LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ cppcon()

 subroutine cppcon ( character uplo, integer n, complex, dimension( * ) ap, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info )

CPPCON

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

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] AP ``` AP is COMPLEX array, dimension (N*(N+1)/2) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=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```

Definition at line 117 of file cppcon.f.

118*
119* -- LAPACK computational routine --
120* -- LAPACK is a software package provided by Univ. of Tennessee, --
121* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
122*
123* .. Scalar Arguments ..
124 CHARACTER UPLO
125 INTEGER INFO, N
126 REAL ANORM, RCOND
127* ..
128* .. Array Arguments ..
129 REAL RWORK( * )
130 COMPLEX AP( * ), WORK( * )
131* ..
132*
133* =====================================================================
134*
135* .. Parameters ..
136 REAL ONE, ZERO
137 parameter( one = 1.0e+0, zero = 0.0e+0 )
138* ..
139* .. Local Scalars ..
140 LOGICAL UPPER
141 CHARACTER NORMIN
142 INTEGER IX, KASE
143 REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
144 COMPLEX ZDUM
145* ..
146* .. Local Arrays ..
147 INTEGER ISAVE( 3 )
148* ..
149* .. External Functions ..
150 LOGICAL LSAME
151 INTEGER ICAMAX
152 REAL SLAMCH
153 EXTERNAL lsame, icamax, slamch
154* ..
155* .. External Subroutines ..
156 EXTERNAL clacn2, clatps, csrscl, xerbla
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC abs, aimag, real
160* ..
161* .. Statement Functions ..
162 REAL CABS1
163* ..
164* .. Statement Function definitions ..
165 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
166* ..
167* .. Executable Statements ..
168*
169* Test the input parameters.
170*
171 info = 0
172 upper = lsame( uplo, 'U' )
173 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
174 info = -1
175 ELSE IF( n.LT.0 ) THEN
176 info = -2
177 ELSE IF( anorm.LT.zero ) THEN
178 info = -4
179 END IF
180 IF( info.NE.0 ) THEN
181 CALL xerbla( 'CPPCON', -info )
182 RETURN
183 END IF
184*
185* Quick return if possible
186*
187 rcond = zero
188 IF( n.EQ.0 ) THEN
189 rcond = one
190 RETURN
191 ELSE IF( anorm.EQ.zero ) THEN
192 RETURN
193 END IF
194*
195 smlnum = slamch( 'Safe minimum' )
196*
197* Estimate the 1-norm of the inverse.
198*
199 kase = 0
200 normin = 'N'
201 10 CONTINUE
202 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
203 IF( kase.NE.0 ) THEN
204 IF( upper ) THEN
205*
206* Multiply by inv(U**H).
207*
208 CALL clatps( 'Upper', 'Conjugate transpose', 'Non-unit',
209 \$ normin, n, ap, work, scalel, rwork, info )
210 normin = 'Y'
211*
212* Multiply by inv(U).
213*
214 CALL clatps( 'Upper', 'No transpose', 'Non-unit', normin, n,
215 \$ ap, work, scaleu, rwork, info )
216 ELSE
217*
218* Multiply by inv(L).
219*
220 CALL clatps( 'Lower', 'No transpose', 'Non-unit', normin, n,
221 \$ ap, work, scalel, rwork, info )
222 normin = 'Y'
223*
224* Multiply by inv(L**H).
225*
226 CALL clatps( 'Lower', 'Conjugate transpose', 'Non-unit',
227 \$ normin, n, ap, work, scaleu, rwork, info )
228 END IF
229*
230* Multiply by 1/SCALE if doing so will not cause overflow.
231*
232 scale = scalel*scaleu
233 IF( scale.NE.one ) THEN
234 ix = icamax( n, work, 1 )
235 IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
236 \$ GO TO 20
237 CALL csrscl( n, scale, work, 1 )
238 END IF
239 GO TO 10
240 END IF
241*
242* Compute the estimate of the reciprocal condition number.
243*
244 IF( ainvnm.NE.zero )
245 \$ rcond = ( one / ainvnm ) / anorm
246*
247 20 CONTINUE
248 RETURN
249*
250* End of CPPCON
251*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function icamax(n, cx, incx)
ICAMAX
Definition icamax.f:71
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
subroutine clatps(uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
CLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition clatps.f:231
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine csrscl(n, sa, sx, incx)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition csrscl.f:84
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