1: *> \brief \b ZSYCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSYCON + dependencies
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14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsycon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSYCON( 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: *> ZSYCON 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.
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.
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.
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 2011
121: *
122: *> \ingroup complex16SYcomputational
123: *
124: * =====================================================================
125: SUBROUTINE ZSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
126: $ INFO )
127: *
128: * -- LAPACK computational routine (version 3.4.0) --
129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131: * November 2011
132: *
133: * .. Scalar Arguments ..
134: CHARACTER UPLO
135: INTEGER INFO, LDA, N
136: DOUBLE PRECISION ANORM, RCOND
137: * ..
138: * .. Array Arguments ..
139: INTEGER IPIV( * )
140: COMPLEX*16 A( LDA, * ), WORK( * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ONE, ZERO
147: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
148: * ..
149: * .. Local Scalars ..
150: LOGICAL UPPER
151: INTEGER I, KASE
152: DOUBLE PRECISION AINVNM
153: * ..
154: * .. Local Arrays ..
155: INTEGER ISAVE( 3 )
156: * ..
157: * .. External Functions ..
158: LOGICAL LSAME
159: EXTERNAL LSAME
160: * ..
161: * .. External Subroutines ..
162: EXTERNAL XERBLA, ZLACN2, ZSYTRS
163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC MAX
166: * ..
167: * .. Executable Statements ..
168: *
169: * Test the input parameters.
170: *
171: INFO = 0
172: UPPER = LSAME( UPLO, 'U' )
173: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
174: INFO = -1
175: ELSE IF( N.LT.0 ) THEN
176: INFO = -2
177: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
178: INFO = -4
179: ELSE IF( ANORM.LT.ZERO ) THEN
180: INFO = -6
181: END IF
182: IF( INFO.NE.0 ) THEN
183: CALL XERBLA( 'ZSYCON', -INFO )
184: RETURN
185: END IF
186: *
187: * Quick return if possible
188: *
189: RCOND = ZERO
190: IF( N.EQ.0 ) THEN
191: RCOND = ONE
192: RETURN
193: ELSE IF( ANORM.LE.ZERO ) THEN
194: RETURN
195: END IF
196: *
197: * Check that the diagonal matrix D is nonsingular.
198: *
199: IF( UPPER ) THEN
200: *
201: * Upper triangular storage: examine D from bottom to top
202: *
203: DO 10 I = N, 1, -1
204: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
205: $ RETURN
206: 10 CONTINUE
207: ELSE
208: *
209: * Lower triangular storage: examine D from top to bottom.
210: *
211: DO 20 I = 1, N
212: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
213: $ RETURN
214: 20 CONTINUE
215: END IF
216: *
217: * Estimate the 1-norm of the inverse.
218: *
219: KASE = 0
220: 30 CONTINUE
221: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
222: IF( KASE.NE.0 ) THEN
223: *
224: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
225: *
226: CALL ZSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
227: GO TO 30
228: END IF
229: *
230: * Compute the estimate of the reciprocal condition number.
231: *
232: IF( AINVNM.NE.ZERO )
233: $ RCOND = ( ONE / AINVNM ) / ANORM
234: *
235: RETURN
236: *
237: * End of ZSYCON
238: *
239: END
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