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

Download CGTCON + dependencies [TGZ] [ZIP] [TXT]

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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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