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

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

Purpose:
```    CLA_GBRCOND_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] 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] 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 155 of file cla_gbrcond_x.f.

155 *
156 * -- LAPACK computational routine (version 3.4.2) --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 * September 2012
160 *
161 * .. Scalar Arguments ..
162  CHARACTER trans
163  INTEGER n, kl, ku, kd, ke, ldab, ldafb, info
164 * ..
165 * .. Array Arguments ..
166  INTEGER ipiv( * )
167  COMPLEX ab( ldab, * ), afb( ldafb, * ), work( * ),
168  \$ x( * )
169  REAL rwork( * )
170 * ..
171 *
172 * =====================================================================
173 *
174 * .. Local Scalars ..
175  LOGICAL notrans
176  INTEGER kase, i, j
177  REAL ainvnm, anorm, tmp
178  COMPLEX zdum
179 * ..
180 * .. Local Arrays ..
181  INTEGER isave( 3 )
182 * ..
183 * .. External Functions ..
184  LOGICAL lsame
185  EXTERNAL lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL clacn2, cgbtrs, xerbla
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC abs, max
192 * ..
193 * .. Statement Functions ..
194  REAL cabs1
195 * ..
196 * .. Statement Function Definitions ..
197  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
198 * ..
199 * .. Executable Statements ..
200 *
201  cla_gbrcond_x = 0.0e+0
202 *
203  info = 0
204  notrans = lsame( trans, 'N' )
205  IF ( .NOT. notrans .AND. .NOT. lsame(trans, 'T') .AND. .NOT.
206  \$ lsame( trans, 'C' ) ) THEN
207  info = -1
208  ELSE IF( n.LT.0 ) THEN
209  info = -2
210  ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN
211  info = -3
212  ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
213  info = -4
214  ELSE IF( ldab.LT.kl+ku+1 ) THEN
215  info = -6
216  ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
217  info = -8
218  END IF
219  IF( info.NE.0 ) THEN
220  CALL xerbla( 'CLA_GBRCOND_X', -info )
221  RETURN
222  END IF
223 *
224 * Compute norm of op(A)*op2(C).
225 *
226  kd = ku + 1
227  ke = kl + 1
228  anorm = 0.0
229  IF ( notrans ) THEN
230  DO i = 1, n
231  tmp = 0.0e+0
232  DO j = max( i-kl, 1 ), min( i+ku, n )
233  tmp = tmp + cabs1( ab( kd+i-j, j) * x( j ) )
234  END DO
235  rwork( i ) = tmp
236  anorm = max( anorm, tmp )
237  END DO
238  ELSE
239  DO i = 1, n
240  tmp = 0.0e+0
241  DO j = max( i-kl, 1 ), min( i+ku, n )
242  tmp = tmp + cabs1( ab( ke-i+j, i ) * x( j ) )
243  END DO
244  rwork( i ) = tmp
245  anorm = max( anorm, tmp )
246  END DO
247  END IF
248 *
249 * Quick return if possible.
250 *
251  IF( n.EQ.0 ) THEN
252  cla_gbrcond_x = 1.0e+0
253  RETURN
254  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
255  RETURN
256  END IF
257 *
258 * Estimate the norm of inv(op(A)).
259 *
260  ainvnm = 0.0e+0
261 *
262  kase = 0
263  10 CONTINUE
264  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
265  IF( kase.NE.0 ) THEN
266  IF( kase.EQ.2 ) THEN
267 *
268 * Multiply by R.
269 *
270  DO i = 1, n
271  work( i ) = work( i ) * rwork( i )
272  END DO
273 *
274  IF ( notrans ) THEN
275  CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
276  \$ ipiv, work, n, info )
277  ELSE
278  CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
279  \$ ldafb, ipiv, work, n, info )
280  ENDIF
281 *
282 * Multiply by inv(X).
283 *
284  DO i = 1, n
285  work( i ) = work( i ) / x( i )
286  END DO
287  ELSE
288 *
289 * Multiply by inv(X**H).
290 *
291  DO i = 1, n
292  work( i ) = work( i ) / x( i )
293  END DO
294 *
295  IF ( notrans ) THEN
296  CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
297  \$ ldafb, ipiv, work, n, info )
298  ELSE
299  CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
300  \$ ipiv, work, n, info )
301  END IF
302 *
303 * Multiply by R.
304 *
305  DO i = 1, n
306  work( i ) = work( i ) * rwork( i )
307  END DO
308  END IF
309  GO TO 10
310  END IF
311 *
312 * Compute the estimate of the reciprocal condition number.
313 *
314  IF( ainvnm .NE. 0.0e+0 )
315  \$ cla_gbrcond_x = 1.0e+0 / ainvnm
316 *
317  RETURN
318 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
real function cla_gbrcond_x(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK)
CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrice...
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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