 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cgtcon()

 subroutine cgtcon ( character NORM, integer N, complex, dimension( * ) DL, complex, dimension( * ) D, complex, dimension( * ) DU, complex, dimension( * ) DU2, integer, dimension( * ) IPIV, real ANORM, real RCOND, complex, dimension( * ) WORK, integer INFO )

CGTCON

Purpose:
``` CGTCON estimates the reciprocal of the condition number of a complex
tridiagonal matrix A using the LU factorization as computed by
CGTTRF.

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] 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] DL ``` DL is COMPLEX array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.``` [in] D ``` D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.``` [in] DU ``` DU is COMPLEX array, dimension (N-1) The (n-1) elements of the first superdiagonal of U.``` [in] DU2 ``` DU2 is COMPLEX array, dimension (N-2) The (n-2) elements of the second superdiagonal of U.``` [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). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.``` [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/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.``` [out] WORK ` WORK is COMPLEX array, dimension (2*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 139 of file cgtcon.f.

141 *
142 * -- LAPACK computational routine --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 *
146 * .. Scalar Arguments ..
147  CHARACTER NORM
148  INTEGER INFO, N
149  REAL ANORM, RCOND
150 * ..
151 * .. Array Arguments ..
152  INTEGER IPIV( * )
153  COMPLEX D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  REAL ONE, ZERO
160  parameter( one = 1.0e+0, zero = 0.0e+0 )
161 * ..
162 * .. Local Scalars ..
163  LOGICAL ONENRM
164  INTEGER I, KASE, KASE1
165  REAL AINVNM
166 * ..
167 * .. Local Arrays ..
168  INTEGER ISAVE( 3 )
169 * ..
170 * .. External Functions ..
171  LOGICAL LSAME
172  EXTERNAL lsame
173 * ..
174 * .. External Subroutines ..
175  EXTERNAL cgttrs, clacn2, xerbla
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC cmplx
179 * ..
180 * .. Executable Statements ..
181 *
182 * Test the input arguments.
183 *
184  info = 0
185  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
186  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
187  info = -1
188  ELSE IF( n.LT.0 ) THEN
189  info = -2
190  ELSE IF( anorm.LT.zero ) THEN
191  info = -8
192  END IF
193  IF( info.NE.0 ) THEN
194  CALL xerbla( 'CGTCON', -info )
195  RETURN
196  END IF
197 *
198 * Quick return if possible
199 *
200  rcond = zero
201  IF( n.EQ.0 ) THEN
202  rcond = one
203  RETURN
204  ELSE IF( anorm.EQ.zero ) THEN
205  RETURN
206  END IF
207 *
208 * Check that D(1:N) is non-zero.
209 *
210  DO 10 i = 1, n
211  IF( d( i ).EQ.cmplx( zero ) )
212  \$ RETURN
213  10 CONTINUE
214 *
215  ainvnm = zero
216  IF( onenrm ) THEN
217  kase1 = 1
218  ELSE
219  kase1 = 2
220  END IF
221  kase = 0
222  20 CONTINUE
223  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
224  IF( kase.NE.0 ) THEN
225  IF( kase.EQ.kase1 ) THEN
226 *
227 * Multiply by inv(U)*inv(L).
228 *
229  CALL cgttrs( 'No transpose', n, 1, dl, d, du, du2, ipiv,
230  \$ work, n, info )
231  ELSE
232 *
233 * Multiply by inv(L**H)*inv(U**H).
234 *
235  CALL cgttrs( 'Conjugate transpose', n, 1, dl, d, du, du2,
236  \$ ipiv, work, n, info )
237  END IF
238  GO TO 20
239  END IF
240 *
241 * Compute the estimate of the reciprocal condition number.
242 *
243  IF( ainvnm.NE.zero )
244  \$ rcond = ( one / ainvnm ) / anorm
245 *
246  RETURN
247 *
248 * End of CGTCON
249 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgttrs(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
CGTTRS
Definition: cgttrs.f:138
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
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