LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cla_syrcond_c()

 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.

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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. [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_syrcond_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
158  REAL AINVNM, ANORM, TMP
159  INTEGER I, J
160  LOGICAL UP, UPPER
161  COMPLEX ZDUM
162 * ..
163 * .. Local Arrays ..
164  INTEGER ISAVE( 3 )
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  EXTERNAL lsame
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL clacn2, csytrs, xerbla
172 * ..
173 * .. Intrinsic Functions ..
174  INTRINSIC abs, max
175 * ..
176 * .. Statement Functions ..
177  REAL CABS1
178 * ..
179 * .. Statement Function Definitions ..
180  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
181 * ..
182 * .. Executable Statements ..
183 *
184  cla_syrcond_c = 0.0e+0
185 *
186  info = 0
187  upper = lsame( uplo, 'U' )
188  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
189  info = -1
190  ELSE IF( n.LT.0 ) THEN
191  info = -2
192  ELSE IF( lda.LT.max( 1, n ) ) THEN
193  info = -4
194  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
195  info = -6
196  END IF
197  IF( info.NE.0 ) THEN
198  CALL xerbla( 'CLA_SYRCOND_C', -info )
199  RETURN
200  END IF
201  up = .false.
202  IF ( lsame( uplo, 'U' ) ) up = .true.
203 *
204 * Compute norm of op(A)*op2(C).
205 *
206  anorm = 0.0e+0
207  IF ( up ) THEN
208  DO i = 1, n
209  tmp = 0.0e+0
210  IF ( capply ) THEN
211  DO j = 1, i
212  tmp = tmp + cabs1( a( j, i ) ) / c( j )
213  END DO
214  DO j = i+1, n
215  tmp = tmp + cabs1( a( i, j ) ) / c( j )
216  END DO
217  ELSE
218  DO j = 1, i
219  tmp = tmp + cabs1( a( j, i ) )
220  END DO
221  DO j = i+1, n
222  tmp = tmp + cabs1( a( i, j ) )
223  END DO
224  END IF
225  rwork( i ) = tmp
226  anorm = max( anorm, tmp )
227  END DO
228  ELSE
229  DO i = 1, n
230  tmp = 0.0e+0
231  IF ( capply ) THEN
232  DO j = 1, i
233  tmp = tmp + cabs1( a( i, j ) ) / c( j )
234  END DO
235  DO j = i+1, n
236  tmp = tmp + cabs1( a( j, i ) ) / c( j )
237  END DO
238  ELSE
239  DO j = 1, i
240  tmp = tmp + cabs1( a( i, j ) )
241  END DO
242  DO j = i+1, n
243  tmp = tmp + cabs1( a( j, i ) )
244  END DO
245  END IF
246  rwork( i ) = tmp
247  anorm = max( anorm, tmp )
248  END DO
249  END IF
250 *
251 * Quick return if possible.
252 *
253  IF( n.EQ.0 ) THEN
254  cla_syrcond_c = 1.0e+0
255  RETURN
256  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
257  RETURN
258  END IF
259 *
260 * Estimate the norm of inv(op(A)).
261 *
262  ainvnm = 0.0e+0
263 *
264  kase = 0
265  10 CONTINUE
266  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
267  IF( kase.NE.0 ) THEN
268  IF( kase.EQ.2 ) THEN
269 *
270 * Multiply by R.
271 *
272  DO i = 1, n
273  work( i ) = work( i ) * rwork( i )
274  END DO
275 *
276  IF ( up ) THEN
277  CALL csytrs( 'U', n, 1, af, ldaf, ipiv,
278  \$ work, n, info )
279  ELSE
280  CALL csytrs( 'L', n, 1, af, ldaf, ipiv,
281  \$ work, n, info )
282  ENDIF
283 *
284 * Multiply by inv(C).
285 *
286  IF ( capply ) THEN
287  DO i = 1, n
288  work( i ) = work( i ) * c( i )
289  END DO
290  END IF
291  ELSE
292 *
293 * Multiply by inv(C**T).
294 *
295  IF ( capply ) THEN
296  DO i = 1, n
297  work( i ) = work( i ) * c( i )
298  END DO
299  END IF
300 *
301  IF ( up ) THEN
302  CALL csytrs( 'U', n, 1, af, ldaf, ipiv,
303  \$ work, n, info )
304  ELSE
305  CALL csytrs( 'L', n, 1, af, ldaf, ipiv,
306  \$ work, n, info )
307  END IF
308 *
309 * Multiply by R.
310 *
311  DO i = 1, n
312  work( i ) = work( i ) * rwork( i )
313  END DO
314  END IF
315  GO TO 10
316  END IF
317 *
318 * Compute the estimate of the reciprocal condition number.
319 *
320  IF( ainvnm .NE. 0.0e+0 )
321  \$ cla_syrcond_c = 1.0e+0 / ainvnm
322 *
323  RETURN
324 *
325 * End of CLA_SYRCOND_C
326 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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...
subroutine csytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CSYTRS
Definition: csytrs.f:120
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