LAPACK  3.9.1 LAPACK: Linear Algebra PACKage
cptt01.f
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1 *> \brief \b CPTT01
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE CPTT01( N, D, E, DF, EF, WORK, RESID )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER N
15 * REAL RESID
16 * ..
17 * .. Array Arguments ..
18 * REAL D( * ), DF( * )
19 * COMPLEX E( * ), EF( * ), WORK( * )
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> CPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
29 *> factorization and computes the residual
30 *> norm(L*D*L' - A) / ( n * norm(A) * EPS ),
31 *> where EPS is the machine epsilon.
32 *> \endverbatim
33 *
34 * Arguments:
35 * ==========
36 *
37 *> \param[in] N
38 *> \verbatim
39 *> N is INTEGTER
40 *> The order of the matrix A.
41 *> \endverbatim
42 *>
43 *> \param[in] D
44 *> \verbatim
45 *> D is REAL array, dimension (N)
46 *> The n diagonal elements of the tridiagonal matrix A.
47 *> \endverbatim
48 *>
49 *> \param[in] E
50 *> \verbatim
51 *> E is COMPLEX array, dimension (N-1)
52 *> The (n-1) subdiagonal elements of the tridiagonal matrix A.
53 *> \endverbatim
54 *>
55 *> \param[in] DF
56 *> \verbatim
57 *> DF is REAL array, dimension (N)
58 *> The n diagonal elements of the factor L from the L*D*L'
59 *> factorization of A.
60 *> \endverbatim
61 *>
62 *> \param[in] EF
63 *> \verbatim
64 *> EF is COMPLEX array, dimension (N-1)
65 *> The (n-1) subdiagonal elements of the factor L from the
66 *> L*D*L' factorization of A.
67 *> \endverbatim
68 *>
69 *> \param[out] WORK
70 *> \verbatim
71 *> WORK is COMPLEX array, dimension (2*N)
72 *> \endverbatim
73 *>
74 *> \param[out] RESID
75 *> \verbatim
76 *> RESID is REAL
77 *> norm(L*D*L' - A) / (n * norm(A) * EPS)
78 *> \endverbatim
79 *
80 * Authors:
81 * ========
82 *
83 *> \author Univ. of Tennessee
84 *> \author Univ. of California Berkeley
85 *> \author Univ. of Colorado Denver
86 *> \author NAG Ltd.
87 *
88 *> \ingroup complex_lin
89 *
90 * =====================================================================
91  SUBROUTINE cptt01( N, D, E, DF, EF, WORK, RESID )
92 *
93 * -- LAPACK test routine --
94 * -- LAPACK is a software package provided by Univ. of Tennessee, --
95 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
96 *
97 * .. Scalar Arguments ..
98  INTEGER N
99  REAL RESID
100 * ..
101 * .. Array Arguments ..
102  REAL D( * ), DF( * )
103  COMPLEX E( * ), EF( * ), WORK( * )
104 * ..
105 *
106 * =====================================================================
107 *
108 * .. Parameters ..
109  REAL ONE, ZERO
110  parameter( one = 1.0e+0, zero = 0.0e+0 )
111 * ..
112 * .. Local Scalars ..
113  INTEGER I
114  REAL ANORM, EPS
115  COMPLEX DE
116 * ..
117 * .. External Functions ..
118  REAL SLAMCH
119  EXTERNAL slamch
120 * ..
121 * .. Intrinsic Functions ..
122  INTRINSIC abs, conjg, max, real
123 * ..
124 * .. Executable Statements ..
125 *
126 * Quick return if possible
127 *
128  IF( n.LE.0 ) THEN
129  resid = zero
130  RETURN
131  END IF
132 *
133  eps = slamch( 'Epsilon' )
134 *
135 * Construct the difference L*D*L' - A.
136 *
137  work( 1 ) = df( 1 ) - d( 1 )
138  DO 10 i = 1, n - 1
139  de = df( i )*ef( i )
140  work( n+i ) = de - e( i )
141  work( 1+i ) = de*conjg( ef( i ) ) + df( i+1 ) - d( i+1 )
142  10 CONTINUE
143 *
144 * Compute the 1-norms of the tridiagonal matrices A and WORK.
145 *
146  IF( n.EQ.1 ) THEN
147  anorm = d( 1 )
148  resid = abs( work( 1 ) )
149  ELSE
150  anorm = max( d( 1 )+abs( e( 1 ) ), d( n )+abs( e( n-1 ) ) )
151  resid = max( abs( work( 1 ) )+abs( work( n+1 ) ),
152  \$ abs( work( n ) )+abs( work( 2*n-1 ) ) )
153  DO 20 i = 2, n - 1
154  anorm = max( anorm, d( i )+abs( e( i ) )+abs( e( i-1 ) ) )
155  resid = max( resid, abs( work( i ) )+abs( work( n+i-1 ) )+
156  \$ abs( work( n+i ) ) )
157  20 CONTINUE
158  END IF
159 *
160 * Compute norm(L*D*L' - A) / (n * norm(A) * EPS)
161 *
162  IF( anorm.LE.zero ) THEN
163  IF( resid.NE.zero )
164  \$ resid = one / eps
165  ELSE
166  resid = ( ( resid / real( n ) ) / anorm ) / eps
167  END IF
168 *
169  RETURN
170 *
171 * End of CPTT01
172 *
173  END
subroutine cptt01(N, D, E, DF, EF, WORK, RESID)
CPTT01
Definition: cptt01.f:92