LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dgbcon ( character NORM, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

DGBCON

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

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 DOUBLE PRECISION array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by DGBTRF. 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 DOUBLE PRECISION array, dimension (3*N)` [out] IWORK ` IWORK is INTEGER array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Date
November 2011

Definition at line 148 of file dgbcon.f.

148 *
149 * -- LAPACK computational routine (version 3.4.0) --
150 * -- LAPACK is a software package provided by Univ. of Tennessee, --
151 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
152 * November 2011
153 *
154 * .. Scalar Arguments ..
155  CHARACTER norm
156  INTEGER info, kl, ku, ldab, n
157  DOUBLE PRECISION anorm, rcond
158 * ..
159 * .. Array Arguments ..
160  INTEGER ipiv( * ), iwork( * )
161  DOUBLE PRECISION ab( ldab, * ), work( * )
162 * ..
163 *
164 * =====================================================================
165 *
166 * .. Parameters ..
167  DOUBLE PRECISION one, zero
168  parameter ( one = 1.0d+0, zero = 0.0d+0 )
169 * ..
170 * .. Local Scalars ..
171  LOGICAL lnoti, onenrm
172  CHARACTER normin
173  INTEGER ix, j, jp, kase, kase1, kd, lm
174  DOUBLE PRECISION ainvnm, scale, smlnum, t
175 * ..
176 * .. Local Arrays ..
177  INTEGER isave( 3 )
178 * ..
179 * .. External Functions ..
180  LOGICAL lsame
181  INTEGER idamax
182  DOUBLE PRECISION ddot, dlamch
183  EXTERNAL lsame, idamax, ddot, dlamch
184 * ..
185 * .. External Subroutines ..
186  EXTERNAL daxpy, dlacn2, dlatbs, drscl, xerbla
187 * ..
188 * .. Intrinsic Functions ..
189  INTRINSIC abs, min
190 * ..
191 * .. Executable Statements ..
192 *
193 * Test the input parameters.
194 *
195  info = 0
196  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
197  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
198  info = -1
199  ELSE IF( n.LT.0 ) THEN
200  info = -2
201  ELSE IF( kl.LT.0 ) THEN
202  info = -3
203  ELSE IF( ku.LT.0 ) THEN
204  info = -4
205  ELSE IF( ldab.LT.2*kl+ku+1 ) THEN
206  info = -6
207  ELSE IF( anorm.LT.zero ) THEN
208  info = -8
209  END IF
210  IF( info.NE.0 ) THEN
211  CALL xerbla( 'DGBCON', -info )
212  RETURN
213  END IF
214 *
215 * Quick return if possible
216 *
217  rcond = zero
218  IF( n.EQ.0 ) THEN
219  rcond = one
220  RETURN
221  ELSE IF( anorm.EQ.zero ) THEN
222  RETURN
223  END IF
224 *
225  smlnum = dlamch( 'Safe minimum' )
226 *
227 * Estimate the norm of inv(A).
228 *
229  ainvnm = zero
230  normin = 'N'
231  IF( onenrm ) THEN
232  kase1 = 1
233  ELSE
234  kase1 = 2
235  END IF
236  kd = kl + ku + 1
237  lnoti = kl.GT.0
238  kase = 0
239  10 CONTINUE
240  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
241  IF( kase.NE.0 ) THEN
242  IF( kase.EQ.kase1 ) THEN
243 *
244 * Multiply by inv(L).
245 *
246  IF( lnoti ) THEN
247  DO 20 j = 1, n - 1
248  lm = min( kl, n-j )
249  jp = ipiv( j )
250  t = work( jp )
251  IF( jp.NE.j ) THEN
252  work( jp ) = work( j )
253  work( j ) = t
254  END IF
255  CALL daxpy( lm, -t, ab( kd+1, j ), 1, work( j+1 ), 1 )
256  20 CONTINUE
257  END IF
258 *
259 * Multiply by inv(U).
260 *
261  CALL dlatbs( 'Upper', 'No transpose', 'Non-unit', normin, n,
262  \$ kl+ku, ab, ldab, work, scale, work( 2*n+1 ),
263  \$ info )
264  ELSE
265 *
266 * Multiply by inv(U**T).
267 *
268  CALL dlatbs( 'Upper', 'Transpose', 'Non-unit', normin, n,
269  \$ kl+ku, ab, ldab, work, scale, work( 2*n+1 ),
270  \$ info )
271 *
272 * Multiply by inv(L**T).
273 *
274  IF( lnoti ) THEN
275  DO 30 j = n - 1, 1, -1
276  lm = min( kl, n-j )
277  work( j ) = work( j ) - ddot( lm, ab( kd+1, j ), 1,
278  \$ work( j+1 ), 1 )
279  jp = ipiv( j )
280  IF( jp.NE.j ) THEN
281  t = work( jp )
282  work( jp ) = work( j )
283  work( j ) = t
284  END IF
285  30 CONTINUE
286  END IF
287  END IF
288 *
289 * Divide X by 1/SCALE if doing so will not cause overflow.
290 *
291  normin = 'Y'
292  IF( scale.NE.one ) THEN
293  ix = idamax( n, work, 1 )
294  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
295  \$ GO TO 40
296  CALL drscl( n, scale, work, 1 )
297  END IF
298  GO TO 10
299  END IF
300 *
301 * Compute the estimate of the reciprocal condition number.
302 *
303  IF( ainvnm.NE.zero )
304  \$ rcond = ( one / ainvnm ) / anorm
305 *
306  40 CONTINUE
307  RETURN
308 *
309 * End of DGBCON
310 *
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:53
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function ddot(N, DX, INCX, DY, INCY)
DDOT
Definition: ddot.f:53
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:54
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:86
subroutine dlatbs(UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
DLATBS solves a triangular banded system of equations.
Definition: dlatbs.f:244
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:138

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