Annotation of rpl/lapack/lapack/dspcon.f, revision 1.16
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: *
1.16 ! bertrand 120: *> \date December 2016
1.10 bertrand 121: *
122: *> \ingroup doubleOTHERcomputational
123: *
124: * =====================================================================
1.1 bertrand 125: SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
126: $ INFO )
127: *
1.16 ! bertrand 128: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.16 ! bertrand 131: * December 2016
1.1 bertrand 132: *
133: * .. Scalar Arguments ..
134: CHARACTER UPLO
135: INTEGER INFO, N
136: DOUBLE PRECISION ANORM, RCOND
137: * ..
138: * .. Array Arguments ..
139: INTEGER IPIV( * ), IWORK( * )
140: DOUBLE PRECISION AP( * ), WORK( * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ONE, ZERO
147: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
148: * ..
149: * .. Local Scalars ..
150: LOGICAL UPPER
151: INTEGER I, IP, KASE
152: DOUBLE PRECISION AINVNM
153: * ..
154: * .. Local Arrays ..
155: INTEGER ISAVE( 3 )
156: * ..
157: * .. External Functions ..
158: LOGICAL LSAME
159: EXTERNAL LSAME
160: * ..
161: * .. External Subroutines ..
162: EXTERNAL DLACN2, DSPTRS, XERBLA
163: * ..
164: * .. Executable Statements ..
165: *
166: * Test the input parameters.
167: *
168: INFO = 0
169: UPPER = LSAME( UPLO, 'U' )
170: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
171: INFO = -1
172: ELSE IF( N.LT.0 ) THEN
173: INFO = -2
174: ELSE IF( ANORM.LT.ZERO ) THEN
175: INFO = -5
176: END IF
177: IF( INFO.NE.0 ) THEN
178: CALL XERBLA( 'DSPCON', -INFO )
179: RETURN
180: END IF
181: *
182: * Quick return if possible
183: *
184: RCOND = ZERO
185: IF( N.EQ.0 ) THEN
186: RCOND = ONE
187: RETURN
188: ELSE IF( ANORM.LE.ZERO ) THEN
189: RETURN
190: END IF
191: *
192: * Check that the diagonal matrix D is nonsingular.
193: *
194: IF( UPPER ) THEN
195: *
196: * Upper triangular storage: examine D from bottom to top
197: *
198: IP = N*( N+1 ) / 2
199: DO 10 I = N, 1, -1
200: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
201: $ RETURN
202: IP = IP - I
203: 10 CONTINUE
204: ELSE
205: *
206: * Lower triangular storage: examine D from top to bottom.
207: *
208: IP = 1
209: DO 20 I = 1, N
210: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
211: $ RETURN
212: IP = IP + N - I + 1
213: 20 CONTINUE
214: END IF
215: *
216: * Estimate the 1-norm of the inverse.
217: *
218: KASE = 0
219: 30 CONTINUE
220: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
221: IF( KASE.NE.0 ) THEN
222: *
1.9 bertrand 223: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
1.1 bertrand 224: *
225: CALL DSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
226: GO TO 30
227: END IF
228: *
229: * Compute the estimate of the reciprocal condition number.
230: *
231: IF( AINVNM.NE.ZERO )
232: $ RCOND = ( ONE / AINVNM ) / ANORM
233: *
234: RETURN
235: *
236: * End of DSPCON
237: *
238: END
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