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

 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.

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

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

Definition at line 158 of file cla_gbrcond_c.f.

161*
162* -- LAPACK computational routine --
163* -- LAPACK is a software package provided by Univ. of Tennessee, --
164* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165*
166* .. Scalar Arguments ..
167 CHARACTER TRANS
168 LOGICAL CAPPLY
169 INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
170* ..
171* .. Array Arguments ..
172 INTEGER IPIV( * )
173 COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
174 REAL C( * ), RWORK( * )
175* ..
176*
177* =====================================================================
178*
179* .. Local Scalars ..
180 LOGICAL NOTRANS
181 INTEGER KASE, I, J
182 REAL AINVNM, ANORM, TMP
183 COMPLEX ZDUM
184* ..
185* .. Local Arrays ..
186 INTEGER ISAVE( 3 )
187* ..
188* .. External Functions ..
189 LOGICAL LSAME
190 EXTERNAL lsame
191* ..
192* .. External Subroutines ..
193 EXTERNAL clacn2, cgbtrs, xerbla
194* ..
195* .. Intrinsic Functions ..
196 INTRINSIC abs, max
197* ..
198* .. Statement Functions ..
199 REAL CABS1
200* ..
201* .. Statement Function Definitions ..
202 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
203* ..
204* .. Executable Statements ..
205 cla_gbrcond_c = 0.0e+0
206*
207 info = 0
208 notrans = lsame( trans, 'N' )
209 IF ( .NOT. notrans .AND. .NOT. lsame( trans, 'T' ) .AND. .NOT.
210 \$ lsame( trans, 'C' ) ) THEN
211 info = -1
212 ELSE IF( n.LT.0 ) THEN
213 info = -2
214 ELSE IF( kl.LT.0 .OR. kl.GT.n-1 ) THEN
215 info = -3
216 ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
217 info = -4
218 ELSE IF( ldab.LT.kl+ku+1 ) THEN
219 info = -6
220 ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
221 info = -8
222 END IF
223 IF( info.NE.0 ) THEN
224 CALL xerbla( 'CLA_GBRCOND_C', -info )
225 RETURN
226 END IF
227*
228* Compute norm of op(A)*op2(C).
229*
230 anorm = 0.0e+0
231 kd = ku + 1
232 ke = kl + 1
233 IF ( notrans ) THEN
234 DO i = 1, n
235 tmp = 0.0e+0
236 IF ( capply ) THEN
237 DO j = max( i-kl, 1 ), min( i+ku, n )
238 tmp = tmp + cabs1( ab( kd+i-j, j ) ) / c( j )
239 END DO
240 ELSE
241 DO j = max( i-kl, 1 ), min( i+ku, n )
242 tmp = tmp + cabs1( ab( kd+i-j, j ) )
243 END DO
244 END IF
245 rwork( i ) = tmp
246 anorm = max( anorm, tmp )
247 END DO
248 ELSE
249 DO i = 1, n
250 tmp = 0.0e+0
251 IF ( capply ) THEN
252 DO j = max( i-kl, 1 ), min( i+ku, n )
253 tmp = tmp + cabs1( ab( ke-i+j, i ) ) / c( j )
254 END DO
255 ELSE
256 DO j = max( i-kl, 1 ), min( i+ku, n )
257 tmp = tmp + cabs1( ab( ke-i+j, i ) )
258 END DO
259 END IF
260 rwork( i ) = tmp
261 anorm = max( anorm, tmp )
262 END DO
263 END IF
264*
265* Quick return if possible.
266*
267 IF( n.EQ.0 ) THEN
268 cla_gbrcond_c = 1.0e+0
269 RETURN
270 ELSE IF( anorm .EQ. 0.0e+0 ) THEN
271 RETURN
272 END IF
273*
274* Estimate the norm of inv(op(A)).
275*
276 ainvnm = 0.0e+0
277*
278 kase = 0
279 10 CONTINUE
280 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
281 IF( kase.NE.0 ) THEN
282 IF( kase.EQ.2 ) THEN
283*
284* Multiply by R.
285*
286 DO i = 1, n
287 work( i ) = work( i ) * rwork( i )
288 END DO
289*
290 IF ( notrans ) THEN
291 CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
292 \$ ipiv, work, n, info )
293 ELSE
294 CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
295 \$ ldafb, ipiv, work, n, info )
296 ENDIF
297*
298* Multiply by inv(C).
299*
300 IF ( capply ) THEN
301 DO i = 1, n
302 work( i ) = work( i ) * c( i )
303 END DO
304 END IF
305 ELSE
306*
307* Multiply by inv(C**H).
308*
309 IF ( capply ) THEN
310 DO i = 1, n
311 work( i ) = work( i ) * c( i )
312 END DO
313 END IF
314*
315 IF ( notrans ) THEN
316 CALL cgbtrs( 'Conjugate transpose', n, kl, ku, 1, afb,
317 \$ ldafb, ipiv, work, n, info )
318 ELSE
319 CALL cgbtrs( 'No transpose', n, kl, ku, 1, afb, ldafb,
320 \$ ipiv, work, n, info )
321 END IF
322*
323* Multiply by R.
324*
325 DO i = 1, n
326 work( i ) = work( i ) * rwork( i )
327 END DO
328 END IF
329 GO TO 10
330 END IF
331*
332* Compute the estimate of the reciprocal condition number.
333*
334 IF( ainvnm .NE. 0.0e+0 )
335 \$ cla_gbrcond_c = 1.0e+0 / ainvnm
336*
337 RETURN
338*
339* End of CLA_GBRCOND_C
340*
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_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...
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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