LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dpocon.f
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1 *> \brief \b DPOCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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 *> \date November 2011
117 *
118 *> \ingroup doublePOcomputational
119 *
120 * =====================================================================
121  SUBROUTINE dpocon( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
122  \$ info )
123 *
124 * -- LAPACK computational routine (version 3.4.0) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * November 2011
128 *
129 * .. Scalar Arguments ..
130  CHARACTER UPLO
131  INTEGER INFO, LDA, N
132  DOUBLE PRECISION ANORM, RCOND
133 * ..
134 * .. Array Arguments ..
135  INTEGER IWORK( * )
136  DOUBLE PRECISION A( lda, * ), WORK( * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  DOUBLE PRECISION ONE, ZERO
143  parameter ( one = 1.0d+0, zero = 0.0d+0 )
144 * ..
145 * .. Local Scalars ..
146  LOGICAL UPPER
147  CHARACTER NORMIN
148  INTEGER IX, KASE
149  DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
150 * ..
151 * .. Local Arrays ..
152  INTEGER ISAVE( 3 )
153 * ..
154 * .. External Functions ..
155  LOGICAL LSAME
156  INTEGER IDAMAX
157  DOUBLE PRECISION DLAMCH
158  EXTERNAL lsame, idamax, dlamch
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL dlacn2, dlatrs, drscl, xerbla
162 * ..
163 * .. Intrinsic Functions ..
164  INTRINSIC abs, max
165 * ..
166 * .. Executable Statements ..
167 *
168 * Test the input parameters.
169 *
170  info = 0
171  upper = lsame( uplo, 'U' )
172  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
173  info = -1
174  ELSE IF( n.LT.0 ) THEN
175  info = -2
176  ELSE IF( lda.LT.max( 1, n ) ) THEN
177  info = -4
178  ELSE IF( anorm.LT.zero ) THEN
179  info = -5
180  END IF
181  IF( info.NE.0 ) THEN
182  CALL xerbla( 'DPOCON', -info )
183  RETURN
184  END IF
185 *
186 * Quick return if possible
187 *
188  rcond = zero
189  IF( n.EQ.0 ) THEN
190  rcond = one
191  RETURN
192  ELSE IF( anorm.EQ.zero ) THEN
193  RETURN
194  END IF
195 *
196  smlnum = dlamch( 'Safe minimum' )
197 *
198 * Estimate the 1-norm of inv(A).
199 *
200  kase = 0
201  normin = 'N'
202  10 CONTINUE
203  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
204  IF( kase.NE.0 ) THEN
205  IF( upper ) THEN
206 *
207 * Multiply by inv(U**T).
208 *
209  CALL dlatrs( 'Upper', 'Transpose', 'Non-unit', normin, n, a,
210  \$ lda, work, scalel, work( 2*n+1 ), info )
211  normin = 'Y'
212 *
213 * Multiply by inv(U).
214 *
215  CALL dlatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
216  \$ a, lda, work, scaleu, work( 2*n+1 ), info )
217  ELSE
218 *
219 * Multiply by inv(L).
220 *
221  CALL dlatrs( 'Lower', 'No transpose', 'Non-unit', normin, n,
222  \$ a, lda, work, scalel, work( 2*n+1 ), info )
223  normin = 'Y'
224 *
225 * Multiply by inv(L**T).
226 *
227  CALL dlatrs( 'Lower', 'Transpose', 'Non-unit', normin, n, a,
228  \$ lda, work, scaleu, work( 2*n+1 ), info )
229  END IF
230 *
231 * Multiply by 1/SCALE if doing so will not cause overflow.
232 *
233  scale = scalel*scaleu
234  IF( scale.NE.one ) THEN
235  ix = idamax( n, work, 1 )
236  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
237  \$ GO TO 20
238  CALL drscl( n, scale, work, 1 )
239  END IF
240  GO TO 10
241  END IF
242 *
243 * Compute the estimate of the reciprocal condition number.
244 *
245  IF( ainvnm.NE.zero )
246  \$ rcond = ( one / ainvnm ) / anorm
247 *
248  20 CONTINUE
249  RETURN
250 *
251 * End of DPOCON
252 *
253  END
subroutine dpocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO)
DPOCON
Definition: dpocon.f:123
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:240
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:86
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