LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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zla_syrcond_c.f
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1*> \brief \b ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric 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_SYRCOND_C + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_syrcond_c.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_syrcond_c.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_syrcond_c.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* DOUBLE PRECISION FUNCTION ZLA_SYRCOND_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_SYRCOND_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 ZSYTRF.
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 ZSYTRF.
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 la_hercond
135*
136* =====================================================================
137 DOUBLE PRECISION FUNCTION zla_syrcond_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
160 DOUBLE PRECISION ainvnm, anorm, tmp
161 INTEGER i, j
162 LOGICAL up, upper
163 COMPLEX*16 zdum
164* ..
165* .. Local Arrays ..
166 INTEGER isave( 3 )
167* ..
168* .. External Functions ..
169 LOGICAL lsame
170 EXTERNAL lsame
171* ..
172* .. External Subroutines ..
173 EXTERNAL zlacn2, zsytrs, xerbla
174* ..
175* .. Intrinsic Functions ..
176 INTRINSIC abs, max
177* ..
178* .. Statement Functions ..
179 DOUBLE PRECISION cabs1
180* ..
181* .. Statement Function Definitions ..
182 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
183* ..
184* .. Executable Statements ..
185*
186 zla_syrcond_c = 0.0d+0
187*
188 info = 0
189 upper = lsame( uplo, 'U' )
190 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
191 info = -1
192 ELSE IF( n.LT.0 ) THEN
193 info = -2
194 ELSE IF( lda.LT.max( 1, n ) ) THEN
195 info = -4
196 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
197 info = -6
198 END IF
199 IF( info.NE.0 ) THEN
200 CALL xerbla( 'ZLA_SYRCOND_C', -info )
201 RETURN
202 END IF
203 up = .false.
204 IF ( lsame( uplo, 'U' ) ) up = .true.
205*
206* Compute norm of op(A)*op2(C).
207*
208 anorm = 0.0d+0
209 IF ( up ) THEN
210 DO i = 1, n
211 tmp = 0.0d+0
212 IF ( capply ) THEN
213 DO j = 1, i
214 tmp = tmp + cabs1( a( j, i ) ) / c( j )
215 END DO
216 DO j = i+1, n
217 tmp = tmp + cabs1( a( i, j ) ) / c( j )
218 END DO
219 ELSE
220 DO j = 1, i
221 tmp = tmp + cabs1( a( j, i ) )
222 END DO
223 DO j = i+1, n
224 tmp = tmp + cabs1( a( i, j ) )
225 END DO
226 END IF
227 rwork( i ) = tmp
228 anorm = max( anorm, tmp )
229 END DO
230 ELSE
231 DO i = 1, n
232 tmp = 0.0d+0
233 IF ( capply ) THEN
234 DO j = 1, i
235 tmp = tmp + cabs1( a( i, j ) ) / c( j )
236 END DO
237 DO j = i+1, n
238 tmp = tmp + cabs1( a( j, i ) ) / c( j )
239 END DO
240 ELSE
241 DO j = 1, i
242 tmp = tmp + cabs1( a( i, j ) )
243 END DO
244 DO j = i+1, n
245 tmp = tmp + cabs1( a( j, i ) )
246 END DO
247 END IF
248 rwork( i ) = tmp
249 anorm = max( anorm, tmp )
250 END DO
251 END IF
252*
253* Quick return if possible.
254*
255 IF( n.EQ.0 ) THEN
256 zla_syrcond_c = 1.0d+0
257 RETURN
258 ELSE IF( anorm .EQ. 0.0d+0 ) THEN
259 RETURN
260 END IF
261*
262* Estimate the norm of inv(op(A)).
263*
264 ainvnm = 0.0d+0
265*
266 kase = 0
267 10 CONTINUE
268 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
269 IF( kase.NE.0 ) THEN
270 IF( kase.EQ.2 ) THEN
271*
272* Multiply by R.
273*
274 DO i = 1, n
275 work( i ) = work( i ) * rwork( i )
276 END DO
277*
278 IF ( up ) THEN
279 CALL zsytrs( 'U', n, 1, af, ldaf, ipiv,
280 $ work, n, info )
281 ELSE
282 CALL zsytrs( 'L', n, 1, af, ldaf, ipiv,
283 $ work, n, info )
284 ENDIF
285*
286* Multiply by inv(C).
287*
288 IF ( capply ) THEN
289 DO i = 1, n
290 work( i ) = work( i ) * c( i )
291 END DO
292 END IF
293 ELSE
294*
295* Multiply by inv(C**T).
296*
297 IF ( capply ) THEN
298 DO i = 1, n
299 work( i ) = work( i ) * c( i )
300 END DO
301 END IF
302*
303 IF ( up ) THEN
304 CALL zsytrs( 'U', n, 1, af, ldaf, ipiv,
305 $ work, n, info )
306 ELSE
307 CALL zsytrs( 'L', n, 1, af, ldaf, ipiv,
308 $ work, n, info )
309 END IF
310*
311* Multiply by R.
312*
313 DO i = 1, n
314 work( i ) = work( i ) * rwork( i )
315 END DO
316 END IF
317 GO TO 10
318 END IF
319*
320* Compute the estimate of the reciprocal condition number.
321*
322 IF( ainvnm .NE. 0.0d+0 )
323 $ zla_syrcond_c = 1.0d+0 / ainvnm
324*
325 RETURN
326*
327* End of ZLA_SYRCOND_C
328*
329 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zsytrs(uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
ZSYTRS
Definition zsytrs.f:120
double precision function zla_syrcond_c(uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)
ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefin...
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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48