LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zgtcon.f
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1 *> \brief \b ZGTCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zgtcon(NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO)
ZGTCON
Definition: zgtcon.f:141
subroutine zgttrs(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
ZGTTRS
Definition: zgttrs.f:138
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:133