LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ csycon_3()

subroutine csycon_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 )

CSYCON_3

Download CSYCON_3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!> CSYCON_3 estimates the reciprocal of the condition number (in the
!> 1-norm) of a complex symmetric matrix A using the factorization
!> computed by CSYTRF_RK or CSYTRF_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 CSYTRS_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 array, dimension (LDA,N)
!>          Diagonal of the block diagonal matrix D and factors U or L
!>          as computed by CSYTRF_RK and CSYTRF_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 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 CSYTRF_RK or CSYTRF_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
!> 
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 162 of file csycon_3.f.

164*
165* -- LAPACK computational routine --
166* -- LAPACK is a software package provided by Univ. of Tennessee, --
167* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168*
169* .. Scalar Arguments ..
170 CHARACTER UPLO
171 INTEGER INFO, LDA, N
172 REAL ANORM, RCOND
173* ..
174* .. Array Arguments ..
175 INTEGER IPIV( * )
176 COMPLEX A( LDA, * ), E( * ), WORK( * )
177* ..
178*
179* =====================================================================
180*
181* .. Parameters ..
182 REAL ONE, ZERO
183 parameter( one = 1.0e+0, zero = 0.0e+0 )
184 COMPLEX CZERO
185 parameter( czero = ( 0.0e+0, 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 clacn2, csytrs_3, 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( 'CSYCON_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.czero )
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.czero )
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**T) or inv(U*D*U**T).
263*
264 CALL csytrs_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 CSYCON_3
276*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine csytrs_3(uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
CSYTRS_3
Definition csytrs_3.f:163
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:131
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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