LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 real function cla_syrcond_c ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * ) IPIV, real, dimension( * ) C, logical CAPPLY, integer INFO, complex, dimension( * ) WORK, real, dimension( * ) RWORK )

CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.

Purpose:
```    CLA_SYRCOND_C Computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a REAL vector.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) On entry, the N-by-N matrix A``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] AF ``` AF is COMPLEX array, dimension (LDAF,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF.``` [in] LDAF ``` LDAF is INTEGER The leading dimension of the array AF. LDAF >= 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.``` [in] C ``` C is REAL array, dimension (N) The vector C in the formula op(A) * inv(diag(C)).``` [in] CAPPLY ``` CAPPLY is LOGICAL If .TRUE. then access the vector C in the formula above.``` [out] INFO ``` INFO is INTEGER = 0: Successful exit. i > 0: The ith argument is invalid.``` [in] WORK ``` WORK is COMPLEX array, dimension (2*N). Workspace.``` [in] RWORK ``` RWORK is REAL array, dimension (N). Workspace.```
Date
September 2012

Definition at line 140 of file cla_syrcond_c.f.

140 *
141 * -- LAPACK computational routine (version 3.4.2) --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 * September 2012
145 *
146 * .. Scalar Arguments ..
147  CHARACTER uplo
148  LOGICAL capply
149  INTEGER n, lda, ldaf, info
150 * ..
151 * .. Array Arguments ..
152  INTEGER ipiv( * )
153  COMPLEX a( lda, * ), af( ldaf, * ), work( * )
154  REAL c( * ), rwork( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Local Scalars ..
160  INTEGER kase
161  REAL ainvnm, anorm, tmp
162  INTEGER i, j
163  LOGICAL up, upper
164  COMPLEX zdum
165 * ..
166 * .. Local Arrays ..
167  INTEGER isave( 3 )
168 * ..
169 * .. External Functions ..
170  LOGICAL lsame
171  EXTERNAL lsame
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL clacn2, csytrs, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, max
178 * ..
179 * .. Statement Functions ..
180  REAL cabs1
181 * ..
182 * .. Statement Function Definitions ..
183  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
184 * ..
185 * .. Executable Statements ..
186 *
187  cla_syrcond_c = 0.0e+0
188 *
189  info = 0
190  upper = lsame( uplo, 'U' )
191  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
192  info = -1
193  ELSE IF( n.LT.0 ) THEN
194  info = -2
195  ELSE IF( lda.LT.max( 1, n ) ) THEN
196  info = -4
197  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
198  info = -6
199  END IF
200  IF( info.NE.0 ) THEN
201  CALL xerbla( 'CLA_SYRCOND_C', -info )
202  RETURN
203  END IF
204  up = .false.
205  IF ( lsame( uplo, 'U' ) ) up = .true.
206 *
207 * Compute norm of op(A)*op2(C).
208 *
209  anorm = 0.0e+0
210  IF ( up ) THEN
211  DO i = 1, n
212  tmp = 0.0e+0
213  IF ( capply ) THEN
214  DO j = 1, i
215  tmp = tmp + cabs1( a( j, i ) ) / c( j )
216  END DO
217  DO j = i+1, n
218  tmp = tmp + cabs1( a( i, j ) ) / c( j )
219  END DO
220  ELSE
221  DO j = 1, i
222  tmp = tmp + cabs1( a( j, i ) )
223  END DO
224  DO j = i+1, n
225  tmp = tmp + cabs1( a( i, j ) )
226  END DO
227  END IF
228  rwork( i ) = tmp
229  anorm = max( anorm, tmp )
230  END DO
231  ELSE
232  DO i = 1, n
233  tmp = 0.0e+0
234  IF ( capply ) THEN
235  DO j = 1, i
236  tmp = tmp + cabs1( a( i, j ) ) / c( j )
237  END DO
238  DO j = i+1, n
239  tmp = tmp + cabs1( a( j, i ) ) / c( j )
240  END DO
241  ELSE
242  DO j = 1, i
243  tmp = tmp + cabs1( a( i, j ) )
244  END DO
245  DO j = i+1, n
246  tmp = tmp + cabs1( a( j, i ) )
247  END DO
248  END IF
249  rwork( i ) = tmp
250  anorm = max( anorm, tmp )
251  END DO
252  END IF
253 *
254 * Quick return if possible.
255 *
256  IF( n.EQ.0 ) THEN
257  cla_syrcond_c = 1.0e+0
258  RETURN
259  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
260  RETURN
261  END IF
262 *
263 * Estimate the norm of inv(op(A)).
264 *
265  ainvnm = 0.0e+0
266 *
267  kase = 0
268  10 CONTINUE
269  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
270  IF( kase.NE.0 ) THEN
271  IF( kase.EQ.2 ) THEN
272 *
273 * Multiply by R.
274 *
275  DO i = 1, n
276  work( i ) = work( i ) * rwork( i )
277  END DO
278 *
279  IF ( up ) THEN
280  CALL csytrs( 'U', n, 1, af, ldaf, ipiv,
281  \$ work, n, info )
282  ELSE
283  CALL csytrs( 'L', n, 1, af, ldaf, ipiv,
284  \$ work, n, info )
285  ENDIF
286 *
287 * Multiply by inv(C).
288 *
289  IF ( capply ) THEN
290  DO i = 1, n
291  work( i ) = work( i ) * c( i )
292  END DO
293  END IF
294  ELSE
295 *
296 * Multiply by inv(C**T).
297 *
298  IF ( capply ) THEN
299  DO i = 1, n
300  work( i ) = work( i ) * c( i )
301  END DO
302  END IF
303 *
304  IF ( up ) THEN
305  CALL csytrs( 'U', n, 1, af, ldaf, ipiv,
306  \$ work, n, info )
307  ELSE
308  CALL csytrs( 'L', n, 1, af, ldaf, ipiv,
309  \$ work, n, info )
310  END IF
311 *
312 * Multiply by R.
313 *
314  DO i = 1, n
315  work( i ) = work( i ) * rwork( i )
316  END DO
317  END IF
318  GO TO 10
319  END IF
320 *
321 * Compute the estimate of the reciprocal condition number.
322 *
323  IF( ainvnm .NE. 0.0e+0 )
324  \$ cla_syrcond_c = 1.0e+0 / ainvnm
325 *
326  RETURN
327 *
subroutine csytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS
Definition: csytrs.f:122
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
real function cla_syrcond_c(UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefin...
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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:135

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