LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches
ssycon_3.f
Go to the documentation of this file.
1*> \brief \b SSYCON_3
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/ssycon_3.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssycon_3.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssycon_3.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SSYCON_3( UPLO, N, A, LDA, E, IPIV, ANORM, RCOND,
22* WORK, IWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER INFO, LDA, N
27* REAL ANORM, RCOND
28* ..
29* .. Array Arguments ..
30* INTEGER IPIV( * ), IWORK( * )
31* REAL A( LDA, * ), E ( * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*> SSYCON_3 estimates the reciprocal of the condition number (in the
40*> 1-norm) of a real symmetric matrix A using the factorization
41*> computed by DSYTRF_RK or DSYTRF_BK:
42*>
43*> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
44*>
45*> where U (or L) is unit upper (or lower) triangular matrix,
46*> U**T (or L**T) is the transpose of U (or L), P is a permutation
47*> matrix, P**T is the transpose of P, and D is symmetric and block
48*> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
49*>
50*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
51*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
52*> This routine uses BLAS3 solver SSYTRS_3.
53*> \endverbatim
54*
55* Arguments:
56* ==========
57*
58*> \param[in] UPLO
59*> \verbatim
60*> UPLO is CHARACTER*1
61*> Specifies whether the details of the factorization are
62*> stored as an upper or lower triangular matrix:
63*> = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T);
64*> = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).
65*> \endverbatim
66*>
67*> \param[in] N
68*> \verbatim
69*> N is INTEGER
70*> The order of the matrix A. N >= 0.
71*> \endverbatim
72*>
73*> \param[in] A
74*> \verbatim
75*> A is REAL array, dimension (LDA,N)
76*> Diagonal of the block diagonal matrix D and factors U or L
77*> as computed by SSYTRF_RK and SSYTRF_BK:
78*> a) ONLY diagonal elements of the symmetric block diagonal
79*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
80*> (superdiagonal (or subdiagonal) elements of D
81*> should be provided on entry in array E), and
82*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
83*> If UPLO = 'L': factor L in the subdiagonal part of A.
84*> \endverbatim
85*>
86*> \param[in] LDA
87*> \verbatim
88*> LDA is INTEGER
89*> The leading dimension of the array A. LDA >= max(1,N).
90*> \endverbatim
91*>
92*> \param[in] E
93*> \verbatim
94*> E is REAL array, dimension (N)
95*> On entry, contains the superdiagonal (or subdiagonal)
96*> elements of the symmetric block diagonal matrix D
97*> with 1-by-1 or 2-by-2 diagonal blocks, where
98*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
99*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
100*>
101*> NOTE: For 1-by-1 diagonal block D(k), where
102*> 1 <= k <= N, the element E(k) is not referenced in both
103*> UPLO = 'U' or UPLO = 'L' cases.
104*> \endverbatim
105*>
106*> \param[in] IPIV
107*> \verbatim
108*> IPIV is INTEGER array, dimension (N)
109*> Details of the interchanges and the block structure of D
110*> as determined by SSYTRF_RK or SSYTRF_BK.
111*> \endverbatim
112*>
113*> \param[in] ANORM
114*> \verbatim
115*> ANORM is REAL
116*> The 1-norm of the original matrix A.
117*> \endverbatim
118*>
119*> \param[out] RCOND
120*> \verbatim
121*> RCOND is REAL
122*> The reciprocal of the condition number of the matrix A,
123*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
124*> estimate of the 1-norm of inv(A) computed in this routine.
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*> WORK is REAL array, dimension (2*N)
130*> \endverbatim
131*>
132*> \param[out] IWORK
133*> \verbatim
134*> IWORK is INTEGER array, dimension (N)
135*> \endverbatim
136*>
137*> \param[out] INFO
138*> \verbatim
139*> INFO is INTEGER
140*> = 0: successful exit
141*> < 0: if INFO = -i, the i-th argument had an illegal value
142*> \endverbatim
143*
144* Authors:
145* ========
146*
147*> \author Univ. of Tennessee
148*> \author Univ. of California Berkeley
149*> \author Univ. of Colorado Denver
150*> \author NAG Ltd.
151*
152*> \ingroup singleSYcomputational
153*
154*> \par Contributors:
155* ==================
156*> \verbatim
157*>
158*> June 2017, Igor Kozachenko,
159*> Computer Science Division,
160*> University of California, Berkeley
161*>
162*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
163*> School of Mathematics,
164*> University of Manchester
165*>
166*> \endverbatim
167*
168* =====================================================================
169 SUBROUTINE ssycon_3( UPLO, N, A, LDA, E, IPIV, ANORM, RCOND,
170 \$ WORK, IWORK, INFO )
171*
172* -- LAPACK computational routine --
173* -- LAPACK is a software package provided by Univ. of Tennessee, --
174* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*
176* .. Scalar Arguments ..
177 CHARACTER UPLO
178 INTEGER INFO, LDA, N
179 REAL ANORM, RCOND
180* ..
181* .. Array Arguments ..
182 INTEGER IPIV( * ), IWORK( * )
183 REAL A( LDA, * ), E( * ), WORK( * )
184* ..
185*
186* =====================================================================
187*
188* .. Parameters ..
189 REAL ONE, ZERO
190 parameter( one = 1.0e+0, zero = 0.0e+0 )
191* ..
192* .. Local Scalars ..
193 LOGICAL UPPER
194 INTEGER I, KASE
195 REAL AINVNM
196* ..
197* .. Local Arrays ..
198 INTEGER ISAVE( 3 )
199* ..
200* .. External Functions ..
201 LOGICAL LSAME
202 EXTERNAL lsame
203* ..
204* .. External Subroutines ..
205 EXTERNAL slacn2, ssytrs_3, xerbla
206* ..
207* .. Intrinsic Functions ..
208 INTRINSIC max
209* ..
210* .. Executable Statements ..
211*
212* Test the input parameters.
213*
214 info = 0
215 upper = lsame( uplo, 'U' )
216 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
217 info = -1
218 ELSE IF( n.LT.0 ) THEN
219 info = -2
220 ELSE IF( lda.LT.max( 1, n ) ) THEN
221 info = -4
222 ELSE IF( anorm.LT.zero ) THEN
223 info = -7
224 END IF
225 IF( info.NE.0 ) THEN
226 CALL xerbla( 'SSYCON_3', -info )
227 RETURN
228 END IF
229*
230* Quick return if possible
231*
232 rcond = zero
233 IF( n.EQ.0 ) THEN
234 rcond = one
235 RETURN
236 ELSE IF( anorm.LE.zero ) THEN
237 RETURN
238 END IF
239*
240* Check that the diagonal matrix D is nonsingular.
241*
242 IF( upper ) THEN
243*
244* Upper triangular storage: examine D from bottom to top
245*
246 DO i = n, 1, -1
247 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
248 \$ RETURN
249 END DO
250 ELSE
251*
252* Lower triangular storage: examine D from top to bottom.
253*
254 DO i = 1, n
255 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
256 \$ RETURN
257 END DO
258 END IF
259*
260* Estimate the 1-norm of the inverse.
261*
262 kase = 0
263 30 CONTINUE
264 CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
265 IF( kase.NE.0 ) THEN
266*
267* Multiply by inv(L*D*L**T) or inv(U*D*U**T).
268*
269 CALL ssytrs_3( uplo, n, 1, a, lda, e, ipiv, work, n, info )
270 GO TO 30
271 END IF
272*
273* Compute the estimate of the reciprocal condition number.
274*
275 IF( ainvnm.NE.zero )
276 \$ rcond = ( one / ainvnm ) / anorm
277*
278 RETURN
279*
280* End of SSYCON_3
281*
282 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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
subroutine ssycon_3(UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
SSYCON_3
Definition: ssycon_3.f:171
subroutine ssytrs_3(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
SSYTRS_3
Definition: ssytrs_3.f:165