Annotation of rpl/lapack/lapack/dsycon.f, revision 1.19
1.10 bertrand 1: *> \brief \b DSYCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.10 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 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">
1.10 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.10 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
22: * IWORK, INFO )
1.16 bertrand 23: *
1.10 bertrand 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: * ..
1.16 bertrand 33: *
1.10 bertrand 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: *
1.16 bertrand 120: *> \author Univ. of Tennessee
121: *> \author Univ. of California Berkeley
122: *> \author Univ. of Colorado Denver
123: *> \author NAG Ltd.
1.10 bertrand 124: *
125: *> \ingroup doubleSYcomputational
126: *
127: * =====================================================================
1.1 bertrand 128: SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
129: $ IWORK, INFO )
130: *
1.19 ! bertrand 131: * -- LAPACK computational routine --
1.1 bertrand 132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134: *
135: * .. Scalar Arguments ..
136: CHARACTER UPLO
137: INTEGER INFO, LDA, N
138: DOUBLE PRECISION ANORM, RCOND
139: * ..
140: * .. Array Arguments ..
141: INTEGER IPIV( * ), IWORK( * )
142: DOUBLE PRECISION A( LDA, * ), WORK( * )
143: * ..
144: *
145: * =====================================================================
146: *
147: * .. Parameters ..
148: DOUBLE PRECISION ONE, ZERO
149: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
150: * ..
151: * .. Local Scalars ..
152: LOGICAL UPPER
153: INTEGER I, KASE
154: DOUBLE PRECISION AINVNM
155: * ..
156: * .. Local Arrays ..
157: INTEGER ISAVE( 3 )
158: * ..
159: * .. External Functions ..
160: LOGICAL LSAME
161: EXTERNAL LSAME
162: * ..
163: * .. External Subroutines ..
164: EXTERNAL DLACN2, DSYTRS, XERBLA
165: * ..
166: * .. Intrinsic Functions ..
167: INTRINSIC MAX
168: * ..
169: * .. Executable Statements ..
170: *
171: * Test the input parameters.
172: *
173: INFO = 0
174: UPPER = LSAME( UPLO, 'U' )
175: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
176: INFO = -1
177: ELSE IF( N.LT.0 ) THEN
178: INFO = -2
179: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
180: INFO = -4
181: ELSE IF( ANORM.LT.ZERO ) THEN
182: INFO = -6
183: END IF
184: IF( INFO.NE.0 ) THEN
185: CALL XERBLA( 'DSYCON', -INFO )
186: RETURN
187: END IF
188: *
189: * Quick return if possible
190: *
191: RCOND = ZERO
192: IF( N.EQ.0 ) THEN
193: RCOND = ONE
194: RETURN
195: ELSE IF( ANORM.LE.ZERO ) THEN
196: RETURN
197: END IF
198: *
199: * Check that the diagonal matrix D is nonsingular.
200: *
201: IF( UPPER ) THEN
202: *
203: * Upper triangular storage: examine D from bottom to top
204: *
205: DO 10 I = N, 1, -1
206: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
207: $ RETURN
208: 10 CONTINUE
209: ELSE
210: *
211: * Lower triangular storage: examine D from top to bottom.
212: *
213: DO 20 I = 1, N
214: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
215: $ RETURN
216: 20 CONTINUE
217: END IF
218: *
219: * Estimate the 1-norm of the inverse.
220: *
221: KASE = 0
222: 30 CONTINUE
223: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
224: IF( KASE.NE.0 ) THEN
225: *
1.9 bertrand 226: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
1.1 bertrand 227: *
228: CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
229: GO TO 30
230: END IF
231: *
232: * Compute the estimate of the reciprocal condition number.
233: *
234: IF( AINVNM.NE.ZERO )
235: $ RCOND = ( ONE / AINVNM ) / ANORM
236: *
237: RETURN
238: *
239: * End of DSYCON
240: *
241: END
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