 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cla_hercond_c()

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

Purpose:
```    CLA_HERCOND_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 CHETRF.``` [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 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.``` [out] WORK ``` WORK is COMPLEX array, dimension (2*N). Workspace.``` [out] RWORK ``` RWORK is REAL array, dimension (N). Workspace.```

Definition at line 136 of file cla_hercond_c.f.

138 *
139 * -- LAPACK computational routine --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 *
143 * .. Scalar Arguments ..
144  CHARACTER UPLO
145  LOGICAL CAPPLY
146  INTEGER N, LDA, LDAF, INFO
147 * ..
148 * .. Array Arguments ..
149  INTEGER IPIV( * )
150  COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * )
151  REAL C ( * ), RWORK( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Local Scalars ..
157  INTEGER KASE, I, J
158  REAL AINVNM, ANORM, TMP
159  LOGICAL UP, UPPER
160  COMPLEX ZDUM
161 * ..
162 * .. Local Arrays ..
163  INTEGER ISAVE( 3 )
164 * ..
165 * .. External Functions ..
166  LOGICAL LSAME
167  EXTERNAL lsame
168 * ..
169 * .. External Subroutines ..
170  EXTERNAL clacn2, chetrs, xerbla
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC abs, max
174 * ..
175 * .. Statement Functions ..
176  REAL CABS1
177 * ..
178 * .. Statement Function Definitions ..
179  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
180 * ..
181 * .. Executable Statements ..
182 *
183  cla_hercond_c = 0.0e+0
184 *
185  info = 0
186  upper = lsame( uplo, 'U' )
187  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
188  info = -1
189  ELSE IF( n.LT.0 ) THEN
190  info = -2
191  ELSE IF( lda.LT.max( 1, n ) ) THEN
192  info = -4
193  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
194  info = -6
195  END IF
196  IF( info.NE.0 ) THEN
197  CALL xerbla( 'CLA_HERCOND_C', -info )
198  RETURN
199  END IF
200  up = .false.
201  IF ( lsame( uplo, 'U' ) ) up = .true.
202 *
203 * Compute norm of op(A)*op2(C).
204 *
205  anorm = 0.0e+0
206  IF ( up ) THEN
207  DO i = 1, n
208  tmp = 0.0e+0
209  IF ( capply ) THEN
210  DO j = 1, i
211  tmp = tmp + cabs1( a( j, i ) ) / c( j )
212  END DO
213  DO j = i+1, n
214  tmp = tmp + cabs1( a( i, j ) ) / c( j )
215  END DO
216  ELSE
217  DO j = 1, i
218  tmp = tmp + cabs1( a( j, i ) )
219  END DO
220  DO j = i+1, n
221  tmp = tmp + cabs1( a( i, j ) )
222  END DO
223  END IF
224  rwork( i ) = tmp
225  anorm = max( anorm, tmp )
226  END DO
227  ELSE
228  DO i = 1, n
229  tmp = 0.0e+0
230  IF ( capply ) THEN
231  DO j = 1, i
232  tmp = tmp + cabs1( a( i, j ) ) / c( j )
233  END DO
234  DO j = i+1, n
235  tmp = tmp + cabs1( a( j, i ) ) / c( j )
236  END DO
237  ELSE
238  DO j = 1, i
239  tmp = tmp + cabs1( a( i, j ) )
240  END DO
241  DO j = i+1, n
242  tmp = tmp + cabs1( a( j, i ) )
243  END DO
244  END IF
245  rwork( i ) = tmp
246  anorm = max( anorm, tmp )
247  END DO
248  END IF
249 *
250 * Quick return if possible.
251 *
252  IF( n.EQ.0 ) THEN
253  cla_hercond_c = 1.0e+0
254  RETURN
255  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
256  RETURN
257  END IF
258 *
259 * Estimate the norm of inv(op(A)).
260 *
261  ainvnm = 0.0e+0
262 *
263  kase = 0
264  10 CONTINUE
265  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
266  IF( kase.NE.0 ) THEN
267  IF( kase.EQ.2 ) THEN
268 *
269 * Multiply by R.
270 *
271  DO i = 1, n
272  work( i ) = work( i ) * rwork( i )
273  END DO
274 *
275  IF ( up ) THEN
276  CALL chetrs( 'U', n, 1, af, ldaf, ipiv,
277  \$ work, n, info )
278  ELSE
279  CALL chetrs( 'L', n, 1, af, ldaf, ipiv,
280  \$ work, n, info )
281  ENDIF
282 *
283 * Multiply by inv(C).
284 *
285  IF ( capply ) THEN
286  DO i = 1, n
287  work( i ) = work( i ) * c( i )
288  END DO
289  END IF
290  ELSE
291 *
292 * Multiply by inv(C**H).
293 *
294  IF ( capply ) THEN
295  DO i = 1, n
296  work( i ) = work( i ) * c( i )
297  END DO
298  END IF
299 *
300  IF ( up ) THEN
301  CALL chetrs( 'U', n, 1, af, ldaf, ipiv,
302  \$ work, n, info )
303  ELSE
304  CALL chetrs( 'L', n, 1, af, ldaf, ipiv,
305  \$ work, n, info )
306  END IF
307 *
308 * Multiply by R.
309 *
310  DO i = 1, n
311  work( i ) = work( i ) * rwork( i )
312  END DO
313  END IF
314  GO TO 10
315  END IF
316 *
317 * Compute the estimate of the reciprocal condition number.
318 *
319  IF( ainvnm .NE. 0.0e+0 )
320  \$ cla_hercond_c = 1.0e+0 / ainvnm
321 *
322  RETURN
323 *
324 * End of CLA_HERCOND_C
325 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine chetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CHETRS
Definition: chetrs.f:120
real function cla_hercond_c(UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefin...
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
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