1: *> \brief <b> DSYCON_ROOK </b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSYCON_ROOK + dependencies
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11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsycon_rook.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsycon_rook.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
22: * WORK, 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_ROOK 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_ROOK.
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_ROOK.
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_ROOK.
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: *> \ingroup doubleSYcomputational
126: *
127: *> \par Contributors:
128: * ==================
129: *> \verbatim
130: *>
131: *> April 2012, Igor Kozachenko,
132: *> Computer Science Division,
133: *> University of California, Berkeley
134: *>
135: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
136: *> School of Mathematics,
137: *> University of Manchester
138: *>
139: *> \endverbatim
140: *
141: * =====================================================================
142: SUBROUTINE DSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
143: $ IWORK, INFO )
144: *
145: * -- LAPACK computational routine --
146: * -- LAPACK is a software package provided by Univ. of Tennessee, --
147: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148: *
149: * .. Scalar Arguments ..
150: CHARACTER UPLO
151: INTEGER INFO, LDA, N
152: DOUBLE PRECISION ANORM, RCOND
153: * ..
154: * .. Array Arguments ..
155: INTEGER IPIV( * ), IWORK( * )
156: DOUBLE PRECISION A( LDA, * ), WORK( * )
157: * ..
158: *
159: * =====================================================================
160: *
161: * .. Parameters ..
162: DOUBLE PRECISION ONE, ZERO
163: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
164: * ..
165: * .. Local Scalars ..
166: LOGICAL UPPER
167: INTEGER I, KASE
168: DOUBLE PRECISION AINVNM
169: * ..
170: * .. Local Arrays ..
171: INTEGER ISAVE( 3 )
172: * ..
173: * .. External Functions ..
174: LOGICAL LSAME
175: EXTERNAL LSAME
176: * ..
177: * .. External Subroutines ..
178: EXTERNAL DLACN2, DSYTRS_ROOK, XERBLA
179: * ..
180: * .. Intrinsic Functions ..
181: INTRINSIC MAX
182: * ..
183: * .. Executable Statements ..
184: *
185: * Test the input parameters.
186: *
187: INFO = 0
188: UPPER = LSAME( UPLO, 'U' )
189: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
190: INFO = -1
191: ELSE IF( N.LT.0 ) THEN
192: INFO = -2
193: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
194: INFO = -4
195: ELSE IF( ANORM.LT.ZERO ) THEN
196: INFO = -6
197: END IF
198: IF( INFO.NE.0 ) THEN
199: CALL XERBLA( 'DSYCON_ROOK', -INFO )
200: RETURN
201: END IF
202: *
203: * Quick return if possible
204: *
205: RCOND = ZERO
206: IF( N.EQ.0 ) THEN
207: RCOND = ONE
208: RETURN
209: ELSE IF( ANORM.LE.ZERO ) THEN
210: RETURN
211: END IF
212: *
213: * Check that the diagonal matrix D is nonsingular.
214: *
215: IF( UPPER ) THEN
216: *
217: * Upper triangular storage: examine D from bottom to top
218: *
219: DO 10 I = N, 1, -1
220: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
221: $ RETURN
222: 10 CONTINUE
223: ELSE
224: *
225: * Lower triangular storage: examine D from top to bottom.
226: *
227: DO 20 I = 1, N
228: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
229: $ RETURN
230: 20 CONTINUE
231: END IF
232: *
233: * Estimate the 1-norm of the inverse.
234: *
235: KASE = 0
236: 30 CONTINUE
237: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
238: IF( KASE.NE.0 ) THEN
239: *
240: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
241: *
242: CALL DSYTRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
243: GO TO 30
244: END IF
245: *
246: * Compute the estimate of the reciprocal condition number.
247: *
248: IF( AINVNM.NE.ZERO )
249: $ RCOND = ( ONE / AINVNM ) / ANORM
250: *
251: RETURN
252: *
253: * End of DSYCON_ROOK
254: *
255: END
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