 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ssycon_rook()

 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

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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```
Contributors:
```   December 2016, 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 ssycon_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  REAL ANORM, RCOND
153 * ..
154 * .. Array Arguments ..
155  INTEGER IPIV( * ), IWORK( * )
156  REAL A( LDA, * ), WORK( * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  REAL ONE, ZERO
163  parameter( one = 1.0e+0, zero = 0.0e+0 )
164 * ..
165 * .. Local Scalars ..
166  LOGICAL UPPER
167  INTEGER I, KASE
168  REAL 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 slacn2, ssytrs_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( 'SSYCON_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 slacn2( 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 ssytrs_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 SSYCON_ROOK
254 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:136
subroutine ssytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS_ROOK
Definition: ssytrs_rook.f:136
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