LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cla_hercond_c.f
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1 *> \brief \b CLA_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 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
22 * CAPPLY, INFO, WORK, RWORK )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * LOGICAL CAPPLY
27 * INTEGER N, LDA, LDAF, INFO
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * )
31 * COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * )
32 * REAL C ( * ), RWORK( * )
33 * ..
34 *
35 *
36 *> \par Purpose:
37 * =============
38 *>
39 *> \verbatim
40 *>
41 *> CLA_HERCOND_C computes the infinity norm condition number of
42 *> op(A) * inv(diag(C)) where C is a REAL vector.
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] UPLO
49 *> \verbatim
50 *> UPLO is CHARACTER*1
51 *> = 'U': Upper triangle of A is stored;
52 *> = 'L': Lower triangle of A is stored.
53 *> \endverbatim
54 *>
55 *> \param[in] N
56 *> \verbatim
57 *> N is INTEGER
58 *> The number of linear equations, i.e., the order of the
59 *> matrix A. N >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] A
63 *> \verbatim
64 *> A is COMPLEX array, dimension (LDA,N)
65 *> On entry, the N-by-N matrix A
66 *> \endverbatim
67 *>
68 *> \param[in] LDA
69 *> \verbatim
70 *> LDA is INTEGER
71 *> The leading dimension of the array A. LDA >= max(1,N).
72 *> \endverbatim
73 *>
74 *> \param[in] AF
75 *> \verbatim
76 *> AF is COMPLEX array, dimension (LDAF,N)
77 *> The block diagonal matrix D and the multipliers used to
78 *> obtain the factor U or L as computed by CHETRF.
79 *> \endverbatim
80 *>
81 *> \param[in] LDAF
82 *> \verbatim
83 *> LDAF is INTEGER
84 *> The leading dimension of the array AF. LDAF >= max(1,N).
85 *> \endverbatim
86 *>
87 *> \param[in] IPIV
88 *> \verbatim
89 *> IPIV is INTEGER array, dimension (N)
90 *> Details of the interchanges and the block structure of D
91 *> as determined by CHETRF.
92 *> \endverbatim
93 *>
94 *> \param[in] C
95 *> \verbatim
96 *> C is REAL array, dimension (N)
97 *> The vector C in the formula op(A) * inv(diag(C)).
98 *> \endverbatim
99 *>
100 *> \param[in] CAPPLY
101 *> \verbatim
102 *> CAPPLY is LOGICAL
103 *> If .TRUE. then access the vector C in the formula above.
104 *> \endverbatim
105 *>
106 *> \param[out] INFO
107 *> \verbatim
108 *> INFO is INTEGER
109 *> = 0: Successful exit.
110 *> i > 0: The ith argument is invalid.
111 *> \endverbatim
112 *>
113 *> \param[out] WORK
114 *> \verbatim
115 *> WORK is COMPLEX array, dimension (2*N).
116 *> Workspace.
117 *> \endverbatim
118 *>
119 *> \param[out] RWORK
120 *> \verbatim
121 *> RWORK is REAL array, dimension (N).
122 *> Workspace.
123 *> \endverbatim
124 *
125 * Authors:
126 * ========
127 *
128 *> \author Univ. of Tennessee
129 *> \author Univ. of California Berkeley
130 *> \author Univ. of Colorado Denver
131 *> \author NAG Ltd.
132 *
133 *> \ingroup complexHEcomputational
134 *
135 * =====================================================================
136  REAL function cla_hercond_c( uplo, n, a, lda, af, ldaf, ipiv, c,
137  $ capply, info, work, rwork )
138 *
139 * -- LAPACK computational routine --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 *
143 * .. Scalar Arguments ..
144  CHARACTER uplo
145  LOGICAL capply
146  INTEGER n, lda, ldaf, info
147 * ..
148 * .. Array Arguments ..
149  INTEGER ipiv( * )
150  COMPLEX a( lda, * ), af( ldaf, * ), work( * )
151  REAL c ( * ), rwork( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Local Scalars ..
157  INTEGER kase, i, j
158  REAL ainvnm, anorm, tmp
159  LOGICAL up, upper
160  COMPLEX zdum
161 * ..
162 * .. Local Arrays ..
163  INTEGER isave( 3 )
164 * ..
165 * .. External Functions ..
166  LOGICAL lsame
167  EXTERNAL lsame
168 * ..
169 * .. External Subroutines ..
170  EXTERNAL clacn2, chetrs, xerbla
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC abs, max
174 * ..
175 * .. Statement Functions ..
176  REAL cabs1
177 * ..
178 * .. Statement Function Definitions ..
179  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
180 * ..
181 * .. Executable Statements ..
182 *
183  cla_hercond_c = 0.0e+0
184 *
185  info = 0
186  upper = lsame( uplo, 'U' )
187  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
188  info = -1
189  ELSE IF( n.LT.0 ) THEN
190  info = -2
191  ELSE IF( lda.LT.max( 1, n ) ) THEN
192  info = -4
193  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
194  info = -6
195  END IF
196  IF( info.NE.0 ) THEN
197  CALL xerbla( 'CLA_HERCOND_C', -info )
198  RETURN
199  END IF
200  up = .false.
201  IF ( lsame( uplo, 'U' ) ) up = .true.
202 *
203 * Compute norm of op(A)*op2(C).
204 *
205  anorm = 0.0e+0
206  IF ( up ) THEN
207  DO i = 1, n
208  tmp = 0.0e+0
209  IF ( capply ) THEN
210  DO j = 1, i
211  tmp = tmp + cabs1( a( j, i ) ) / c( j )
212  END DO
213  DO j = i+1, n
214  tmp = tmp + cabs1( a( i, j ) ) / c( j )
215  END DO
216  ELSE
217  DO j = 1, i
218  tmp = tmp + cabs1( a( j, i ) )
219  END DO
220  DO j = i+1, n
221  tmp = tmp + cabs1( a( i, j ) )
222  END DO
223  END IF
224  rwork( i ) = tmp
225  anorm = max( anorm, tmp )
226  END DO
227  ELSE
228  DO i = 1, n
229  tmp = 0.0e+0
230  IF ( capply ) THEN
231  DO j = 1, i
232  tmp = tmp + cabs1( a( i, j ) ) / c( j )
233  END DO
234  DO j = i+1, n
235  tmp = tmp + cabs1( a( j, i ) ) / c( j )
236  END DO
237  ELSE
238  DO j = 1, i
239  tmp = tmp + cabs1( a( i, j ) )
240  END DO
241  DO j = i+1, n
242  tmp = tmp + cabs1( a( j, i ) )
243  END DO
244  END IF
245  rwork( i ) = tmp
246  anorm = max( anorm, tmp )
247  END DO
248  END IF
249 *
250 * Quick return if possible.
251 *
252  IF( n.EQ.0 ) THEN
253  cla_hercond_c = 1.0e+0
254  RETURN
255  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
256  RETURN
257  END IF
258 *
259 * Estimate the norm of inv(op(A)).
260 *
261  ainvnm = 0.0e+0
262 *
263  kase = 0
264  10 CONTINUE
265  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
266  IF( kase.NE.0 ) THEN
267  IF( kase.EQ.2 ) THEN
268 *
269 * Multiply by R.
270 *
271  DO i = 1, n
272  work( i ) = work( i ) * rwork( i )
273  END DO
274 *
275  IF ( up ) THEN
276  CALL chetrs( 'U', n, 1, af, ldaf, ipiv,
277  $ work, n, info )
278  ELSE
279  CALL chetrs( 'L', n, 1, af, ldaf, ipiv,
280  $ work, n, info )
281  ENDIF
282 *
283 * Multiply by inv(C).
284 *
285  IF ( capply ) THEN
286  DO i = 1, n
287  work( i ) = work( i ) * c( i )
288  END DO
289  END IF
290  ELSE
291 *
292 * Multiply by inv(C**H).
293 *
294  IF ( capply ) THEN
295  DO i = 1, n
296  work( i ) = work( i ) * c( i )
297  END DO
298  END IF
299 *
300  IF ( up ) THEN
301  CALL chetrs( 'U', n, 1, af, ldaf, ipiv,
302  $ work, n, info )
303  ELSE
304  CALL chetrs( 'L', n, 1, af, ldaf, ipiv,
305  $ work, n, info )
306  END IF
307 *
308 * Multiply by R.
309 *
310  DO i = 1, n
311  work( i ) = work( i ) * rwork( i )
312  END DO
313  END IF
314  GO TO 10
315  END IF
316 *
317 * Compute the estimate of the reciprocal condition number.
318 *
319  IF( ainvnm .NE. 0.0e+0 )
320  $ cla_hercond_c = 1.0e+0 / ainvnm
321 *
322  RETURN
323 *
324 * End of CLA_HERCOND_C
325 *
326  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine chetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CHETRS
Definition: chetrs.f:120
real function cla_hercond_c(UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefin...
subroutine clacn2(N, V, X, EST, KASE, ISAVE)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: clacn2.f:133