 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dtrcon()

 subroutine dtrcon ( character NORM, character UPLO, character DIAG, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision RCOND, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

DTRCON

Purpose:
``` DTRCON estimates the reciprocal of the condition number of a
triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * 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] UPLO ``` UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.``` [in] DIAG ``` DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (3*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 135 of file dtrcon.f.

137 *
138 * -- LAPACK computational routine --
139 * -- LAPACK is a software package provided by Univ. of Tennessee, --
140 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141 *
142 * .. Scalar Arguments ..
143  CHARACTER DIAG, NORM, UPLO
144  INTEGER INFO, LDA, N
145  DOUBLE PRECISION RCOND
146 * ..
147 * .. Array Arguments ..
148  INTEGER IWORK( * )
149  DOUBLE PRECISION A( LDA, * ), WORK( * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  DOUBLE PRECISION ONE, ZERO
156  parameter( one = 1.0d+0, zero = 0.0d+0 )
157 * ..
158 * .. Local Scalars ..
159  LOGICAL NOUNIT, ONENRM, UPPER
160  CHARACTER NORMIN
161  INTEGER IX, KASE, KASE1
162  DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
163 * ..
164 * .. Local Arrays ..
165  INTEGER ISAVE( 3 )
166 * ..
167 * .. External Functions ..
168  LOGICAL LSAME
169  INTEGER IDAMAX
170  DOUBLE PRECISION DLAMCH, DLANTR
171  EXTERNAL lsame, idamax, dlamch, dlantr
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL dlacn2, dlatrs, drscl, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, dble, max
178 * ..
179 * .. Executable Statements ..
180 *
181 * Test the input parameters.
182 *
183  info = 0
184  upper = lsame( uplo, 'U' )
185  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
186  nounit = lsame( diag, 'N' )
187 *
188  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
189  info = -1
190  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
191  info = -2
192  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
193  info = -3
194  ELSE IF( n.LT.0 ) THEN
195  info = -4
196  ELSE IF( lda.LT.max( 1, n ) ) THEN
197  info = -6
198  END IF
199  IF( info.NE.0 ) THEN
200  CALL xerbla( 'DTRCON', -info )
201  RETURN
202  END IF
203 *
204 * Quick return if possible
205 *
206  IF( n.EQ.0 ) THEN
207  rcond = one
208  RETURN
209  END IF
210 *
211  rcond = zero
212  smlnum = dlamch( 'Safe minimum' )*dble( max( 1, n ) )
213 *
214 * Compute the norm of the triangular matrix A.
215 *
216  anorm = dlantr( norm, uplo, diag, n, n, a, lda, work )
217 *
218 * Continue only if ANORM > 0.
219 *
220  IF( anorm.GT.zero ) THEN
221 *
222 * Estimate the norm of the inverse of A.
223 *
224  ainvnm = zero
225  normin = 'N'
226  IF( onenrm ) THEN
227  kase1 = 1
228  ELSE
229  kase1 = 2
230  END IF
231  kase = 0
232  10 CONTINUE
233  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
234  IF( kase.NE.0 ) THEN
235  IF( kase.EQ.kase1 ) THEN
236 *
237 * Multiply by inv(A).
238 *
239  CALL dlatrs( uplo, 'No transpose', diag, normin, n, a,
240  \$ lda, work, scale, work( 2*n+1 ), info )
241  ELSE
242 *
243 * Multiply by inv(A**T).
244 *
245  CALL dlatrs( uplo, 'Transpose', diag, normin, n, a, lda,
246  \$ work, scale, work( 2*n+1 ), info )
247  END IF
248  normin = 'Y'
249 *
250 * Multiply by 1/SCALE if doing so will not cause overflow.
251 *
252  IF( scale.NE.one ) THEN
253  ix = idamax( n, work, 1 )
254  xnorm = abs( work( ix ) )
255  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
256  \$ GO TO 20
257  CALL drscl( n, scale, work, 1 )
258  END IF
259  GO TO 10
260  END IF
261 *
262 * Compute the estimate of the reciprocal condition number.
263 *
264  IF( ainvnm.NE.zero )
265  \$ rcond = ( one / anorm ) / ainvnm
266  END IF
267 *
268  20 CONTINUE
269  RETURN
270 *
271 * End of DTRCON
272 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:84
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
subroutine dlatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
DLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: dlatrs.f:238
double precision function dlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlantr.f:141
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