LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zla_hercond_x.f
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1*> \brief \b ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) 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_x.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_x.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF,
22* LDAF, IPIV, X, INFO,
23* WORK, RWORK )
24*
25* .. Scalar Arguments ..
26* CHARACTER UPLO
27* INTEGER N, LDA, LDAF, INFO
28* ..
29* .. Array Arguments ..
30* INTEGER IPIV( * )
31* COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
32* DOUBLE PRECISION RWORK( * )
33* ..
34*
35*
36*> \par Purpose:
37* =============
38*>
39*> \verbatim
40*>
41*> ZLA_HERCOND_X computes the infinity norm condition number of
42*> op(A) * diag(X) where X is a COMPLEX*16 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 block diagonal matrix D and the multipliers used to
78*> obtain the factor U or L as computed by ZHETRF.
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] X
95*> \verbatim
96*> X is COMPLEX*16 array, dimension (N)
97*> The vector X in the formula op(A) * diag(X).
98*> \endverbatim
99*>
100*> \param[out] INFO
101*> \verbatim
102*> INFO is INTEGER
103*> = 0: Successful exit.
104*> i > 0: The ith argument is invalid.
105*> \endverbatim
106*>
107*> \param[out] WORK
108*> \verbatim
109*> WORK is COMPLEX*16 array, dimension (2*N).
110*> Workspace.
111*> \endverbatim
112*>
113*> \param[out] RWORK
114*> \verbatim
115*> RWORK is DOUBLE PRECISION array, dimension (N).
116*> Workspace.
117*> \endverbatim
118*
119* Authors:
120* ========
121*
122*> \author Univ. of Tennessee
123*> \author Univ. of California Berkeley
124*> \author Univ. of Colorado Denver
125*> \author NAG Ltd.
126*
127*> \ingroup complex16HEcomputational
128*
129* =====================================================================
130 DOUBLE PRECISION FUNCTION zla_hercond_x( UPLO, N, A, LDA, AF,
131 \$ LDAF, IPIV, X, INFO,
132 \$ WORK, RWORK )
133*
134* -- LAPACK computational routine --
135* -- LAPACK is a software package provided by Univ. of Tennessee, --
136* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137*
138* .. Scalar Arguments ..
139 CHARACTER uplo
140 INTEGER n, lda, ldaf, info
141* ..
142* .. Array Arguments ..
143 INTEGER ipiv( * )
144 COMPLEX*16 a( lda, * ), af( ldaf, * ), work( * ), x( * )
145 DOUBLE PRECISION rwork( * )
146* ..
147*
148* =====================================================================
149*
150* .. Local Scalars ..
151 INTEGER kase, i, j
152 DOUBLE PRECISION ainvnm, anorm, tmp
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, zhetrs, xerbla
165* ..
166* .. Intrinsic Functions ..
167 INTRINSIC abs, max
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_hercond_x = 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_HERCOND_X', -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 DO j = 1, i
204 tmp = tmp + cabs1( a( j, i ) * x( j ) )
205 END DO
206 DO j = i+1, n
207 tmp = tmp + cabs1( a( i, j ) * x( j ) )
208 END DO
209 rwork( i ) = tmp
210 anorm = max( anorm, tmp )
211 END DO
212 ELSE
213 DO i = 1, n
214 tmp = 0.0d+0
215 DO j = 1, i
216 tmp = tmp + cabs1( a( i, j ) * x( j ) )
217 END DO
218 DO j = i+1, n
219 tmp = tmp + cabs1( a( j, i ) * x( j ) )
220 END DO
221 rwork( i ) = tmp
222 anorm = max( anorm, tmp )
223 END DO
224 END IF
225*
226* Quick return if possible.
227*
228 IF( n.EQ.0 ) THEN
229 zla_hercond_x = 1.0d+0
230 RETURN
231 ELSE IF( anorm .EQ. 0.0d+0 ) THEN
232 RETURN
233 END IF
234*
235* Estimate the norm of inv(op(A)).
236*
237 ainvnm = 0.0d+0
238*
239 kase = 0
240 10 CONTINUE
241 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
242 IF( kase.NE.0 ) THEN
243 IF( kase.EQ.2 ) THEN
244*
245* Multiply by R.
246*
247 DO i = 1, n
248 work( i ) = work( i ) * rwork( i )
249 END DO
250*
251 IF ( up ) THEN
252 CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
253 \$ work, n, info )
254 ELSE
255 CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
256 \$ work, n, info )
257 ENDIF
258*
259* Multiply by inv(X).
260*
261 DO i = 1, n
262 work( i ) = work( i ) / x( i )
263 END DO
264 ELSE
265*
266* Multiply by inv(X**H).
267*
268 DO i = 1, n
269 work( i ) = work( i ) / x( i )
270 END DO
271*
272 IF ( up ) THEN
273 CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
274 \$ work, n, info )
275 ELSE
276 CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
277 \$ work, n, info )
278 END IF
279*
280* Multiply by R.
281*
282 DO i = 1, n
283 work( i ) = work( i ) * rwork( i )
284 END DO
285 END IF
286 GO TO 10
287 END IF
288*
289* Compute the estimate of the reciprocal condition number.
290*
291 IF( ainvnm .NE. 0.0d+0 )
292 \$ zla_hercond_x = 1.0d+0 / ainvnm
293*
294 RETURN
295*
296* End of ZLA_HERCOND_X
297*
298 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_x(UPLO, N, A, LDA, AF, LDAF, IPIV, X, INFO, WORK, RWORK)
ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite m...
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