LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dpbcon()

subroutine dpbcon ( character  UPLO,
integer  N,
integer  KD,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision  ANORM,
double precision  RCOND,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

DPBCON

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Purpose:
 DPBCON estimates the reciprocal of the condition number (in the
 1-norm) of a real symmetric positive definite band matrix using the
 Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.

 An estimate is obtained for norm(inv(A)), and the reciprocal of the
 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangular factor stored in AB;
          = 'L':  Lower triangular factor stored in AB.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]KD
          KD is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The triangular factor U or L from the Cholesky factorization
          A = U**T*U or A = L*L**T of the band matrix A, stored in the
          first KD+1 rows of the array.  The j-th column of U or L is
          stored in the j-th column of the array AB as follows:
          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in]ANORM
          ANORM is DOUBLE PRECISION
          The 1-norm (or infinity-norm) of the symmetric band matrix A.
[out]RCOND
          RCOND is DOUBLE PRECISION
          The reciprocal of the condition number of the matrix A,
          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
          estimate of the 1-norm of inv(A) computed in this routine.
[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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 134 of file dpbcon.f.

134 *
135 * -- LAPACK computational routine (version 3.7.0) --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 * December 2016
139 *
140 * .. Scalar Arguments ..
141  CHARACTER uplo
142  INTEGER info, kd, ldab, n
143  DOUBLE PRECISION anorm, rcond
144 * ..
145 * .. Array Arguments ..
146  INTEGER iwork( * )
147  DOUBLE PRECISION ab( ldab, * ), work( * )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  DOUBLE PRECISION one, zero
154  parameter( one = 1.0d+0, zero = 0.0d+0 )
155 * ..
156 * .. Local Scalars ..
157  LOGICAL upper
158  CHARACTER normin
159  INTEGER ix, kase
160  DOUBLE PRECISION ainvnm, scale, scalel, scaleu, smlnum
161 * ..
162 * .. Local Arrays ..
163  INTEGER isave( 3 )
164 * ..
165 * .. External Functions ..
166  LOGICAL lsame
167  INTEGER idamax
168  DOUBLE PRECISION dlamch
169  EXTERNAL lsame, idamax, dlamch
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL dlacn2, dlatbs, drscl, xerbla
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC abs
176 * ..
177 * .. Executable Statements ..
178 *
179 * Test the input parameters.
180 *
181  info = 0
182  upper = lsame( uplo, 'U' )
183  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
184  info = -1
185  ELSE IF( n.LT.0 ) THEN
186  info = -2
187  ELSE IF( kd.LT.0 ) THEN
188  info = -3
189  ELSE IF( ldab.LT.kd+1 ) THEN
190  info = -5
191  ELSE IF( anorm.LT.zero ) THEN
192  info = -6
193  END IF
194  IF( info.NE.0 ) THEN
195  CALL xerbla( 'DPBCON', -info )
196  RETURN
197  END IF
198 *
199 * Quick return if possible
200 *
201  rcond = zero
202  IF( n.EQ.0 ) THEN
203  rcond = one
204  RETURN
205  ELSE IF( anorm.EQ.zero ) THEN
206  RETURN
207  END IF
208 *
209  smlnum = dlamch( 'Safe minimum' )
210 *
211 * Estimate the 1-norm of the inverse.
212 *
213  kase = 0
214  normin = 'N'
215  10 CONTINUE
216  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
217  IF( kase.NE.0 ) THEN
218  IF( upper ) THEN
219 *
220 * Multiply by inv(U**T).
221 *
222  CALL dlatbs( 'Upper', 'Transpose', 'Non-unit', normin, n,
223  $ kd, ab, ldab, work, scalel, work( 2*n+1 ),
224  $ info )
225  normin = 'Y'
226 *
227 * Multiply by inv(U).
228 *
229  CALL dlatbs( 'Upper', 'No transpose', 'Non-unit', normin, n,
230  $ kd, ab, ldab, work, scaleu, work( 2*n+1 ),
231  $ info )
232  ELSE
233 *
234 * Multiply by inv(L).
235 *
236  CALL dlatbs( 'Lower', 'No transpose', 'Non-unit', normin, n,
237  $ kd, ab, ldab, work, scalel, work( 2*n+1 ),
238  $ info )
239  normin = 'Y'
240 *
241 * Multiply by inv(L**T).
242 *
243  CALL dlatbs( 'Lower', 'Transpose', 'Non-unit', normin, n,
244  $ kd, ab, ldab, work, scaleu, work( 2*n+1 ),
245  $ info )
246  END IF
247 *
248 * Multiply by 1/SCALE if doing so will not cause overflow.
249 *
250  scale = scalel*scaleu
251  IF( scale.NE.one ) THEN
252  ix = idamax( n, work, 1 )
253  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
254  $ GO TO 20
255  CALL drscl( n, scale, work, 1 )
256  END IF
257  GO TO 10
258  END IF
259 *
260 * Compute the estimate of the reciprocal condition number.
261 *
262  IF( ainvnm.NE.zero )
263  $ rcond = ( one / ainvnm ) / anorm
264 *
265  20 CONTINUE
266 *
267  RETURN
268 *
269 * End of DPBCON
270 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:73
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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:86
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