1*> \brief \b SPTT01
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 SPTT01( 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( * ), E( * ), EF( * ), WORK( * )
19*       ..
20*
21*
22*> \par Purpose:
23*  =============
24*>
25*> \verbatim
26*>
27*> SPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
28*> factorization and computes the residual
29*>    norm(L*D*L' - A) / ( n * norm(A) * EPS ),
30*> where EPS is the machine epsilon.
31*> \endverbatim
32*
33*  Arguments:
34*  ==========
35*
36*> \param[in] N
37*> \verbatim
38*>          N is INTEGTER
39*>          The order of the matrix A.
40*> \endverbatim
41*>
42*> \param[in] D
43*> \verbatim
44*>          D is REAL array, dimension (N)
45*>          The n diagonal elements of the tridiagonal matrix A.
46*> \endverbatim
47*>
48*> \param[in] E
49*> \verbatim
50*>          E is REAL array, dimension (N-1)
51*>          The (n-1) subdiagonal elements of the tridiagonal matrix A.
52*> \endverbatim
53*>
54*> \param[in] DF
55*> \verbatim
56*>          DF is REAL array, dimension (N)
57*>          The n diagonal elements of the factor L from the L*D*L'
58*>          factorization of A.
59*> \endverbatim
60*>
61*> \param[in] EF
62*> \verbatim
63*>          EF is REAL array, dimension (N-1)
64*>          The (n-1) subdiagonal elements of the factor L from the
65*>          L*D*L' factorization of A.
66*> \endverbatim
67*>
68*> \param[out] WORK
69*> \verbatim
70*>          WORK is REAL array, dimension (2*N)
71*> \endverbatim
72*>
73*> \param[out] RESID
74*> \verbatim
75*>          RESID is REAL
76*>          norm(L*D*L' - A) / (n * norm(A) * EPS)
77*> \endverbatim
78*
79*  Authors:
80*  ========
81*
82*> \author Univ. of Tennessee
83*> \author Univ. of California Berkeley
84*> \author Univ. of Colorado Denver
85*> \author NAG Ltd.
86*
87*> \date November 2011
88*
89*> \ingroup single_lin
90*
91*  =====================================================================
92      SUBROUTINE SPTT01( N, D, E, DF, EF, WORK, RESID )
93*
94*  -- LAPACK test routine (version 3.4.0) --
95*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
96*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
97*     November 2011
98*
99*     .. Scalar Arguments ..
100      INTEGER            N
101      REAL               RESID
102*     ..
103*     .. Array Arguments ..
104      REAL               D( * ), DF( * ), E( * ), EF( * ), WORK( * )
105*     ..
106*
107*  =====================================================================
108*
109*     .. Parameters ..
110      REAL               ONE, ZERO
111      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
112*     ..
113*     .. Local Scalars ..
114      INTEGER            I
115      REAL               ANORM, DE, EPS
116*     ..
117*     .. External Functions ..
118      REAL               SLAMCH
119      EXTERNAL           SLAMCH
120*     ..
121*     .. Intrinsic Functions ..
122      INTRINSIC          ABS, 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*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 SPTT01
172*
173      END
174