LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dsycon_3()

subroutine dsycon_3 ( character uplo,
integer n,
double precision, dimension( lda, * ) a,
integer lda,
double precision, dimension( * ) e,
integer, dimension( * ) ipiv,
double precision anorm,
double precision rcond,
double precision, dimension( * ) work,
integer, dimension( * ) iwork,
integer info )

DSYCON_3

Download DSYCON_3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!> DSYCON_3 estimates the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric matrix A using the factorization
!> computed by DSYTRF_RK or DSYTRF_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 DSYTRS_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 DOUBLE PRECISION array, dimension (LDA,N)
!>          Diagonal of the block diagonal matrix D and factors U or L
!>          as computed by DSYTRF_RK and DSYTRF_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 DOUBLE PRECISION 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 DSYTRF_RK or DSYTRF_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 DOUBLE PRECISION array, dimension (2*N)
!>
[out]IWORK
!>          IWORK is INTEGER array, dimension (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 167 of file dsycon_3.f.

169*
170* -- LAPACK computational routine --
171* -- LAPACK is a software package provided by Univ. of Tennessee, --
172* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
173*
174* .. Scalar Arguments ..
175 CHARACTER UPLO
176 INTEGER INFO, LDA, N
177 DOUBLE PRECISION ANORM, RCOND
178* ..
179* .. Array Arguments ..
180 INTEGER IPIV( * ), IWORK( * )
181 DOUBLE PRECISION A( LDA, * ), E( * ), WORK( * )
182* ..
183*
184* =====================================================================
185*
186* .. Parameters ..
187 DOUBLE PRECISION ONE, ZERO
188 parameter( one = 1.0d+0, zero = 0.0d+0 )
189* ..
190* .. Local Scalars ..
191 LOGICAL UPPER
192 INTEGER I, KASE
193 DOUBLE PRECISION AINVNM
194* ..
195* .. Local Arrays ..
196 INTEGER ISAVE( 3 )
197* ..
198* .. External Functions ..
199 LOGICAL LSAME
200 EXTERNAL lsame
201* ..
202* .. External Subroutines ..
203 EXTERNAL dlacn2, dsytrs_3, xerbla
204* ..
205* .. Intrinsic Functions ..
206 INTRINSIC max
207* ..
208* .. Executable Statements ..
209*
210* Test the input parameters.
211*
212 info = 0
213 upper = lsame( uplo, 'U' )
214 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
215 info = -1
216 ELSE IF( n.LT.0 ) THEN
217 info = -2
218 ELSE IF( lda.LT.max( 1, n ) ) THEN
219 info = -4
220 ELSE IF( anorm.LT.zero ) THEN
221 info = -7
222 END IF
223 IF( info.NE.0 ) THEN
224 CALL xerbla( 'DSYCON_3', -info )
225 RETURN
226 END IF
227*
228* Quick return if possible
229*
230 rcond = zero
231 IF( n.EQ.0 ) THEN
232 rcond = one
233 RETURN
234 ELSE IF( anorm.LE.zero ) THEN
235 RETURN
236 END IF
237*
238* Check that the diagonal matrix D is nonsingular.
239*
240 IF( upper ) THEN
241*
242* Upper triangular storage: examine D from bottom to top
243*
244 DO i = n, 1, -1
245 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
246 $ RETURN
247 END DO
248 ELSE
249*
250* Lower triangular storage: examine D from top to bottom.
251*
252 DO i = 1, n
253 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
254 $ RETURN
255 END DO
256 END IF
257*
258* Estimate the 1-norm of the inverse.
259*
260 kase = 0
261 30 CONTINUE
262 CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
263 IF( kase.NE.0 ) THEN
264*
265* Multiply by inv(L*D*L**T) or inv(U*D*U**T).
266*
267 CALL dsytrs_3( uplo, n, 1, a, lda, e, ipiv, work, n, info )
268 GO TO 30
269 END IF
270*
271* Compute the estimate of the reciprocal condition number.
272*
273 IF( ainvnm.NE.zero )
274 $ rcond = ( one / ainvnm ) / anorm
275*
276 RETURN
277*
278* End of DSYCON_3
279*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dsytrs_3
subroutine dsytrs_3(uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
DSYTRS_3
Definition dsytrs_3.f:163
dlacn2
subroutine dlacn2(n, v, x, isgn, est, kase, isave)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition dlacn2.f:134
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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