 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ sgbcon()

 subroutine sgbcon ( character NORM, integer N, integer KL, integer KU, real, dimension( ldab, * ) AB, integer LDAB, integer, dimension( * ) IPIV, real ANORM, real RCOND, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

SGBCON

Purpose:
``` SGBCON 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 SGBTRF.

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 REAL array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by SGBTRF. 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 REAL 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 REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).``` [out] WORK ` WORK is REAL 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```

Definition at line 144 of file sgbcon.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 REAL ANORM, RCOND
155* ..
156* .. Array Arguments ..
157 INTEGER IPIV( * ), IWORK( * )
158 REAL AB( LDAB, * ), WORK( * )
159* ..
160*
161* =====================================================================
162*
163* .. Parameters ..
164 REAL ONE, ZERO
165 parameter( one = 1.0e+0, zero = 0.0e+0 )
166* ..
167* .. Local Scalars ..
168 LOGICAL LNOTI, ONENRM
169 CHARACTER NORMIN
170 INTEGER IX, J, JP, KASE, KASE1, KD, LM
171 REAL AINVNM, SCALE, SMLNUM, T
172* ..
173* .. Local Arrays ..
174 INTEGER ISAVE( 3 )
175* ..
176* .. External Functions ..
177 LOGICAL LSAME
178 INTEGER ISAMAX
179 REAL SDOT, SLAMCH
180 EXTERNAL lsame, isamax, sdot, slamch
181* ..
182* .. External Subroutines ..
183 EXTERNAL saxpy, slacn2, slatbs, srscl, 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( 'SGBCON', -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 = slamch( '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 slacn2( 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 saxpy( 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 slatbs( '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 slatbs( '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 ) - sdot( 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 = isamax( n, work, 1 )
291 IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
292 \$ GO TO 40
293 CALL srscl( 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 SGBCON
307*
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
subroutine slatbs(UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
SLATBS solves a triangular banded system of equations.
Definition: slatbs.f:242
subroutine srscl(N, SA, SX, INCX)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: srscl.f:84
real function sdot(N, SX, INCX, SY, INCY)
SDOT
Definition: sdot.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
Here is the call graph for this function:
Here is the caller graph for this function: