LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cla_gercond_c()

 real function cla_gercond_c ( character TRANS, 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_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices.

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Purpose:
```    CLA_GERCOND_C computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a REAL 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 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 factors L and U from the factorization A = P*L*U as computed by CGETRF.``` [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 CGETRF; row i of the matrix was interchanged with row IPIV(i).``` [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 140 of file cla_gercond_c.f.

142 *
143 * -- LAPACK computational routine --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 *
147 * .. Scalar Arguments ..
148  CHARACTER TRANS
149  LOGICAL CAPPLY
150  INTEGER N, LDA, LDAF, INFO
151 * ..
152 * .. Array Arguments ..
153  INTEGER IPIV( * )
154  COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * )
155  REAL C( * ), RWORK( * )
156 * ..
157 *
158 * =====================================================================
159 *
160 * .. Local Scalars ..
161  LOGICAL NOTRANS
162  INTEGER KASE, I, J
163  REAL AINVNM, ANORM, TMP
164  COMPLEX ZDUM
165 * ..
166 * .. Local Arrays ..
167  INTEGER ISAVE( 3 )
168 * ..
169 * .. External Functions ..
170  LOGICAL LSAME
171  EXTERNAL lsame
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL clacn2, cgetrs, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, max, real, aimag
178 * ..
179 * .. Statement Functions ..
180  REAL CABS1
181 * ..
182 * .. Statement Function Definitions ..
183  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
184 * ..
185 * .. Executable Statements ..
186  cla_gercond_c = 0.0e+0
187 *
188  info = 0
189  notrans = lsame( trans, 'N' )
190  IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
191  \$ lsame( trans, 'C' ) ) THEN
192  info = -1
193  ELSE IF( n.LT.0 ) THEN
194  info = -2
195  ELSE IF( lda.LT.max( 1, n ) ) THEN
196  info = -4
197  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
198  info = -6
199  END IF
200  IF( info.NE.0 ) THEN
201  CALL xerbla( 'CLA_GERCOND_C', -info )
202  RETURN
203  END IF
204 *
205 * Compute norm of op(A)*op2(C).
206 *
207  anorm = 0.0e+0
208  IF ( notrans ) THEN
209  DO i = 1, n
210  tmp = 0.0e+0
211  IF ( capply ) THEN
212  DO j = 1, n
213  tmp = tmp + cabs1( a( i, j ) ) / c( j )
214  END DO
215  ELSE
216  DO j = 1, n
217  tmp = tmp + cabs1( a( i, j ) )
218  END DO
219  END IF
220  rwork( i ) = tmp
221  anorm = max( anorm, tmp )
222  END DO
223  ELSE
224  DO i = 1, n
225  tmp = 0.0e+0
226  IF ( capply ) THEN
227  DO j = 1, n
228  tmp = tmp + cabs1( a( j, i ) ) / c( j )
229  END DO
230  ELSE
231  DO j = 1, n
232  tmp = tmp + cabs1( a( j, i ) )
233  END DO
234  END IF
235  rwork( i ) = tmp
236  anorm = max( anorm, tmp )
237  END DO
238  END IF
239 *
240 * Quick return if possible.
241 *
242  IF( n.EQ.0 ) THEN
243  cla_gercond_c = 1.0e+0
244  RETURN
245  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
246  RETURN
247  END IF
248 *
249 * Estimate the norm of inv(op(A)).
250 *
251  ainvnm = 0.0e+0
252 *
253  kase = 0
254  10 CONTINUE
255  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
256  IF( kase.NE.0 ) THEN
257  IF( kase.EQ.2 ) THEN
258 *
259 * Multiply by R.
260 *
261  DO i = 1, n
262  work( i ) = work( i ) * rwork( i )
263  END DO
264 *
265  IF (notrans) THEN
266  CALL cgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
267  \$ work, n, info )
268  ELSE
269  CALL cgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
270  \$ work, n, info )
271  ENDIF
272 *
273 * Multiply by inv(C).
274 *
275  IF ( capply ) THEN
276  DO i = 1, n
277  work( i ) = work( i ) * c( i )
278  END DO
279  END IF
280  ELSE
281 *
282 * Multiply by inv(C**H).
283 *
284  IF ( capply ) THEN
285  DO i = 1, n
286  work( i ) = work( i ) * c( i )
287  END DO
288  END IF
289 *
290  IF ( notrans ) THEN
291  CALL cgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
292  \$ work, n, info )
293  ELSE
294  CALL cgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
295  \$ work, n, info )
296  END IF
297 *
298 * Multiply by R.
299 *
300  DO i = 1, n
301  work( i ) = work( i ) * rwork( i )
302  END DO
303  END IF
304  GO TO 10
305  END IF
306 *
307 * Compute the estimate of the reciprocal condition number.
308 *
309  IF( ainvnm .NE. 0.0e+0 )
310  \$ cla_gercond_c = 1.0e+0 / ainvnm
311 *
312  RETURN
313 *
314 * End of CLA_GERCOND_C
315 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CGETRS
Definition: cgetrs.f:121
real function cla_gercond_c(TRANS, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO, WORK, RWORK)
CLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices.
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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