Annotation of rpl/lapack/lapack/dsycon.f, revision 1.11
1.10 bertrand 1: *> \brief \b DSYCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSYCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsycon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsycon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsycon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
22: * IWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER UPLO
26: * INTEGER INFO, LDA, N
27: * DOUBLE PRECISION ANORM, RCOND
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * ), IWORK( * )
31: * DOUBLE PRECISION A( LDA, * ), WORK( * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DSYCON 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 DSYTRF.
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 DOUBLE PRECISION 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 DSYTRF.
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 DSYTRF.
84: *> \endverbatim
85: *>
86: *> \param[in] ANORM
87: *> \verbatim
88: *> ANORM is DOUBLE PRECISION
89: *> The 1-norm of the original matrix A.
90: *> \endverbatim
91: *>
92: *> \param[out] RCOND
93: *> \verbatim
94: *> RCOND is DOUBLE PRECISION
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 DOUBLE PRECISION 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: *> \date November 2011
126: *
127: *> \ingroup doubleSYcomputational
128: *
129: * =====================================================================
1.1 bertrand 130: SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
131: $ IWORK, INFO )
132: *
1.10 bertrand 133: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 bertrand 136: * November 2011
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: CHARACTER UPLO
140: INTEGER INFO, LDA, N
141: DOUBLE PRECISION ANORM, RCOND
142: * ..
143: * .. Array Arguments ..
144: INTEGER IPIV( * ), IWORK( * )
145: DOUBLE PRECISION A( LDA, * ), WORK( * )
146: * ..
147: *
148: * =====================================================================
149: *
150: * .. Parameters ..
151: DOUBLE PRECISION ONE, ZERO
152: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
153: * ..
154: * .. Local Scalars ..
155: LOGICAL UPPER
156: INTEGER I, KASE
157: DOUBLE PRECISION AINVNM
158: * ..
159: * .. Local Arrays ..
160: INTEGER ISAVE( 3 )
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: EXTERNAL LSAME
165: * ..
166: * .. External Subroutines ..
167: EXTERNAL DLACN2, DSYTRS, XERBLA
168: * ..
169: * .. Intrinsic Functions ..
170: INTRINSIC MAX
171: * ..
172: * .. Executable Statements ..
173: *
174: * Test the input parameters.
175: *
176: INFO = 0
177: UPPER = LSAME( UPLO, 'U' )
178: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
179: INFO = -1
180: ELSE IF( N.LT.0 ) THEN
181: INFO = -2
182: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
183: INFO = -4
184: ELSE IF( ANORM.LT.ZERO ) THEN
185: INFO = -6
186: END IF
187: IF( INFO.NE.0 ) THEN
188: CALL XERBLA( 'DSYCON', -INFO )
189: RETURN
190: END IF
191: *
192: * Quick return if possible
193: *
194: RCOND = ZERO
195: IF( N.EQ.0 ) THEN
196: RCOND = ONE
197: RETURN
198: ELSE IF( ANORM.LE.ZERO ) THEN
199: RETURN
200: END IF
201: *
202: * Check that the diagonal matrix D is nonsingular.
203: *
204: IF( UPPER ) THEN
205: *
206: * Upper triangular storage: examine D from bottom to top
207: *
208: DO 10 I = N, 1, -1
209: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
210: $ RETURN
211: 10 CONTINUE
212: ELSE
213: *
214: * Lower triangular storage: examine D from top to bottom.
215: *
216: DO 20 I = 1, N
217: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
218: $ RETURN
219: 20 CONTINUE
220: END IF
221: *
222: * Estimate the 1-norm of the inverse.
223: *
224: KASE = 0
225: 30 CONTINUE
226: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
227: IF( KASE.NE.0 ) THEN
228: *
1.9 bertrand 229: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
1.1 bertrand 230: *
231: CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
232: GO TO 30
233: END IF
234: *
235: * Compute the estimate of the reciprocal condition number.
236: *
237: IF( AINVNM.NE.ZERO )
238: $ RCOND = ( ONE / AINVNM ) / ANORM
239: *
240: RETURN
241: *
242: * End of DSYCON
243: *
244: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dsycon.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack