LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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csycon.f
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1*> \brief \b CSYCON
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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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/csycon.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
22* INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER INFO, LDA, N
27* REAL ANORM, RCOND
28* ..
29* .. Array Arguments ..
30* INTEGER IPIV( * )
31* COMPLEX A( LDA, * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> CSYCON estimates the reciprocal of the condition number (in the
41*> 1-norm) of a complex symmetric matrix A using the factorization
42*> A = U*D*U**T or A = L*D*L**T computed by CSYTRF.
43*>
44*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
45*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
46*> \endverbatim
47*
48* Arguments:
49* ==========
50*
51*> \param[in] UPLO
52*> \verbatim
53*> UPLO is CHARACTER*1
54*> Specifies whether the details of the factorization are stored
55*> as an upper or lower triangular matrix.
56*> = 'U': Upper triangular, form is A = U*D*U**T;
57*> = 'L': Lower triangular, form is A = L*D*L**T.
58*> \endverbatim
59*>
60*> \param[in] N
61*> \verbatim
62*> N is INTEGER
63*> The order of the matrix A. N >= 0.
64*> \endverbatim
65*>
66*> \param[in] A
67*> \verbatim
68*> A is COMPLEX array, dimension (LDA,N)
69*> The block diagonal matrix D and the multipliers used to
70*> obtain the factor U or L as computed by CSYTRF.
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] IPIV
80*> \verbatim
81*> IPIV is INTEGER array, dimension (N)
82*> Details of the interchanges and the block structure of D
83*> as determined by CSYTRF.
84*> \endverbatim
85*>
86*> \param[in] ANORM
87*> \verbatim
88*> ANORM is REAL
89*> The 1-norm of the original matrix A.
90*> \endverbatim
91*>
92*> \param[out] RCOND
93*> \verbatim
94*> RCOND is REAL
95*> The reciprocal of the condition number of the matrix A,
96*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
97*> estimate of the 1-norm of inv(A) computed in this routine.
98*> \endverbatim
99*>
100*> \param[out] WORK
101*> \verbatim
102*> WORK is COMPLEX array, dimension (2*N)
103*> \endverbatim
104*>
105*> \param[out] INFO
106*> \verbatim
107*> INFO is INTEGER
108*> = 0: successful exit
109*> < 0: if INFO = -i, the i-th argument had an illegal value
110*> \endverbatim
111*
112* Authors:
113* ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \ingroup complexSYcomputational
121*
122* =====================================================================
123 SUBROUTINE csycon( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
124 \$ INFO )
125*
126* -- LAPACK computational routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER UPLO
132 INTEGER INFO, LDA, N
133 REAL ANORM, RCOND
134* ..
135* .. Array Arguments ..
136 INTEGER IPIV( * )
137 COMPLEX A( LDA, * ), WORK( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ONE, ZERO
144 parameter( one = 1.0e+0, zero = 0.0e+0 )
145* ..
146* .. Local Scalars ..
147 LOGICAL UPPER
148 INTEGER I, KASE
149 REAL AINVNM
150* ..
151* .. Local Arrays ..
152 INTEGER ISAVE( 3 )
153* ..
154* .. External Functions ..
155 LOGICAL LSAME
156 EXTERNAL lsame
157* ..
158* .. External Subroutines ..
159 EXTERNAL clacn2, csytrs, xerbla
160* ..
161* .. Intrinsic Functions ..
162 INTRINSIC max
163* ..
164* .. Executable Statements ..
165*
166* Test the input parameters.
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( anorm.LT.zero ) THEN
177 info = -6
178 END IF
179 IF( info.NE.0 ) THEN
180 CALL xerbla( 'CSYCON', -info )
181 RETURN
182 END IF
183*
184* Quick return if possible
185*
186 rcond = zero
187 IF( n.EQ.0 ) THEN
188 rcond = one
189 RETURN
190 ELSE IF( anorm.LE.zero ) THEN
191 RETURN
192 END IF
193*
194* Check that the diagonal matrix D is nonsingular.
195*
196 IF( upper ) THEN
197*
198* Upper triangular storage: examine D from bottom to top
199*
200 DO 10 i = n, 1, -1
201 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
202 \$ RETURN
203 10 CONTINUE
204 ELSE
205*
206* Lower triangular storage: examine D from top to bottom.
207*
208 DO 20 i = 1, n
209 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
210 \$ RETURN
211 20 CONTINUE
212 END IF
213*
214* Estimate the 1-norm of the inverse.
215*
216 kase = 0
217 30 CONTINUE
218 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
219 IF( kase.NE.0 ) THEN
220*
221* Multiply by inv(L*D*L**T) or inv(U*D*U**T).
222*
223 CALL csytrs( uplo, n, 1, a, lda, ipiv, work, n, info )
224 GO TO 30
225 END IF
226*
227* Compute the estimate of the reciprocal condition number.
228*
229 IF( ainvnm.NE.zero )
230 \$ rcond = ( one / ainvnm ) / anorm
231*
232 RETURN
233*
234* End of CSYCON
235*
236 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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
subroutine csycon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
CSYCON
Definition: csycon.f:125
subroutine csytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS
Definition: csytrs.f:120