LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dgecon.f
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1 *> \brief \b DGECON
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER NORM
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 *> DGECON estimates the reciprocal of the condition number of a general
41 *> real matrix A, in either the 1-norm or the infinity-norm, using
42 *> the LU factorization computed by DGETRF.
43 *>
44 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
45 *> condition number is computed as
46 *> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
47 *> \endverbatim
48 *
49 * Arguments:
50 * ==========
51 *
52 *> \param[in] NORM
53 *> \verbatim
54 *> NORM is CHARACTER*1
55 *> Specifies whether the 1-norm condition number or the
56 *> infinity-norm condition number is required:
57 *> = '1' or 'O': 1-norm;
58 *> = 'I': Infinity-norm.
59 *> \endverbatim
60 *>
61 *> \param[in] N
62 *> \verbatim
63 *> N is INTEGER
64 *> The order of the matrix A. N >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in] A
68 *> \verbatim
69 *> A is DOUBLE PRECISION array, dimension (LDA,N)
70 *> The factors L and U from the factorization A = P*L*U
71 *> as computed by DGETRF.
72 *> \endverbatim
73 *>
74 *> \param[in] LDA
75 *> \verbatim
76 *> LDA is INTEGER
77 *> The leading dimension of the array A. LDA >= max(1,N).
78 *> \endverbatim
79 *>
80 *> \param[in] ANORM
81 *> \verbatim
82 *> ANORM is DOUBLE PRECISION
83 *> If NORM = '1' or 'O', the 1-norm of the original matrix A.
84 *> If NORM = 'I', the infinity-norm of the original matrix A.
85 *> \endverbatim
86 *>
87 *> \param[out] RCOND
88 *> \verbatim
89 *> RCOND is DOUBLE PRECISION
90 *> The reciprocal of the condition number of the matrix A,
91 *> computed as RCOND = 1/(norm(A) * norm(inv(A))).
92 *> \endverbatim
93 *>
94 *> \param[out] WORK
95 *> \verbatim
96 *> WORK is DOUBLE PRECISION array, dimension (4*N)
97 *> \endverbatim
98 *>
99 *> \param[out] IWORK
100 *> \verbatim
101 *> IWORK is INTEGER array, dimension (N)
102 *> \endverbatim
103 *>
104 *> \param[out] INFO
105 *> \verbatim
106 *> INFO is INTEGER
107 *> = 0: successful exit
108 *> < 0: if INFO = -i, the i-th argument had an illegal value
109 *> \endverbatim
110 *
111 * Authors:
112 * ========
113 *
114 *> \author Univ. of Tennessee
115 *> \author Univ. of California Berkeley
116 *> \author Univ. of Colorado Denver
117 *> \author NAG Ltd.
118 *
119 *> \ingroup doubleGEcomputational
120 *
121 * =====================================================================
122  SUBROUTINE dgecon( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
123  $ INFO )
124 *
125 * -- LAPACK computational routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER NORM
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 ONENRM
147  CHARACTER NORMIN
148  INTEGER IX, KASE, KASE1
149  DOUBLE PRECISION AINVNM, SCALE, SL, SMLNUM, SU
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  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
172  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) 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( 'DGECON', -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 norm of inv(A).
199 *
200  ainvnm = zero
201  normin = 'N'
202  IF( onenrm ) THEN
203  kase1 = 1
204  ELSE
205  kase1 = 2
206  END IF
207  kase = 0
208  10 CONTINUE
209  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
210  IF( kase.NE.0 ) THEN
211  IF( kase.EQ.kase1 ) THEN
212 *
213 * Multiply by inv(L).
214 *
215  CALL dlatrs( 'Lower', 'No transpose', 'Unit', normin, n, a,
216  $ lda, work, sl, work( 2*n+1 ), info )
217 *
218 * Multiply by inv(U).
219 *
220  CALL dlatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
221  $ a, lda, work, su, work( 3*n+1 ), info )
222  ELSE
223 *
224 * Multiply by inv(U**T).
225 *
226  CALL dlatrs( 'Upper', 'Transpose', 'Non-unit', normin, n, a,
227  $ lda, work, su, work( 3*n+1 ), info )
228 *
229 * Multiply by inv(L**T).
230 *
231  CALL dlatrs( 'Lower', 'Transpose', 'Unit', normin, n, a,
232  $ lda, work, sl, work( 2*n+1 ), info )
233  END IF
234 *
235 * Divide X by 1/(SL*SU) if doing so will not cause overflow.
236 *
237  scale = sl*su
238  normin = 'Y'
239  IF( scale.NE.one ) THEN
240  ix = idamax( n, work, 1 )
241  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
242  $ GO TO 20
243  CALL drscl( n, scale, work, 1 )
244  END IF
245  GO TO 10
246  END IF
247 *
248 * Compute the estimate of the reciprocal condition number.
249 *
250  IF( ainvnm.NE.zero )
251  $ rcond = ( one / ainvnm ) / anorm
252 *
253  20 CONTINUE
254  RETURN
255 *
256 * End of DGECON
257 *
258  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dgecon(NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO)
DGECON
Definition: dgecon.f:124
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