LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zppcon.f
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1*> \brief \b ZPPCON
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zppcon.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER UPLO
25* INTEGER INFO, N
26* DOUBLE PRECISION ANORM, RCOND
27* ..
28* .. Array Arguments ..
29* DOUBLE PRECISION RWORK( * )
30* COMPLEX*16 AP( * ), WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> ZPPCON estimates the reciprocal of the condition number (in the
40*> 1-norm) of a complex Hermitian positive definite packed matrix using
41*> the Cholesky factorization A = U**H*U or A = L*L**H computed by
42*> ZPPTRF.
43*>
44*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
45*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
46*> \endverbatim
47*
48* Arguments:
49* ==========
50*
51*> \param[in] UPLO
52*> \verbatim
53*> UPLO is CHARACTER*1
54*> = 'U': Upper triangle of A is stored;
55*> = 'L': Lower triangle of A is stored.
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*> N is INTEGER
61*> The order of the matrix A. N >= 0.
62*> \endverbatim
63*>
64*> \param[in] AP
65*> \verbatim
66*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
67*> The triangular factor U or L from the Cholesky factorization
68*> A = U**H*U or A = L*L**H, packed columnwise in a linear
69*> array. The j-th column of U or L is stored in the array AP
70*> as follows:
71*> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
72*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
73*> \endverbatim
74*>
75*> \param[in] ANORM
76*> \verbatim
77*> ANORM is DOUBLE PRECISION
78*> The 1-norm (or infinity-norm) of the Hermitian matrix A.
79*> \endverbatim
80*>
81*> \param[out] RCOND
82*> \verbatim
83*> RCOND is DOUBLE PRECISION
84*> The reciprocal of the condition number of the matrix A,
85*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
86*> estimate of the 1-norm of inv(A) computed in this routine.
87*> \endverbatim
88*>
89*> \param[out] WORK
90*> \verbatim
91*> WORK is COMPLEX*16 array, dimension (2*N)
92*> \endverbatim
93*>
94*> \param[out] RWORK
95*> \verbatim
96*> RWORK is DOUBLE PRECISION array, dimension (N)
97*> \endverbatim
98*>
99*> \param[out] INFO
100*> \verbatim
101*> INFO is INTEGER
102*> = 0: successful exit
103*> < 0: if INFO = -i, the i-th argument had an illegal value
104*> \endverbatim
105*
106* Authors:
107* ========
108*
109*> \author Univ. of Tennessee
110*> \author Univ. of California Berkeley
111*> \author Univ. of Colorado Denver
112*> \author NAG Ltd.
113*
114*> \ingroup ppcon
115*
116* =====================================================================
117 SUBROUTINE zppcon( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
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 DOUBLE PRECISION ANORM, RCOND
127* ..
128* .. Array Arguments ..
129 DOUBLE PRECISION RWORK( * )
130 COMPLEX*16 AP( * ), WORK( * )
131* ..
132*
133* =====================================================================
134*
135* .. Parameters ..
136 DOUBLE PRECISION ONE, ZERO
137 parameter( one = 1.0d+0, zero = 0.0d+0 )
138* ..
139* .. Local Scalars ..
140 LOGICAL UPPER
141 CHARACTER NORMIN
142 INTEGER IX, KASE
143 DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
144 COMPLEX*16 ZDUM
145* ..
146* .. Local Arrays ..
147 INTEGER ISAVE( 3 )
148* ..
149* .. External Functions ..
150 LOGICAL LSAME
151 INTEGER IZAMAX
152 DOUBLE PRECISION DLAMCH
153 EXTERNAL lsame, izamax, dlamch
154* ..
155* .. External Subroutines ..
156 EXTERNAL xerbla, zdrscl, zlacn2, zlatps
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC abs, dble, dimag
160* ..
161* .. Statement Functions ..
162 DOUBLE PRECISION CABS1
163* ..
164* .. Statement Function definitions ..
165 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( 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( 'ZPPCON', -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 = dlamch( 'Safe minimum' )
196*
197* Estimate the 1-norm of the inverse.
198*
199 kase = 0
200 normin = 'N'
201 10 CONTINUE
202 CALL zlacn2( 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 zlatps( '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 zlatps( 'Upper', 'No transpose', 'Non-unit', normin, n,
215 \$ ap, work, scaleu, rwork, info )
216 ELSE
217*
218* Multiply by inv(L).
219*
220 CALL zlatps( '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 zlatps( '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 = izamax( n, work, 1 )
235 IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
236 \$ GO TO 20
237 CALL zdrscl( 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 ZPPCON
251*
252 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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
subroutine zlatps(uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
ZLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition zlatps.f:231
subroutine zppcon(uplo, n, ap, anorm, rcond, work, rwork, info)
ZPPCON
Definition zppcon.f:118
subroutine zdrscl(n, sa, sx, incx)
ZDRSCL multiplies a vector by the reciprocal of a real scalar.
Definition zdrscl.f:84