 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zla_syrcond_x()

 double precision function zla_syrcond_x ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * ) IPIV, complex*16, dimension( * ) X, integer INFO, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK )

ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.

Purpose:
```    ZLA_SYRCOND_X Computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX*16 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 ZSYTRF.``` [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 ZSYTRF.``` [in] X ``` X is COMPLEX*16 array, dimension (N) The vector X in the formula op(A) * diag(X).``` [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 130 of file zla_syrcond_x.f.

133 *
134 * -- LAPACK computational routine --
135 * -- LAPACK is a software package provided by Univ. of Tennessee, --
136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137 *
138 * .. Scalar Arguments ..
139  CHARACTER UPLO
140  INTEGER N, LDA, LDAF, INFO
141 * ..
142 * .. Array Arguments ..
143  INTEGER IPIV( * )
144  COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
145  DOUBLE PRECISION RWORK( * )
146 * ..
147 *
148 * =====================================================================
149 *
150 * .. Local Scalars ..
151  INTEGER KASE
152  DOUBLE PRECISION AINVNM, ANORM, TMP
153  INTEGER I, J
154  LOGICAL UP, UPPER
155  COMPLEX*16 ZDUM
156 * ..
157 * .. Local Arrays ..
158  INTEGER ISAVE( 3 )
159 * ..
160 * .. External Functions ..
161  LOGICAL LSAME
162  EXTERNAL lsame
163 * ..
164 * .. External Subroutines ..
165  EXTERNAL zlacn2, zsytrs, xerbla
166 * ..
167 * .. Intrinsic Functions ..
168  INTRINSIC abs, max
169 * ..
170 * .. Statement Functions ..
171  DOUBLE PRECISION CABS1
172 * ..
173 * .. Statement Function Definitions ..
174  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
175 * ..
176 * .. Executable Statements ..
177 *
178  zla_syrcond_x = 0.0d+0
179 *
180  info = 0
181  upper = lsame( uplo, 'U' )
182  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
183  info = -1
184  ELSE IF( n.LT.0 ) THEN
185  info = -2
186  ELSE IF( lda.LT.max( 1, n ) ) THEN
187  info = -4
188  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
189  info = -6
190  END IF
191  IF( info.NE.0 ) THEN
192  CALL xerbla( 'ZLA_SYRCOND_X', -info )
193  RETURN
194  END IF
195  up = .false.
196  IF ( lsame( uplo, 'U' ) ) up = .true.
197 *
198 * Compute norm of op(A)*op2(C).
199 *
200  anorm = 0.0d+0
201  IF ( up ) THEN
202  DO i = 1, n
203  tmp = 0.0d+0
204  DO j = 1, i
205  tmp = tmp + cabs1( a( j, i ) * x( j ) )
206  END DO
207  DO j = i+1, n
208  tmp = tmp + cabs1( a( i, j ) * x( j ) )
209  END DO
210  rwork( i ) = tmp
211  anorm = max( anorm, tmp )
212  END DO
213  ELSE
214  DO i = 1, n
215  tmp = 0.0d+0
216  DO j = 1, i
217  tmp = tmp + cabs1( a( i, j ) * x( j ) )
218  END DO
219  DO j = i+1, n
220  tmp = tmp + cabs1( a( j, i ) * x( j ) )
221  END DO
222  rwork( i ) = tmp
223  anorm = max( anorm, tmp )
224  END DO
225  END IF
226 *
227 * Quick return if possible.
228 *
229  IF( n.EQ.0 ) THEN
230  zla_syrcond_x = 1.0d+0
231  RETURN
232  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
233  RETURN
234  END IF
235 *
236 * Estimate the norm of inv(op(A)).
237 *
238  ainvnm = 0.0d+0
239 *
240  kase = 0
241  10 CONTINUE
242  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
243  IF( kase.NE.0 ) THEN
244  IF( kase.EQ.2 ) THEN
245 *
246 * Multiply by R.
247 *
248  DO i = 1, n
249  work( i ) = work( i ) * rwork( i )
250  END DO
251 *
252  IF ( up ) THEN
253  CALL zsytrs( 'U', n, 1, af, ldaf, ipiv,
254  \$ work, n, info )
255  ELSE
256  CALL zsytrs( 'L', n, 1, af, ldaf, ipiv,
257  \$ work, n, info )
258  ENDIF
259 *
260 * Multiply by inv(X).
261 *
262  DO i = 1, n
263  work( i ) = work( i ) / x( i )
264  END DO
265  ELSE
266 *
267 * Multiply by inv(X**T).
268 *
269  DO i = 1, n
270  work( i ) = work( i ) / x( i )
271  END DO
272 *
273  IF ( up ) THEN
274  CALL zsytrs( 'U', n, 1, af, ldaf, ipiv,
275  \$ work, n, info )
276  ELSE
277  CALL zsytrs( 'L', n, 1, af, ldaf, ipiv,
278  \$ work, n, info )
279  END IF
280 *
281 * Multiply by R.
282 *
283  DO i = 1, n
284  work( i ) = work( i ) * rwork( i )
285  END DO
286  END IF
287  GO TO 10
288  END IF
289 *
290 * Compute the estimate of the reciprocal condition number.
291 *
292  IF( ainvnm .NE. 0.0d+0 )
293  \$ zla_syrcond_x = 1.0d+0 / ainvnm
294 *
295  RETURN
296 *
297 * End of ZLA_SYRCOND_X
298 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
double precision function zla_syrcond_x(UPLO, N, A, LDA, AF, LDAF, IPIV, X, INFO, WORK, RWORK)
ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite m...
subroutine zsytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZSYTRS
Definition: zsytrs.f:120
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