LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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

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```

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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