LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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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