1*> \brief \b CPTT02
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 CPTT02( UPLO, N, NRHS, D, E, X, LDX, B, LDB, RESID )
12*
13*       .. Scalar Arguments ..
14*       CHARACTER          UPLO
15*       INTEGER            LDB, LDX, N, NRHS
16*       REAL               RESID
17*       ..
18*       .. Array Arguments ..
19*       REAL               D( * )
20*       COMPLEX            B( LDB, * ), E( * ), X( LDX, * )
21*       ..
22*
23*
24*> \par Purpose:
25*  =============
26*>
27*> \verbatim
28*>
29*> CPTT02 computes the residual for the solution to a symmetric
30*> tridiagonal system of equations:
31*>    RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
32*> where EPS is the machine epsilon.
33*> \endverbatim
34*
35*  Arguments:
36*  ==========
37*
38*> \param[in] UPLO
39*> \verbatim
40*>          UPLO is CHARACTER*1
41*>          Specifies whether the superdiagonal or the subdiagonal of the
42*>          tridiagonal matrix A is stored.
43*>          = 'U':  E is the superdiagonal of A
44*>          = 'L':  E is the subdiagonal of A
45*> \endverbatim
46*>
47*> \param[in] N
48*> \verbatim
49*>          N is INTEGTER
50*>          The order of the matrix A.
51*> \endverbatim
52*>
53*> \param[in] NRHS
54*> \verbatim
55*>          NRHS is INTEGER
56*>          The number of right hand sides, i.e., the number of columns
57*>          of the matrices B and X.  NRHS >= 0.
58*> \endverbatim
59*>
60*> \param[in] D
61*> \verbatim
62*>          D is REAL array, dimension (N)
63*>          The n diagonal elements of the tridiagonal matrix A.
64*> \endverbatim
65*>
66*> \param[in] E
67*> \verbatim
68*>          E is COMPLEX array, dimension (N-1)
69*>          The (n-1) subdiagonal elements of the tridiagonal matrix A.
70*> \endverbatim
71*>
72*> \param[in] X
73*> \verbatim
74*>          X is COMPLEX array, dimension (LDX,NRHS)
75*>          The n by nrhs matrix of solution vectors X.
76*> \endverbatim
77*>
78*> \param[in] LDX
79*> \verbatim
80*>          LDX is INTEGER
81*>          The leading dimension of the array X.  LDX >= max(1,N).
82*> \endverbatim
83*>
84*> \param[in,out] B
85*> \verbatim
86*>          B is COMPLEX array, dimension (LDB,NRHS)
87*>          On entry, the n by nrhs matrix of right hand side vectors B.
88*>          On exit, B is overwritten with the difference B - A*X.
89*> \endverbatim
90*>
91*> \param[in] LDB
92*> \verbatim
93*>          LDB is INTEGER
94*>          The leading dimension of the array B.  LDB >= max(1,N).
95*> \endverbatim
96*>
97*> \param[out] RESID
98*> \verbatim
99*>          RESID is REAL
100*>          norm(B - A*X) / (norm(A) * norm(X) * EPS)
101*> \endverbatim
102*
103*  Authors:
104*  ========
105*
106*> \author Univ. of Tennessee
107*> \author Univ. of California Berkeley
108*> \author Univ. of Colorado Denver
109*> \author NAG Ltd.
110*
111*> \ingroup complex_lin
112*
113*  =====================================================================
114      SUBROUTINE CPTT02( UPLO, N, NRHS, D, E, X, LDX, B, LDB, RESID )
115*
116*  -- LAPACK test routine --
117*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
118*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119*
120*     .. Scalar Arguments ..
121      CHARACTER          UPLO
122      INTEGER            LDB, LDX, N, NRHS
123      REAL               RESID
124*     ..
125*     .. Array Arguments ..
126      REAL               D( * )
127      COMPLEX            B( LDB, * ), E( * ), X( LDX, * )
128*     ..
129*
130*  =====================================================================
131*
132*     .. Parameters ..
133      REAL               ONE, ZERO
134      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
135*     ..
136*     .. Local Scalars ..
137      INTEGER            J
138      REAL               ANORM, BNORM, EPS, XNORM
139*     ..
140*     .. External Functions ..
141      REAL               CLANHT, SCASUM, SLAMCH
142      EXTERNAL           CLANHT, SCASUM, SLAMCH
143*     ..
144*     .. Intrinsic Functions ..
145      INTRINSIC          MAX
146*     ..
147*     .. External Subroutines ..
148      EXTERNAL           CLAPTM
149*     ..
150*     .. Executable Statements ..
151*
152*     Quick return if possible
153*
154      IF( N.LE.0 ) THEN
155         RESID = ZERO
156         RETURN
157      END IF
158*
159*     Compute the 1-norm of the tridiagonal matrix A.
160*
161      ANORM = CLANHT( '1', N, D, E )
162*
163*     Exit with RESID = 1/EPS if ANORM = 0.
164*
165      EPS = SLAMCH( 'Epsilon' )
166      IF( ANORM.LE.ZERO ) THEN
167         RESID = ONE / EPS
168         RETURN
169      END IF
170*
171*     Compute B - A*X.
172*
173      CALL CLAPTM( UPLO, N, NRHS, -ONE, D, E, X, LDX, ONE, B, LDB )
174*
175*     Compute the maximum over the number of right hand sides of
176*        norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
177*
178      RESID = ZERO
179      DO 10 J = 1, NRHS
180         BNORM = SCASUM( N, B( 1, J ), 1 )
181         XNORM = SCASUM( N, X( 1, J ), 1 )
182         IF( XNORM.LE.ZERO ) THEN
183            RESID = ONE / EPS
184         ELSE
185            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
186         END IF
187   10 CONTINUE
188*
189      RETURN
190*
191*     End of CPTT02
192*
193      END
194