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

 subroutine dsycon_rook ( character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

DSYCON_ROOK

Purpose:
``` DSYCON_ROOK estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by DSYTRF_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 DOUBLE PRECISION array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF_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 DSYTRF_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 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```
Contributors:
```   April 2012, 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 142 of file dsycon_rook.f.

144*
145* -- LAPACK computational routine --
146* -- LAPACK is a software package provided by Univ. of Tennessee, --
147* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148*
149* .. Scalar Arguments ..
150 CHARACTER UPLO
151 INTEGER INFO, LDA, N
152 DOUBLE PRECISION ANORM, RCOND
153* ..
154* .. Array Arguments ..
155 INTEGER IPIV( * ), IWORK( * )
156 DOUBLE PRECISION A( LDA, * ), WORK( * )
157* ..
158*
159* =====================================================================
160*
161* .. Parameters ..
162 DOUBLE PRECISION ONE, ZERO
163 parameter( one = 1.0d+0, zero = 0.0d+0 )
164* ..
165* .. Local Scalars ..
166 LOGICAL UPPER
167 INTEGER I, KASE
168 DOUBLE PRECISION AINVNM
169* ..
170* .. Local Arrays ..
171 INTEGER ISAVE( 3 )
172* ..
173* .. External Functions ..
174 LOGICAL LSAME
175 EXTERNAL lsame
176* ..
177* .. External Subroutines ..
178 EXTERNAL dlacn2, dsytrs_rook, xerbla
179* ..
180* .. Intrinsic Functions ..
181 INTRINSIC max
182* ..
183* .. Executable Statements ..
184*
185* Test the input parameters.
186*
187 info = 0
188 upper = lsame( uplo, 'U' )
189 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
190 info = -1
191 ELSE IF( n.LT.0 ) THEN
192 info = -2
193 ELSE IF( lda.LT.max( 1, n ) ) THEN
194 info = -4
195 ELSE IF( anorm.LT.zero ) THEN
196 info = -6
197 END IF
198 IF( info.NE.0 ) THEN
199 CALL xerbla( 'DSYCON_ROOK', -info )
200 RETURN
201 END IF
202*
203* Quick return if possible
204*
205 rcond = zero
206 IF( n.EQ.0 ) THEN
207 rcond = one
208 RETURN
209 ELSE IF( anorm.LE.zero ) THEN
210 RETURN
211 END IF
212*
213* Check that the diagonal matrix D is nonsingular.
214*
215 IF( upper ) THEN
216*
217* Upper triangular storage: examine D from bottom to top
218*
219 DO 10 i = n, 1, -1
220 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
221 \$ RETURN
222 10 CONTINUE
223 ELSE
224*
225* Lower triangular storage: examine D from top to bottom.
226*
227 DO 20 i = 1, n
228 IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
229 \$ RETURN
230 20 CONTINUE
231 END IF
232*
233* Estimate the 1-norm of the inverse.
234*
235 kase = 0
236 30 CONTINUE
237 CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
238 IF( kase.NE.0 ) THEN
239*
240* Multiply by inv(L*D*L**T) or inv(U*D*U**T).
241*
242 CALL dsytrs_rook( uplo, n, 1, a, lda, ipiv, work, n, info )
243 GO TO 30
244 END IF
245*
246* Compute the estimate of the reciprocal condition number.
247*
248 IF( ainvnm.NE.zero )
249 \$ rcond = ( one / ainvnm ) / anorm
250*
251 RETURN
252*
253* End of DSYCON_ROOK
254*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:136
subroutine dsytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DSYTRS_ROOK
Definition: dsytrs_rook.f:136
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