Annotation of rpl/lapack/lapack/dspcon.f, revision 1.19
1.10 bertrand 1: *> \brief \b DSPCON
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 DSPCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspcon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspcon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspcon.f">
1.10 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.10 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
22: * INFO )
1.16 bertrand 23: *
1.10 bertrand 24: * .. Scalar Arguments ..
25: * CHARACTER UPLO
26: * INTEGER INFO, N
27: * DOUBLE PRECISION ANORM, RCOND
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * ), IWORK( * )
31: * DOUBLE PRECISION AP( * ), WORK( * )
32: * ..
1.16 bertrand 33: *
1.10 bertrand 34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DSPCON estimates the reciprocal of the condition number (in the
41: *> 1-norm) of a real symmetric packed matrix A using the factorization
42: *> A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
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] AP
67: *> \verbatim
68: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
69: *> The block diagonal matrix D and the multipliers used to
70: *> obtain the factor U or L as computed by DSPTRF, stored as a
71: *> packed triangular matrix.
72: *> \endverbatim
73: *>
74: *> \param[in] IPIV
75: *> \verbatim
76: *> IPIV is INTEGER array, dimension (N)
77: *> Details of the interchanges and the block structure of D
78: *> as determined by DSPTRF.
79: *> \endverbatim
80: *>
81: *> \param[in] ANORM
82: *> \verbatim
83: *> ANORM is DOUBLE PRECISION
84: *> The 1-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/(ANORM * AINVNM), where AINVNM is an
92: *> estimate of the 1-norm of inv(A) computed in this routine.
93: *> \endverbatim
94: *>
95: *> \param[out] WORK
96: *> \verbatim
97: *> WORK is DOUBLE PRECISION array, dimension (2*N)
98: *> \endverbatim
99: *>
100: *> \param[out] IWORK
101: *> \verbatim
102: *> IWORK is INTEGER array, dimension (N)
103: *> \endverbatim
104: *>
105: *> \param[out] INFO
106: *> \verbatim
107: *> INFO is INTEGER
108: *> = 0: successful exit
109: *> < 0: if INFO = -i, the i-th argument had an illegal value
110: *> \endverbatim
111: *
112: * Authors:
113: * ========
114: *
1.16 bertrand 115: *> \author Univ. of Tennessee
116: *> \author Univ. of California Berkeley
117: *> \author Univ. of Colorado Denver
118: *> \author NAG Ltd.
1.10 bertrand 119: *
120: *> \ingroup doubleOTHERcomputational
121: *
122: * =====================================================================
1.1 bertrand 123: SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
124: $ INFO )
125: *
1.19 ! bertrand 126: * -- LAPACK computational routine --
1.1 bertrand 127: * -- LAPACK is a software package provided by Univ. of Tennessee, --
128: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129: *
130: * .. Scalar Arguments ..
131: CHARACTER UPLO
132: INTEGER INFO, N
133: DOUBLE PRECISION ANORM, RCOND
134: * ..
135: * .. Array Arguments ..
136: INTEGER IPIV( * ), IWORK( * )
137: DOUBLE PRECISION AP( * ), WORK( * )
138: * ..
139: *
140: * =====================================================================
141: *
142: * .. Parameters ..
143: DOUBLE PRECISION ONE, ZERO
144: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
145: * ..
146: * .. Local Scalars ..
147: LOGICAL UPPER
148: INTEGER I, IP, KASE
149: DOUBLE PRECISION AINVNM
150: * ..
151: * .. Local Arrays ..
152: INTEGER ISAVE( 3 )
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME
156: EXTERNAL LSAME
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL DLACN2, DSPTRS, XERBLA
160: * ..
161: * .. Executable Statements ..
162: *
163: * Test the input parameters.
164: *
165: INFO = 0
166: UPPER = LSAME( UPLO, 'U' )
167: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
168: INFO = -1
169: ELSE IF( N.LT.0 ) THEN
170: INFO = -2
171: ELSE IF( ANORM.LT.ZERO ) THEN
172: INFO = -5
173: END IF
174: IF( INFO.NE.0 ) THEN
175: CALL XERBLA( 'DSPCON', -INFO )
176: RETURN
177: END IF
178: *
179: * Quick return if possible
180: *
181: RCOND = ZERO
182: IF( N.EQ.0 ) THEN
183: RCOND = ONE
184: RETURN
185: ELSE IF( ANORM.LE.ZERO ) THEN
186: RETURN
187: END IF
188: *
189: * Check that the diagonal matrix D is nonsingular.
190: *
191: IF( UPPER ) THEN
192: *
193: * Upper triangular storage: examine D from bottom to top
194: *
195: IP = N*( N+1 ) / 2
196: DO 10 I = N, 1, -1
197: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
198: $ RETURN
199: IP = IP - I
200: 10 CONTINUE
201: ELSE
202: *
203: * Lower triangular storage: examine D from top to bottom.
204: *
205: IP = 1
206: DO 20 I = 1, N
207: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
208: $ RETURN
209: IP = IP + N - I + 1
210: 20 CONTINUE
211: END IF
212: *
213: * Estimate the 1-norm of the inverse.
214: *
215: KASE = 0
216: 30 CONTINUE
217: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
218: IF( KASE.NE.0 ) THEN
219: *
1.9 bertrand 220: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
1.1 bertrand 221: *
222: CALL DSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
223: GO TO 30
224: END IF
225: *
226: * Compute the estimate of the reciprocal condition number.
227: *
228: IF( AINVNM.NE.ZERO )
229: $ RCOND = ( ONE / AINVNM ) / ANORM
230: *
231: RETURN
232: *
233: * End of DSPCON
234: *
235: END
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