LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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.

Download ZLA_GERCOND_C + dependencies [TGZ] [ZIP] [TXT]

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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zgetrs
subroutine zgetrs(trans, n, nrhs, a, lda, ipiv, b, ldb, info)
ZGETRS
Definition zgetrs.f:121
zla_gercond_c
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.
Definition zla_gercond_c.f:143
zlacn2
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
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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