 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 double precision function zla_gercond_c ( character TRANS, 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_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices.

Purpose:
```    ZLA_GERCOND_C computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate Transpose = Transpose)``` [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 factors L and U from the factorization A = P*L*U as computed by ZGETRF.``` [in] LDAF ``` LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices from the factorization A = P*L*U as computed by ZGETRF; row i of the matrix was interchanged with row IPIV(i).``` [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 145 of file zla_gercond_c.f.

145 *
146 * -- LAPACK computational routine (version 3.4.2) --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 * September 2012
150 *
151 * .. Scalar Aguments ..
152  CHARACTER trans
153  LOGICAL capply
154  INTEGER n, lda, ldaf, info
155 * ..
156 * .. Array Arguments ..
157  INTEGER ipiv( * )
158  COMPLEX*16 a( lda, * ), af( ldaf, * ), work( * )
159  DOUBLE PRECISION c( * ), rwork( * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Local Scalars ..
165  LOGICAL notrans
166  INTEGER kase, i, j
167  DOUBLE PRECISION ainvnm, anorm, tmp
168  COMPLEX*16 zdum
169 * ..
170 * .. Local Arrays ..
171  INTEGER isave( 3 )
172 * ..
173 * .. External Functions ..
174  LOGICAL lsame
175  EXTERNAL lsame
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL zlacn2, zgetrs, xerbla
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC abs, max, REAL, dimag
182 * ..
183 * .. Statement Functions ..
184  DOUBLE PRECISION cabs1
185 * ..
186 * .. Statement Function Definitions ..
187  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
188 * ..
189 * .. Executable Statements ..
190  zla_gercond_c = 0.0d+0
191 *
192  info = 0
193  notrans = lsame( trans, 'N' )
194  IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
195  \$ lsame( trans, 'C' ) ) THEN
196  info = -1
197  ELSE IF( n.LT.0 ) THEN
198  info = -2
199  ELSE IF( lda.LT.max( 1, n ) ) THEN
200  info = -4
201  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
202  info = -6
203  END IF
204  IF( info.NE.0 ) THEN
205  CALL xerbla( 'ZLA_GERCOND_C', -info )
206  RETURN
207  END IF
208 *
209 * Compute norm of op(A)*op2(C).
210 *
211  anorm = 0.0d+0
212  IF ( notrans ) THEN
213  DO i = 1, n
214  tmp = 0.0d+0
215  IF ( capply ) THEN
216  DO j = 1, n
217  tmp = tmp + cabs1( a( i, j ) ) / c( j )
218  END DO
219  ELSE
220  DO j = 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 = 0.0d+0
230  IF ( capply ) THEN
231  DO j = 1, n
232  tmp = tmp + cabs1( a( j, i ) ) / c( j )
233  END DO
234  ELSE
235  DO j = 1, n
236  tmp = tmp + cabs1( a( j, i ) )
237  END DO
238  END IF
239  rwork( i ) = tmp
240  anorm = max( anorm, tmp )
241  END DO
242  END IF
243 *
244 * Quick return if possible.
245 *
246  IF( n.EQ.0 ) THEN
247  zla_gercond_c = 1.0d+0
248  RETURN
249  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
250  RETURN
251  END IF
252 *
253 * Estimate the norm of inv(op(A)).
254 *
255  ainvnm = 0.0d+0
256 *
257  kase = 0
258  10 CONTINUE
259  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
260  IF( kase.NE.0 ) THEN
261  IF( kase.EQ.2 ) THEN
262 *
263 * Multiply by R.
264 *
265  DO i = 1, n
266  work( i ) = work( i ) * rwork( i )
267  END DO
268 *
269  IF (notrans) THEN
270  CALL zgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
271  \$ work, n, info )
272  ELSE
273  CALL zgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
274  \$ work, n, info )
275  ENDIF
276 *
277 * Multiply by inv(C).
278 *
279  IF ( capply ) THEN
280  DO i = 1, n
281  work( i ) = work( i ) * c( i )
282  END DO
283  END IF
284  ELSE
285 *
286 * Multiply by inv(C**H).
287 *
288  IF ( capply ) THEN
289  DO i = 1, n
290  work( i ) = work( i ) * c( i )
291  END DO
292  END IF
293 *
294  IF ( notrans ) THEN
295  CALL zgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
296  \$ work, n, info )
297  ELSE
298  CALL zgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
299  \$ work, n, info )
300  END IF
301 *
302 * Multiply by R.
303 *
304  DO i = 1, n
305  work( i ) = work( i ) * rwork( i )
306  END DO
307  END IF
308  GO TO 10
309  END IF
310 *
311 * Compute the estimate of the reciprocal condition number.
312 *
313  IF( ainvnm .NE. 0.0d+0 )
314  \$ zla_gercond_c = 1.0d+0 / ainvnm
315 *
316  RETURN
317 *
subroutine zgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZGETRS
Definition: zgetrs.f:123
double precision function zla_gercond_c(TRANS, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices...
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
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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