Annotation of rpl/lapack/lapack/dpocon.f, revision 1.16
1.9 bertrand 1: *> \brief \b DPOCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download DPOCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpocon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpocon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpocon.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
22: * INFO )
1.15 bertrand 23: *
1.9 bertrand 24: * .. Scalar Arguments ..
25: * CHARACTER UPLO
26: * INTEGER INFO, LDA, N
27: * DOUBLE PRECISION ANORM, RCOND
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IWORK( * )
31: * DOUBLE PRECISION A( LDA, * ), WORK( * )
32: * ..
1.15 bertrand 33: *
1.9 bertrand 34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DPOCON estimates the reciprocal of the condition number (in the
41: *> 1-norm) of a real symmetric positive definite matrix using the
42: *> Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.
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: *> = 'U': Upper triangle of A is stored;
55: *> = 'L': Lower triangle of A is stored.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] A
65: *> \verbatim
66: *> A is DOUBLE PRECISION array, dimension (LDA,N)
67: *> The triangular factor U or L from the Cholesky factorization
68: *> A = U**T*U or A = L*L**T, as computed by DPOTRF.
69: *> \endverbatim
70: *>
71: *> \param[in] LDA
72: *> \verbatim
73: *> LDA is INTEGER
74: *> The leading dimension of the array A. LDA >= max(1,N).
75: *> \endverbatim
76: *>
77: *> \param[in] ANORM
78: *> \verbatim
79: *> ANORM is DOUBLE PRECISION
80: *> The 1-norm (or infinity-norm) of the symmetric matrix A.
81: *> \endverbatim
82: *>
83: *> \param[out] RCOND
84: *> \verbatim
85: *> RCOND is DOUBLE PRECISION
86: *> The reciprocal of the condition number of the matrix A,
87: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
88: *> estimate of the 1-norm of inv(A) computed in this routine.
89: *> \endverbatim
90: *>
91: *> \param[out] WORK
92: *> \verbatim
93: *> WORK is DOUBLE PRECISION array, dimension (3*N)
94: *> \endverbatim
95: *>
96: *> \param[out] IWORK
97: *> \verbatim
98: *> IWORK is INTEGER array, dimension (N)
99: *> \endverbatim
100: *>
101: *> \param[out] INFO
102: *> \verbatim
103: *> INFO is INTEGER
104: *> = 0: successful exit
105: *> < 0: if INFO = -i, the i-th argument had an illegal value
106: *> \endverbatim
107: *
108: * Authors:
109: * ========
110: *
1.15 bertrand 111: *> \author Univ. of Tennessee
112: *> \author Univ. of California Berkeley
113: *> \author Univ. of Colorado Denver
114: *> \author NAG Ltd.
1.9 bertrand 115: *
1.15 bertrand 116: *> \date December 2016
1.9 bertrand 117: *
118: *> \ingroup doublePOcomputational
119: *
120: * =====================================================================
1.1 bertrand 121: SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
122: $ INFO )
123: *
1.15 bertrand 124: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 127: * December 2016
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: CHARACTER UPLO
131: INTEGER INFO, LDA, N
132: DOUBLE PRECISION ANORM, RCOND
133: * ..
134: * .. Array Arguments ..
135: INTEGER IWORK( * )
136: DOUBLE PRECISION A( LDA, * ), WORK( * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: DOUBLE PRECISION ONE, ZERO
143: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
144: * ..
145: * .. Local Scalars ..
146: LOGICAL UPPER
147: CHARACTER NORMIN
148: INTEGER IX, KASE
149: DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
150: * ..
151: * .. Local Arrays ..
152: INTEGER ISAVE( 3 )
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME
156: INTEGER IDAMAX
157: DOUBLE PRECISION DLAMCH
158: EXTERNAL LSAME, IDAMAX, DLAMCH
159: * ..
160: * .. External Subroutines ..
161: EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA
162: * ..
163: * .. Intrinsic Functions ..
164: INTRINSIC ABS, MAX
165: * ..
166: * .. Executable Statements ..
167: *
168: * Test the input parameters.
169: *
170: INFO = 0
171: UPPER = LSAME( UPLO, 'U' )
172: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
173: INFO = -1
174: ELSE IF( N.LT.0 ) THEN
175: INFO = -2
176: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
177: INFO = -4
178: ELSE IF( ANORM.LT.ZERO ) THEN
179: INFO = -5
180: END IF
181: IF( INFO.NE.0 ) THEN
182: CALL XERBLA( 'DPOCON', -INFO )
183: RETURN
184: END IF
185: *
186: * Quick return if possible
187: *
188: RCOND = ZERO
189: IF( N.EQ.0 ) THEN
190: RCOND = ONE
191: RETURN
192: ELSE IF( ANORM.EQ.ZERO ) THEN
193: RETURN
194: END IF
195: *
196: SMLNUM = DLAMCH( 'Safe minimum' )
197: *
198: * Estimate the 1-norm of inv(A).
199: *
200: KASE = 0
201: NORMIN = 'N'
202: 10 CONTINUE
203: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
204: IF( KASE.NE.0 ) THEN
205: IF( UPPER ) THEN
206: *
1.8 bertrand 207: * Multiply by inv(U**T).
1.1 bertrand 208: *
209: CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
210: $ LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
211: NORMIN = 'Y'
212: *
213: * Multiply by inv(U).
214: *
215: CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
216: $ A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
217: ELSE
218: *
219: * Multiply by inv(L).
220: *
221: CALL DLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
222: $ A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
223: NORMIN = 'Y'
224: *
1.8 bertrand 225: * Multiply by inv(L**T).
1.1 bertrand 226: *
227: CALL DLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A,
228: $ LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
229: END IF
230: *
231: * Multiply by 1/SCALE if doing so will not cause overflow.
232: *
233: SCALE = SCALEL*SCALEU
234: IF( SCALE.NE.ONE ) THEN
235: IX = IDAMAX( N, WORK, 1 )
236: IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
237: $ GO TO 20
238: CALL DRSCL( N, SCALE, WORK, 1 )
239: END IF
240: GO TO 10
241: END IF
242: *
243: * Compute the estimate of the reciprocal condition number.
244: *
245: IF( AINVNM.NE.ZERO )
246: $ RCOND = ( ONE / AINVNM ) / ANORM
247: *
248: 20 CONTINUE
249: RETURN
250: *
251: * End of DPOCON
252: *
253: END
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