 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ zla_gercond_c()

 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.``` [out] WORK ``` WORK is COMPLEX*16 array, dimension (2*N). Workspace.``` [out] RWORK ``` RWORK is DOUBLE PRECISION array, dimension (N). Workspace.```

Definition at line 140 of file zla_gercond_c.f.

143*
144* -- LAPACK computational routine --
145* -- LAPACK is a software package provided by Univ. of Tennessee, --
146* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147*
148* .. Scalar Arguments ..
149 CHARACTER TRANS
150 LOGICAL CAPPLY
151 INTEGER N, LDA, LDAF, INFO
152* ..
153* .. Array Arguments ..
154 INTEGER IPIV( * )
155 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
156 DOUBLE PRECISION C( * ), RWORK( * )
157* ..
158*
159* =====================================================================
160*
161* .. Local Scalars ..
162 LOGICAL NOTRANS
163 INTEGER KASE, I, J
164 DOUBLE PRECISION AINVNM, ANORM, TMP
165 COMPLEX*16 ZDUM
166* ..
167* .. Local Arrays ..
168 INTEGER ISAVE( 3 )
169* ..
170* .. External Functions ..
171 LOGICAL LSAME
172 EXTERNAL lsame
173* ..
174* .. External Subroutines ..
175 EXTERNAL zlacn2, zgetrs, xerbla
176* ..
177* .. Intrinsic Functions ..
178 INTRINSIC abs, max, real, dimag
179* ..
180* .. Statement Functions ..
181 DOUBLE PRECISION CABS1
182* ..
183* .. Statement Function Definitions ..
184 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
185* ..
186* .. Executable Statements ..
187 zla_gercond_c = 0.0d+0
188*
189 info = 0
190 notrans = lsame( trans, 'N' )
191 IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
192 \$ lsame( trans, 'C' ) ) THEN
193 info = -1
194 ELSE IF( n.LT.0 ) THEN
195 info = -2
196 ELSE IF( lda.LT.max( 1, n ) ) THEN
197 info = -4
198 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
199 info = -6
200 END IF
201 IF( info.NE.0 ) THEN
202 CALL xerbla( 'ZLA_GERCOND_C', -info )
203 RETURN
204 END IF
205*
206* Compute norm of op(A)*op2(C).
207*
208 anorm = 0.0d+0
209 IF ( notrans ) THEN
210 DO i = 1, n
211 tmp = 0.0d+0
212 IF ( capply ) THEN
213 DO j = 1, n
214 tmp = tmp + cabs1( a( i, j ) ) / c( j )
215 END DO
216 ELSE
217 DO j = 1, n
218 tmp = tmp + cabs1( a( i, j ) )
219 END DO
220 END IF
221 rwork( i ) = tmp
222 anorm = max( anorm, tmp )
223 END DO
224 ELSE
225 DO i = 1, n
226 tmp = 0.0d+0
227 IF ( capply ) THEN
228 DO j = 1, n
229 tmp = tmp + cabs1( a( j, i ) ) / c( j )
230 END DO
231 ELSE
232 DO j = 1, n
233 tmp = tmp + cabs1( a( j, i ) )
234 END DO
235 END IF
236 rwork( i ) = tmp
237 anorm = max( anorm, tmp )
238 END DO
239 END IF
240*
241* Quick return if possible.
242*
243 IF( n.EQ.0 ) THEN
244 zla_gercond_c = 1.0d+0
245 RETURN
246 ELSE IF( anorm .EQ. 0.0d+0 ) THEN
247 RETURN
248 END IF
249*
250* Estimate the norm of inv(op(A)).
251*
252 ainvnm = 0.0d+0
253*
254 kase = 0
255 10 CONTINUE
256 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
257 IF( kase.NE.0 ) THEN
258 IF( kase.EQ.2 ) THEN
259*
260* Multiply by R.
261*
262 DO i = 1, n
263 work( i ) = work( i ) * rwork( i )
264 END DO
265*
266 IF (notrans) THEN
267 CALL zgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
268 \$ work, n, info )
269 ELSE
270 CALL zgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
271 \$ work, n, info )
272 ENDIF
273*
274* Multiply by inv(C).
275*
276 IF ( capply ) THEN
277 DO i = 1, n
278 work( i ) = work( i ) * c( i )
279 END DO
280 END IF
281 ELSE
282*
283* Multiply by inv(C**H).
284*
285 IF ( capply ) THEN
286 DO i = 1, n
287 work( i ) = work( i ) * c( i )
288 END DO
289 END IF
290*
291 IF ( notrans ) THEN
292 CALL zgetrs( 'Conjugate transpose', n, 1, af, ldaf, ipiv,
293 \$ work, n, info )
294 ELSE
295 CALL zgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
296 \$ work, n, info )
297 END IF
298*
299* Multiply by R.
300*
301 DO i = 1, n
302 work( i ) = work( i ) * rwork( i )
303 END DO
304 END IF
305 GO TO 10
306 END IF
307*
308* Compute the estimate of the reciprocal condition number.
309*
310 IF( ainvnm .NE. 0.0d+0 )
311 \$ zla_gercond_c = 1.0d+0 / ainvnm
312*
313 RETURN
314*
315* End of ZLA_GERCOND_C
316*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZGETRS
Definition: zgetrs.f:121
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 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
Here is the call graph for this function:
Here is the caller graph for this function: