LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zla_hercond_c.f
Go to the documentation of this file.
1 *> \brief \b ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download ZLA_HERCOND_C + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_hercond_c.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_hercond_c.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_hercond_c.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLA_HERCOND_C( UPLO, N, A, LDA, AF,
22 * LDAF, IPIV, C, CAPPLY,
23 * INFO, WORK, RWORK )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER UPLO
27 * LOGICAL CAPPLY
28 * INTEGER N, LDA, LDAF, INFO
29 * ..
30 * .. Array Arguments ..
31 * INTEGER IPIV( * )
32 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
33 * DOUBLE PRECISION C ( * ), RWORK( * )
34 * ..
35 *
36 *
37 *> \par Purpose:
38 * =============
39 *>
40 *> \verbatim
41 *>
42 *> ZLA_HERCOND_C computes the infinity norm condition number of
43 *> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] UPLO
50 *> \verbatim
51 *> UPLO is CHARACTER*1
52 *> = 'U': Upper triangle of A is stored;
53 *> = 'L': Lower triangle of A is stored.
54 *> \endverbatim
55 *>
56 *> \param[in] N
57 *> \verbatim
58 *> N is INTEGER
59 *> The number of linear equations, i.e., the order of the
60 *> matrix A. N >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in] A
64 *> \verbatim
65 *> A is COMPLEX*16 array, dimension (LDA,N)
66 *> On entry, the N-by-N matrix A
67 *> \endverbatim
68 *>
69 *> \param[in] LDA
70 *> \verbatim
71 *> LDA is INTEGER
72 *> The leading dimension of the array A. LDA >= max(1,N).
73 *> \endverbatim
74 *>
75 *> \param[in] AF
76 *> \verbatim
77 *> AF is COMPLEX*16 array, dimension (LDAF,N)
78 *> The block diagonal matrix D and the multipliers used to
79 *> obtain the factor U or L as computed by ZHETRF.
80 *> \endverbatim
81 *>
82 *> \param[in] LDAF
83 *> \verbatim
84 *> LDAF is INTEGER
85 *> The leading dimension of the array AF. LDAF >= max(1,N).
86 *> \endverbatim
87 *>
88 *> \param[in] IPIV
89 *> \verbatim
90 *> IPIV is INTEGER array, dimension (N)
91 *> Details of the interchanges and the block structure of D
92 *> as determined by CHETRF.
93 *> \endverbatim
94 *>
95 *> \param[in] C
96 *> \verbatim
97 *> C is DOUBLE PRECISION array, dimension (N)
98 *> The vector C in the formula op(A) * inv(diag(C)).
99 *> \endverbatim
100 *>
101 *> \param[in] CAPPLY
102 *> \verbatim
103 *> CAPPLY is LOGICAL
104 *> If .TRUE. then access the vector C in the formula above.
105 *> \endverbatim
106 *>
107 *> \param[out] INFO
108 *> \verbatim
109 *> INFO is INTEGER
110 *> = 0: Successful exit.
111 *> i > 0: The ith argument is invalid.
112 *> \endverbatim
113 *>
114 *> \param[out] WORK
115 *> \verbatim
116 *> WORK is COMPLEX*16 array, dimension (2*N).
117 *> Workspace.
118 *> \endverbatim
119 *>
120 *> \param[out] RWORK
121 *> \verbatim
122 *> RWORK is DOUBLE PRECISION array, dimension (N).
123 *> Workspace.
124 *> \endverbatim
125 *
126 * Authors:
127 * ========
128 *
129 *> \author Univ. of Tennessee
130 *> \author Univ. of California Berkeley
131 *> \author Univ. of Colorado Denver
132 *> \author NAG Ltd.
133 *
134 *> \ingroup complex16HEcomputational
135 *
136 * =====================================================================
137  DOUBLE PRECISION FUNCTION zla_hercond_c( UPLO, N, A, LDA, AF,
138  $ LDAF, IPIV, C, CAPPLY,
139  $ INFO, WORK, RWORK )
140 *
141 * -- LAPACK computational routine --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 *
145 * .. Scalar Arguments ..
146  CHARACTER uplo
147  LOGICAL capply
148  INTEGER n, lda, ldaf, info
149 * ..
150 * .. Array Arguments ..
151  INTEGER ipiv( * )
152  COMPLEX*16 a( lda, * ), af( ldaf, * ), work( * )
153  DOUBLE PRECISION c ( * ), rwork( * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Local Scalars ..
159  INTEGER kase, i, j
160  DOUBLE PRECISION ainvnm, anorm, tmp
161  LOGICAL up, upper
162  COMPLEX*16 zdum
163 * ..
164 * .. Local Arrays ..
165  INTEGER isave( 3 )
166 * ..
167 * .. External Functions ..
168  LOGICAL lsame
169  EXTERNAL lsame
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL zlacn2, zhetrs, xerbla
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC abs, max
176 * ..
177 * .. Statement Functions ..
178  DOUBLE PRECISION cabs1
179 * ..
180 * .. Statement Function Definitions ..
181  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
182 * ..
183 * .. Executable Statements ..
184 *
185  zla_hercond_c = 0.0d+0
186 *
187  info = 0
188  upper = lsame( uplo, 'U' )
189  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
190  info = -1
191  ELSE IF( n.LT.0 ) THEN
192  info = -2
193  ELSE IF( lda.LT.max( 1, n ) ) THEN
194  info = -4
195  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
196  info = -6
197  END IF
198  IF( info.NE.0 ) THEN
199  CALL xerbla( 'ZLA_HERCOND_C', -info )
200  RETURN
201  END IF
202  up = .false.
203  IF ( lsame( uplo, 'U' ) ) up = .true.
204 *
205 * Compute norm of op(A)*op2(C).
206 *
207  anorm = 0.0d+0
208  IF ( up ) THEN
209  DO i = 1, n
210  tmp = 0.0d+0
211  IF ( capply ) THEN
212  DO j = 1, i
213  tmp = tmp + cabs1( a( j, i ) ) / c( j )
214  END DO
215  DO j = i+1, n
216  tmp = tmp + cabs1( a( i, j ) ) / c( j )
217  END DO
218  ELSE
219  DO j = 1, i
220  tmp = tmp + cabs1( a( j, i ) )
221  END DO
222  DO j = i+1, n
223  tmp = tmp + cabs1( a( i, j ) )
224  END DO
225  END IF
226  rwork( i ) = tmp
227  anorm = max( anorm, tmp )
228  END DO
229  ELSE
230  DO i = 1, n
231  tmp = 0.0d+0
232  IF ( capply ) THEN
233  DO j = 1, i
234  tmp = tmp + cabs1( a( i, j ) ) / c( j )
235  END DO
236  DO j = i+1, n
237  tmp = tmp + cabs1( a( j, i ) ) / c( j )
238  END DO
239  ELSE
240  DO j = 1, i
241  tmp = tmp + cabs1( a( i, j ) )
242  END DO
243  DO j = i+1, n
244  tmp = tmp + cabs1( a( j, i ) )
245  END DO
246  END IF
247  rwork( i ) = tmp
248  anorm = max( anorm, tmp )
249  END DO
250  END IF
251 *
252 * Quick return if possible.
253 *
254  IF( n.EQ.0 ) THEN
255  zla_hercond_c = 1.0d+0
256  RETURN
257  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
258  RETURN
259  END IF
260 *
261 * Estimate the norm of inv(op(A)).
262 *
263  ainvnm = 0.0d+0
264 *
265  kase = 0
266  10 CONTINUE
267  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
268  IF( kase.NE.0 ) THEN
269  IF( kase.EQ.2 ) THEN
270 *
271 * Multiply by R.
272 *
273  DO i = 1, n
274  work( i ) = work( i ) * rwork( i )
275  END DO
276 *
277  IF ( up ) THEN
278  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
279  $ work, n, info )
280  ELSE
281  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
282  $ work, n, info )
283  ENDIF
284 *
285 * Multiply by inv(C).
286 *
287  IF ( capply ) THEN
288  DO i = 1, n
289  work( i ) = work( i ) * c( i )
290  END DO
291  END IF
292  ELSE
293 *
294 * Multiply by inv(C**H).
295 *
296  IF ( capply ) THEN
297  DO i = 1, n
298  work( i ) = work( i ) * c( i )
299  END DO
300  END IF
301 *
302  IF ( up ) THEN
303  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
304  $ work, n, info )
305  ELSE
306  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
307  $ work, n, info )
308  END IF
309 *
310 * Multiply by R.
311 *
312  DO i = 1, n
313  work( i ) = work( i ) * rwork( i )
314  END DO
315  END IF
316  GO TO 10
317  END IF
318 *
319 * Compute the estimate of the reciprocal condition number.
320 *
321  IF( ainvnm .NE. 0.0d+0 )
322  $ zla_hercond_c = 1.0d+0 / ainvnm
323 *
324  RETURN
325 *
326 * End of ZLA_HERCOND_C
327 *
328  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function zla_hercond_c(UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefin...
subroutine zhetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS
Definition: zhetrs.f:120
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:133