1: *> \brief \b ZGTCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGTCON + dependencies
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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/zgtcon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
22: * WORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER NORM
26: * INTEGER INFO, N
27: * DOUBLE PRECISION ANORM, RCOND
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * )
31: * COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZGTCON estimates the reciprocal of the condition number of a complex
41: *> tridiagonal matrix A using the LU factorization as computed by
42: *> ZGTTRF.
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] NORM
52: *> \verbatim
53: *> NORM is CHARACTER*1
54: *> Specifies whether the 1-norm condition number or the
55: *> infinity-norm condition number is required:
56: *> = '1' or 'O': 1-norm;
57: *> = 'I': Infinity-norm.
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] DL
67: *> \verbatim
68: *> DL is COMPLEX*16 array, dimension (N-1)
69: *> The (n-1) multipliers that define the matrix L from the
70: *> LU factorization of A as computed by ZGTTRF.
71: *> \endverbatim
72: *>
73: *> \param[in] D
74: *> \verbatim
75: *> D is COMPLEX*16 array, dimension (N)
76: *> The n diagonal elements of the upper triangular matrix U from
77: *> the LU factorization of A.
78: *> \endverbatim
79: *>
80: *> \param[in] DU
81: *> \verbatim
82: *> DU is COMPLEX*16 array, dimension (N-1)
83: *> The (n-1) elements of the first superdiagonal of U.
84: *> \endverbatim
85: *>
86: *> \param[in] DU2
87: *> \verbatim
88: *> DU2 is COMPLEX*16 array, dimension (N-2)
89: *> The (n-2) elements of the second superdiagonal of U.
90: *> \endverbatim
91: *>
92: *> \param[in] IPIV
93: *> \verbatim
94: *> IPIV is INTEGER array, dimension (N)
95: *> The pivot indices; for 1 <= i <= n, row i of the matrix was
96: *> interchanged with row IPIV(i). IPIV(i) will always be either
97: *> i or i+1; IPIV(i) = i indicates a row interchange was not
98: *> required.
99: *> \endverbatim
100: *>
101: *> \param[in] ANORM
102: *> \verbatim
103: *> ANORM is DOUBLE PRECISION
104: *> If NORM = '1' or 'O', the 1-norm of the original matrix A.
105: *> If NORM = 'I', the infinity-norm of the original matrix A.
106: *> \endverbatim
107: *>
108: *> \param[out] RCOND
109: *> \verbatim
110: *> RCOND is DOUBLE PRECISION
111: *> The reciprocal of the condition number of the matrix A,
112: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
113: *> estimate of the 1-norm of inv(A) computed in this routine.
114: *> \endverbatim
115: *>
116: *> \param[out] WORK
117: *> \verbatim
118: *> WORK is COMPLEX*16 array, dimension (2*N)
119: *> \endverbatim
120: *>
121: *> \param[out] INFO
122: *> \verbatim
123: *> INFO is INTEGER
124: *> = 0: successful exit
125: *> < 0: if INFO = -i, the i-th argument had an illegal value
126: *> \endverbatim
127: *
128: * Authors:
129: * ========
130: *
131: *> \author Univ. of Tennessee
132: *> \author Univ. of California Berkeley
133: *> \author Univ. of Colorado Denver
134: *> \author NAG Ltd.
135: *
136: *> \ingroup complex16GTcomputational
137: *
138: * =====================================================================
139: SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
140: $ WORK, INFO )
141: *
142: * -- LAPACK computational routine --
143: * -- LAPACK is a software package provided by Univ. of Tennessee, --
144: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145: *
146: * .. Scalar Arguments ..
147: CHARACTER NORM
148: INTEGER INFO, N
149: DOUBLE PRECISION ANORM, RCOND
150: * ..
151: * .. Array Arguments ..
152: INTEGER IPIV( * )
153: COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
154: * ..
155: *
156: * =====================================================================
157: *
158: * .. Parameters ..
159: DOUBLE PRECISION ONE, ZERO
160: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
161: * ..
162: * .. Local Scalars ..
163: LOGICAL ONENRM
164: INTEGER I, KASE, KASE1
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 XERBLA, ZGTTRS, ZLACN2
176: * ..
177: * .. Intrinsic Functions ..
178: INTRINSIC DCMPLX
179: * ..
180: * .. Executable Statements ..
181: *
182: * Test the input arguments.
183: *
184: INFO = 0
185: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
186: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
187: INFO = -1
188: ELSE IF( N.LT.0 ) THEN
189: INFO = -2
190: ELSE IF( ANORM.LT.ZERO ) THEN
191: INFO = -8
192: END IF
193: IF( INFO.NE.0 ) THEN
194: CALL XERBLA( 'ZGTCON', -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.EQ.ZERO ) THEN
205: RETURN
206: END IF
207: *
208: * Check that D(1:N) is non-zero.
209: *
210: DO 10 I = 1, N
211: IF( D( I ).EQ.DCMPLX( ZERO ) )
212: $ RETURN
213: 10 CONTINUE
214: *
215: AINVNM = ZERO
216: IF( ONENRM ) THEN
217: KASE1 = 1
218: ELSE
219: KASE1 = 2
220: END IF
221: KASE = 0
222: 20 CONTINUE
223: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
224: IF( KASE.NE.0 ) THEN
225: IF( KASE.EQ.KASE1 ) THEN
226: *
227: * Multiply by inv(U)*inv(L).
228: *
229: CALL ZGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV,
230: $ WORK, N, INFO )
231: ELSE
232: *
233: * Multiply by inv(L**H)*inv(U**H).
234: *
235: CALL ZGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2,
236: $ IPIV, WORK, N, INFO )
237: END IF
238: GO TO 20
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 ZGTCON
249: *
250: END
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