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
174