Annotation of rpl/lapack/lapack/zhecon.f, revision 1.18
1.9 bertrand 1: *> \brief \b ZHECON
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 ZHECON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhecon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhecon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhecon.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
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 IPIV( * )
31: * COMPLEX*16 A( LDA, * ), WORK( * )
32: * ..
1.15 bertrand 33: *
1.9 bertrand 34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZHECON estimates the reciprocal of the condition number of a complex
41: *> Hermitian matrix A using the factorization A = U*D*U**H or
42: *> A = L*D*L**H computed by ZHETRF.
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**H;
57: *> = 'L': Lower triangular, form is A = L*D*L**H.
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] A
67: *> \verbatim
68: *> A is COMPLEX*16 array, dimension (LDA,N)
69: *> The block diagonal matrix D and the multipliers used to
70: *> obtain the factor U or L as computed by ZHETRF.
71: *> \endverbatim
72: *>
73: *> \param[in] LDA
74: *> \verbatim
75: *> LDA is INTEGER
76: *> The leading dimension of the array A. LDA >= max(1,N).
77: *> \endverbatim
78: *>
79: *> \param[in] IPIV
80: *> \verbatim
81: *> IPIV is INTEGER array, dimension (N)
82: *> Details of the interchanges and the block structure of D
83: *> as determined by ZHETRF.
84: *> \endverbatim
85: *>
86: *> \param[in] ANORM
87: *> \verbatim
88: *> ANORM is DOUBLE PRECISION
89: *> The 1-norm of the original matrix A.
90: *> \endverbatim
91: *>
92: *> \param[out] RCOND
93: *> \verbatim
94: *> RCOND is DOUBLE PRECISION
95: *> The reciprocal of the condition number of the matrix A,
96: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
97: *> estimate of the 1-norm of inv(A) computed in this routine.
98: *> \endverbatim
99: *>
100: *> \param[out] WORK
101: *> \verbatim
102: *> WORK is COMPLEX*16 array, dimension (2*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: *
1.15 bertrand 115: *> \author Univ. of Tennessee
116: *> \author Univ. of California Berkeley
117: *> \author Univ. of Colorado Denver
118: *> \author NAG Ltd.
1.9 bertrand 119: *
120: *> \ingroup complex16HEcomputational
121: *
122: * =====================================================================
1.1 bertrand 123: SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
124: $ INFO )
125: *
1.18 ! 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, LDA, N
133: DOUBLE PRECISION ANORM, RCOND
134: * ..
135: * .. Array Arguments ..
136: INTEGER IPIV( * )
137: COMPLEX*16 A( LDA, * ), 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, 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 XERBLA, ZHETRS, ZLACN2
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC MAX
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( LDA.LT.MAX( 1, N ) ) THEN
175: INFO = -4
176: ELSE IF( ANORM.LT.ZERO ) THEN
177: INFO = -6
178: END IF
179: IF( INFO.NE.0 ) THEN
180: CALL XERBLA( 'ZHECON', -INFO )
181: RETURN
182: END IF
183: *
184: * Quick return if possible
185: *
186: RCOND = ZERO
187: IF( N.EQ.0 ) THEN
188: RCOND = ONE
189: RETURN
190: ELSE IF( ANORM.LE.ZERO ) THEN
191: RETURN
192: END IF
193: *
194: * Check that the diagonal matrix D is nonsingular.
195: *
196: IF( UPPER ) THEN
197: *
198: * Upper triangular storage: examine D from bottom to top
199: *
200: DO 10 I = N, 1, -1
201: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
202: $ RETURN
203: 10 CONTINUE
204: ELSE
205: *
206: * Lower triangular storage: examine D from top to bottom.
207: *
208: DO 20 I = 1, N
209: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
210: $ RETURN
211: 20 CONTINUE
212: END IF
213: *
214: * Estimate the 1-norm of the inverse.
215: *
216: KASE = 0
217: 30 CONTINUE
218: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
219: IF( KASE.NE.0 ) THEN
220: *
1.8 bertrand 221: * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
1.1 bertrand 222: *
223: CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
224: GO TO 30
225: END IF
226: *
227: * Compute the estimate of the reciprocal condition number.
228: *
229: IF( AINVNM.NE.ZERO )
230: $ RCOND = ( ONE / AINVNM ) / ANORM
231: *
232: RETURN
233: *
234: * End of ZHECON
235: *
236: END
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