LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ctbcon()

 subroutine ctbcon ( character NORM, character UPLO, character DIAG, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real RCOND, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CTBCON

Purpose:
``` CTBCON estimates the reciprocal of the condition number of a
triangular band matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then 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] UPLO ``` UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.``` [in] DIAG ``` DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] KD ``` KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.``` [in] AB ``` AB is COMPLEX array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.``` [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 COMPLEX array, dimension (2*N)` [out] RWORK ` RWORK is REAL 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 141 of file ctbcon.f.

143*
144* -- LAPACK computational routine --
145* -- LAPACK is a software package provided by Univ. of Tennessee, --
146* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147*
148* .. Scalar Arguments ..
149 CHARACTER DIAG, NORM, UPLO
150 INTEGER INFO, KD, LDAB, N
151 REAL RCOND
152* ..
153* .. Array Arguments ..
154 REAL RWORK( * )
155 COMPLEX AB( LDAB, * ), WORK( * )
156* ..
157*
158* =====================================================================
159*
160* .. Parameters ..
161 REAL ONE, ZERO
162 parameter( one = 1.0e+0, zero = 0.0e+0 )
163* ..
164* .. Local Scalars ..
165 LOGICAL NOUNIT, ONENRM, UPPER
166 CHARACTER NORMIN
167 INTEGER IX, KASE, KASE1
168 REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
169 COMPLEX ZDUM
170* ..
171* .. Local Arrays ..
172 INTEGER ISAVE( 3 )
173* ..
174* .. External Functions ..
175 LOGICAL LSAME
176 INTEGER ICAMAX
177 REAL CLANTB, SLAMCH
178 EXTERNAL lsame, icamax, clantb, slamch
179* ..
180* .. External Subroutines ..
181 EXTERNAL clacn2, clatbs, csrscl, xerbla
182* ..
183* .. Intrinsic Functions ..
184 INTRINSIC abs, aimag, max, real
185* ..
186* .. Statement Functions ..
187 REAL CABS1
188* ..
189* .. Statement Function definitions ..
190 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
191* ..
192* .. Executable Statements ..
193*
194* Test the input parameters.
195*
196 info = 0
197 upper = lsame( uplo, 'U' )
198 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
199 nounit = lsame( diag, 'N' )
200*
201 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
202 info = -1
203 ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
204 info = -2
205 ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
206 info = -3
207 ELSE IF( n.LT.0 ) THEN
208 info = -4
209 ELSE IF( kd.LT.0 ) THEN
210 info = -5
211 ELSE IF( ldab.LT.kd+1 ) THEN
212 info = -7
213 END IF
214 IF( info.NE.0 ) THEN
215 CALL xerbla( 'CTBCON', -info )
216 RETURN
217 END IF
218*
219* Quick return if possible
220*
221 IF( n.EQ.0 ) THEN
222 rcond = one
223 RETURN
224 END IF
225*
226 rcond = zero
227 smlnum = slamch( 'Safe minimum' )*real( max( n, 1 ) )
228*
229* Compute the 1-norm of the triangular matrix A or A**H.
230*
231 anorm = clantb( norm, uplo, diag, n, kd, ab, ldab, rwork )
232*
233* Continue only if ANORM > 0.
234*
235 IF( anorm.GT.zero ) THEN
236*
237* Estimate the 1-norm of the inverse of A.
238*
239 ainvnm = zero
240 normin = 'N'
241 IF( onenrm ) THEN
242 kase1 = 1
243 ELSE
244 kase1 = 2
245 END IF
246 kase = 0
247 10 CONTINUE
248 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
249 IF( kase.NE.0 ) THEN
250 IF( kase.EQ.kase1 ) THEN
251*
252* Multiply by inv(A).
253*
254 CALL clatbs( uplo, 'No transpose', diag, normin, n, kd,
255 \$ ab, ldab, work, scale, rwork, info )
256 ELSE
257*
258* Multiply by inv(A**H).
259*
260 CALL clatbs( uplo, 'Conjugate transpose', diag, normin,
261 \$ n, kd, ab, ldab, work, scale, rwork, info )
262 END IF
263 normin = 'Y'
264*
265* Multiply by 1/SCALE if doing so will not cause overflow.
266*
267 IF( scale.NE.one ) THEN
268 ix = icamax( n, work, 1 )
269 xnorm = cabs1( work( ix ) )
270 IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
271 \$ GO TO 20
272 CALL csrscl( n, scale, work, 1 )
273 END IF
274 GO TO 10
275 END IF
276*
277* Compute the estimate of the reciprocal condition number.
278*
279 IF( ainvnm.NE.zero )
280 \$ rcond = ( one / anorm ) / ainvnm
281 END IF
282*
283 20 CONTINUE
284 RETURN
285*
286* End of CTBCON
287*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function clantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clantb.f:141
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:84
subroutine clatbs(UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
CLATBS solves a triangular banded system of equations.
Definition: clatbs.f:243
subroutine clacn2(N, V, X, EST, KASE, ISAVE)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: clacn2.f:133
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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