LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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```
Date
November 2011

Definition at line 139 of file dtrcon.f.

139 *
140 * -- LAPACK computational routine (version 3.4.0) --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 * November 2011
144 *
145 * .. Scalar Arguments ..
146  CHARACTER diag, norm, uplo
147  INTEGER info, lda, n
148  DOUBLE PRECISION rcond
149 * ..
150 * .. Array Arguments ..
151  INTEGER iwork( * )
152  DOUBLE PRECISION a( lda, * ), work( * )
153 * ..
154 *
155 * =====================================================================
156 *
157 * .. Parameters ..
158  DOUBLE PRECISION one, zero
159  parameter ( one = 1.0d+0, zero = 0.0d+0 )
160 * ..
161 * .. Local Scalars ..
162  LOGICAL nounit, onenrm, upper
163  CHARACTER normin
164  INTEGER ix, kase, kase1
165  DOUBLE PRECISION ainvnm, anorm, scale, smlnum, xnorm
166 * ..
167 * .. Local Arrays ..
168  INTEGER isave( 3 )
169 * ..
170 * .. External Functions ..
171  LOGICAL lsame
172  INTEGER idamax
173  DOUBLE PRECISION dlamch, dlantr
174  EXTERNAL lsame, idamax, dlamch, dlantr
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL dlacn2, dlatrs, drscl, xerbla
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC abs, dble, max
181 * ..
182 * .. Executable Statements ..
183 *
184 * Test the input parameters.
185 *
186  info = 0
187  upper = lsame( uplo, 'U' )
188  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
189  nounit = lsame( diag, 'N' )
190 *
191  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
192  info = -1
193  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
194  info = -2
195  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
196  info = -3
197  ELSE IF( n.LT.0 ) THEN
198  info = -4
199  ELSE IF( lda.LT.max( 1, n ) ) THEN
200  info = -6
201  END IF
202  IF( info.NE.0 ) THEN
203  CALL xerbla( 'DTRCON', -info )
204  RETURN
205  END IF
206 *
207 * Quick return if possible
208 *
209  IF( n.EQ.0 ) THEN
210  rcond = one
211  RETURN
212  END IF
213 *
214  rcond = zero
215  smlnum = dlamch( 'Safe minimum' )*dble( max( 1, n ) )
216 *
217 * Compute the norm of the triangular matrix A.
218 *
219  anorm = dlantr( norm, uplo, diag, n, n, a, lda, work )
220 *
221 * Continue only if ANORM > 0.
222 *
223  IF( anorm.GT.zero ) THEN
224 *
225 * Estimate the norm of the inverse of A.
226 *
227  ainvnm = zero
228  normin = 'N'
229  IF( onenrm ) THEN
230  kase1 = 1
231  ELSE
232  kase1 = 2
233  END IF
234  kase = 0
235  10 CONTINUE
236  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
237  IF( kase.NE.0 ) THEN
238  IF( kase.EQ.kase1 ) THEN
239 *
240 * Multiply by inv(A).
241 *
242  CALL dlatrs( uplo, 'No transpose', diag, normin, n, a,
243  \$ lda, work, scale, work( 2*n+1 ), info )
244  ELSE
245 *
246 * Multiply by inv(A**T).
247 *
248  CALL dlatrs( uplo, 'Transpose', diag, normin, n, a, lda,
249  \$ work, scale, work( 2*n+1 ), info )
250  END IF
251  normin = 'Y'
252 *
253 * Multiply by 1/SCALE if doing so will not cause overflow.
254 *
255  IF( scale.NE.one ) THEN
256  ix = idamax( n, work, 1 )
257  xnorm = abs( work( ix ) )
258  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
259  \$ GO TO 20
260  CALL drscl( n, scale, work, 1 )
261  END IF
262  GO TO 10
263  END IF
264 *
265 * Compute the estimate of the reciprocal condition number.
266 *
267  IF( ainvnm.NE.zero )
268  \$ rcond = ( one / anorm ) / ainvnm
269  END IF
270 *
271  20 CONTINUE
272  RETURN
273 *
274 * End of DTRCON
275 *
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:53
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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:240
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:86
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, or the element of largest absolute value of a trapezoidal or triangular matrix.
Definition: dlantr.f:143
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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:138

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