 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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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