LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zla_gbrcond_c()

double precision function zla_gbrcond_c ( character  TRANS,
integer  N,
integer  KL,
integer  KU,
complex*16, dimension( ldab, * )  AB,
integer  LDAB,
complex*16, dimension( ldafb, * )  AFB,
integer  LDAFB,
integer, dimension( * )  IPIV,
double precision, dimension( * )  C,
logical  CAPPLY,
integer  INFO,
complex*16, dimension( * )  WORK,
double precision, dimension( * )  RWORK 
)

ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.

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

Purpose:
    ZLA_GBRCOND_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]KL
          KL is INTEGER
     The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
     The number of superdiagonals within the band of A.  KU >= 0.
[in]AB
          AB is COMPLEX*16 array, dimension (LDAB,N)
     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
     The j-th column of A is stored in the j-th column of the
     array AB as follows:
     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
[in]LDAB
          LDAB is INTEGER
     The leading dimension of the array AB.  LDAB >= KL+KU+1.
[in]AFB
          AFB is COMPLEX*16 array, dimension (LDAFB,N)
     Details of the LU factorization of the band matrix A, as
     computed by ZGBTRF.  U is stored as an upper triangular
     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
     and the multipliers used during the factorization are stored
     in rows KL+KU+2 to 2*KL+KU+1.
[in]LDAFB
          LDAFB is INTEGER
     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
     The pivot indices from the factorization A = P*L*U
     as computed by ZGBTRF; 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 159 of file zla_gbrcond_c.f.

163 *
164 * -- LAPACK computational routine --
165 * -- LAPACK is a software package provided by Univ. of Tennessee, --
166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
167 *
168 * .. Scalar Arguments ..
169  CHARACTER TRANS
170  LOGICAL CAPPLY
171  INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
172 * ..
173 * .. Array Arguments ..
174  INTEGER IPIV( * )
175  COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
176  DOUBLE PRECISION C( * ), RWORK( * )
177 *
178 *
179 * =====================================================================
180 *
181 * .. Local Scalars ..
182  LOGICAL NOTRANS
183  INTEGER KASE, I, J
184  DOUBLE PRECISION AINVNM, ANORM, TMP
185  COMPLEX*16 ZDUM
186 * ..
187 * .. Local Arrays ..
188  INTEGER ISAVE( 3 )
189 * ..
190 * .. External Functions ..
191  LOGICAL LSAME
192  EXTERNAL lsame
193 * ..
194 * .. External Subroutines ..
195  EXTERNAL zlacn2, zgbtrs, xerbla
196 * ..
197 * .. Intrinsic Functions ..
198  INTRINSIC abs, max
199 * ..
200 * .. Statement Functions ..
201  DOUBLE PRECISION CABS1
202 * ..
203 * .. Statement Function Definitions ..
204  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
205 * ..
206 * .. Executable Statements ..
207  zla_gbrcond_c = 0.0d+0
208 *
209  info = 0
210  notrans = lsame( trans, 'N' )
211  IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
212  $ lsame( trans, 'C' ) ) THEN
213  info = -1
214  ELSE IF( n.LT.0 ) THEN
215  info = -2
216  ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN
217  info = -3
218  ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
219  info = -4
220  ELSE IF( ldab.LT.kl+ku+1 ) THEN
221  info = -6
222  ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
223  info = -8
224  END IF
225  IF( info.NE.0 ) THEN
226  CALL xerbla( 'ZLA_GBRCOND_C', -info )
227  RETURN
228  END IF
229 *
230 * Compute norm of op(A)*op2(C).
231 *
232  anorm = 0.0d+0
233  kd = ku + 1
234  ke = kl + 1
235  IF ( notrans ) THEN
236  DO i = 1, n
237  tmp = 0.0d+0
238  IF ( capply ) THEN
239  DO j = max( i-kl, 1 ), min( i+ku, n )
240  tmp = tmp + cabs1( ab( kd+i-j, j ) ) / c( j )
241  END DO
242  ELSE
243  DO j = max( i-kl, 1 ), min( i+ku, n )
244  tmp = tmp + cabs1( ab( kd+i-j, j ) )
245  END DO
246  END IF
247  rwork( i ) = tmp
248  anorm = max( anorm, tmp )
249  END DO
250  ELSE
251  DO i = 1, n
252  tmp = 0.0d+0
253  IF ( capply ) THEN
254  DO j = max( i-kl, 1 ), min( i+ku, n )
255  tmp = tmp + cabs1( ab( ke-i+j, i ) ) / c( j )
256  END DO
257  ELSE
258  DO j = max( i-kl, 1 ), min( i+ku, n )
259  tmp = tmp + cabs1( ab( ke-i+j, i ) )
260  END DO
261  END IF
262  rwork( i ) = tmp
263  anorm = max( anorm, tmp )
264  END DO
265  END IF
266 *
267 * Quick return if possible.
268 *
269  IF( n.EQ.0 ) THEN
270  zla_gbrcond_c = 1.0d+0
271  RETURN
272  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
273  RETURN
274  END IF
275 *
276 * Estimate the norm of inv(op(A)).
277 *
278  ainvnm = 0.0d+0
279 *
280  kase = 0
281  10 CONTINUE
282  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
283  IF( kase.NE.0 ) THEN
284  IF( kase.EQ.2 ) THEN
285 *
286 * Multiply by R.
287 *
288  DO i = 1, n
289  work( i ) = work( i ) * rwork( i )
290  END DO
291 *
292  IF ( notrans ) THEN
293  CALL zgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
294  $ ipiv, work, n, info )
295  ELSE
296  CALL zgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
297  $ ldafb, ipiv, work, n, info )
298  ENDIF
299 *
300 * Multiply by inv(C).
301 *
302  IF ( capply ) THEN
303  DO i = 1, n
304  work( i ) = work( i ) * c( i )
305  END DO
306  END IF
307  ELSE
308 *
309 * Multiply by inv(C**H).
310 *
311  IF ( capply ) THEN
312  DO i = 1, n
313  work( i ) = work( i ) * c( i )
314  END DO
315  END IF
316 *
317  IF ( notrans ) THEN
318  CALL zgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
319  $ ldafb, ipiv, work, n, info )
320  ELSE
321  CALL zgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
322  $ ipiv, work, n, info )
323  END IF
324 *
325 * Multiply by R.
326 *
327  DO i = 1, n
328  work( i ) = work( i ) * rwork( i )
329  END DO
330  END IF
331  GO TO 10
332  END IF
333 *
334 * Compute the estimate of the reciprocal condition number.
335 *
336  IF( ainvnm .NE. 0.0d+0 )
337  $ zla_gbrcond_c = 1.0d+0 / ainvnm
338 *
339  RETURN
340 *
341 * End of ZLA_GBRCOND_C
342 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function zla_gbrcond_c(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, C, CAPPLY, INFO, WORK, RWORK)
ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded ma...
subroutine zgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
ZGBTRS
Definition: zgbtrs.f:138
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
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