LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sgtcon()

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

SGTCON

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

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 REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.``` [in] D ``` D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.``` [in] DU ``` DU is REAL array, dimension (N-1) The (n-1) elements of the first superdiagonal of U.``` [in] DU2 ``` DU2 is REAL 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 REAL 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 sgtcon.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  REAL ANORM, RCOND
155 * ..
156 * .. Array Arguments ..
157  INTEGER IPIV( * ), IWORK( * )
158  REAL D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
159 * ..
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164  REAL ONE, ZERO
165  parameter( one = 1.0e+0, zero = 0.0e+0 )
166 * ..
167 * .. Local Scalars ..
168  LOGICAL ONENRM
169  INTEGER I, KASE, KASE1
170  REAL 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 sgttrs, slacn2, 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( 'SGTCON', -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 slacn2( 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 sgttrs( '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 sgttrs( '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 SGTCON
251 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sgttrs(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
SGTTRS
Definition: sgttrs.f:138
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
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