LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
dspcon.f
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1 *> \brief \b DSPCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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