LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches
cla_porcond_x.f
Go to the documentation of this file.
1*> \brief \b CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite 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/cla_porcond_x.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_porcond_x.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_porcond_x.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION CLA_PORCOND_X( UPLO, N, A, LDA, AF, LDAF, X, INFO,
22* WORK, RWORK )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER N, LDA, LDAF, INFO
27* ..
28* .. Array Arguments ..
29* COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
30* REAL RWORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> CLA_PORCOND_X Computes the infinity norm condition number of
40*> op(A) * diag(X) where X is a COMPLEX vector.
41*> \endverbatim
42*
43* Arguments:
44* ==========
45*
46*> \param[in] UPLO
47*> \verbatim
48*> UPLO is CHARACTER*1
49*> = 'U': Upper triangle of A is stored;
50*> = 'L': Lower triangle of A is stored.
51*> \endverbatim
52*>
53*> \param[in] N
54*> \verbatim
55*> N is INTEGER
56*> The number of linear equations, i.e., the order of the
57*> matrix A. N >= 0.
58*> \endverbatim
59*>
60*> \param[in] A
61*> \verbatim
62*> A is COMPLEX array, dimension (LDA,N)
63*> On entry, the N-by-N matrix A.
64*> \endverbatim
65*>
66*> \param[in] LDA
67*> \verbatim
68*> LDA is INTEGER
69*> The leading dimension of the array A. LDA >= max(1,N).
70*> \endverbatim
71*>
72*> \param[in] AF
73*> \verbatim
74*> AF is COMPLEX array, dimension (LDAF,N)
75*> The triangular factor U or L from the Cholesky factorization
76*> A = U**H*U or A = L*L**H, as computed by CPOTRF.
77*> \endverbatim
78*>
79*> \param[in] LDAF
80*> \verbatim
81*> LDAF is INTEGER
82*> The leading dimension of the array AF. LDAF >= max(1,N).
83*> \endverbatim
84*>
85*> \param[in] X
86*> \verbatim
87*> X is COMPLEX array, dimension (N)
88*> The vector X in the formula op(A) * diag(X).
89*> \endverbatim
90*>
91*> \param[out] INFO
92*> \verbatim
93*> INFO is INTEGER
94*> = 0: Successful exit.
95*> i > 0: The ith argument is invalid.
96*> \endverbatim
97*>
98*> \param[out] WORK
99*> \verbatim
100*> WORK is COMPLEX array, dimension (2*N).
101*> Workspace.
102*> \endverbatim
103*>
104*> \param[out] RWORK
105*> \verbatim
106*> RWORK is REAL array, dimension (N).
107*> Workspace.
108*> \endverbatim
109*
110* Authors:
111* ========
112*
113*> \author Univ. of Tennessee
114*> \author Univ. of California Berkeley
115*> \author Univ. of Colorado Denver
116*> \author NAG Ltd.
117*
118*> \ingroup la_porcond
119*
120* =====================================================================
121 REAL function cla_porcond_x( uplo, n, a, lda, af, ldaf, x, info,
122 \$ work, rwork )
123*
124* -- LAPACK computational routine --
125* -- LAPACK is a software package provided by Univ. of Tennessee, --
126* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127*
128* .. Scalar Arguments ..
129 CHARACTER uplo
130 INTEGER n, lda, ldaf, info
131* ..
132* .. Array Arguments ..
133 COMPLEX a( lda, * ), af( ldaf, * ), work( * ), x( * )
134 REAL rwork( * )
135* ..
136*
137* =====================================================================
138*
139* .. Local Scalars ..
140 INTEGER kase, i, j
141 REAL ainvnm, anorm, tmp
142 LOGICAL up, upper
143 COMPLEX zdum
144* ..
145* .. Local Arrays ..
146 INTEGER isave( 3 )
147* ..
148* .. External Functions ..
149 LOGICAL lsame
150 EXTERNAL lsame
151* ..
152* .. External Subroutines ..
153 EXTERNAL clacn2, cpotrs, xerbla
154* ..
155* .. Intrinsic Functions ..
156 INTRINSIC abs, max, real, aimag
157* ..
158* .. Statement Functions ..
159 REAL cabs1
160* ..
161* .. Statement Function Definitions ..
162 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
163* ..
164* .. Executable Statements ..
165*
166 cla_porcond_x = 0.0e+0
167*
168 info = 0
169 upper = lsame( uplo, 'U' )
170 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
171 info = -1
172 ELSE IF ( n.LT.0 ) THEN
173 info = -2
174 ELSE IF( lda.LT.max( 1, n ) ) THEN
175 info = -4
176 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
177 info = -6
178 END IF
179 IF( info.NE.0 ) THEN
180 CALL xerbla( 'CLA_PORCOND_X', -info )
181 RETURN
182 END IF
183 up = .false.
184 IF ( lsame( uplo, 'U' ) ) up = .true.
185*
186* Compute norm of op(A)*op2(C).
187*
188 anorm = 0.0
189 IF ( up ) THEN
190 DO i = 1, n
191 tmp = 0.0e+0
192 DO j = 1, i
193 tmp = tmp + cabs1( a( j, i ) * x( j ) )
194 END DO
195 DO j = i+1, n
196 tmp = tmp + cabs1( a( i, j ) * x( j ) )
197 END DO
198 rwork( i ) = tmp
199 anorm = max( anorm, tmp )
200 END DO
201 ELSE
202 DO i = 1, n
203 tmp = 0.0e+0
204 DO j = 1, i
205 tmp = tmp + cabs1( a( i, j ) * x( j ) )
206 END DO
207 DO j = i+1, n
208 tmp = tmp + cabs1( a( j, i ) * x( j ) )
209 END DO
210 rwork( i ) = tmp
211 anorm = max( anorm, tmp )
212 END DO
213 END IF
214*
215* Quick return if possible.
216*
217 IF( n.EQ.0 ) THEN
218 cla_porcond_x = 1.0e+0
219 RETURN
220 ELSE IF( anorm .EQ. 0.0e+0 ) THEN
221 RETURN
222 END IF
223*
224* Estimate the norm of inv(op(A)).
225*
226 ainvnm = 0.0e+0
227*
228 kase = 0
229 10 CONTINUE
230 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
231 IF( kase.NE.0 ) THEN
232 IF( kase.EQ.2 ) THEN
233*
234* Multiply by R.
235*
236 DO i = 1, n
237 work( i ) = work( i ) * rwork( i )
238 END DO
239*
240 IF ( up ) THEN
241 CALL cpotrs( 'U', n, 1, af, ldaf,
242 \$ work, n, info )
243 ELSE
244 CALL cpotrs( 'L', n, 1, af, ldaf,
245 \$ work, n, info )
246 ENDIF
247*
248* Multiply by inv(X).
249*
250 DO i = 1, n
251 work( i ) = work( i ) / x( i )
252 END DO
253 ELSE
254*
255* Multiply by inv(X**H).
256*
257 DO i = 1, n
258 work( i ) = work( i ) / x( i )
259 END DO
260*
261 IF ( up ) THEN
262 CALL cpotrs( 'U', n, 1, af, ldaf,
263 \$ work, n, info )
264 ELSE
265 CALL cpotrs( 'L', n, 1, af, ldaf,
266 \$ work, n, info )
267 END IF
268*
269* Multiply by R.
270*
271 DO i = 1, n
272 work( i ) = work( i ) * rwork( i )
273 END DO
274 END IF
275 GO TO 10
276 END IF
277*
278* Compute the estimate of the reciprocal condition number.
279*
280 IF( ainvnm .NE. 0.0e+0 )
281 \$ cla_porcond_x = 1.0e+0 / ainvnm
282*
283 RETURN
284*
285* End of CLA_PORCOND_X
286*
287 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
real function cla_porcond_x(uplo, n, a, lda, af, ldaf, x, info, work, rwork)
CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-def...
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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine cpotrs(uplo, n, nrhs, a, lda, b, ldb, info)
CPOTRS
Definition cpotrs.f:110