LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ dgbcon()

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

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

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

Definition at line 144 of file dgbcon.f.

146*
147* -- LAPACK computational routine --
148* -- LAPACK is a software package provided by Univ. of Tennessee, --
149* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150*
151* .. Scalar Arguments ..
152 CHARACTER NORM
153 INTEGER INFO, KL, KU, LDAB, N
154 DOUBLE PRECISION ANORM, RCOND
155* ..
156* .. Array Arguments ..
157 INTEGER IPIV( * ), IWORK( * )
158 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
159* ..
160*
161* =====================================================================
162*
163* .. Parameters ..
164 DOUBLE PRECISION ONE, ZERO
165 parameter( one = 1.0d+0, zero = 0.0d+0 )
166* ..
167* .. Local Scalars ..
168 LOGICAL LNOTI, ONENRM
169 CHARACTER NORMIN
170 INTEGER IX, J, JP, KASE, KASE1, KD, LM
171 DOUBLE PRECISION AINVNM, SCALE, SMLNUM, T
172* ..
173* .. Local Arrays ..
174 INTEGER ISAVE( 3 )
175* ..
176* .. External Functions ..
177 LOGICAL LSAME
178 INTEGER IDAMAX
179 DOUBLE PRECISION DDOT, DLAMCH
180 EXTERNAL lsame, idamax, ddot, dlamch
181* ..
182* .. External Subroutines ..
183 EXTERNAL daxpy, dlacn2, dlatbs, drscl, xerbla
184* ..
185* .. Intrinsic Functions ..
186 INTRINSIC abs, min
187* ..
188* .. Executable Statements ..
189*
190* Test the input parameters.
191*
192 info = 0
193 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
194 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
195 info = -1
196 ELSE IF( n.LT.0 ) THEN
197 info = -2
198 ELSE IF( kl.LT.0 ) THEN
199 info = -3
200 ELSE IF( ku.LT.0 ) THEN
201 info = -4
202 ELSE IF( ldab.LT.2*kl+ku+1 ) THEN
203 info = -6
204 ELSE IF( anorm.LT.zero ) THEN
205 info = -8
206 END IF
207 IF( info.NE.0 ) THEN
208 CALL xerbla( 'DGBCON', -info )
209 RETURN
210 END IF
211*
212* Quick return if possible
213*
214 rcond = zero
215 IF( n.EQ.0 ) THEN
216 rcond = one
217 RETURN
218 ELSE IF( anorm.EQ.zero ) THEN
219 RETURN
220 END IF
221*
222 smlnum = dlamch( 'Safe minimum' )
223*
224* Estimate the norm of inv(A).
225*
226 ainvnm = zero
227 normin = 'N'
228 IF( onenrm ) THEN
229 kase1 = 1
230 ELSE
231 kase1 = 2
232 END IF
233 kd = kl + ku + 1
234 lnoti = kl.GT.0
235 kase = 0
236 10 CONTINUE
237 CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
238 IF( kase.NE.0 ) THEN
239 IF( kase.EQ.kase1 ) THEN
240*
241* Multiply by inv(L).
242*
243 IF( lnoti ) THEN
244 DO 20 j = 1, n - 1
245 lm = min( kl, n-j )
246 jp = ipiv( j )
247 t = work( jp )
248 IF( jp.NE.j ) THEN
249 work( jp ) = work( j )
250 work( j ) = t
251 END IF
252 CALL daxpy( lm, -t, ab( kd+1, j ), 1, work( j+1 ), 1 )
253 20 CONTINUE
254 END IF
255*
256* Multiply by inv(U).
257*
258 CALL dlatbs( 'Upper', 'No transpose', 'Non-unit', normin, n,
259 $ kl+ku, ab, ldab, work, scale, work( 2*n+1 ),
260 $ info )
261 ELSE
262*
263* Multiply by inv(U**T).
264*
265 CALL dlatbs( 'Upper', 'Transpose', 'Non-unit', normin, n,
266 $ kl+ku, ab, ldab, work, scale, work( 2*n+1 ),
267 $ info )
268*
269* Multiply by inv(L**T).
270*
271 IF( lnoti ) THEN
272 DO 30 j = n - 1, 1, -1
273 lm = min( kl, n-j )
274 work( j ) = work( j ) - ddot( lm, ab( kd+1, j ), 1,
275 $ work( j+1 ), 1 )
276 jp = ipiv( j )
277 IF( jp.NE.j ) THEN
278 t = work( jp )
279 work( jp ) = work( j )
280 work( j ) = t
281 END IF
282 30 CONTINUE
283 END IF
284 END IF
285*
286* Divide X by 1/SCALE if doing so will not cause overflow.
287*
288 normin = 'Y'
289 IF( scale.NE.one ) THEN
290 ix = idamax( n, work, 1 )
291 IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
292 $ GO TO 40
293 CALL drscl( n, scale, work, 1 )
294 END IF
295 GO TO 10
296 END IF
297*
298* Compute the estimate of the reciprocal condition number.
299*
300 IF( ainvnm.NE.zero )
301 $ rcond = ( one / ainvnm ) / anorm
302*
303 40 CONTINUE
304 RETURN
305*
306* End of DGBCON
307*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
daxpy
subroutine daxpy(n, da, dx, incx, dy, incy)
DAXPY
Definition daxpy.f:89
ddot
double precision function ddot(n, dx, incx, dy, incy)
DDOT
Definition ddot.f:82
idamax
integer function idamax(n, dx, incx)
IDAMAX
Definition idamax.f:71
dlacn2
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:136
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
dlatbs
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:242
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
drscl
subroutine drscl(n, sa, sx, incx)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition drscl.f:84
Here is the call graph for this function:
Here is the caller graph for this function: