 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zsycon_3()

 subroutine zsycon_3 ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, integer INFO )

ZSYCON_3

Purpose:
``` ZSYCON_3 estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
computed by ZSYTRF_RK or ZSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
This routine uses BLAS3 solver ZSYTRS_3.```
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 = P*U*D*(U**T)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] E ``` E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK.``` [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:
```  June 2017,  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 164 of file zsycon_3.f.

166 *
167 * -- LAPACK computational routine --
168 * -- LAPACK is a software package provided by Univ. of Tennessee, --
169 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
170 *
171 * .. Scalar Arguments ..
172  CHARACTER UPLO
173  INTEGER INFO, LDA, N
174  DOUBLE PRECISION ANORM, RCOND
175 * ..
176 * .. Array Arguments ..
177  INTEGER IPIV( * )
178  COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
179 * ..
180 *
181 * =====================================================================
182 *
183 * .. Parameters ..
184  DOUBLE PRECISION ONE, ZERO
185  parameter( one = 1.0d+0, zero = 0.0d+0 )
186  COMPLEX*16 CZERO
187  parameter( czero = ( 0.0d+0, 0.0d+0 ) )
188 * ..
189 * .. Local Scalars ..
190  LOGICAL UPPER
191  INTEGER I, KASE
192  DOUBLE PRECISION AINVNM
193 * ..
194 * .. Local Arrays ..
195  INTEGER ISAVE( 3 )
196 * ..
197 * .. External Functions ..
198  LOGICAL LSAME
199  EXTERNAL lsame
200 * ..
201 * .. External Subroutines ..
202  EXTERNAL zlacn2, zsytrs_3, xerbla
203 * ..
204 * .. Intrinsic Functions ..
205  INTRINSIC max
206 * ..
207 * .. Executable Statements ..
208 *
209 * Test the input parameters.
210 *
211  info = 0
212  upper = lsame( uplo, 'U' )
213  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
214  info = -1
215  ELSE IF( n.LT.0 ) THEN
216  info = -2
217  ELSE IF( lda.LT.max( 1, n ) ) THEN
218  info = -4
219  ELSE IF( anorm.LT.zero ) THEN
220  info = -7
221  END IF
222  IF( info.NE.0 ) THEN
223  CALL xerbla( 'ZSYCON_3', -info )
224  RETURN
225  END IF
226 *
227 * Quick return if possible
228 *
229  rcond = zero
230  IF( n.EQ.0 ) THEN
231  rcond = one
232  RETURN
233  ELSE IF( anorm.LE.zero ) THEN
234  RETURN
235  END IF
236 *
237 * Check that the diagonal matrix D is nonsingular.
238 *
239  IF( upper ) THEN
240 *
241 * Upper triangular storage: examine D from bottom to top
242 *
243  DO i = n, 1, -1
244  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.czero )
245  \$ RETURN
246  END DO
247  ELSE
248 *
249 * Lower triangular storage: examine D from top to bottom.
250 *
251  DO i = 1, n
252  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.czero )
253  \$ RETURN
254  END DO
255  END IF
256 *
257 * Estimate the 1-norm of the inverse.
258 *
259  kase = 0
260  30 CONTINUE
261  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
262  IF( kase.NE.0 ) THEN
263 *
264 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
265 *
266  CALL zsytrs_3( uplo, n, 1, a, lda, e, ipiv, work, n, info )
267  GO TO 30
268  END IF
269 *
270 * Compute the estimate of the reciprocal condition number.
271 *
272  IF( ainvnm.NE.zero )
273  \$ rcond = ( one / ainvnm ) / anorm
274 *
275  RETURN
276 *
277 * End of ZSYCON_3
278 *
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_3(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
ZSYTRS_3
Definition: zsytrs_3.f:165
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