LAPACK 3.12.0
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.

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

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

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*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
cgbtrs
subroutine cgbtrs(trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
CGBTRS
Definition cgbtrs.f:138
cla_gbrcond_x
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...
Definition cla_gbrcond_x.f:153
clacn2
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
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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