LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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chpcon.f
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1*> \brief \b CHPCON
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chpcon.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chpcon.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chpcon.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER UPLO
25* INTEGER INFO, N
26* REAL ANORM, RCOND
27* ..
28* .. Array Arguments ..
29* INTEGER IPIV( * )
30* COMPLEX AP( * ), WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> CHPCON estimates the reciprocal of the condition number of a complex
40*> Hermitian packed matrix A using the factorization A = U*D*U**H or
41*> A = L*D*L**H computed by CHPTRF.
42*>
43*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
44*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
45*> \endverbatim
46*
47* Arguments:
48* ==========
49*
50*> \param[in] UPLO
51*> \verbatim
52*> UPLO is CHARACTER*1
53*> Specifies whether the details of the factorization are stored
54*> as an upper or lower triangular matrix.
55*> = 'U': Upper triangular, form is A = U*D*U**H;
56*> = 'L': Lower triangular, form is A = L*D*L**H.
57*> \endverbatim
58*>
59*> \param[in] N
60*> \verbatim
61*> N is INTEGER
62*> The order of the matrix A. N >= 0.
63*> \endverbatim
64*>
65*> \param[in] AP
66*> \verbatim
67*> AP is COMPLEX array, dimension (N*(N+1)/2)
68*> The block diagonal matrix D and the multipliers used to
69*> obtain the factor U or L as computed by CHPTRF, stored as a
70*> packed triangular matrix.
71*> \endverbatim
72*>
73*> \param[in] IPIV
74*> \verbatim
75*> IPIV is INTEGER array, dimension (N)
76*> Details of the interchanges and the block structure of D
77*> as determined by CHPTRF.
78*> \endverbatim
79*>
80*> \param[in] ANORM
81*> \verbatim
82*> ANORM is REAL
83*> The 1-norm of the original matrix A.
84*> \endverbatim
85*>
86*> \param[out] RCOND
87*> \verbatim
88*> RCOND is REAL
89*> The reciprocal of the condition number of the matrix A,
90*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
91*> estimate of the 1-norm of inv(A) computed in this routine.
92*> \endverbatim
93*>
94*> \param[out] WORK
95*> \verbatim
96*> WORK is COMPLEX array, dimension (2*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 hpcon
115*
116* =====================================================================
117 SUBROUTINE chpcon( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, 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 REAL ANORM, RCOND
127* ..
128* .. Array Arguments ..
129 INTEGER IPIV( * )
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 INTEGER I, IP, KASE
142 REAL AINVNM
143* ..
144* .. Local Arrays ..
145 INTEGER ISAVE( 3 )
146* ..
147* .. External Functions ..
148 LOGICAL LSAME
149 EXTERNAL lsame
150* ..
151* .. External Subroutines ..
152 EXTERNAL chptrs, clacn2, xerbla
153* ..
154* .. Executable Statements ..
155*
156* Test the input parameters.
157*
158 info = 0
159 upper = lsame( uplo, 'U' )
160 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
161 info = -1
162 ELSE IF( n.LT.0 ) THEN
163 info = -2
164 ELSE IF( anorm.LT.zero ) THEN
165 info = -5
166 END IF
167 IF( info.NE.0 ) THEN
168 CALL xerbla( 'CHPCON', -info )
169 RETURN
170 END IF
171*
172* Quick return if possible
173*
174 rcond = zero
175 IF( n.EQ.0 ) THEN
176 rcond = one
177 RETURN
178 ELSE IF( anorm.LE.zero ) THEN
179 RETURN
180 END IF
181*
182* Check that the diagonal matrix D is nonsingular.
183*
184 IF( upper ) THEN
185*
186* Upper triangular storage: examine D from bottom to top
187*
188 ip = n*( n+1 ) / 2
189 DO 10 i = n, 1, -1
190 IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
191 \$ RETURN
192 ip = ip - i
193 10 CONTINUE
194 ELSE
195*
196* Lower triangular storage: examine D from top to bottom.
197*
198 ip = 1
199 DO 20 i = 1, n
200 IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
201 \$ RETURN
202 ip = ip + n - i + 1
203 20 CONTINUE
204 END IF
205*
206* Estimate the 1-norm of the inverse.
207*
208 kase = 0
209 30 CONTINUE
210 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
211 IF( kase.NE.0 ) THEN
212*
213* Multiply by inv(L*D*L**H) or inv(U*D*U**H).
214*
215 CALL chptrs( uplo, n, 1, ap, ipiv, work, n, info )
216 GO TO 30
217 END IF
218*
219* Compute the estimate of the reciprocal condition number.
220*
221 IF( ainvnm.NE.zero )
222 \$ rcond = ( one / ainvnm ) / anorm
223*
224 RETURN
225*
226* End of CHPCON
227*
228 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine chpcon(uplo, n, ap, ipiv, anorm, rcond, work, info)
CHPCON
Definition chpcon.f:118
subroutine chptrs(uplo, n, nrhs, ap, ipiv, b, ldb, info)
CHPTRS
Definition chptrs.f:115
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