1: *> \brief \b ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHECON_ROOK + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhecon_rook.f">
11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhecon_rook.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHECON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
22: * INFO )
23: *
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: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZHECON_ROOK 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 CHETRF_ROOK.
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 CHETRF_ROOK.
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 CHETRF_ROOK.
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: *
115: *> \author Univ. of Tennessee
116: *> \author Univ. of California Berkeley
117: *> \author Univ. of Colorado Denver
118: *> \author NAG Ltd.
119: *
120: *> \date November 2013
121: *
122: *> \ingroup complex16HEcomputational
123: *
124: *> \par Contributors:
125: * ==================
126: *> \verbatim
127: *>
128: *> November 2013, Igor Kozachenko,
129: *> Computer Science Division,
130: *> University of California, Berkeley
131: *>
132: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
133: *> School of Mathematics,
134: *> University of Manchester
135: *>
136: *> \endverbatim
137: *
138: * =====================================================================
139: SUBROUTINE ZHECON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
140: $ INFO )
141: *
142: * -- LAPACK computational routine (version 3.5.0) --
143: * -- LAPACK is a software package provided by Univ. of Tennessee, --
144: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145: * November 2013
146: *
147: * .. Scalar Arguments ..
148: CHARACTER UPLO
149: INTEGER INFO, LDA, N
150: DOUBLE PRECISION ANORM, RCOND
151: * ..
152: * .. Array Arguments ..
153: INTEGER IPIV( * )
154: COMPLEX*16 A( LDA, * ), WORK( * )
155: * ..
156: *
157: * =====================================================================
158: *
159: * .. Parameters ..
160: REAL ONE, ZERO
161: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
162: * ..
163: * .. Local Scalars ..
164: LOGICAL UPPER
165: INTEGER I, KASE
166: DOUBLE PRECISION AINVNM
167: * ..
168: * .. Local Arrays ..
169: INTEGER ISAVE( 3 )
170: * ..
171: * .. External Functions ..
172: LOGICAL LSAME
173: EXTERNAL LSAME
174: * ..
175: * .. External Subroutines ..
176: EXTERNAL ZHETRS_ROOK, ZLACN2, XERBLA
177: * ..
178: * .. Intrinsic Functions ..
179: INTRINSIC MAX
180: * ..
181: * .. Executable Statements ..
182: *
183: * Test the input parameters.
184: *
185: INFO = 0
186: UPPER = LSAME( UPLO, 'U' )
187: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
188: INFO = -1
189: ELSE IF( N.LT.0 ) THEN
190: INFO = -2
191: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
192: INFO = -4
193: ELSE IF( ANORM.LT.ZERO ) THEN
194: INFO = -6
195: END IF
196: IF( INFO.NE.0 ) THEN
197: CALL XERBLA( 'ZHECON_ROOK', -INFO )
198: RETURN
199: END IF
200: *
201: * Quick return if possible
202: *
203: RCOND = ZERO
204: IF( N.EQ.0 ) THEN
205: RCOND = ONE
206: RETURN
207: ELSE IF( ANORM.LE.ZERO ) THEN
208: RETURN
209: END IF
210: *
211: * Check that the diagonal matrix D is nonsingular.
212: *
213: IF( UPPER ) THEN
214: *
215: * Upper triangular storage: examine D from bottom to top
216: *
217: DO 10 I = N, 1, -1
218: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
219: $ RETURN
220: 10 CONTINUE
221: ELSE
222: *
223: * Lower triangular storage: examine D from top to bottom.
224: *
225: DO 20 I = 1, N
226: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
227: $ RETURN
228: 20 CONTINUE
229: END IF
230: *
231: * Estimate the 1-norm of the inverse.
232: *
233: KASE = 0
234: 30 CONTINUE
235: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
236: IF( KASE.NE.0 ) THEN
237: *
238: * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
239: *
240: CALL ZHETRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
241: GO TO 30
242: END IF
243: *
244: * Compute the estimate of the reciprocal condition number.
245: *
246: IF( AINVNM.NE.ZERO )
247: $ RCOND = ( ONE / AINVNM ) / ANORM
248: *
249: RETURN
250: *
251: * End of ZHECON_ROOK
252: *
253: END
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