE PRECISION RMAX
96 * ..
97 *
98 * =====================================================================
99 *
100 * .. Parameters ..
101  DOUBLE PRECISION ZERO, ONE
102  parameter ( zero = 0.0d+0, one = 1.0d+0 )
103  COMPLEX*16 CZERO, CONE
104  parameter ( czero = ( 0.0d+0, 0.0d+0 ),
105  \$ cone = ( 1.0d+0, 0.0d+0 ) )
106  INTEGER LDT, LWORK
107  parameter ( ldt = 10, lwork = 2*ldt*ldt )
108 * ..
109 * .. Local Scalars ..
110  INTEGER I, IFST, ILST, INFO1, INFO2, J, N
111  DOUBLE PRECISION EPS, RES
112  COMPLEX*16 CTEMP
113 * ..
114 * .. Local Arrays ..
115  DOUBLE PRECISION RESULT( 2 ), RWORK( ldt )
116  COMPLEX*16 DIAG( ldt ), Q( ldt, ldt ), T1( ldt, ldt ),
117  \$ t2( ldt, ldt ), tmp( ldt, ldt ), work( lwork )
118 * ..
119 * .. External Functions ..
120  DOUBLE PRECISION DLAMCH
121  EXTERNAL dlamch
122 * ..
123 * .. External Subroutines ..
124  EXTERNAL zcopy, zhst01, zlacpy, zlaset, ztrexc
125 * ..
126 * .. Executable Statements ..
127 *
128  eps = dlamch( 'P' )
129  rmax = zero
130  lmax = 0
131  knt = 0
132  ninfo = 0
133 *
134 * Read input data until N=0
135 *
136  10 CONTINUE
137  READ( nin, fmt = * )n, ifst, ilst
138  IF( n.EQ.0 )
139  \$ RETURN
140  knt = knt + 1
141  DO 20 i = 1, n
142  READ( nin, fmt = * )( tmp( i, j ), j = 1, n )
143  20 CONTINUE
144  CALL zlacpy( 'F', n, n, tmp, ldt, t1, ldt )
145  CALL zlacpy( 'F', n, n, tmp, ldt, t2, ldt )
146  res = zero
147 *
148 * Test without accumulating Q
149 *
150  CALL zlaset( 'Full', n, n, czero, cone, q, ldt )
151  CALL ztrexc( 'N', n, t1, ldt, q, ldt, ifst, ilst, info1 )
152  DO 40 i = 1, n
153  DO 30 j = 1, n
154  IF( i.EQ.j .AND. q( i, j ).NE.cone )
155  \$ res = res + one / eps
156  IF( i.NE.j .AND. q( i, j ).NE.czero )
157  \$ res = res + one / eps
158  30 CONTINUE
159  40 CONTINUE
160 *
161 * Test with accumulating Q
162 *
163  CALL zlaset( 'Full', n, n, czero, cone, q, ldt )
164  CALL ztrexc( 'V', n, t2, ldt, q, ldt, ifst, ilst, info2 )
165 *
166 * Compare T1 with T2
167 *
168  DO 60 i = 1, n
169  DO 50 j = 1, n
170  IF( t1( i, j ).NE.t2( i, j ) )
171  \$ res = res + one / eps
172  50 CONTINUE
173  60 CONTINUE
174  IF( info1.NE.0 .OR. info2.NE.0 )
175  \$ ninfo = ninfo + 1
176  IF( info1.NE.info2 )
177  \$ res = res + one / eps
178 *
179 * Test for successful reordering of T2
180 *
181  CALL zcopy( n, tmp, ldt+1, diag, 1 )
182  IF( ifst.LT.ilst ) THEN
183  DO 70 i = ifst + 1, ilst
184  ctemp = diag( i )
185  diag( i ) = diag( i-1 )
186  diag( i-1 ) = ctemp
187  70 CONTINUE
188  ELSE IF( ifst.GT.ilst ) THEN
189  DO 80 i = ifst - 1, ilst, -1
190  ctemp = diag( i+1 )
191  diag( i+1 ) = diag( i )
192  diag( i ) = ctemp
193  80 CONTINUE
194  END IF
195  DO 90 i = 1, n
196  IF( t2( i, i ).NE.diag( i ) )
197  \$ res = res + one / eps
198  90 CONTINUE
199 *
200 * Test for small residual, and orthogonality of Q
201 *
202  CALL zhst01( n, 1, n, tmp, ldt, t2, ldt, q, ldt, work, lwork,
203  \$ rwork, result )
204  res = res + result( 1 ) + result( 2 )
205 *
206 * Test for T2 being in Schur form
207 *
208  DO 110 j = 1, n - 1
209  DO 100 i = j + 1, n
210  IF( t2( i, j ).NE.czero )
211  \$ res = res + one / eps
212  100 CONTINUE
213  110 CONTINUE
214  IF( res.GT.rmax ) THEN
215  rmax = res
216  lmax = knt
217  END IF
218  GO TO 10
219 *
220 * End of ZGET36
221 *
222  END
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:52
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zhst01(N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK, LWORK, RWORK, RESULT)
ZHST01
Definition: zhst01.f:142
subroutine zget36(RMAX, LMAX, NINFO, KNT, NIN)
ZGET36
Definition: zget36.f:87
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: zlaset.f:108
subroutine ztrexc(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO)
ZTREXC
Definition: ztrexc.f:128