LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zsycon_rook()

 subroutine zsycon_rook ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, integer INFO )

ZSYCON_ROOK

Purpose:
``` ZSYCON_ROOK 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 ZSYTRF_ROOK.

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*16 array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF_ROOK.``` [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 ZSYTRF_ROOK.``` [in] ANORM ``` ANORM is DOUBLE PRECISION The 1-norm of the original matrix A.``` [out] RCOND ``` RCOND is DOUBLE PRECISION 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*16 array, dimension (2*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Contributors:
```   December 2016, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester```

Definition at line 137 of file zsycon_rook.f.

139*
140* -- LAPACK computational routine --
141* -- LAPACK is a software package provided by Univ. of Tennessee, --
142* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143*
144* .. Scalar Arguments ..
145 CHARACTER UPLO
146 INTEGER INFO, LDA, N
147 DOUBLE PRECISION ANORM, RCOND
148* ..
149* .. Array Arguments ..
150 INTEGER IPIV( * )
151 COMPLEX*16 A( LDA, * ), WORK( * )
152* ..
153*
154* =====================================================================
155*
156* .. Parameters ..
157 DOUBLE PRECISION ONE, ZERO
158 parameter( one = 1.0d+0, zero = 0.0d+0 )
159 COMPLEX*16 CZERO
160 parameter( czero = ( 0.0d+0, 0.0d+0 ) )
161* ..
162* .. Local Scalars ..
163 LOGICAL UPPER
164 INTEGER I, KASE
165 DOUBLE PRECISION AINVNM
166* ..
167* .. Local Arrays ..
168 INTEGER ISAVE( 3 )
169* ..
170* .. External Functions ..
171 LOGICAL LSAME
172 EXTERNAL lsame
173* ..
174* .. External Subroutines ..
175 EXTERNAL zlacn2, zsytrs_rook, xerbla
176* ..
177* .. Intrinsic Functions ..
178 INTRINSIC max
179* ..
180* .. Executable Statements ..
181*
182* Test the input parameters.
183*
184 info = 0
185 upper = lsame( uplo, 'U' )
186 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
187 info = -1
188 ELSE IF( n.LT.0 ) THEN
189 info = -2
190 ELSE IF( lda.LT.max( 1, n ) ) THEN
191 info = -4
192 ELSE IF( anorm.LT.zero ) THEN
193 info = -6
194 END IF
195 IF( info.NE.0 ) THEN
196 CALL xerbla( 'ZSYCON_ROOK', -info )
197 RETURN
198 END IF
199*
200* Quick return if possible
201*
202 rcond = zero
203 IF( n.EQ.0 ) THEN
204 rcond = one
205 RETURN
206 ELSE IF( anorm.LE.zero ) THEN
207 RETURN
208 END IF
209*
210* Check that the diagonal matrix D is nonsingular.
211*
212 IF( upper ) THEN
213*
214* Upper triangular storage: examine D from bottom to top
215*
216 DO 10 i = n, 1, -1
217 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.czero )
218 \$ RETURN
219 10 CONTINUE
220 ELSE
221*
222* Lower triangular storage: examine D from top to bottom.
223*
224 DO 20 i = 1, n
225 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.czero )
226 \$ RETURN
227 20 CONTINUE
228 END IF
229*
230* Estimate the 1-norm of the inverse.
231*
232 kase = 0
233 30 CONTINUE
234 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
235 IF( kase.NE.0 ) THEN
236*
237* Multiply by inv(L*D*L**T) or inv(U*D*U**T).
238*
239 CALL zsytrs_rook( uplo, n, 1, a, lda, ipiv, work, n, info )
240 GO TO 30
241 END IF
242*
243* Compute the estimate of the reciprocal condition number.
244*
245 IF( ainvnm.NE.zero )
246 \$ rcond = ( one / ainvnm ) / anorm
247*
248 RETURN
249*
250* End of ZSYCON_ROOK
251*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:133
subroutine zsytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZSYTRS_ROOK
Definition: zsytrs_rook.f:136
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