LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ csycon()

 subroutine csycon ( character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info )

CSYCON

Purpose:
``` CSYCON estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by CSYTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSYTRF.``` [in] ANORM ``` ANORM is REAL The 1-norm of the original matrix A.``` [out] RCOND ``` RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.``` [out] WORK ` WORK is COMPLEX array, dimension (2*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 123 of file csycon.f.

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*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine csytrs(uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
CSYTRS
Definition csytrs.f:120
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
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