LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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◆ zpocon()

 subroutine zpocon ( character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info )

ZPOCON

Purpose:
``` ZPOCON 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 ZPOTRF.

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*16 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 ZPOTRF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] ANORM ``` ANORM is DOUBLE PRECISION The 1-norm (or infinity-norm) of the Hermitian matrix A.``` [out] RCOND ``` RCOND is DOUBLE PRECISION 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*16 array, dimension (2*N)` [out] RWORK ` RWORK is DOUBLE PRECISION 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 119 of file zpocon.f.

121*
122* -- LAPACK computational routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER UPLO
128 INTEGER INFO, LDA, N
129 DOUBLE PRECISION ANORM, RCOND
130* ..
131* .. Array Arguments ..
132 DOUBLE PRECISION RWORK( * )
133 COMPLEX*16 A( LDA, * ), WORK( * )
134* ..
135*
136* =====================================================================
137*
138* .. Parameters ..
139 DOUBLE PRECISION ONE, ZERO
140 parameter( one = 1.0d+0, zero = 0.0d+0 )
141* ..
142* .. Local Scalars ..
143 LOGICAL UPPER
144 CHARACTER NORMIN
145 INTEGER IX, KASE
146 DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147 COMPLEX*16 ZDUM
148* ..
149* .. Local Arrays ..
150 INTEGER ISAVE( 3 )
151* ..
152* .. External Functions ..
153 LOGICAL LSAME
154 INTEGER IZAMAX
155 DOUBLE PRECISION DLAMCH
156 EXTERNAL lsame, izamax, dlamch
157* ..
158* .. External Subroutines ..
159 EXTERNAL xerbla, zdrscl, zlacn2, zlatrs
160* ..
161* .. Intrinsic Functions ..
162 INTRINSIC abs, dble, dimag, max
163* ..
164* .. Statement Functions ..
165 DOUBLE PRECISION CABS1
166* ..
167* .. Statement Function definitions ..
168 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
169* ..
170* .. Executable Statements ..
171*
172* Test the input parameters.
173*
174 info = 0
175 upper = lsame( uplo, 'U' )
176 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
177 info = -1
178 ELSE IF( n.LT.0 ) THEN
179 info = -2
180 ELSE IF( lda.LT.max( 1, n ) ) THEN
181 info = -4
182 ELSE IF( anorm.LT.zero ) THEN
183 info = -5
184 END IF
185 IF( info.NE.0 ) THEN
186 CALL xerbla( 'ZPOCON', -info )
187 RETURN
188 END IF
189*
190* Quick return if possible
191*
192 rcond = zero
193 IF( n.EQ.0 ) THEN
194 rcond = one
195 RETURN
196 ELSE IF( anorm.EQ.zero ) THEN
197 RETURN
198 END IF
199*
200 smlnum = dlamch( 'Safe minimum' )
201*
202* Estimate the 1-norm of inv(A).
203*
204 kase = 0
205 normin = 'N'
206 10 CONTINUE
207 CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
208 IF( kase.NE.0 ) THEN
209 IF( upper ) THEN
210*
211* Multiply by inv(U**H).
212*
213 CALL zlatrs( 'Upper', 'Conjugate transpose', 'Non-unit',
214 \$ normin, n, a, lda, work, scalel, rwork, info )
215 normin = 'Y'
216*
217* Multiply by inv(U).
218*
219 CALL zlatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
220 \$ a, lda, work, scaleu, rwork, info )
221 ELSE
222*
223* Multiply by inv(L).
224*
225 CALL zlatrs( 'Lower', 'No transpose', 'Non-unit', normin, n,
226 \$ a, lda, work, scalel, rwork, info )
227 normin = 'Y'
228*
229* Multiply by inv(L**H).
230*
231 CALL zlatrs( 'Lower', 'Conjugate transpose', 'Non-unit',
232 \$ normin, n, a, lda, work, scaleu, rwork, info )
233 END IF
234*
235* Multiply by 1/SCALE if doing so will not cause overflow.
236*
237 scale = scalel*scaleu
238 IF( scale.NE.one ) THEN
239 ix = izamax( n, work, 1 )
240 IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
241 \$ GO TO 20
242 CALL zdrscl( n, scale, work, 1 )
243 END IF
244 GO TO 10
245 END IF
246*
247* Compute the estimate of the reciprocal condition number.
248*
249 IF( ainvnm.NE.zero )
250 \$ rcond = ( one / ainvnm ) / anorm
251*
252 20 CONTINUE
253 RETURN
254*
255* End of ZPOCON
256*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function izamax(n, zx, incx)
IZAMAX
Definition izamax.f:71
subroutine zlacn2(n, v, x, est, kase, isave)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition zlacn2.f:133
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
subroutine zlatrs(uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info)
ZLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition zlatrs.f:239
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine zdrscl(n, sa, sx, incx)
ZDRSCL multiplies a vector by the reciprocal of a real scalar.
Definition zdrscl.f:84
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