LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 real function cla_gercond_x ( character TRANS, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * ) IPIV, complex, dimension( * ) X, integer INFO, complex, dimension( * ) WORK, real, dimension( * ) RWORK )

CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices.

Purpose:
```    CLA_GERCOND_X computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX 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] X ``` X is COMPLEX 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.``` [in] WORK ``` WORK is COMPLEX array, dimension (2*N). Workspace.``` [in] RWORK ``` RWORK is REAL array, dimension (N). Workspace.```
Date
September 2012

Definition at line 137 of file cla_gercond_x.f.

137 *
138 * -- LAPACK computational routine (version 3.4.2) --
139 * -- LAPACK is a software package provided by Univ. of Tennessee, --
140 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141 * September 2012
142 *
143 * .. Scalar Arguments ..
144  CHARACTER trans
145  INTEGER n, lda, ldaf, info
146 * ..
147 * .. Array Arguments ..
148  INTEGER ipiv( * )
149  COMPLEX a( lda, * ), af( ldaf, * ), work( * ), x( * )
150  REAL rwork( * )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Local Scalars ..
156  LOGICAL notrans
157  INTEGER kase
158  REAL ainvnm, anorm, tmp
159  INTEGER i, j
160  COMPLEX zdum
161 * ..
162 * .. Local Arrays ..
163  INTEGER isave( 3 )
164 * ..
165 * .. External Functions ..
166  LOGICAL lsame
167  EXTERNAL lsame
168 * ..
169 * .. External Subroutines ..
170  EXTERNAL clacn2, cgetrs, xerbla
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC abs, max, REAL, aimag
174 * ..
175 * .. Statement Functions ..
176  REAL cabs1
177 * ..
178 * .. Statement Function Definitions ..
179  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
180 * ..
181 * .. Executable Statements ..
182 *
183  cla_gercond_x = 0.0e+0
184 *
185  info = 0
186  notrans = lsame( trans, 'N' )
187  IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
188  \$ lsame( trans, 'C' ) ) 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_GERCOND_X', -info )
199  RETURN
200  END IF
201 *
202 * Compute norm of op(A)*op2(C).
203 *
204  anorm = 0.0
205  IF ( notrans ) THEN
206  DO i = 1, n
207  tmp = 0.0e+0
208  DO j = 1, n
209  tmp = tmp + cabs1( a( i, j ) * x( j ) )
210  END DO
211  rwork( i ) = tmp
212  anorm = max( anorm, tmp )
213  END DO
214  ELSE
215  DO i = 1, n
216  tmp = 0.0e+0
217  DO j = 1, n
218  tmp = tmp + cabs1( a( j, i ) * x( j ) )
219  END DO
220  rwork( i ) = tmp
221  anorm = max( anorm, tmp )
222  END DO
223  END IF
224 *
225 * Quick return if possible.
226 *
227  IF( n.EQ.0 ) THEN
228  cla_gercond_x = 1.0e+0
229  RETURN
230  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
231  RETURN
232  END IF
233 *
234 * Estimate the norm of inv(op(A)).
235 *
236  ainvnm = 0.0e+0
237 *
238  kase = 0
239  10 CONTINUE
240  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
241  IF( kase.NE.0 ) THEN
242  IF( kase.EQ.2 ) THEN
243 * Multiply by R.
244  DO i = 1, n
245  work( i ) = work( i ) * rwork( i )
246  END DO
247 *
248  IF ( notrans ) THEN
249  CALL cgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
250  \$ work, n, info )
251  ELSE
252  CALL cgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
253  \$ work, n, info )
254  ENDIF
255 *
256 * Multiply by inv(X).
257 *
258  DO i = 1, n
259  work( i ) = work( i ) / x( i )
260  END DO
261  ELSE
262 *
263 * Multiply by inv(X**H).
264 *
265  DO i = 1, n
266  work( i ) = work( i ) / x( i )
267  END DO
268 *
269  IF ( notrans ) THEN
270  CALL cgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
271  \$ work, n, info )
272  ELSE
273  CALL cgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
274  \$ work, n, info )
275  END IF
276 *
277 * Multiply by R.
278 *
279  DO i = 1, n
280  work( i ) = work( i ) * rwork( i )
281  END DO
282  END IF
283  GO TO 10
284  END IF
285 *
286 * Compute the estimate of the reciprocal condition number.
287 *
288  IF( ainvnm .NE. 0.0e+0 )
289  \$ cla_gercond_x = 1.0e+0 / ainvnm
290 *
291  RETURN
292 *
real function cla_gercond_x(TRANS, N, A, LDA, AF, LDAF, IPIV, X, INFO, WORK, RWORK)
CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices...
subroutine cgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CGETRS
Definition: cgetrs.f:123
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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:135

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