1*> \brief \b ZPTT01
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 ZPTT01( N, D, E, DF, EF, WORK, RESID )
12*
13*       .. Scalar Arguments ..
14*       INTEGER            N
15*       DOUBLE PRECISION   RESID
16*       ..
17*       .. Array Arguments ..
18*       DOUBLE PRECISION   D( * ), DF( * )
19*       COMPLEX*16         E( * ), EF( * ), WORK( * )
20*       ..
21*
22*
23*> \par Purpose:
24*  =============
25*>
26*> \verbatim
27*>
28*> ZPTT01 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 DOUBLE PRECISION 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*16 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 DOUBLE PRECISION 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*16 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*16 array, dimension (2*N)
72*> \endverbatim
73*>
74*> \param[out] RESID
75*> \verbatim
76*>          RESID is DOUBLE PRECISION
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*> \date December 2016
89*
90*> \ingroup complex16_lin
91*
92*  =====================================================================
93      SUBROUTINE ZPTT01( N, D, E, DF, EF, WORK, RESID )
94*
95*  -- LAPACK test routine (version 3.7.0) --
96*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
97*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
98*     December 2016
99*
100*     .. Scalar Arguments ..
101      INTEGER            N
102      DOUBLE PRECISION   RESID
103*     ..
104*     .. Array Arguments ..
105      DOUBLE PRECISION   D( * ), DF( * )
106      COMPLEX*16         E( * ), EF( * ), WORK( * )
107*     ..
108*
109*  =====================================================================
110*
111*     .. Parameters ..
112      DOUBLE PRECISION   ONE, ZERO
113      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
114*     ..
115*     .. Local Scalars ..
116      INTEGER            I
117      DOUBLE PRECISION   ANORM, EPS
118      COMPLEX*16         DE
119*     ..
120*     .. External Functions ..
121      DOUBLE PRECISION   DLAMCH
122      EXTERNAL           DLAMCH
123*     ..
124*     .. Intrinsic Functions ..
125      INTRINSIC          ABS, DBLE, DCONJG, MAX
126*     ..
127*     .. Executable Statements ..
128*
129*     Quick return if possible
130*
131      IF( N.LE.0 ) THEN
132         RESID = ZERO
133         RETURN
134      END IF
135*
136      EPS = DLAMCH( 'Epsilon' )
137*
138*     Construct the difference L*D*L' - A.
139*
140      WORK( 1 ) = DF( 1 ) - D( 1 )
141      DO 10 I = 1, N - 1
142         DE = DF( I )*EF( I )
143         WORK( N+I ) = DE - E( I )
144         WORK( 1+I ) = DE*DCONJG( EF( I ) ) + DF( I+1 ) - D( I+1 )
145   10 CONTINUE
146*
147*     Compute the 1-norms of the tridiagonal matrices A and WORK.
148*
149      IF( N.EQ.1 ) THEN
150         ANORM = D( 1 )
151         RESID = ABS( WORK( 1 ) )
152      ELSE
153         ANORM = MAX( D( 1 )+ABS( E( 1 ) ), D( N )+ABS( E( N-1 ) ) )
154         RESID = MAX( ABS( WORK( 1 ) )+ABS( WORK( N+1 ) ),
155     $           ABS( WORK( N ) )+ABS( WORK( 2*N-1 ) ) )
156         DO 20 I = 2, N - 1
157            ANORM = MAX( ANORM, D( I )+ABS( E( I ) )+ABS( E( I-1 ) ) )
158            RESID = MAX( RESID, ABS( WORK( I ) )+ABS( WORK( N+I-1 ) )+
159     $              ABS( WORK( N+I ) ) )
160   20    CONTINUE
161      END IF
162*
163*     Compute norm(L*D*L' - A) / (n * norm(A) * EPS)
164*
165      IF( ANORM.LE.ZERO ) THEN
166         IF( RESID.NE.ZERO )
167     $      RESID = ONE / EPS
168      ELSE
169         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
170      END IF
171*
172      RETURN
173*
174*     End of ZPTT01
175*
176      END
177