LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zla_hercond_c()

 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.``` [out] WORK ``` WORK is COMPLEX*16 array, dimension (2*N). Workspace.``` [out] RWORK ``` RWORK is DOUBLE PRECISION array, dimension (N). Workspace.```

Definition at line 137 of file zla_hercond_c.f.

140 *
141 * -- LAPACK computational routine --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 *
145 * .. Scalar Arguments ..
146  CHARACTER UPLO
147  LOGICAL CAPPLY
148  INTEGER N, LDA, LDAF, INFO
149 * ..
150 * .. Array Arguments ..
151  INTEGER IPIV( * )
152  COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
153  DOUBLE PRECISION C ( * ), RWORK( * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Local Scalars ..
159  INTEGER KASE, I, J
160  DOUBLE PRECISION AINVNM, ANORM, TMP
161  LOGICAL UP, UPPER
162  COMPLEX*16 ZDUM
163 * ..
164 * .. Local Arrays ..
165  INTEGER ISAVE( 3 )
166 * ..
167 * .. External Functions ..
168  LOGICAL LSAME
169  EXTERNAL lsame
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL zlacn2, zhetrs, xerbla
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC abs, max
176 * ..
177 * .. Statement Functions ..
178  DOUBLE PRECISION CABS1
179 * ..
180 * .. Statement Function Definitions ..
181  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
182 * ..
183 * .. Executable Statements ..
184 *
185  zla_hercond_c = 0.0d+0
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( ldaf.LT.max( 1, n ) ) THEN
196  info = -6
197  END IF
198  IF( info.NE.0 ) THEN
199  CALL xerbla( 'ZLA_HERCOND_C', -info )
200  RETURN
201  END IF
202  up = .false.
203  IF ( lsame( uplo, 'U' ) ) up = .true.
204 *
205 * Compute norm of op(A)*op2(C).
206 *
207  anorm = 0.0d+0
208  IF ( up ) THEN
209  DO i = 1, n
210  tmp = 0.0d+0
211  IF ( capply ) THEN
212  DO j = 1, i
213  tmp = tmp + cabs1( a( j, i ) ) / c( j )
214  END DO
215  DO j = i+1, n
216  tmp = tmp + cabs1( a( i, j ) ) / c( j )
217  END DO
218  ELSE
219  DO j = 1, i
220  tmp = tmp + cabs1( a( j, i ) )
221  END DO
222  DO j = i+1, n
223  tmp = tmp + cabs1( a( i, j ) )
224  END DO
225  END IF
226  rwork( i ) = tmp
227  anorm = max( anorm, tmp )
228  END DO
229  ELSE
230  DO i = 1, n
231  tmp = 0.0d+0
232  IF ( capply ) THEN
233  DO j = 1, i
234  tmp = tmp + cabs1( a( i, j ) ) / c( j )
235  END DO
236  DO j = i+1, n
237  tmp = tmp + cabs1( a( j, i ) ) / c( j )
238  END DO
239  ELSE
240  DO j = 1, i
241  tmp = tmp + cabs1( a( i, j ) )
242  END DO
243  DO j = i+1, n
244  tmp = tmp + cabs1( a( j, i ) )
245  END DO
246  END IF
247  rwork( i ) = tmp
248  anorm = max( anorm, tmp )
249  END DO
250  END IF
251 *
252 * Quick return if possible.
253 *
254  IF( n.EQ.0 ) THEN
255  zla_hercond_c = 1.0d+0
256  RETURN
257  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
258  RETURN
259  END IF
260 *
261 * Estimate the norm of inv(op(A)).
262 *
263  ainvnm = 0.0d+0
264 *
265  kase = 0
266  10 CONTINUE
267  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
268  IF( kase.NE.0 ) THEN
269  IF( kase.EQ.2 ) THEN
270 *
271 * Multiply by R.
272 *
273  DO i = 1, n
274  work( i ) = work( i ) * rwork( i )
275  END DO
276 *
277  IF ( up ) THEN
278  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
279  \$ work, n, info )
280  ELSE
281  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
282  \$ work, n, info )
283  ENDIF
284 *
285 * Multiply by inv(C).
286 *
287  IF ( capply ) THEN
288  DO i = 1, n
289  work( i ) = work( i ) * c( i )
290  END DO
291  END IF
292  ELSE
293 *
294 * Multiply by inv(C**H).
295 *
296  IF ( capply ) THEN
297  DO i = 1, n
298  work( i ) = work( i ) * c( i )
299  END DO
300  END IF
301 *
302  IF ( up ) THEN
303  CALL zhetrs( 'U', n, 1, af, ldaf, ipiv,
304  \$ work, n, info )
305  ELSE
306  CALL zhetrs( 'L', n, 1, af, ldaf, ipiv,
307  \$ work, n, info )
308  END IF
309 *
310 * Multiply by R.
311 *
312  DO i = 1, n
313  work( i ) = work( i ) * rwork( i )
314  END DO
315  END IF
316  GO TO 10
317  END IF
318 *
319 * Compute the estimate of the reciprocal condition number.
320 *
321  IF( ainvnm .NE. 0.0d+0 )
322  \$ zla_hercond_c = 1.0d+0 / ainvnm
323 *
324  RETURN
325 *
326 * End of ZLA_HERCOND_C
327 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:120
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:133
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