 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 double precision function zla_hercond_c ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * ) IPIV, double precision, dimension ( * ) C, logical CAPPLY, integer INFO, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK )

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

Purpose:
```    ZLA_HERCOND_C computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a DOUBLE PRECISION 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*16 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*16 array, dimension (LDAF,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF.``` [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 CHETRF.``` [in] C ``` C is DOUBLE PRECISION 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*16 array, dimension (2*N). Workspace.``` [in] RWORK ``` RWORK is DOUBLE PRECISION array, dimension (N). Workspace.```
Date
September 2012

Definition at line 142 of file zla_hercond_c.f.

142 *
143 * -- LAPACK computational routine (version 3.4.2) --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 * September 2012
147 *
148 * .. Scalar Arguments ..
149  CHARACTER uplo
150  LOGICAL capply
151  INTEGER n, lda, ldaf, info
152 * ..
153 * .. Array Arguments ..
154  INTEGER ipiv( * )
155  COMPLEX*16 a( lda, * ), af( ldaf, * ), work( * )
156  DOUBLE PRECISION c ( * ), rwork( * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Local Scalars ..
162  INTEGER kase, i, j
163  DOUBLE PRECISION ainvnm, anorm, tmp
164  LOGICAL up, upper
165  COMPLEX*16 zdum
166 * ..
167 * .. Local Arrays ..
168  INTEGER isave( 3 )
169 * ..
170 * .. External Functions ..
171  LOGICAL lsame
172  EXTERNAL lsame
173 * ..
174 * .. External Subroutines ..
175  EXTERNAL zlacn2, zhetrs, xerbla
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC abs, max
179 * ..
180 * .. Statement Functions ..
181  DOUBLE PRECISION cabs1
182 * ..
183 * .. Statement Function Definitions ..
184  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
185 * ..
186 * .. Executable Statements ..
187 *
188  zla_hercond_c = 0.0d+0
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( ldaf.LT.max( 1, n ) ) THEN
199  info = -6
200  END IF
201  IF( info.NE.0 ) THEN
202  CALL xerbla( 'ZLA_HERCOND_C', -info )
203  RETURN
204  END IF
205  up = .false.
206  IF ( lsame( uplo, 'U' ) ) up = .true.
207 *
208 * Compute norm of op(A)*op2(C).
209 *
210  anorm = 0.0d+0
211  IF ( up ) THEN
212  DO i = 1, n
213  tmp = 0.0d+0
214  IF ( capply ) THEN
215  DO j = 1, i
216  tmp = tmp + cabs1( a( j, i ) ) / c( j )
217  END DO
218  DO j = i+1, n
219  tmp = tmp + cabs1( a( i, j ) ) / c( j )
220  END DO
221  ELSE
222  DO j = 1, i
223  tmp = tmp + cabs1( a( j, i ) )
224  END DO
225  DO j = i+1, n
226  tmp = tmp + cabs1( a( i, j ) )
227  END DO
228  END IF
229  rwork( i ) = tmp
230  anorm = max( anorm, tmp )
231  END DO
232  ELSE
233  DO i = 1, n
234  tmp = 0.0d+0
235  IF ( capply ) THEN
236  DO j = 1, i
237  tmp = tmp + cabs1( a( i, j ) ) / c( j )
238  END DO
239  DO j = i+1, n
240  tmp = tmp + cabs1( a( j, i ) ) / c( j )
241  END DO
242  ELSE
243  DO j = 1, i
244  tmp = tmp + cabs1( a( i, j ) )
245  END DO
246  DO j = i+1, n
247  tmp = tmp + cabs1( a( j, i ) )
248  END DO
249  END IF
250  rwork( i ) = tmp
251  anorm = max( anorm, tmp )
252  END DO
253  END IF
254 *
255 * Quick return if possible.
256 *
257  IF( n.EQ.0 ) THEN
258  zla_hercond_c = 1.0d+0
259  RETURN
260  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
261  RETURN
262  END IF
263 *
264 * Estimate the norm of inv(op(A)).
265 *
266  ainvnm = 0.0d+0
267 *
268  kase = 0
269  10 CONTINUE
270  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
271  IF( kase.NE.0 ) THEN
272  IF( kase.EQ.2 ) THEN
273 *
274 * Multiply by R.
275 *
276  DO i = 1, n
277  work( i ) = work( i ) * rwork( i )
278  END DO
279 *
280  IF ( up ) THEN
281  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
282  \$ work, n, info )
283  ELSE
284  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
285  \$ work, n, info )
286  ENDIF
287 *
288 * Multiply by inv(C).
289 *
290  IF ( capply ) THEN
291  DO i = 1, n
292  work( i ) = work( i ) * c( i )
293  END DO
294  END IF
295  ELSE
296 *
297 * Multiply by inv(C**H).
298 *
299  IF ( capply ) THEN
300  DO i = 1, n
301  work( i ) = work( i ) * c( i )
302  END DO
303  END IF
304 *
305  IF ( up ) THEN
306  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
307  \$ work, n, info )
308  ELSE
309  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
310  \$ work, n, info )
311  END IF
312 *
313 * Multiply by R.
314 *
315  DO i = 1, n
316  work( i ) = work( i ) * rwork( i )
317  END DO
318  END IF
319  GO TO 10
320  END IF
321 *
322 * Compute the estimate of the reciprocal condition number.
323 *
324  IF( ainvnm .NE. 0.0d+0 )
325  \$ zla_hercond_c = 1.0d+0 / ainvnm
326 *
327  RETURN
328 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:135
double precision function zla_hercond_c(UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefin...
subroutine zhetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS
Definition: zhetrs.f:122
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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