LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ctrcon()

 subroutine ctrcon ( character NORM, character UPLO, character DIAG, integer N, complex, dimension( lda, * ) A, integer LDA, real RCOND, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CTRCON

Purpose:
``` CTRCON 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 COMPLEX 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 REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).``` [out] WORK ` WORK is COMPLEX array, dimension (2*N)` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Date
December 2016

Definition at line 139 of file ctrcon.f.

139 *
140 * -- LAPACK computational routine (version 3.7.0) --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 * December 2016
144 *
145 * .. Scalar Arguments ..
146  CHARACTER diag, norm, uplo
147  INTEGER info, lda, n
148  REAL rcond
149 * ..
150 * .. Array Arguments ..
151  REAL rwork( * )
152  COMPLEX a( lda, * ), work( * )
153 * ..
154 *
155 * =====================================================================
156 *
157 * .. Parameters ..
158  REAL one, zero
159  parameter( one = 1.0e+0, zero = 0.0e+0 )
160 * ..
161 * .. Local Scalars ..
162  LOGICAL nounit, onenrm, upper
163  CHARACTER normin
164  INTEGER ix, kase, kase1
165  REAL ainvnm, anorm, scale, smlnum, xnorm
166  COMPLEX zdum
167 * ..
168 * .. Local Arrays ..
169  INTEGER isave( 3 )
170 * ..
171 * .. External Functions ..
172  LOGICAL lsame
173  INTEGER icamax
174  REAL clantr, slamch
175  EXTERNAL lsame, icamax, clantr, slamch
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL clacn2, clatrs, csrscl, xerbla
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC abs, aimag, max, real
182 * ..
183 * .. Statement Functions ..
184  REAL cabs1
185 * ..
186 * .. Statement Function definitions ..
187  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
188 * ..
189 * .. Executable Statements ..
190 *
191 * Test the input parameters.
192 *
193  info = 0
194  upper = lsame( uplo, 'U' )
195  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
196  nounit = lsame( diag, 'N' )
197 *
198  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
199  info = -1
200  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
201  info = -2
202  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
203  info = -3
204  ELSE IF( n.LT.0 ) THEN
205  info = -4
206  ELSE IF( lda.LT.max( 1, n ) ) THEN
207  info = -6
208  END IF
209  IF( info.NE.0 ) THEN
210  CALL xerbla( 'CTRCON', -info )
211  RETURN
212  END IF
213 *
214 * Quick return if possible
215 *
216  IF( n.EQ.0 ) THEN
217  rcond = one
218  RETURN
219  END IF
220 *
221  rcond = zero
222  smlnum = slamch( 'Safe minimum' )*REAL( MAX( 1, N ) )
223 *
224 * Compute the norm of the triangular matrix A.
225 *
226  anorm = clantr( norm, uplo, diag, n, n, a, lda, rwork )
227 *
228 * Continue only if ANORM > 0.
229 *
230  IF( anorm.GT.zero ) THEN
231 *
232 * Estimate the norm of the inverse of A.
233 *
234  ainvnm = zero
235  normin = 'N'
236  IF( onenrm ) THEN
237  kase1 = 1
238  ELSE
239  kase1 = 2
240  END IF
241  kase = 0
242  10 CONTINUE
243  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
244  IF( kase.NE.0 ) THEN
245  IF( kase.EQ.kase1 ) THEN
246 *
247 * Multiply by inv(A).
248 *
249  CALL clatrs( uplo, 'No transpose', diag, normin, n, a,
250  \$ lda, work, scale, rwork, info )
251  ELSE
252 *
253 * Multiply by inv(A**H).
254 *
255  CALL clatrs( uplo, 'Conjugate transpose', diag, normin,
256  \$ n, a, lda, work, scale, rwork, info )
257  END IF
258  normin = 'Y'
259 *
260 * Multiply by 1/SCALE if doing so will not cause overflow.
261 *
262  IF( scale.NE.one ) THEN
263  ix = icamax( n, work, 1 )
264  xnorm = cabs1( work( ix ) )
265  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
266  \$ GO TO 20
267  CALL csrscl( n, scale, work, 1 )
268  END IF
269  GO TO 10
270  END IF
271 *
272 * Compute the estimate of the reciprocal condition number.
273 *
274  IF( ainvnm.NE.zero )
275  \$ rcond = ( one / anorm ) / ainvnm
276  END IF
277 *
278  20 CONTINUE
279  RETURN
280 *
281 * End of CTRCON
282 *
subroutine clacn2(N, V, X, EST, KASE, ISAVE)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: clacn2.f:135
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:73
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine clatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
CLATRS solves a triangular system of equations with the scale factor set to prevent overflow...
Definition: clatrs.f:241
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:86
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
real function clantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
CLANTR 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: clantr.f:144
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