 LAPACK  3.10.0 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```

Definition at line 135 of file ctrcon.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  REAL RCOND
146 * ..
147 * .. Array Arguments ..
148  REAL RWORK( * )
149  COMPLEX A( LDA, * ), WORK( * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  REAL ONE, ZERO
156  parameter( one = 1.0e+0, zero = 0.0e+0 )
157 * ..
158 * .. Local Scalars ..
159  LOGICAL NOUNIT, ONENRM, UPPER
160  CHARACTER NORMIN
161  INTEGER IX, KASE, KASE1
162  REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
163  COMPLEX ZDUM
164 * ..
165 * .. Local Arrays ..
166  INTEGER ISAVE( 3 )
167 * ..
168 * .. External Functions ..
169  LOGICAL LSAME
170  INTEGER ICAMAX
171  REAL CLANTR, SLAMCH
172  EXTERNAL lsame, icamax, clantr, slamch
173 * ..
174 * .. External Subroutines ..
175  EXTERNAL clacn2, clatrs, csrscl, xerbla
176 * ..
177 * .. Intrinsic Functions ..
178  INTRINSIC abs, aimag, max, real
179 * ..
180 * .. Statement Functions ..
181  REAL CABS1
182 * ..
183 * .. Statement Function definitions ..
184  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
185 * ..
186 * .. Executable Statements ..
187 *
188 * Test the input parameters.
189 *
190  info = 0
191  upper = lsame( uplo, 'U' )
192  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
193  nounit = lsame( diag, 'N' )
194 *
195  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
196  info = -1
197  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
198  info = -2
199  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
200  info = -3
201  ELSE IF( n.LT.0 ) THEN
202  info = -4
203  ELSE IF( lda.LT.max( 1, n ) ) THEN
204  info = -6
205  END IF
206  IF( info.NE.0 ) THEN
207  CALL xerbla( 'CTRCON', -info )
208  RETURN
209  END IF
210 *
211 * Quick return if possible
212 *
213  IF( n.EQ.0 ) THEN
214  rcond = one
215  RETURN
216  END IF
217 *
218  rcond = zero
219  smlnum = slamch( 'Safe minimum' )*real( max( 1, n ) )
220 *
221 * Compute the norm of the triangular matrix A.
222 *
223  anorm = clantr( norm, uplo, diag, n, n, a, lda, rwork )
224 *
225 * Continue only if ANORM > 0.
226 *
227  IF( anorm.GT.zero ) THEN
228 *
229 * Estimate the norm of the inverse of A.
230 *
231  ainvnm = zero
232  normin = 'N'
233  IF( onenrm ) THEN
234  kase1 = 1
235  ELSE
236  kase1 = 2
237  END IF
238  kase = 0
239  10 CONTINUE
240  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
241  IF( kase.NE.0 ) THEN
242  IF( kase.EQ.kase1 ) THEN
243 *
244 * Multiply by inv(A).
245 *
246  CALL clatrs( uplo, 'No transpose', diag, normin, n, a,
247  \$ lda, work, scale, rwork, info )
248  ELSE
249 *
250 * Multiply by inv(A**H).
251 *
252  CALL clatrs( uplo, 'Conjugate transpose', diag, normin,
253  \$ n, a, lda, work, scale, rwork, info )
254  END IF
255  normin = 'Y'
256 *
257 * Multiply by 1/SCALE if doing so will not cause overflow.
258 *
259  IF( scale.NE.one ) THEN
260  ix = icamax( n, work, 1 )
261  xnorm = cabs1( work( ix ) )
262  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
263  \$ GO TO 20
264  CALL csrscl( n, scale, work, 1 )
265  END IF
266  GO TO 10
267  END IF
268 *
269 * Compute the estimate of the reciprocal condition number.
270 *
271  IF( ainvnm.NE.zero )
272  \$ rcond = ( one / anorm ) / ainvnm
273  END IF
274 *
275  20 CONTINUE
276  RETURN
277 *
278 * End of CTRCON
279 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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:239
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,...
Definition: clantr.f:142
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:84
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:133
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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