LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ checon_3()

 subroutine checon_3 ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) E, integer, dimension( * ) IPIV, real ANORM, real RCOND, complex, dimension( * ) WORK, integer INFO )

CHECON_3

Purpose:
``` CHECON_3 estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian matrix A using the factorization
computed by CHETRF_RK or CHETRF_BK:

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

where U (or L) is unit upper (or lower) triangular matrix,
U**H (or L**H) is the conjugate of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is Hermitian 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 CHETRS_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**H)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T).``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_BK: a) ONLY diagonal elements of the Hermitian 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 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian 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 CHETRF_RK or CHETRF_BK.``` [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```
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 checon_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 REAL ANORM, RCOND
175* ..
176* .. Array Arguments ..
177 INTEGER IPIV( * )
178 COMPLEX A( LDA, * ), E( * ), WORK( * )
179* ..
180*
181* =====================================================================
182*
183* .. Parameters ..
184 REAL ONE, ZERO
185 parameter( one = 1.0e+0, zero = 0.0e+0 )
186* ..
187* .. Local Scalars ..
188 LOGICAL UPPER
189 INTEGER I, KASE
190 REAL AINVNM
191* ..
192* .. Local Arrays ..
193 INTEGER ISAVE( 3 )
194* ..
195* .. External Functions ..
196 LOGICAL LSAME
197 EXTERNAL lsame
198* ..
199* .. External Subroutines ..
200 EXTERNAL chetrs_3, clacn2, xerbla
201* ..
202* .. Intrinsic Functions ..
203 INTRINSIC max
204* ..
205* .. Executable Statements ..
206*
207* Test the input parameters.
208*
209 info = 0
210 upper = lsame( uplo, 'U' )
211 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
212 info = -1
213 ELSE IF( n.LT.0 ) THEN
214 info = -2
215 ELSE IF( lda.LT.max( 1, n ) ) THEN
216 info = -4
217 ELSE IF( anorm.LT.zero ) THEN
218 info = -7
219 END IF
220 IF( info.NE.0 ) THEN
221 CALL xerbla( 'CHECON_3', -info )
222 RETURN
223 END IF
224*
225* Quick return if possible
226*
227 rcond = zero
228 IF( n.EQ.0 ) THEN
229 rcond = one
230 RETURN
231 ELSE IF( anorm.LE.zero ) THEN
232 RETURN
233 END IF
234*
235* Check that the diagonal matrix D is nonsingular.
236*
237 IF( upper ) THEN
238*
239* Upper triangular storage: examine D from bottom to top
240*
241 DO i = n, 1, -1
242 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
243 \$ RETURN
244 END DO
245 ELSE
246*
247* Lower triangular storage: examine D from top to bottom.
248*
249 DO i = 1, n
250 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
251 \$ RETURN
252 END DO
253 END IF
254*
255* Estimate the 1-norm of the inverse.
256*
257 kase = 0
258 30 CONTINUE
259 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
260 IF( kase.NE.0 ) THEN
261*
262* Multiply by inv(L*D*L**H) or inv(U*D*U**H).
263*
264 CALL chetrs_3( uplo, n, 1, a, lda, e, ipiv, work, n, info )
265 GO TO 30
266 END IF
267*
268* Compute the estimate of the reciprocal condition number.
269*
270 IF( ainvnm.NE.zero )
271 \$ rcond = ( one / ainvnm ) / anorm
272*
273 RETURN
274*
275* End of CHECON_3
276*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine chetrs_3(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
CHETRS_3
Definition: chetrs_3.f:165
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
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