1: *> \brief \b ZSYCON_ROOK
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSYCON_ROOK + dependencies
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsycon_rook.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
22: * WORK, 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: *> ZSYCON_ROOK estimates the reciprocal of the condition number (in the
41: *> 1-norm) of a complex symmetric matrix A using the factorization
42: *> A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_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**T;
57: *> = 'L': Lower triangular, form is A = L*D*L**T.
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 ZSYTRF_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 ZSYTRF_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 complex16SYcomputational
121: *
122: *> \par Contributors:
123: * ==================
124: *> \verbatim
125: *>
126: *> December 2016, Igor Kozachenko,
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 ZSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
138: $ INFO )
139: *
140: * -- LAPACK computational routine --
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 ..
157: DOUBLE PRECISION ONE, ZERO
158: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
159: COMPLEX*16 CZERO
160: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
161: * ..
162: * .. Local Scalars ..
163: LOGICAL UPPER
164: INTEGER I, KASE
165: DOUBLE PRECISION AINVNM
166: * ..
167: * .. Local Arrays ..
168: INTEGER ISAVE( 3 )
169: * ..
170: * .. External Functions ..
171: LOGICAL LSAME
172: EXTERNAL LSAME
173: * ..
174: * .. External Subroutines ..
175: EXTERNAL ZLACN2, ZSYTRS_ROOK, XERBLA
176: * ..
177: * .. Intrinsic Functions ..
178: INTRINSIC MAX
179: * ..
180: * .. Executable Statements ..
181: *
182: * Test the input parameters.
183: *
184: INFO = 0
185: UPPER = LSAME( UPLO, 'U' )
186: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
187: INFO = -1
188: ELSE IF( N.LT.0 ) THEN
189: INFO = -2
190: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
191: INFO = -4
192: ELSE IF( ANORM.LT.ZERO ) THEN
193: INFO = -6
194: END IF
195: IF( INFO.NE.0 ) THEN
196: CALL XERBLA( 'ZSYCON_ROOK', -INFO )
197: RETURN
198: END IF
199: *
200: * Quick return if possible
201: *
202: RCOND = ZERO
203: IF( N.EQ.0 ) THEN
204: RCOND = ONE
205: RETURN
206: ELSE IF( ANORM.LE.ZERO ) THEN
207: RETURN
208: END IF
209: *
210: * Check that the diagonal matrix D is nonsingular.
211: *
212: IF( UPPER ) THEN
213: *
214: * Upper triangular storage: examine D from bottom to top
215: *
216: DO 10 I = N, 1, -1
217: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
218: $ RETURN
219: 10 CONTINUE
220: ELSE
221: *
222: * Lower triangular storage: examine D from top to bottom.
223: *
224: DO 20 I = 1, N
225: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
226: $ RETURN
227: 20 CONTINUE
228: END IF
229: *
230: * Estimate the 1-norm of the inverse.
231: *
232: KASE = 0
233: 30 CONTINUE
234: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
235: IF( KASE.NE.0 ) THEN
236: *
237: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
238: *
239: CALL ZSYTRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
240: GO TO 30
241: END IF
242: *
243: * Compute the estimate of the reciprocal condition number.
244: *
245: IF( AINVNM.NE.ZERO )
246: $ RCOND = ( ONE / AINVNM ) / ANORM
247: *
248: RETURN
249: *
250: * End of ZSYCON_ROOK
251: *
252: END
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