Annotation of rpl/lapack/lapack/zhecon_rook.f, revision 1.8
1.4 bertrand 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) </b>
1.1 bertrand 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>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhecon_rook.f">
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: *> \ingroup complex16HEcomputational
121: *
122: *> \par Contributors:
123: * ==================
124: *> \verbatim
125: *>
1.6 bertrand 126: *> June 2017, Igor Kozachenko,
1.1 bertrand 127: *> Computer Science Division,
128: *> University of California, Berkeley
129: *>
130: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
131: *> School of Mathematics,
132: *> University of Manchester
133: *>
134: *> \endverbatim
135: *
136: * =====================================================================
137: SUBROUTINE ZHECON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
138: $ INFO )
139: *
1.8 ! bertrand 140: * -- LAPACK computational routine --
1.1 bertrand 141: * -- LAPACK is a software package provided by Univ. of Tennessee, --
142: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143: *
144: * .. Scalar Arguments ..
145: CHARACTER UPLO
146: INTEGER INFO, LDA, N
147: DOUBLE PRECISION ANORM, RCOND
148: * ..
149: * .. Array Arguments ..
150: INTEGER IPIV( * )
151: COMPLEX*16 A( LDA, * ), WORK( * )
152: * ..
153: *
154: * =====================================================================
155: *
156: * .. Parameters ..
1.6 bertrand 157: DOUBLE PRECISION ONE, ZERO
1.1 bertrand 158: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
159: * ..
160: * .. Local Scalars ..
161: LOGICAL UPPER
162: INTEGER I, KASE
163: DOUBLE PRECISION AINVNM
164: * ..
165: * .. Local Arrays ..
166: INTEGER ISAVE( 3 )
167: * ..
168: * .. External Functions ..
169: LOGICAL LSAME
170: EXTERNAL LSAME
171: * ..
172: * .. External Subroutines ..
173: EXTERNAL ZHETRS_ROOK, ZLACN2, XERBLA
174: * ..
175: * .. Intrinsic Functions ..
176: INTRINSIC MAX
177: * ..
178: * .. Executable Statements ..
179: *
180: * Test the input parameters.
181: *
182: INFO = 0
183: UPPER = LSAME( UPLO, 'U' )
184: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
185: INFO = -1
186: ELSE IF( N.LT.0 ) THEN
187: INFO = -2
188: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
189: INFO = -4
190: ELSE IF( ANORM.LT.ZERO ) THEN
191: INFO = -6
192: END IF
193: IF( INFO.NE.0 ) THEN
194: CALL XERBLA( 'ZHECON_ROOK', -INFO )
195: RETURN
196: END IF
197: *
198: * Quick return if possible
199: *
200: RCOND = ZERO
201: IF( N.EQ.0 ) THEN
202: RCOND = ONE
203: RETURN
204: ELSE IF( ANORM.LE.ZERO ) THEN
205: RETURN
206: END IF
207: *
208: * Check that the diagonal matrix D is nonsingular.
209: *
210: IF( UPPER ) THEN
211: *
212: * Upper triangular storage: examine D from bottom to top
213: *
214: DO 10 I = N, 1, -1
215: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
216: $ RETURN
217: 10 CONTINUE
218: ELSE
219: *
220: * Lower triangular storage: examine D from top to bottom.
221: *
222: DO 20 I = 1, N
223: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
224: $ RETURN
225: 20 CONTINUE
226: END IF
227: *
228: * Estimate the 1-norm of the inverse.
229: *
230: KASE = 0
231: 30 CONTINUE
232: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
233: IF( KASE.NE.0 ) THEN
234: *
235: * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
236: *
237: CALL ZHETRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
238: GO TO 30
239: END IF
240: *
241: * Compute the estimate of the reciprocal condition number.
242: *
243: IF( AINVNM.NE.ZERO )
244: $ RCOND = ( ONE / AINVNM ) / ANORM
245: *
246: RETURN
247: *
248: * End of ZHECON_ROOK
249: *
250: END
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