LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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sla_syrcond.f
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1*> \brief \b SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_syrcond.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE,
22* C, INFO, WORK, IWORK )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER N, LDA, LDAF, INFO, CMODE
27* ..
28* .. Array Arguments
29* INTEGER IWORK( * ), IPIV( * )
30* REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> SLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
40*> where op2 is determined by CMODE as follows
41*> CMODE = 1 op2(C) = C
42*> CMODE = 0 op2(C) = I
43*> CMODE = -1 op2(C) = inv(C)
44*> The Skeel condition number cond(A) = norminf( |inv(A)||A| )
45*> is computed by computing scaling factors R such that
46*> diag(R)*A*op2(C) is row equilibrated and computing the standard
47*> infinity-norm condition number.
48*> \endverbatim
49*
50* Arguments:
51* ==========
52*
53*> \param[in] UPLO
54*> \verbatim
55*> UPLO is CHARACTER*1
56*> = 'U': Upper triangle of A is stored;
57*> = 'L': Lower triangle of A is stored.
58*> \endverbatim
59*>
60*> \param[in] N
61*> \verbatim
62*> N is INTEGER
63*> The number of linear equations, i.e., the order of the
64*> matrix A. N >= 0.
65*> \endverbatim
66*>
67*> \param[in] A
68*> \verbatim
69*> A is REAL array, dimension (LDA,N)
70*> On entry, the N-by-N matrix A.
71*> \endverbatim
72*>
73*> \param[in] LDA
74*> \verbatim
75*> LDA is INTEGER
76*> The leading dimension of the array A. LDA >= max(1,N).
77*> \endverbatim
78*>
79*> \param[in] AF
80*> \verbatim
81*> AF is REAL array, dimension (LDAF,N)
82*> The block diagonal matrix D and the multipliers used to
83*> obtain the factor U or L as computed by SSYTRF.
84*> \endverbatim
85*>
86*> \param[in] LDAF
87*> \verbatim
88*> LDAF is INTEGER
89*> The leading dimension of the array AF. LDAF >= max(1,N).
90*> \endverbatim
91*>
92*> \param[in] IPIV
93*> \verbatim
94*> IPIV is INTEGER array, dimension (N)
95*> Details of the interchanges and the block structure of D
96*> as determined by SSYTRF.
97*> \endverbatim
98*>
99*> \param[in] CMODE
100*> \verbatim
101*> CMODE is INTEGER
102*> Determines op2(C) in the formula op(A) * op2(C) as follows:
103*> CMODE = 1 op2(C) = C
104*> CMODE = 0 op2(C) = I
105*> CMODE = -1 op2(C) = inv(C)
106*> \endverbatim
107*>
108*> \param[in] C
109*> \verbatim
110*> C is REAL array, dimension (N)
111*> The vector C in the formula op(A) * op2(C).
112*> \endverbatim
113*>
114*> \param[out] INFO
115*> \verbatim
116*> INFO is INTEGER
117*> = 0: Successful exit.
118*> i > 0: The ith argument is invalid.
119*> \endverbatim
120*>
121*> \param[out] WORK
122*> \verbatim
123*> WORK is REAL array, dimension (3*N).
124*> Workspace.
125*> \endverbatim
126*>
127*> \param[out] IWORK
128*> \verbatim
129*> IWORK is INTEGER array, dimension (N).
130*> Workspace.
131*> \endverbatim
132*
133* Authors:
134* ========
135*
136*> \author Univ. of Tennessee
137*> \author Univ. of California Berkeley
138*> \author Univ. of Colorado Denver
139*> \author NAG Ltd.
140*
141*> \ingroup la_hercond
142*
143* =====================================================================
144 REAL function sla_syrcond( uplo, n, a, lda, af, ldaf, ipiv, cmode,
145 \$ c, info, work, iwork )
146*
147* -- LAPACK computational routine --
148* -- LAPACK is a software package provided by Univ. of Tennessee, --
149* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150*
151* .. Scalar Arguments ..
152 CHARACTER uplo
153 INTEGER n, lda, ldaf, info, cmode
154* ..
155* .. Array Arguments
156 INTEGER iwork( * ), ipiv( * )
157 REAL a( lda, * ), af( ldaf, * ), work( * ), c( * )
158* ..
159*
160* =====================================================================
161*
162* .. Local Scalars ..
163 CHARACTER normin
164 INTEGER kase, i, j
165 REAL ainvnm, smlnum, tmp
166 LOGICAL up
167* ..
168* .. Local Arrays ..
169 INTEGER isave( 3 )
170* ..
171* .. External Functions ..
172 LOGICAL lsame
173 REAL slamch
174 EXTERNAL lsame, slamch
175* ..
176* .. External Subroutines ..
177 EXTERNAL slacn2, xerbla, ssytrs
178* ..
179* .. Intrinsic Functions ..
180 INTRINSIC abs, max
181* ..
182* .. Executable Statements ..
183*
184 sla_syrcond = 0.0
185*
186 info = 0
187 IF( n.LT.0 ) THEN
188 info = -2
189 ELSE IF( lda.LT.max( 1, n ) ) THEN
190 info = -4
191 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
192 info = -6
193 END IF
194 IF( info.NE.0 ) THEN
195 CALL xerbla( 'SLA_SYRCOND', -info )
196 RETURN
197 END IF
198 IF( n.EQ.0 ) THEN
199 sla_syrcond = 1.0
200 RETURN
201 END IF
202 up = .false.
203 IF ( lsame( uplo, 'U' ) ) up = .true.
204*
205* Compute the equilibration matrix R such that
206* inv(R)*A*C has unit 1-norm.
207*
208 IF ( up ) THEN
209 DO i = 1, n
210 tmp = 0.0
211 IF ( cmode .EQ. 1 ) THEN
212 DO j = 1, i
213 tmp = tmp + abs( a( j, i ) * c( j ) )
214 END DO
215 DO j = i+1, n
216 tmp = tmp + abs( a( i, j ) * c( j ) )
217 END DO
218 ELSE IF ( cmode .EQ. 0 ) THEN
219 DO j = 1, i
220 tmp = tmp + abs( a( j, i ) )
221 END DO
222 DO j = i+1, n
223 tmp = tmp + abs( a( i, j ) )
224 END DO
225 ELSE
226 DO j = 1, i
227 tmp = tmp + abs( a( j, i ) / c( j ) )
228 END DO
229 DO j = i+1, n
230 tmp = tmp + abs( a( i, j ) / c( j ) )
231 END DO
232 END IF
233 work( 2*n+i ) = tmp
234 END DO
235 ELSE
236 DO i = 1, n
237 tmp = 0.0
238 IF ( cmode .EQ. 1 ) THEN
239 DO j = 1, i
240 tmp = tmp + abs( a( i, j ) * c( j ) )
241 END DO
242 DO j = i+1, n
243 tmp = tmp + abs( a( j, i ) * c( j ) )
244 END DO
245 ELSE IF ( cmode .EQ. 0 ) THEN
246 DO j = 1, i
247 tmp = tmp + abs( a( i, j ) )
248 END DO
249 DO j = i+1, n
250 tmp = tmp + abs( a( j, i ) )
251 END DO
252 ELSE
253 DO j = 1, i
254 tmp = tmp + abs( a( i, j) / c( j ) )
255 END DO
256 DO j = i+1, n
257 tmp = tmp + abs( a( j, i) / c( j ) )
258 END DO
259 END IF
260 work( 2*n+i ) = tmp
261 END DO
262 ENDIF
263*
264* Estimate the norm of inv(op(A)).
265*
266 smlnum = slamch( 'Safe minimum' )
267 ainvnm = 0.0
268 normin = 'N'
269
270 kase = 0
271 10 CONTINUE
272 CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
273 IF( kase.NE.0 ) THEN
274 IF( kase.EQ.2 ) THEN
275*
276* Multiply by R.
277*
278 DO i = 1, n
279 work( i ) = work( i ) * work( 2*n+i )
280 END DO
281
282 IF ( up ) THEN
283 CALL ssytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info )
284 ELSE
285 CALL ssytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info )
286 ENDIF
287*
288* Multiply by inv(C).
289*
290 IF ( cmode .EQ. 1 ) THEN
291 DO i = 1, n
292 work( i ) = work( i ) / c( i )
293 END DO
294 ELSE IF ( cmode .EQ. -1 ) THEN
295 DO i = 1, n
296 work( i ) = work( i ) * c( i )
297 END DO
298 END IF
299 ELSE
300*
301* Multiply by inv(C**T).
302*
303 IF ( cmode .EQ. 1 ) THEN
304 DO i = 1, n
305 work( i ) = work( i ) / c( i )
306 END DO
307 ELSE IF ( cmode .EQ. -1 ) THEN
308 DO i = 1, n
309 work( i ) = work( i ) * c( i )
310 END DO
311 END IF
312
313 IF ( up ) THEN
314 CALL ssytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info )
315 ELSE
316 CALL ssytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info )
317 ENDIF
318*
319* Multiply by R.
320*
321 DO i = 1, n
322 work( i ) = work( i ) * work( 2*n+i )
323 END DO
324 END IF
325*
326 GO TO 10
327 END IF
328*
329* Compute the estimate of the reciprocal condition number.
330*
331 IF( ainvnm .NE. 0.0 )
332 \$ sla_syrcond = ( 1.0 / ainvnm )
333*
334 RETURN
335*
336* End of SLA_SYRCOND
337*
338 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ssytrs(uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
SSYTRS
Definition ssytrs.f:120
real function sla_syrcond(uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.
subroutine slacn2(n, v, x, isgn, est, kase, isave)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition slacn2.f:136
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48