 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine ssycon_rook ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, real ANORM, real RCOND, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

SSYCON_ROOK

Purpose:
``` SSYCON_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 SSYTRF_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 REAL array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF_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 SSYTRF_ROOK.``` [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 REAL 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```
Date
November 2015
Contributors:

November 2015, 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 146 of file ssycon_rook.f.

146 *
147 * -- LAPACK computational routine (version 3.6.0) --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 * November 2015
151 *
152 * .. Scalar Arguments ..
153  CHARACTER uplo
154  INTEGER info, lda, n
155  REAL anorm, rcond
156 * ..
157 * .. Array Arguments ..
158  INTEGER ipiv( * ), iwork( * )
159  REAL a( lda, * ), work( * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  REAL one, zero
166  parameter ( one = 1.0e+0, zero = 0.0e+0 )
167 * ..
168 * .. Local Scalars ..
169  LOGICAL upper
170  INTEGER i, kase
171  REAL ainvnm
172 * ..
173 * .. Local Arrays ..
174  INTEGER isave( 3 )
175 * ..
176 * .. External Functions ..
177  LOGICAL lsame
178  EXTERNAL lsame
179 * ..
180 * .. External Subroutines ..
181  EXTERNAL slacn2, ssytrs_rook, xerbla
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC max
185 * ..
186 * .. Executable Statements ..
187 *
188 * Test the input parameters.
189 *
190  info = 0
191  upper = lsame( uplo, 'U' )
192  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
193  info = -1
194  ELSE IF( n.LT.0 ) THEN
195  info = -2
196  ELSE IF( lda.LT.max( 1, n ) ) THEN
197  info = -4
198  ELSE IF( anorm.LT.zero ) THEN
199  info = -6
200  END IF
201  IF( info.NE.0 ) THEN
202  CALL xerbla( 'SSYCON_ROOK', -info )
203  RETURN
204  END IF
205 *
206 * Quick return if possible
207 *
208  rcond = zero
209  IF( n.EQ.0 ) THEN
210  rcond = one
211  RETURN
212  ELSE IF( anorm.LE.zero ) THEN
213  RETURN
214  END IF
215 *
216 * Check that the diagonal matrix D is nonsingular.
217 *
218  IF( upper ) THEN
219 *
220 * Upper triangular storage: examine D from bottom to top
221 *
222  DO 10 i = n, 1, -1
223  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
224  \$ RETURN
225  10 CONTINUE
226  ELSE
227 *
228 * Lower triangular storage: examine D from top to bottom.
229 *
230  DO 20 i = 1, n
231  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
232  \$ RETURN
233  20 CONTINUE
234  END IF
235 *
236 * Estimate the 1-norm of the inverse.
237 *
238  kase = 0
239  30 CONTINUE
240  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
241  IF( kase.NE.0 ) THEN
242 *
243 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
244 *
245  CALL ssytrs_rook( uplo, n, 1, a, lda, ipiv, work, n, info )
246  GO TO 30
247  END IF
248 *
249 * Compute the estimate of the reciprocal condition number.
250 *
251  IF( ainvnm.NE.zero )
252  \$ rcond = ( one / ainvnm ) / anorm
253 *
254  RETURN
255 *
256 * End of SSYCON_ROOK
257 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ssytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS_ROOK
Definition: ssytrs_rook.f:138
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:138
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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