LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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◆ zgbcon()

 subroutine zgbcon ( character norm, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info )

ZGBCON

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Purpose:
``` ZGBCON estimates the reciprocal of the condition number of a complex
general band matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by ZGBTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).```
Parameters
 [in] NORM ``` NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.``` [in] N ``` N is INTEGER 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*16 array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by ZGBTRF. 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] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).``` [in] ANORM ``` ANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.``` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).``` [out] WORK ` WORK is COMPLEX*16 array, dimension (2*N)` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 145 of file zgbcon.f.

147*
148* -- LAPACK computational routine --
149* -- LAPACK is a software package provided by Univ. of Tennessee, --
150* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151*
152* .. Scalar Arguments ..
153 CHARACTER NORM
154 INTEGER INFO, KL, KU, LDAB, N
155 DOUBLE PRECISION ANORM, RCOND
156* ..
157* .. Array Arguments ..
158 INTEGER IPIV( * )
159 DOUBLE PRECISION RWORK( * )
160 COMPLEX*16 AB( LDAB, * ), WORK( * )
161* ..
162*
163* =====================================================================
164*
165* .. Parameters ..
166 DOUBLE PRECISION ONE, ZERO
167 parameter( one = 1.0d+0, zero = 0.0d+0 )
168* ..
169* .. Local Scalars ..
170 LOGICAL LNOTI, ONENRM
171 CHARACTER NORMIN
172 INTEGER IX, J, JP, KASE, KASE1, KD, LM
173 DOUBLE PRECISION AINVNM, SCALE, SMLNUM
174 COMPLEX*16 T, ZDUM
175* ..
176* .. Local Arrays ..
177 INTEGER ISAVE( 3 )
178* ..
179* .. External Functions ..
180 LOGICAL LSAME
181 INTEGER IZAMAX
182 DOUBLE PRECISION DLAMCH
183 COMPLEX*16 ZDOTC
184 EXTERNAL lsame, izamax, dlamch, zdotc
185* ..
186* .. External Subroutines ..
187 EXTERNAL xerbla, zaxpy, zdrscl, zlacn2, zlatbs
188* ..
189* .. Intrinsic Functions ..
190 INTRINSIC abs, dble, dimag, min
191* ..
192* .. Statement Functions ..
193 DOUBLE PRECISION CABS1
194* ..
195* .. Statement Function definitions ..
196 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
197* ..
198* .. Executable Statements ..
199*
200* Test the input parameters.
201*
202 info = 0
203 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
204 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
205 info = -1
206 ELSE IF( n.LT.0 ) THEN
207 info = -2
208 ELSE IF( kl.LT.0 ) THEN
209 info = -3
210 ELSE IF( ku.LT.0 ) THEN
211 info = -4
212 ELSE IF( ldab.LT.2*kl+ku+1 ) THEN
213 info = -6
214 ELSE IF( anorm.LT.zero ) THEN
215 info = -8
216 END IF
217 IF( info.NE.0 ) THEN
218 CALL xerbla( 'ZGBCON', -info )
219 RETURN
220 END IF
221*
222* Quick return if possible
223*
224 rcond = zero
225 IF( n.EQ.0 ) THEN
226 rcond = one
227 RETURN
228 ELSE IF( anorm.EQ.zero ) THEN
229 RETURN
230 END IF
231*
232 smlnum = dlamch( 'Safe minimum' )
233*
234* Estimate the norm of inv(A).
235*
236 ainvnm = zero
237 normin = 'N'
238 IF( onenrm ) THEN
239 kase1 = 1
240 ELSE
241 kase1 = 2
242 END IF
243 kd = kl + ku + 1
244 lnoti = kl.GT.0
245 kase = 0
246 10 CONTINUE
247 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
248 IF( kase.NE.0 ) THEN
249 IF( kase.EQ.kase1 ) THEN
250*
251* Multiply by inv(L).
252*
253 IF( lnoti ) THEN
254 DO 20 j = 1, n - 1
255 lm = min( kl, n-j )
256 jp = ipiv( j )
257 t = work( jp )
258 IF( jp.NE.j ) THEN
259 work( jp ) = work( j )
260 work( j ) = t
261 END IF
262 CALL zaxpy( lm, -t, ab( kd+1, j ), 1, work( j+1 ), 1 )
263 20 CONTINUE
264 END IF
265*
266* Multiply by inv(U).
267*
268 CALL zlatbs( 'Upper', 'No transpose', 'Non-unit', normin, n,
269 \$ kl+ku, ab, ldab, work, scale, rwork, info )
270 ELSE
271*
272* Multiply by inv(U**H).
273*
274 CALL zlatbs( 'Upper', 'Conjugate transpose', 'Non-unit',
275 \$ normin, n, kl+ku, ab, ldab, work, scale, rwork,
276 \$ info )
277*
278* Multiply by inv(L**H).
279*
280 IF( lnoti ) THEN
281 DO 30 j = n - 1, 1, -1
282 lm = min( kl, n-j )
283 work( j ) = work( j ) - zdotc( lm, ab( kd+1, j ), 1,
284 \$ work( j+1 ), 1 )
285 jp = ipiv( j )
286 IF( jp.NE.j ) THEN
287 t = work( jp )
288 work( jp ) = work( j )
289 work( j ) = t
290 END IF
291 30 CONTINUE
292 END IF
293 END IF
294*
295* Divide X by 1/SCALE if doing so will not cause overflow.
296*
297 normin = 'Y'
298 IF( scale.NE.one ) THEN
299 ix = izamax( n, work, 1 )
300 IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
301 \$ GO TO 40
302 CALL zdrscl( n, scale, work, 1 )
303 END IF
304 GO TO 10
305 END IF
306*
307* Compute the estimate of the reciprocal condition number.
308*
309 IF( ainvnm.NE.zero )
310 \$ rcond = ( one / ainvnm ) / anorm
311*
312 40 CONTINUE
313 RETURN
314*
315* End of ZGBCON
316*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zaxpy(n, za, zx, incx, zy, incy)
ZAXPY
Definition zaxpy.f:88
complex *16 function zdotc(n, zx, incx, zy, incy)
ZDOTC
Definition zdotc.f:83
integer function izamax(n, zx, incx)
IZAMAX
Definition izamax.f:71
subroutine zlacn2(n, v, x, est, kase, isave)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition zlacn2.f:133
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
subroutine zlatbs(uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info)
ZLATBS solves a triangular banded system of equations.
Definition zlatbs.f:243
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine zdrscl(n, sa, sx, incx)
ZDRSCL multiplies a vector by the reciprocal of a real scalar.
Definition zdrscl.f:84
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