LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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```
Date
November 2011

Definition at line 145 of file ctbcon.f.

145 *
146 * -- LAPACK computational routine (version 3.4.0) --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 * November 2011
150 *
151 * .. Scalar Arguments ..
152  CHARACTER diag, norm, uplo
153  INTEGER info, kd, ldab, n
154  REAL rcond
155 * ..
156 * .. Array Arguments ..
157  REAL rwork( * )
158  COMPLEX 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 nounit, onenrm, upper
169  CHARACTER normin
170  INTEGER ix, kase, kase1
171  REAL ainvnm, anorm, scale, smlnum, xnorm
172  COMPLEX zdum
173 * ..
174 * .. Local Arrays ..
175  INTEGER isave( 3 )
176 * ..
177 * .. External Functions ..
178  LOGICAL lsame
179  INTEGER icamax
180  REAL clantb, slamch
181  EXTERNAL lsame, icamax, clantb, slamch
182 * ..
183 * .. External Subroutines ..
184  EXTERNAL clacn2, clatbs, csrscl, xerbla
185 * ..
186 * .. Intrinsic Functions ..
187  INTRINSIC abs, aimag, max, real
188 * ..
189 * .. Statement Functions ..
190  REAL cabs1
191 * ..
192 * .. Statement Function definitions ..
193  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
194 * ..
195 * .. Executable Statements ..
196 *
197 * Test the input parameters.
198 *
199  info = 0
200  upper = lsame( uplo, 'U' )
201  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
202  nounit = lsame( diag, 'N' )
203 *
204  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
205  info = -1
206  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
207  info = -2
208  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
209  info = -3
210  ELSE IF( n.LT.0 ) THEN
211  info = -4
212  ELSE IF( kd.LT.0 ) THEN
213  info = -5
214  ELSE IF( ldab.LT.kd+1 ) THEN
215  info = -7
216  END IF
217  IF( info.NE.0 ) THEN
218  CALL xerbla( 'CTBCON', -info )
219  RETURN
220  END IF
221 *
222 * Quick return if possible
223 *
224  IF( n.EQ.0 ) THEN
225  rcond = one
226  RETURN
227  END IF
228 *
229  rcond = zero
230  smlnum = slamch( 'Safe minimum' )*REAL( MAX( N, 1 ) )
231 *
232 * Compute the 1-norm of the triangular matrix A or A**H.
233 *
234  anorm = clantb( norm, uplo, diag, n, kd, ab, ldab, rwork )
235 *
236 * Continue only if ANORM > 0.
237 *
238  IF( anorm.GT.zero ) THEN
239 *
240 * Estimate the 1-norm of the inverse of A.
241 *
242  ainvnm = zero
243  normin = 'N'
244  IF( onenrm ) THEN
245  kase1 = 1
246  ELSE
247  kase1 = 2
248  END IF
249  kase = 0
250  10 CONTINUE
251  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
252  IF( kase.NE.0 ) THEN
253  IF( kase.EQ.kase1 ) THEN
254 *
255 * Multiply by inv(A).
256 *
257  CALL clatbs( uplo, 'No transpose', diag, normin, n, kd,
258  \$ ab, ldab, work, scale, rwork, info )
259  ELSE
260 *
261 * Multiply by inv(A**H).
262 *
263  CALL clatbs( uplo, 'Conjugate transpose', diag, normin,
264  \$ n, kd, ab, ldab, work, scale, rwork, info )
265  END IF
266  normin = 'Y'
267 *
268 * Multiply by 1/SCALE if doing so will not cause overflow.
269 *
270  IF( scale.NE.one ) THEN
271  ix = icamax( n, work, 1 )
272  xnorm = cabs1( work( ix ) )
273  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
274  \$ GO TO 20
275  CALL csrscl( n, scale, work, 1 )
276  END IF
277  GO TO 10
278  END IF
279 *
280 * Compute the estimate of the reciprocal condition number.
281 *
282  IF( ainvnm.NE.zero )
283  \$ rcond = ( one / anorm ) / ainvnm
284  END IF
285 *
286  20 CONTINUE
287  RETURN
288 *
289 * End of CTBCON
290 *
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:245
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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, or the element of largest absolute value of a triangular band matrix.
Definition: clantb.f:143
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:53
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:86
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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:135

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