 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cgecon()

 subroutine cgecon ( character NORM, integer N, complex, dimension( lda, * ) A, integer LDA, real ANORM, real RCOND, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CGECON

Purpose:
``` CGECON estimates the reciprocal of the condition number of a general
complex matrix A, in either the 1-norm or the infinity-norm, using
the LU factorization computed by CGETRF.

An estimate is obtained for norm(inv(A)), and 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] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by CGETRF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [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/(norm(A) * norm(inv(A))).``` [out] WORK ` WORK is COMPLEX array, dimension (2*N)` [out] RWORK ` RWORK is REAL array, dimension (2*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 122 of file cgecon.f.

124*
125* -- LAPACK computational routine --
126* -- LAPACK is a software package provided by Univ. of Tennessee, --
127* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128*
129* .. Scalar Arguments ..
130 CHARACTER NORM
131 INTEGER INFO, LDA, N
132 REAL ANORM, RCOND
133* ..
134* .. Array Arguments ..
135 REAL RWORK( * )
136 COMPLEX A( LDA, * ), WORK( * )
137* ..
138*
139* =====================================================================
140*
141* .. Parameters ..
142 REAL ONE, ZERO
143 parameter( one = 1.0e+0, zero = 0.0e+0 )
144* ..
145* .. Local Scalars ..
146 LOGICAL ONENRM
147 CHARACTER NORMIN
148 INTEGER IX, KASE, KASE1
149 REAL AINVNM, SCALE, SL, SMLNUM, SU
150 COMPLEX ZDUM
151* ..
152* .. Local Arrays ..
153 INTEGER ISAVE( 3 )
154* ..
155* .. External Functions ..
156 LOGICAL LSAME
157 INTEGER ICAMAX
158 REAL SLAMCH
159 EXTERNAL lsame, icamax, slamch
160* ..
161* .. External Subroutines ..
162 EXTERNAL clacn2, clatrs, csrscl, xerbla
163* ..
164* .. Intrinsic Functions ..
165 INTRINSIC abs, aimag, max, real
166* ..
167* .. Statement Functions ..
168 REAL CABS1
169* ..
170* .. Statement Function definitions ..
171 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
172* ..
173* .. Executable Statements ..
174*
175* Test the input parameters.
176*
177 info = 0
178 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
179 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
180 info = -1
181 ELSE IF( n.LT.0 ) THEN
182 info = -2
183 ELSE IF( lda.LT.max( 1, n ) ) THEN
184 info = -4
185 ELSE IF( anorm.LT.zero ) THEN
186 info = -5
187 END IF
188 IF( info.NE.0 ) THEN
189 CALL xerbla( 'CGECON', -info )
190 RETURN
191 END IF
192*
193* Quick return if possible
194*
195 rcond = zero
196 IF( n.EQ.0 ) THEN
197 rcond = one
198 RETURN
199 ELSE IF( anorm.EQ.zero ) THEN
200 RETURN
201 END IF
202*
203 smlnum = slamch( 'Safe minimum' )
204*
205* Estimate the norm of inv(A).
206*
207 ainvnm = zero
208 normin = 'N'
209 IF( onenrm ) THEN
210 kase1 = 1
211 ELSE
212 kase1 = 2
213 END IF
214 kase = 0
215 10 CONTINUE
216 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
217 IF( kase.NE.0 ) THEN
218 IF( kase.EQ.kase1 ) THEN
219*
220* Multiply by inv(L).
221*
222 CALL clatrs( 'Lower', 'No transpose', 'Unit', normin, n, a,
223 \$ lda, work, sl, rwork, info )
224*
225* Multiply by inv(U).
226*
227 CALL clatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
228 \$ a, lda, work, su, rwork( n+1 ), info )
229 ELSE
230*
231* Multiply by inv(U**H).
232*
233 CALL clatrs( 'Upper', 'Conjugate transpose', 'Non-unit',
234 \$ normin, n, a, lda, work, su, rwork( n+1 ),
235 \$ info )
236*
237* Multiply by inv(L**H).
238*
239 CALL clatrs( 'Lower', 'Conjugate transpose', 'Unit', normin,
240 \$ n, a, lda, work, sl, rwork, info )
241 END IF
242*
243* Divide X by 1/(SL*SU) if doing so will not cause overflow.
244*
245 scale = sl*su
246 normin = 'Y'
247 IF( scale.NE.one ) THEN
248 ix = icamax( n, work, 1 )
249 IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
250 \$ GO TO 20
251 CALL csrscl( n, scale, work, 1 )
252 END IF
253 GO TO 10
254 END IF
255*
256* Compute the estimate of the reciprocal condition number.
257*
258 IF( ainvnm.NE.zero )
259 \$ rcond = ( one / ainvnm ) / anorm
260*
261 20 CONTINUE
262 RETURN
263*
264* End of CGECON
265*
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
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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