Annotation of rpl/lapack/lapack/zhpcon.f, revision 1.14
1.9 bertrand 1: *> \brief \b ZHPCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHPCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpcon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpcon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpcon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, N
26: * DOUBLE PRECISION ANORM, RCOND
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IPIV( * )
30: * COMPLEX*16 AP( * ), WORK( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZHPCON estimates the reciprocal of the condition number of a complex
40: *> Hermitian packed matrix A using the factorization A = U*D*U**H or
41: *> A = L*D*L**H computed by ZHPTRF.
42: *>
43: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
44: *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
45: *> \endverbatim
46: *
47: * Arguments:
48: * ==========
49: *
50: *> \param[in] UPLO
51: *> \verbatim
52: *> UPLO is CHARACTER*1
53: *> Specifies whether the details of the factorization are stored
54: *> as an upper or lower triangular matrix.
55: *> = 'U': Upper triangular, form is A = U*D*U**H;
56: *> = 'L': Lower triangular, form is A = L*D*L**H.
57: *> \endverbatim
58: *>
59: *> \param[in] N
60: *> \verbatim
61: *> N is INTEGER
62: *> The order of the matrix A. N >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] AP
66: *> \verbatim
67: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
68: *> The block diagonal matrix D and the multipliers used to
69: *> obtain the factor U or L as computed by ZHPTRF, stored as a
70: *> packed triangular matrix.
71: *> \endverbatim
72: *>
73: *> \param[in] IPIV
74: *> \verbatim
75: *> IPIV is INTEGER array, dimension (N)
76: *> Details of the interchanges and the block structure of D
77: *> as determined by ZHPTRF.
78: *> \endverbatim
79: *>
80: *> \param[in] ANORM
81: *> \verbatim
82: *> ANORM is DOUBLE PRECISION
83: *> The 1-norm of the original matrix A.
84: *> \endverbatim
85: *>
86: *> \param[out] RCOND
87: *> \verbatim
88: *> RCOND is DOUBLE PRECISION
89: *> The reciprocal of the condition number of the matrix A,
90: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
91: *> estimate of the 1-norm of inv(A) computed in this routine.
92: *> \endverbatim
93: *>
94: *> \param[out] WORK
95: *> \verbatim
96: *> WORK is COMPLEX*16 array, dimension (2*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 November 2011
115: *
116: *> \ingroup complex16OTHERcomputational
117: *
118: * =====================================================================
1.1 bertrand 119: SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
120: *
1.9 bertrand 121: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 122: * -- LAPACK is a software package provided by Univ. of Tennessee, --
123: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 124: * November 2011
1.1 bertrand 125: *
126: * .. Scalar Arguments ..
127: CHARACTER UPLO
128: INTEGER INFO, N
129: DOUBLE PRECISION ANORM, RCOND
130: * ..
131: * .. Array Arguments ..
132: INTEGER IPIV( * )
133: COMPLEX*16 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: INTEGER I, IP, KASE
145: DOUBLE PRECISION AINVNM
146: * ..
147: * .. Local Arrays ..
148: INTEGER ISAVE( 3 )
149: * ..
150: * .. External Functions ..
151: LOGICAL LSAME
152: EXTERNAL LSAME
153: * ..
154: * .. External Subroutines ..
155: EXTERNAL XERBLA, ZHPTRS, ZLACN2
156: * ..
157: * .. Executable Statements ..
158: *
159: * Test the input parameters.
160: *
161: INFO = 0
162: UPPER = LSAME( UPLO, 'U' )
163: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
164: INFO = -1
165: ELSE IF( N.LT.0 ) THEN
166: INFO = -2
167: ELSE IF( ANORM.LT.ZERO ) THEN
168: INFO = -5
169: END IF
170: IF( INFO.NE.0 ) THEN
171: CALL XERBLA( 'ZHPCON', -INFO )
172: RETURN
173: END IF
174: *
175: * Quick return if possible
176: *
177: RCOND = ZERO
178: IF( N.EQ.0 ) THEN
179: RCOND = ONE
180: RETURN
181: ELSE IF( ANORM.LE.ZERO ) THEN
182: RETURN
183: END IF
184: *
185: * Check that the diagonal matrix D is nonsingular.
186: *
187: IF( UPPER ) THEN
188: *
189: * Upper triangular storage: examine D from bottom to top
190: *
191: IP = N*( N+1 ) / 2
192: DO 10 I = N, 1, -1
193: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
194: $ RETURN
195: IP = IP - I
196: 10 CONTINUE
197: ELSE
198: *
199: * Lower triangular storage: examine D from top to bottom.
200: *
201: IP = 1
202: DO 20 I = 1, N
203: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
204: $ RETURN
205: IP = IP + N - I + 1
206: 20 CONTINUE
207: END IF
208: *
209: * Estimate the 1-norm of the inverse.
210: *
211: KASE = 0
212: 30 CONTINUE
213: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
214: IF( KASE.NE.0 ) THEN
215: *
1.8 bertrand 216: * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
1.1 bertrand 217: *
218: CALL ZHPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
219: GO TO 30
220: END IF
221: *
222: * Compute the estimate of the reciprocal condition number.
223: *
224: IF( AINVNM.NE.ZERO )
225: $ RCOND = ( ONE / AINVNM ) / ANORM
226: *
227: RETURN
228: *
229: * End of ZHPCON
230: *
231: END
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