LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dpocon.f
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1 *> \brief \b DPOCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download DPOCON + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpocon.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER UPLO
26 * INTEGER INFO, LDA, N
27 * DOUBLE PRECISION ANORM, RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IWORK( * )
31 * DOUBLE PRECISION A( LDA, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> DPOCON estimates the reciprocal of the condition number (in the
41 *> 1-norm) of a real symmetric positive definite matrix using the
42 *> Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.
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 *> = 'U': Upper triangle of A is stored;
55 *> = 'L': Lower triangle of A is stored.
56 *> \endverbatim
57 *>
58 *> \param[in] N
59 *> \verbatim
60 *> N is INTEGER
61 *> The order of the matrix A. N >= 0.
62 *> \endverbatim
63 *>
64 *> \param[in] A
65 *> \verbatim
66 *> A is DOUBLE PRECISION array, dimension (LDA,N)
67 *> The triangular factor U or L from the Cholesky factorization
68 *> A = U**T*U or A = L*L**T, as computed by DPOTRF.
69 *> \endverbatim
70 *>
71 *> \param[in] LDA
72 *> \verbatim
73 *> LDA is INTEGER
74 *> The leading dimension of the array A. LDA >= max(1,N).
75 *> \endverbatim
76 *>
77 *> \param[in] ANORM
78 *> \verbatim
79 *> ANORM is DOUBLE PRECISION
80 *> The 1-norm (or infinity-norm) of the symmetric matrix A.
81 *> \endverbatim
82 *>
83 *> \param[out] RCOND
84 *> \verbatim
85 *> RCOND is DOUBLE PRECISION
86 *> The reciprocal of the condition number of the matrix A,
87 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
88 *> estimate of the 1-norm of inv(A) computed in this routine.
89 *> \endverbatim
90 *>
91 *> \param[out] WORK
92 *> \verbatim
93 *> WORK is DOUBLE PRECISION array, dimension (3*N)
94 *> \endverbatim
95 *>
96 *> \param[out] IWORK
97 *> \verbatim
98 *> IWORK is INTEGER array, dimension (N)
99 *> \endverbatim
100 *>
101 *> \param[out] INFO
102 *> \verbatim
103 *> INFO is INTEGER
104 *> = 0: successful exit
105 *> < 0: if INFO = -i, the i-th argument had an illegal value
106 *> \endverbatim
107 *
108 * Authors:
109 * ========
110 *
111 *> \author Univ. of Tennessee
112 *> \author Univ. of California Berkeley
113 *> \author Univ. of Colorado Denver
114 *> \author NAG Ltd.
115 *
116 *> \ingroup doublePOcomputational
117 *
118 * =====================================================================
119  SUBROUTINE dpocon( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
120  $ INFO )
121 *
122 * -- LAPACK computational routine --
123 * -- LAPACK is a software package provided by Univ. of Tennessee, --
124 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125 *
126 * .. Scalar Arguments ..
127  CHARACTER UPLO
128  INTEGER INFO, LDA, N
129  DOUBLE PRECISION ANORM, RCOND
130 * ..
131 * .. Array Arguments ..
132  INTEGER IWORK( * )
133  DOUBLE PRECISION A( LDA, * ), WORK( * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  DOUBLE PRECISION ONE, ZERO
140  parameter( one = 1.0d+0, zero = 0.0d+0 )
141 * ..
142 * .. Local Scalars ..
143  LOGICAL UPPER
144  CHARACTER NORMIN
145  INTEGER IX, KASE
146  DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147 * ..
148 * .. Local Arrays ..
149  INTEGER ISAVE( 3 )
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME
153  INTEGER IDAMAX
154  DOUBLE PRECISION DLAMCH
155  EXTERNAL lsame, idamax, dlamch
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL dlacn2, dlatrs, drscl, xerbla
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC abs, max
162 * ..
163 * .. Executable Statements ..
164 *
165 * Test the input parameters.
166 *
167  info = 0
168  upper = lsame( uplo, 'U' )
169  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
170  info = -1
171  ELSE IF( n.LT.0 ) THEN
172  info = -2
173  ELSE IF( lda.LT.max( 1, n ) ) THEN
174  info = -4
175  ELSE IF( anorm.LT.zero ) THEN
176  info = -5
177  END IF
178  IF( info.NE.0 ) THEN
179  CALL xerbla( 'DPOCON', -info )
180  RETURN
181  END IF
182 *
183 * Quick return if possible
184 *
185  rcond = zero
186  IF( n.EQ.0 ) THEN
187  rcond = one
188  RETURN
189  ELSE IF( anorm.EQ.zero ) THEN
190  RETURN
191  END IF
192 *
193  smlnum = dlamch( 'Safe minimum' )
194 *
195 * Estimate the 1-norm of inv(A).
196 *
197  kase = 0
198  normin = 'N'
199  10 CONTINUE
200  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
201  IF( kase.NE.0 ) THEN
202  IF( upper ) THEN
203 *
204 * Multiply by inv(U**T).
205 *
206  CALL dlatrs( 'Upper', 'Transpose', 'Non-unit', normin, n, a,
207  $ lda, work, scalel, work( 2*n+1 ), info )
208  normin = 'Y'
209 *
210 * Multiply by inv(U).
211 *
212  CALL dlatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
213  $ a, lda, work, scaleu, work( 2*n+1 ), info )
214  ELSE
215 *
216 * Multiply by inv(L).
217 *
218  CALL dlatrs( 'Lower', 'No transpose', 'Non-unit', normin, n,
219  $ a, lda, work, scalel, work( 2*n+1 ), info )
220  normin = 'Y'
221 *
222 * Multiply by inv(L**T).
223 *
224  CALL dlatrs( 'Lower', 'Transpose', 'Non-unit', normin, n, a,
225  $ lda, work, scaleu, work( 2*n+1 ), info )
226  END IF
227 *
228 * Multiply by 1/SCALE if doing so will not cause overflow.
229 *
230  scale = scalel*scaleu
231  IF( scale.NE.one ) THEN
232  ix = idamax( n, work, 1 )
233  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
234  $ GO TO 20
235  CALL drscl( n, scale, work, 1 )
236  END IF
237  GO TO 10
238  END IF
239 *
240 * Compute the estimate of the reciprocal condition number.
241 *
242  IF( ainvnm.NE.zero )
243  $ rcond = ( one / ainvnm ) / anorm
244 *
245  20 CONTINUE
246  RETURN
247 *
248 * End of DPOCON
249 *
250  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:84
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 dlatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
DLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: dlatrs.f:238
subroutine dpocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO)
DPOCON
Definition: dpocon.f:121