LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dspcon.f
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1*> \brief \b DSPCON
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DSPCON + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspcon.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspcon.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspcon.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
22* INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER UPLO
26* INTEGER INFO, N
27* DOUBLE PRECISION ANORM, RCOND
28* ..
29* .. Array Arguments ..
30* INTEGER IPIV( * ), IWORK( * )
31* DOUBLE PRECISION AP( * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> DSPCON estimates the reciprocal of the condition number (in the
41*> 1-norm) of a real symmetric packed matrix A using the factorization
42*> A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
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*> Specifies whether the details of the factorization are stored
55*> as an upper or lower triangular matrix.
56*> = 'U': Upper triangular, form is A = U*D*U**T;
57*> = 'L': Lower triangular, form is A = L*D*L**T.
58*> \endverbatim
59*>
60*> \param[in] N
61*> \verbatim
62*> N is INTEGER
63*> The order of the matrix A. N >= 0.
64*> \endverbatim
65*>
66*> \param[in] AP
67*> \verbatim
68*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
69*> The block diagonal matrix D and the multipliers used to
70*> obtain the factor U or L as computed by DSPTRF, stored as a
71*> packed triangular matrix.
72*> \endverbatim
73*>
74*> \param[in] IPIV
75*> \verbatim
76*> IPIV is INTEGER array, dimension (N)
77*> Details of the interchanges and the block structure of D
78*> as determined by DSPTRF.
79*> \endverbatim
80*>
81*> \param[in] ANORM
82*> \verbatim
83*> ANORM is DOUBLE PRECISION
84*> The 1-norm of the original matrix A.
85*> \endverbatim
86*>
87*> \param[out] RCOND
88*> \verbatim
89*> RCOND is DOUBLE PRECISION
90*> The reciprocal of the condition number of the matrix A,
91*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
92*> estimate of the 1-norm of inv(A) computed in this routine.
93*> \endverbatim
94*>
95*> \param[out] WORK
96*> \verbatim
97*> WORK is DOUBLE PRECISION array, dimension (2*N)
98*> \endverbatim
99*>
100*> \param[out] IWORK
101*> \verbatim
102*> IWORK is INTEGER array, dimension (N)
103*> \endverbatim
104*>
105*> \param[out] INFO
106*> \verbatim
107*> INFO is INTEGER
108*> = 0: successful exit
109*> < 0: if INFO = -i, the i-th argument had an illegal value
110*> \endverbatim
111*
112* Authors:
113* ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \ingroup doubleOTHERcomputational
121*
122* =====================================================================
123 SUBROUTINE dspcon( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
124 $ INFO )
125*
126* -- LAPACK computational routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER UPLO
132 INTEGER INFO, N
133 DOUBLE PRECISION ANORM, RCOND
134* ..
135* .. Array Arguments ..
136 INTEGER IPIV( * ), IWORK( * )
137 DOUBLE PRECISION AP( * ), WORK( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ONE, ZERO
144 parameter( one = 1.0d+0, zero = 0.0d+0 )
145* ..
146* .. Local Scalars ..
147 LOGICAL UPPER
148 INTEGER I, IP, KASE
149 DOUBLE PRECISION AINVNM
150* ..
151* .. Local Arrays ..
152 INTEGER ISAVE( 3 )
153* ..
154* .. External Functions ..
155 LOGICAL LSAME
156 EXTERNAL lsame
157* ..
158* .. External Subroutines ..
159 EXTERNAL dlacn2, dsptrs, xerbla
160* ..
161* .. Executable Statements ..
162*
163* Test the input parameters.
164*
165 info = 0
166 upper = lsame( uplo, 'U' )
167 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
168 info = -1
169 ELSE IF( n.LT.0 ) THEN
170 info = -2
171 ELSE IF( anorm.LT.zero ) THEN
172 info = -5
173 END IF
174 IF( info.NE.0 ) THEN
175 CALL xerbla( 'DSPCON', -info )
176 RETURN
177 END IF
178*
179* Quick return if possible
180*
181 rcond = zero
182 IF( n.EQ.0 ) THEN
183 rcond = one
184 RETURN
185 ELSE IF( anorm.LE.zero ) THEN
186 RETURN
187 END IF
188*
189* Check that the diagonal matrix D is nonsingular.
190*
191 IF( upper ) THEN
192*
193* Upper triangular storage: examine D from bottom to top
194*
195 ip = n*( n+1 ) / 2
196 DO 10 i = n, 1, -1
197 IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
198 $ RETURN
199 ip = ip - i
200 10 CONTINUE
201 ELSE
202*
203* Lower triangular storage: examine D from top to bottom.
204*
205 ip = 1
206 DO 20 i = 1, n
207 IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
208 $ RETURN
209 ip = ip + n - i + 1
210 20 CONTINUE
211 END IF
212*
213* Estimate the 1-norm of the inverse.
214*
215 kase = 0
216 30 CONTINUE
217 CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
218 IF( kase.NE.0 ) THEN
219*
220* Multiply by inv(L*D*L**T) or inv(U*D*U**T).
221*
222 CALL dsptrs( uplo, n, 1, ap, ipiv, work, n, info )
223 GO TO 30
224 END IF
225*
226* Compute the estimate of the reciprocal condition number.
227*
228 IF( ainvnm.NE.zero )
229 $ rcond = ( one / ainvnm ) / anorm
230*
231 RETURN
232*
233* End of DSPCON
234*
235 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:136
subroutine dsptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
DSPTRS
Definition: dsptrs.f:115
subroutine dspcon(UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
DSPCON
Definition: dspcon.f:125