 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ csycon_rook()

 subroutine csycon_rook ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, real ANORM, real RCOND, complex, dimension( * ) WORK, integer INFO )

CSYCON_ROOK

Purpose:
CSYCON_ROOK estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by CSYTRF_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 COMPLEX array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF_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 CSYTRF_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 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
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 137 of file csycon_rook.f.

139 *
140 * -- LAPACK computational routine --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 *
144 * .. Scalar Arguments ..
145  CHARACTER UPLO
146  INTEGER INFO, LDA, N
147  REAL ANORM, RCOND
148 * ..
149 * .. Array Arguments ..
150  INTEGER IPIV( * )
151  COMPLEX A( LDA, * ), WORK( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  REAL ONE, ZERO
158  parameter( one = 1.0e+0, zero = 0.0e+0 )
159  COMPLEX CZERO
160  parameter( czero = ( 0.0e+0, 0.0e+0 ) )
161 * ..
162 * .. Local Scalars ..
163  LOGICAL UPPER
164  INTEGER I, KASE
165  REAL AINVNM
166 * ..
167 * .. Local Arrays ..
168  INTEGER ISAVE( 3 )
169 * ..
170 * .. External Functions ..
171  LOGICAL LSAME
172  EXTERNAL lsame
173 * ..
174 * .. External Subroutines ..
175  EXTERNAL clacn2, csytrs_rook, xerbla
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC max
179 * ..
180 * .. Executable Statements ..
181 *
182 * Test the input parameters.
183 *
184  info = 0
185  upper = lsame( uplo, 'U' )
186  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
187  info = -1
188  ELSE IF( n.LT.0 ) THEN
189  info = -2
190  ELSE IF( lda.LT.max( 1, n ) ) THEN
191  info = -4
192  ELSE IF( anorm.LT.zero ) THEN
193  info = -6
194  END IF
195  IF( info.NE.0 ) THEN
196  CALL xerbla( 'CSYCON_ROOK', -info )
197  RETURN
198  END IF
199 *
200 * Quick return if possible
201 *
202  rcond = zero
203  IF( n.EQ.0 ) THEN
204  rcond = one
205  RETURN
206  ELSE IF( anorm.LE.zero ) THEN
207  RETURN
208  END IF
209 *
210 * Check that the diagonal matrix D is nonsingular.
211 *
212  IF( upper ) THEN
213 *
214 * Upper triangular storage: examine D from bottom to top
215 *
216  DO 10 i = n, 1, -1
217  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.czero )
218  \$ RETURN
219  10 CONTINUE
220  ELSE
221 *
222 * Lower triangular storage: examine D from top to bottom.
223 *
224  DO 20 i = 1, n
225  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.czero )
226  \$ RETURN
227  20 CONTINUE
228  END IF
229 *
230 * Estimate the 1-norm of the inverse.
231 *
232  kase = 0
233  30 CONTINUE
234  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
235  IF( kase.NE.0 ) THEN
236 *
237 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
238 *
239  CALL csytrs_rook( uplo, n, 1, a, lda, ipiv, work, n, info )
240  GO TO 30
241  END IF
242 *
243 * Compute the estimate of the reciprocal condition number.
244 *
245  IF( ainvnm.NE.zero )
246  \$ rcond = ( one / ainvnm ) / anorm
247 *
248  RETURN
249 *
250 * End of CSYCON_ROOK
251 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:133
subroutine csytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS_ROOK
Definition: csytrs_rook.f:136
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