LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine cpocon ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real ANORM, real RCOND, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CPOCON

Purpose:
``` CPOCON estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite matrix using the
Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] ANORM ``` ANORM is REAL The 1-norm (or infinity-norm) of the Hermitian matrix A.``` [out] RCOND ``` RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.``` [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
November 2011

Definition at line 123 of file cpocon.f.

123 *
124 * -- LAPACK computational routine (version 3.4.0) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * November 2011
128 *
129 * .. Scalar Arguments ..
130  CHARACTER uplo
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 upper
147  CHARACTER normin
148  INTEGER ix, kase
149  REAL ainvnm, scale, scalel, scaleu, smlnum
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  upper = lsame( uplo, 'U' )
179  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) 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( 'CPOCON', -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 1-norm of inv(A).
206 *
207  kase = 0
208  normin = 'N'
209  10 CONTINUE
210  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
211  IF( kase.NE.0 ) THEN
212  IF( upper ) THEN
213 *
214 * Multiply by inv(U**H).
215 *
216  CALL clatrs( 'Upper', 'Conjugate transpose', 'Non-unit',
217  \$ normin, n, a, lda, work, scalel, rwork, info )
218  normin = 'Y'
219 *
220 * Multiply by inv(U).
221 *
222  CALL clatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
223  \$ a, lda, work, scaleu, rwork, info )
224  ELSE
225 *
226 * Multiply by inv(L).
227 *
228  CALL clatrs( 'Lower', 'No transpose', 'Non-unit', normin, n,
229  \$ a, lda, work, scalel, rwork, info )
230  normin = 'Y'
231 *
232 * Multiply by inv(L**H).
233 *
234  CALL clatrs( 'Lower', 'Conjugate transpose', 'Non-unit',
235  \$ normin, n, a, lda, work, scaleu, rwork, info )
236  END IF
237 *
238 * Multiply by 1/SCALE if doing so will not cause overflow.
239 *
240  scale = scalel*scaleu
241  IF( scale.NE.one ) THEN
242  ix = icamax( n, work, 1 )
243  IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
244  \$ GO TO 20
245  CALL csrscl( n, scale, work, 1 )
246  END IF
247  GO TO 10
248  END IF
249 *
250 * Compute the estimate of the reciprocal condition number.
251 *
252  IF( ainvnm.NE.zero )
253  \$ rcond = ( one / ainvnm ) / anorm
254 *
255  20 CONTINUE
256  RETURN
257 *
258 * End of CPOCON
259 *
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 xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:53
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:86
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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

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