 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cla_gbrcond_x()

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

Definition at line 151 of file cla_gbrcond_x.f.

153*
154* -- LAPACK computational routine --
155* -- LAPACK is a software package provided by Univ. of Tennessee, --
156* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157*
158* .. Scalar Arguments ..
159 CHARACTER TRANS
160 INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
161* ..
162* .. Array Arguments ..
163 INTEGER IPIV( * )
164 COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
165 \$ X( * )
166 REAL RWORK( * )
167* ..
168*
169* =====================================================================
170*
171* .. Local Scalars ..
172 LOGICAL NOTRANS
173 INTEGER KASE, I, J
174 REAL AINVNM, ANORM, TMP
175 COMPLEX ZDUM
176* ..
177* .. Local Arrays ..
178 INTEGER ISAVE( 3 )
179* ..
180* .. External Functions ..
181 LOGICAL LSAME
182 EXTERNAL lsame
183* ..
184* .. External Subroutines ..
185 EXTERNAL clacn2, cgbtrs, xerbla
186* ..
187* .. Intrinsic Functions ..
188 INTRINSIC abs, max
189* ..
190* .. Statement Functions ..
191 REAL CABS1
192* ..
193* .. Statement Function Definitions ..
194 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
195* ..
196* .. Executable Statements ..
197*
198 cla_gbrcond_x = 0.0e+0
199*
200 info = 0
201 notrans = lsame( trans, 'N' )
202 IF ( .NOT. notrans .AND. .NOT. lsame(trans, 'T') .AND. .NOT.
203 \$ lsame( trans, 'C' ) ) THEN
204 info = -1
205 ELSE IF( n.LT.0 ) THEN
206 info = -2
207 ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN
208 info = -3
209 ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
210 info = -4
211 ELSE IF( ldab.LT.kl+ku+1 ) THEN
212 info = -6
213 ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
214 info = -8
215 END IF
216 IF( info.NE.0 ) THEN
217 CALL xerbla( 'CLA_GBRCOND_X', -info )
218 RETURN
219 END IF
220*
221* Compute norm of op(A)*op2(C).
222*
223 kd = ku + 1
224 ke = kl + 1
225 anorm = 0.0
226 IF ( notrans ) THEN
227 DO i = 1, n
228 tmp = 0.0e+0
229 DO j = max( i-kl, 1 ), min( i+ku, n )
230 tmp = tmp + cabs1( ab( kd+i-j, j) * x( j ) )
231 END DO
232 rwork( i ) = tmp
233 anorm = max( anorm, tmp )
234 END DO
235 ELSE
236 DO i = 1, n
237 tmp = 0.0e+0
238 DO j = max( i-kl, 1 ), min( i+ku, n )
239 tmp = tmp + cabs1( ab( ke-i+j, i ) * x( j ) )
240 END DO
241 rwork( i ) = tmp
242 anorm = max( anorm, tmp )
243 END DO
244 END IF
245*
246* Quick return if possible.
247*
248 IF( n.EQ.0 ) THEN
249 cla_gbrcond_x = 1.0e+0
250 RETURN
251 ELSE IF( anorm .EQ. 0.0e+0 ) THEN
252 RETURN
253 END IF
254*
255* Estimate the norm of inv(op(A)).
256*
257 ainvnm = 0.0e+0
258*
259 kase = 0
260 10 CONTINUE
261 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
262 IF( kase.NE.0 ) THEN
263 IF( kase.EQ.2 ) THEN
264*
265* Multiply by R.
266*
267 DO i = 1, n
268 work( i ) = work( i ) * rwork( i )
269 END DO
270*
271 IF ( notrans ) THEN
272 CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
273 \$ ipiv, work, n, info )
274 ELSE
275 CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
276 \$ ldafb, ipiv, work, n, info )
277 ENDIF
278*
279* Multiply by inv(X).
280*
281 DO i = 1, n
282 work( i ) = work( i ) / x( i )
283 END DO
284 ELSE
285*
286* Multiply by inv(X**H).
287*
288 DO i = 1, n
289 work( i ) = work( i ) / x( i )
290 END DO
291*
292 IF ( notrans ) THEN
293 CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
294 \$ ldafb, ipiv, work, n, info )
295 ELSE
296 CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
297 \$ ipiv, work, n, info )
298 END IF
299*
300* Multiply by R.
301*
302 DO i = 1, n
303 work( i ) = work( i ) * rwork( i )
304 END DO
305 END IF
306 GO TO 10
307 END IF
308*
309* Compute the estimate of the reciprocal condition number.
310*
311 IF( ainvnm .NE. 0.0e+0 )
312 \$ cla_gbrcond_x = 1.0e+0 / ainvnm
313*
314 RETURN
315*
316* End of CLA_GBRCOND_X
317*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
CGBTRS
Definition: cgbtrs.f:138
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...
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:133
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