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