LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 real function cla_gbrcond_c ( character TRANS, integer N, integer KL, integer KU, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldafb, * ) AFB, integer LDAFB, integer, dimension( * ) IPIV, real, dimension( * ) C, logical CAPPLY, integer INFO, complex, dimension( * ) WORK, real, dimension( * ) RWORK )

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

Purpose:
CLA_GBRCOND_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] 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 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 array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by CGBTRF. 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 CGBTRF; 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. [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 163 of file cla_gbrcond_c.f.

163 *
164 * -- LAPACK computational routine (version 3.4.2) --
165 * -- LAPACK is a software package provided by Univ. of Tennessee, --
166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
167 * September 2012
168 *
169 * .. Scalar Arguments ..
170  CHARACTER trans
171  LOGICAL capply
172  INTEGER n, kl, ku, kd, ke, ldab, ldafb, info
173 * ..
174 * .. Array Arguments ..
175  INTEGER ipiv( * )
176  COMPLEX ab( ldab, * ), afb( ldafb, * ), work( * )
177  REAL c( * ), rwork( * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Local Scalars ..
183  LOGICAL notrans
184  INTEGER kase, i, j
185  REAL ainvnm, anorm, tmp
186  COMPLEX zdum
187 * ..
188 * .. Local Arrays ..
189  INTEGER isave( 3 )
190 * ..
191 * .. External Functions ..
192  LOGICAL lsame
193  EXTERNAL lsame
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL clacn2, cgbtrs, xerbla
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC abs, max
200 * ..
201 * .. Statement Functions ..
202  REAL cabs1
203 * ..
204 * .. Statement Function Definitions ..
205  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
206 * ..
207 * .. Executable Statements ..
208  cla_gbrcond_c = 0.0e+0
209 *
210  info = 0
211  notrans = lsame( trans, 'N' )
212  IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
213  \$ lsame( trans, 'C' ) ) THEN
214  info = -1
215  ELSE IF( n.LT.0 ) THEN
216  info = -2
217  ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN
218  info = -3
219  ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
220  info = -4
221  ELSE IF( ldab.LT.kl+ku+1 ) THEN
222  info = -6
223  ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
224  info = -8
225  END IF
226  IF( info.NE.0 ) THEN
227  CALL xerbla( 'CLA_GBRCOND_C', -info )
228  RETURN
229  END IF
230 *
231 * Compute norm of op(A)*op2(C).
232 *
233  anorm = 0.0e+0
234  kd = ku + 1
235  ke = kl + 1
236  IF ( notrans ) THEN
237  DO i = 1, n
238  tmp = 0.0e+0
239  IF ( capply ) THEN
240  DO j = max( i-kl, 1 ), min( i+ku, n )
241  tmp = tmp + cabs1( ab( kd+i-j, j ) ) / c( j )
242  END DO
243  ELSE
244  DO j = max( i-kl, 1 ), min( i+ku, n )
245  tmp = tmp + cabs1( ab( kd+i-j, j ) )
246  END DO
247  END IF
248  rwork( i ) = tmp
249  anorm = max( anorm, tmp )
250  END DO
251  ELSE
252  DO i = 1, n
253  tmp = 0.0e+0
254  IF ( capply ) THEN
255  DO j = max( i-kl, 1 ), min( i+ku, n )
256  tmp = tmp + cabs1( ab( ke-i+j, i ) ) / c( j )
257  END DO
258  ELSE
259  DO j = max( i-kl, 1 ), min( i+ku, n )
260  tmp = tmp + cabs1( ab( ke-i+j, i ) )
261  END DO
262  END IF
263  rwork( i ) = tmp
264  anorm = max( anorm, tmp )
265  END DO
266  END IF
267 *
268 * Quick return if possible.
269 *
270  IF( n.EQ.0 ) THEN
271  cla_gbrcond_c = 1.0e+0
272  RETURN
273  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
274  RETURN
275  END IF
276 *
277 * Estimate the norm of inv(op(A)).
278 *
279  ainvnm = 0.0e+0
280 *
281  kase = 0
282  10 CONTINUE
283  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
284  IF( kase.NE.0 ) THEN
285  IF( kase.EQ.2 ) THEN
286 *
287 * Multiply by R.
288 *
289  DO i = 1, n
290  work( i ) = work( i ) * rwork( i )
291  END DO
292 *
293  IF ( notrans ) THEN
294  CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
295  \$ ipiv, work, n, info )
296  ELSE
297  CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
298  \$ ldafb, ipiv, work, n, info )
299  ENDIF
300 *
301 * Multiply by inv(C).
302 *
303  IF ( capply ) THEN
304  DO i = 1, n
305  work( i ) = work( i ) * c( i )
306  END DO
307  END IF
308  ELSE
309 *
310 * Multiply by inv(C**H).
311 *
312  IF ( capply ) THEN
313  DO i = 1, n
314  work( i ) = work( i ) * c( i )
315  END DO
316  END IF
317 *
318  IF ( notrans ) THEN
319  CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
320  \$ ldafb, ipiv, work, n, info )
321  ELSE
322  CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
323  \$ ipiv, work, n, info )
324  END IF
325 *
326 * Multiply by R.
327 *
328  DO i = 1, n
329  work( i ) = work( i ) * rwork( i )
330  END DO
331  END IF
332  GO TO 10
333  END IF
334 *
335 * Compute the estimate of the reciprocal condition number.
336 *
337  IF( ainvnm .NE. 0.0e+0 )
338  \$ cla_gbrcond_c = 1.0e+0 / ainvnm
339 *
340  RETURN
341 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
real function cla_gbrcond_c(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, C, CAPPLY, INFO, WORK, RWORK)
CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded ma...
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine cgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
CGBTRS
Definition: cgbtrs.f:140
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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