LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zla_porcond_c.f
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1 *> \brief \b ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_porcond_c.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLA_PORCOND_C( UPLO, N, A, LDA, AF,
22 * LDAF, C, CAPPLY, INFO,
23 * WORK, RWORK )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER UPLO
27 * LOGICAL CAPPLY
28 * INTEGER N, LDA, LDAF, INFO
29 * ..
30 * .. Array Arguments ..
31 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
32 * DOUBLE PRECISION C( * ), RWORK( * )
33 * ..
34 *
35 *
36 *> \par Purpose:
37 * =============
38 *>
39 *> \verbatim
40 *>
41 *> ZLA_PORCOND_C Computes the infinity norm condition number of
42 *> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION 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*16 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*16 array, dimension (LDAF,N)
77 *> The triangular factor U or L from the Cholesky factorization
78 *> A = U**H*U or A = L*L**H, as computed by ZPOTRF.
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] C
88 *> \verbatim
89 *> C is DOUBLE PRECISION array, dimension (N)
90 *> The vector C in the formula op(A) * inv(diag(C)).
91 *> \endverbatim
92 *>
93 *> \param[in] CAPPLY
94 *> \verbatim
95 *> CAPPLY is LOGICAL
96 *> If .TRUE. then access the vector C in the formula above.
97 *> \endverbatim
98 *>
99 *> \param[out] INFO
100 *> \verbatim
101 *> INFO is INTEGER
102 *> = 0: Successful exit.
103 *> i > 0: The ith argument is invalid.
104 *> \endverbatim
105 *>
106 *> \param[out] WORK
107 *> \verbatim
108 *> WORK is COMPLEX*16 array, dimension (2*N).
109 *> Workspace.
110 *> \endverbatim
111 *>
112 *> \param[out] RWORK
113 *> \verbatim
114 *> RWORK is DOUBLE PRECISION array, dimension (N).
115 *> Workspace.
116 *> \endverbatim
117 *
118 * Authors:
119 * ========
120 *
121 *> \author Univ. of Tennessee
122 *> \author Univ. of California Berkeley
123 *> \author Univ. of Colorado Denver
124 *> \author NAG Ltd.
125 *
126 *> \ingroup complex16POcomputational
127 *
128 * =====================================================================
129  DOUBLE PRECISION FUNCTION zla_porcond_c( UPLO, N, A, LDA, AF,
130  $ LDAF, C, CAPPLY, INFO,
131  $ WORK, RWORK )
132 *
133 * -- LAPACK computational routine --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 *
137 * .. Scalar Arguments ..
138  CHARACTER uplo
139  LOGICAL capply
140  INTEGER n, lda, ldaf, info
141 * ..
142 * .. Array Arguments ..
143  COMPLEX*16 a( lda, * ), af( ldaf, * ), work( * )
144  DOUBLE PRECISION c( * ), rwork( * )
145 * ..
146 *
147 * =====================================================================
148 *
149 * .. Local Scalars ..
150  INTEGER kase
151  DOUBLE PRECISION ainvnm, anorm, tmp
152  INTEGER i, j
153  LOGICAL up, upper
154  COMPLEX*16 zdum
155 * ..
156 * .. Local Arrays ..
157  INTEGER isave( 3 )
158 * ..
159 * .. External Functions ..
160  LOGICAL lsame
161  EXTERNAL lsame
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL zlacn2, zpotrs, xerbla
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC abs, max, real, dimag
168 * ..
169 * .. Statement Functions ..
170  DOUBLE PRECISION cabs1
171 * ..
172 * .. Statement Function Definitions ..
173  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
174 * ..
175 * .. Executable Statements ..
176 *
177  zla_porcond_c = 0.0d+0
178 *
179  info = 0
180  upper = lsame( uplo, 'U' )
181  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
182  info = -1
183  ELSE IF( n.LT.0 ) THEN
184  info = -2
185  ELSE IF( lda.LT.max( 1, n ) ) THEN
186  info = -4
187  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
188  info = -6
189  END IF
190  IF( info.NE.0 ) THEN
191  CALL xerbla( 'ZLA_PORCOND_C', -info )
192  RETURN
193  END IF
194  up = .false.
195  IF ( lsame( uplo, 'U' ) ) up = .true.
196 *
197 * Compute norm of op(A)*op2(C).
198 *
199  anorm = 0.0d+0
200  IF ( up ) THEN
201  DO i = 1, n
202  tmp = 0.0d+0
203  IF ( capply ) THEN
204  DO j = 1, i
205  tmp = tmp + cabs1( a( j, i ) ) / c( j )
206  END DO
207  DO j = i+1, n
208  tmp = tmp + cabs1( a( i, j ) ) / c( j )
209  END DO
210  ELSE
211  DO j = 1, i
212  tmp = tmp + cabs1( a( j, i ) )
213  END DO
214  DO j = i+1, n
215  tmp = tmp + cabs1( a( i, j ) )
216  END DO
217  END IF
218  rwork( i ) = tmp
219  anorm = max( anorm, tmp )
220  END DO
221  ELSE
222  DO i = 1, n
223  tmp = 0.0d+0
224  IF ( capply ) THEN
225  DO j = 1, i
226  tmp = tmp + cabs1( a( i, j ) ) / c( j )
227  END DO
228  DO j = i+1, n
229  tmp = tmp + cabs1( a( j, i ) ) / c( j )
230  END DO
231  ELSE
232  DO j = 1, i
233  tmp = tmp + cabs1( a( i, j ) )
234  END DO
235  DO j = i+1, n
236  tmp = tmp + cabs1( a( j, i ) )
237  END DO
238  END IF
239  rwork( i ) = tmp
240  anorm = max( anorm, tmp )
241  END DO
242  END IF
243 *
244 * Quick return if possible.
245 *
246  IF( n.EQ.0 ) THEN
247  zla_porcond_c = 1.0d+0
248  RETURN
249  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
250  RETURN
251  END IF
252 *
253 * Estimate the norm of inv(op(A)).
254 *
255  ainvnm = 0.0d+0
256 *
257  kase = 0
258  10 CONTINUE
259  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
260  IF( kase.NE.0 ) THEN
261  IF( kase.EQ.2 ) THEN
262 *
263 * Multiply by R.
264 *
265  DO i = 1, n
266  work( i ) = work( i ) * rwork( i )
267  END DO
268 *
269  IF ( up ) THEN
270  CALL zpotrs( 'U', n, 1, af, ldaf,
271  $ work, n, info )
272  ELSE
273  CALL zpotrs( 'L', n, 1, af, ldaf,
274  $ work, n, info )
275  ENDIF
276 *
277 * Multiply by inv(C).
278 *
279  IF ( capply ) THEN
280  DO i = 1, n
281  work( i ) = work( i ) * c( i )
282  END DO
283  END IF
284  ELSE
285 *
286 * Multiply by inv(C**H).
287 *
288  IF ( capply ) THEN
289  DO i = 1, n
290  work( i ) = work( i ) * c( i )
291  END DO
292  END IF
293 *
294  IF ( up ) THEN
295  CALL zpotrs( 'U', n, 1, af, ldaf,
296  $ work, n, info )
297  ELSE
298  CALL zpotrs( 'L', n, 1, af, ldaf,
299  $ work, n, info )
300  END IF
301 *
302 * Multiply by R.
303 *
304  DO i = 1, n
305  work( i ) = work( i ) * rwork( i )
306  END DO
307  END IF
308  GO TO 10
309  END IF
310 *
311 * Compute the estimate of the reciprocal condition number.
312 *
313  IF( ainvnm .NE. 0.0d+0 )
314  $ zla_porcond_c = 1.0d+0 / ainvnm
315 *
316  RETURN
317 *
318 * End of ZLA_PORCOND_C
319 *
320  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
double precision function zla_porcond_c(UPLO, N, A, LDA, AF, LDAF, C, CAPPLY, INFO, WORK, RWORK)
ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positiv...
subroutine zpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
ZPOTRS
Definition: zpotrs.f:110