LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dsycon.f
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1 *> \brief \b DSYCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
22 * IWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER INFO, LDA, N
27 * DOUBLE PRECISION ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * ), IWORK( * )
31 * DOUBLE PRECISION A( LDA, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> DSYCON estimates the reciprocal of the condition number (in the
41 *> 1-norm) of a real symmetric matrix A using the factorization
42 *> A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
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] A
67 *> \verbatim
68 *> A is DOUBLE PRECISION array, dimension (LDA,N)
69 *> The block diagonal matrix D and the multipliers used to
70 *> obtain the factor U or L as computed by DSYTRF.
71 *> \endverbatim
72 *>
73 *> \param[in] LDA
74 *> \verbatim
75 *> LDA is INTEGER
76 *> The leading dimension of the array A. LDA >= max(1,N).
77 *> \endverbatim
78 *>
79 *> \param[in] IPIV
80 *> \verbatim
81 *> IPIV is INTEGER array, dimension (N)
82 *> Details of the interchanges and the block structure of D
83 *> as determined by DSYTRF.
84 *> \endverbatim
85 *>
86 *> \param[in] ANORM
87 *> \verbatim
88 *> ANORM is DOUBLE PRECISION
89 *> The 1-norm of the original matrix A.
90 *> \endverbatim
91 *>
92 *> \param[out] RCOND
93 *> \verbatim
94 *> RCOND is DOUBLE PRECISION
95 *> The reciprocal of the condition number of the matrix A,
96 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
97 *> estimate of the 1-norm of inv(A) computed in this routine.
98 *> \endverbatim
99 *>
100 *> \param[out] WORK
101 *> \verbatim
102 *> WORK is DOUBLE PRECISION array, dimension (2*N)
103 *> \endverbatim
104 *>
105 *> \param[out] IWORK
106 *> \verbatim
107 *> IWORK is INTEGER array, dimension (N)
108 *> \endverbatim
109 *>
110 *> \param[out] INFO
111 *> \verbatim
112 *> INFO is INTEGER
113 *> = 0: successful exit
114 *> < 0: if INFO = -i, the i-th argument had an illegal value
115 *> \endverbatim
116 *
117 * Authors:
118 * ========
119 *
120 *> \author Univ. of Tennessee
121 *> \author Univ. of California Berkeley
122 *> \author Univ. of Colorado Denver
123 *> \author NAG Ltd.
124 *
125 *> \date November 2011
126 *
127 *> \ingroup doubleSYcomputational
128 *
129 * =====================================================================
130  SUBROUTINE dsycon( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
131  \$ iwork, info )
132 *
133 * -- LAPACK computational routine (version 3.4.0) --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 * November 2011
137 *
138 * .. Scalar Arguments ..
139  CHARACTER UPLO
140  INTEGER INFO, LDA, N
141  DOUBLE PRECISION ANORM, RCOND
142 * ..
143 * .. Array Arguments ..
144  INTEGER IPIV( * ), IWORK( * )
145  DOUBLE PRECISION A( lda, * ), WORK( * )
146 * ..
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151  DOUBLE PRECISION ONE, ZERO
152  parameter ( one = 1.0d+0, zero = 0.0d+0 )
153 * ..
154 * .. Local Scalars ..
155  LOGICAL UPPER
156  INTEGER I, KASE
157  DOUBLE PRECISION AINVNM
158 * ..
159 * .. Local Arrays ..
160  INTEGER ISAVE( 3 )
161 * ..
162 * .. External Functions ..
163  LOGICAL LSAME
164  EXTERNAL lsame
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL dlacn2, dsytrs, xerbla
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC max
171 * ..
172 * .. Executable Statements ..
173 *
174 * Test the input parameters.
175 *
176  info = 0
177  upper = lsame( uplo, 'U' )
178  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
179  info = -1
180  ELSE IF( n.LT.0 ) THEN
181  info = -2
182  ELSE IF( lda.LT.max( 1, n ) ) THEN
183  info = -4
184  ELSE IF( anorm.LT.zero ) THEN
185  info = -6
186  END IF
187  IF( info.NE.0 ) THEN
188  CALL xerbla( 'DSYCON', -info )
189  RETURN
190  END IF
191 *
192 * Quick return if possible
193 *
194  rcond = zero
195  IF( n.EQ.0 ) THEN
196  rcond = one
197  RETURN
198  ELSE IF( anorm.LE.zero ) THEN
199  RETURN
200  END IF
201 *
202 * Check that the diagonal matrix D is nonsingular.
203 *
204  IF( upper ) THEN
205 *
206 * Upper triangular storage: examine D from bottom to top
207 *
208  DO 10 i = n, 1, -1
209  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
210  \$ RETURN
211  10 CONTINUE
212  ELSE
213 *
214 * Lower triangular storage: examine D from top to bottom.
215 *
216  DO 20 i = 1, n
217  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
218  \$ RETURN
219  20 CONTINUE
220  END IF
221 *
222 * Estimate the 1-norm of the inverse.
223 *
224  kase = 0
225  30 CONTINUE
226  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
227  IF( kase.NE.0 ) THEN
228 *
229 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
230 *
231  CALL dsytrs( uplo, n, 1, a, lda, ipiv, work, n, info )
232  GO TO 30
233  END IF
234 *
235 * Compute the estimate of the reciprocal condition number.
236 *
237  IF( ainvnm.NE.zero )
238  \$ rcond = ( one / ainvnm ) / anorm
239 *
240  RETURN
241 *
242 * End of DSYCON
243 *
244  END
subroutine dsycon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
DSYCON
Definition: dsycon.f:132
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dsytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DSYTRS
Definition: dsytrs.f:122
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:138