LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dgtcon()

subroutine dgtcon ( character  NORM,
integer  N,
double precision, dimension( * )  DL,
double precision, dimension( * )  D,
double precision, dimension( * )  DU,
double precision, dimension( * )  DU2,
integer, dimension( * )  IPIV,
double precision  ANORM,
double precision  RCOND,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

DGTCON

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

Purpose:
 DGTCON estimates the reciprocal of the condition number of a real
 tridiagonal matrix A using the LU factorization as computed by
 DGTTRF.

 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 DOUBLE PRECISION array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A as computed by DGTTRF.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.
[in]DU
          DU is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) elements of the first superdiagonal of U.
[in]DU2
          DU2 is DOUBLE PRECISION 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 DOUBLE PRECISION
          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 DOUBLE PRECISION
          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 DOUBLE PRECISION array, dimension (2*N)
[out]IWORK
          IWORK is INTEGER array, dimension (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 144 of file dgtcon.f.

146 *
147 * -- LAPACK computational routine --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 *
151 * .. Scalar Arguments ..
152  CHARACTER NORM
153  INTEGER INFO, N
154  DOUBLE PRECISION ANORM, RCOND
155 * ..
156 * .. Array Arguments ..
157  INTEGER IPIV( * ), IWORK( * )
158  DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
159 * ..
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164  DOUBLE PRECISION ONE, ZERO
165  parameter( one = 1.0d+0, zero = 0.0d+0 )
166 * ..
167 * .. Local Scalars ..
168  LOGICAL ONENRM
169  INTEGER I, KASE, KASE1
170  DOUBLE PRECISION AINVNM
171 * ..
172 * .. Local Arrays ..
173  INTEGER ISAVE( 3 )
174 * ..
175 * .. External Functions ..
176  LOGICAL LSAME
177  EXTERNAL lsame
178 * ..
179 * .. External Subroutines ..
180  EXTERNAL dgttrs, dlacn2, xerbla
181 * ..
182 * .. Executable Statements ..
183 *
184 * Test the input arguments.
185 *
186  info = 0
187  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
188  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
189  info = -1
190  ELSE IF( n.LT.0 ) THEN
191  info = -2
192  ELSE IF( anorm.LT.zero ) THEN
193  info = -8
194  END IF
195  IF( info.NE.0 ) THEN
196  CALL xerbla( 'DGTCON', -info )
197  RETURN
198  END IF
199 *
200 * Quick return if possible
201 *
202  rcond = zero
203  IF( n.EQ.0 ) THEN
204  rcond = one
205  RETURN
206  ELSE IF( anorm.EQ.zero ) THEN
207  RETURN
208  END IF
209 *
210 * Check that D(1:N) is non-zero.
211 *
212  DO 10 i = 1, n
213  IF( d( i ).EQ.zero )
214  $ RETURN
215  10 CONTINUE
216 *
217  ainvnm = zero
218  IF( onenrm ) THEN
219  kase1 = 1
220  ELSE
221  kase1 = 2
222  END IF
223  kase = 0
224  20 CONTINUE
225  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
226  IF( kase.NE.0 ) THEN
227  IF( kase.EQ.kase1 ) THEN
228 *
229 * Multiply by inv(U)*inv(L).
230 *
231  CALL dgttrs( 'No transpose', n, 1, dl, d, du, du2, ipiv,
232  $ work, n, info )
233  ELSE
234 *
235 * Multiply by inv(L**T)*inv(U**T).
236 *
237  CALL dgttrs( 'Transpose', n, 1, dl, d, du, du2, ipiv, work,
238  $ n, info )
239  END IF
240  GO TO 20
241  END IF
242 *
243 * Compute the estimate of the reciprocal condition number.
244 *
245  IF( ainvnm.NE.zero )
246  $ rcond = ( one / ainvnm ) / anorm
247 *
248  RETURN
249 *
250 * End of DGTCON
251 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dgttrs(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
DGTTRS
Definition: dgttrs.f:138
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:136
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