1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
|
SUBROUTINE CGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
$ RWORK, RESID )
*
* -- LAPACK test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER LDB, LDX, N, NRHS
REAL RESID
* ..
* .. Array Arguments ..
REAL RWORK( * )
COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ),
$ X( LDX, * )
* ..
*
* Purpose
* =======
*
* CGTT02 computes the residual for the solution to a tridiagonal
* system of equations:
* RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
* where EPS is the machine epsilon.
*
* Arguments
* =========
*
* TRANS (input) CHARACTER
* Specifies the form of the residual.
* = 'N': B - A * X (No transpose)
* = 'T': B - A**T * X (Transpose)
* = 'C': B - A**H * X (Conjugate transpose)
*
* N (input) INTEGTER
* The order of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrices B and X. NRHS >= 0.
*
* DL (input) COMPLEX array, dimension (N-1)
* The (n-1) sub-diagonal elements of A.
*
* D (input) COMPLEX array, dimension (N)
* The diagonal elements of A.
*
* DU (input) COMPLEX array, dimension (N-1)
* The (n-1) super-diagonal elements of A.
*
* X (input) COMPLEX array, dimension (LDX,NRHS)
* The computed solution vectors X.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* B (input/output) COMPLEX array, dimension (LDB,NRHS)
* On entry, the right hand side vectors for the system of
* linear equations.
* On exit, B is overwritten with the difference B - op(A)*X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* RWORK (workspace) REAL array, dimension (N)
*
* RESID (output) REAL
* norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER J
REAL ANORM, BNORM, EPS, XNORM
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANGT, SCASUM, SLAMCH
EXTERNAL LSAME, CLANGT, SCASUM, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CLAGTM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0
*
RESID = ZERO
IF( N.LE.0 .OR. NRHS.EQ.0 )
$ RETURN
*
* Compute the maximum over the number of right hand sides of
* norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ).
*
IF( LSAME( TRANS, 'N' ) ) THEN
ANORM = CLANGT( '1', N, DL, D, DU )
ELSE
ANORM = CLANGT( 'I', N, DL, D, DU )
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = SLAMCH( 'Epsilon' )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute B - op(A)*X.
*
CALL CLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
$ LDB )
*
DO 10 J = 1, NRHS
BNORM = SCASUM( N, B( 1, J ), 1 )
XNORM = SCASUM( N, X( 1, J ), 1 )
IF( XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
END IF
10 CONTINUE
*
RETURN
*
* End of CGTT02
*
END
|
