LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
sspcon.f
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1 *> \brief \b SSPCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER INFO, N
27 * REAL ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IPIV( * ), IWORK( * )
31 * REAL AP( * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> SSPCON 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 SSPTRF.
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 REAL 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 SSPTRF, 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 SSPTRF.
79 *> \endverbatim
80 *>
81 *> \param[in] ANORM
82 *> \verbatim
83 *> ANORM is REAL
84 *> The 1-norm of the original matrix A.
85 *> \endverbatim
86 *>
87 *> \param[out] RCOND
88 *> \verbatim
89 *> RCOND is REAL
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 REAL 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 *> \date December 2016
121 *
122 *> \ingroup realOTHERcomputational
123 *
124 * =====================================================================
125  SUBROUTINE sspcon( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
126  \$ INFO )
127 *
128 * -- LAPACK computational routine (version 3.7.0) --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * December 2016
132 *
133 * .. Scalar Arguments ..
134  CHARACTER UPLO
135  INTEGER INFO, N
136  REAL ANORM, RCOND
137 * ..
138 * .. Array Arguments ..
139  INTEGER IPIV( * ), IWORK( * )
140  REAL AP( * ), WORK( * )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  REAL ONE, ZERO
147  parameter( one = 1.0e+0, zero = 0.0e+0 )
148 * ..
149 * .. Local Scalars ..
150  LOGICAL UPPER
151  INTEGER I, IP, KASE
152  REAL AINVNM
153 * ..
154 * .. Local Arrays ..
155  INTEGER ISAVE( 3 )
156 * ..
157 * .. External Functions ..
158  LOGICAL LSAME
159  EXTERNAL lsame
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL slacn2, ssptrs, xerbla
163 * ..
164 * .. Executable Statements ..
165 *
166 * Test the input parameters.
167 *
168  info = 0
169  upper = lsame( uplo, 'U' )
170  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
171  info = -1
172  ELSE IF( n.LT.0 ) THEN
173  info = -2
174  ELSE IF( anorm.LT.zero ) THEN
175  info = -5
176  END IF
177  IF( info.NE.0 ) THEN
178  CALL xerbla( 'SSPCON', -info )
179  RETURN
180  END IF
181 *
182 * Quick return if possible
183 *
184  rcond = zero
185  IF( n.EQ.0 ) THEN
186  rcond = one
187  RETURN
188  ELSE IF( anorm.LE.zero ) THEN
189  RETURN
190  END IF
191 *
192 * Check that the diagonal matrix D is nonsingular.
193 *
194  IF( upper ) THEN
195 *
196 * Upper triangular storage: examine D from bottom to top
197 *
198  ip = n*( n+1 ) / 2
199  DO 10 i = n, 1, -1
200  IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
201  \$ RETURN
202  ip = ip - i
203  10 CONTINUE
204  ELSE
205 *
206 * Lower triangular storage: examine D from top to bottom.
207 *
208  ip = 1
209  DO 20 i = 1, n
210  IF( ipiv( i ).GT.0 .AND. ap( ip ).EQ.zero )
211  \$ RETURN
212  ip = ip + n - i + 1
213  20 CONTINUE
214  END IF
215 *
216 * Estimate the 1-norm of the inverse.
217 *
218  kase = 0
219  30 CONTINUE
220  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
221  IF( kase.NE.0 ) THEN
222 *
223 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
224 *
225  CALL ssptrs( uplo, n, 1, ap, ipiv, work, n, info )
226  GO TO 30
227  END IF
228 *
229 * Compute the estimate of the reciprocal condition number.
230 *
231  IF( ainvnm.NE.zero )
232  \$ rcond = ( one / ainvnm ) / anorm
233 *
234  RETURN
235 *
236 * End of SSPCON
237 *
238  END
subroutine sspcon(UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
SSPCON
Definition: sspcon.f:127
subroutine ssptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPTRS
Definition: ssptrs.f:117
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:138