LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zla_hercond_c.f
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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
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_hercond_c.f">
11*> [TGZ]</a>
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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_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