LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
ssycon.f
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1 *> \brief \b SSYCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
22 * IWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER INFO, LDA, N
27 * REAL ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * ), IWORK( * )
31 * REAL A( LDA, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> SSYCON 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 SSYTRF.
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 REAL 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 SSYTRF.
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 SSYTRF.
84 *> \endverbatim
85 *>
86 *> \param[in] ANORM
87 *> \verbatim
88 *> ANORM is REAL
89 *> The 1-norm of the original matrix A.
90 *> \endverbatim
91 *>
92 *> \param[out] RCOND
93 *> \verbatim
94 *> RCOND is REAL
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 REAL 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 *> \ingroup realSYcomputational
126 *
127 * =====================================================================
128  SUBROUTINE ssycon( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
129  $ IWORK, INFO )
130 *
131 * -- LAPACK computational routine --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 *
135 * .. Scalar Arguments ..
136  CHARACTER UPLO
137  INTEGER INFO, LDA, N
138  REAL ANORM, RCOND
139 * ..
140 * .. Array Arguments ..
141  INTEGER IPIV( * ), IWORK( * )
142  REAL A( LDA, * ), WORK( * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  REAL ONE, ZERO
149  parameter( one = 1.0e+0, zero = 0.0e+0 )
150 * ..
151 * .. Local Scalars ..
152  LOGICAL UPPER
153  INTEGER I, KASE
154  REAL AINVNM
155 * ..
156 * .. Local Arrays ..
157  INTEGER ISAVE( 3 )
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  EXTERNAL lsame
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL slacn2, ssytrs, xerbla
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC max
168 * ..
169 * .. Executable Statements ..
170 *
171 * Test the input parameters.
172 *
173  info = 0
174  upper = lsame( uplo, 'U' )
175  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
176  info = -1
177  ELSE IF( n.LT.0 ) THEN
178  info = -2
179  ELSE IF( lda.LT.max( 1, n ) ) THEN
180  info = -4
181  ELSE IF( anorm.LT.zero ) THEN
182  info = -6
183  END IF
184  IF( info.NE.0 ) THEN
185  CALL xerbla( 'SSYCON', -info )
186  RETURN
187  END IF
188 *
189 * Quick return if possible
190 *
191  rcond = zero
192  IF( n.EQ.0 ) THEN
193  rcond = one
194  RETURN
195  ELSE IF( anorm.LE.zero ) THEN
196  RETURN
197  END IF
198 *
199 * Check that the diagonal matrix D is nonsingular.
200 *
201  IF( upper ) THEN
202 *
203 * Upper triangular storage: examine D from bottom to top
204 *
205  DO 10 i = n, 1, -1
206  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
207  $ RETURN
208  10 CONTINUE
209  ELSE
210 *
211 * Lower triangular storage: examine D from top to bottom.
212 *
213  DO 20 i = 1, n
214  IF( ipiv( i ).GT.0 .AND. a( i, i ).EQ.zero )
215  $ RETURN
216  20 CONTINUE
217  END IF
218 *
219 * Estimate the 1-norm of the inverse.
220 *
221  kase = 0
222  30 CONTINUE
223  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
224  IF( kase.NE.0 ) THEN
225 *
226 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
227 *
228  CALL ssytrs( uplo, n, 1, a, lda, ipiv, work, n, info )
229  GO TO 30
230  END IF
231 *
232 * Compute the estimate of the reciprocal condition number.
233 *
234  IF( ainvnm.NE.zero )
235  $ rcond = ( one / ainvnm ) / anorm
236 *
237  RETURN
238 *
239 * End of SSYCON
240 *
241  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
subroutine ssycon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
SSYCON
Definition: ssycon.f:130
subroutine ssytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS
Definition: ssytrs.f:120