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 ZSPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
$ RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDB, LDX, N, NRHS
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( * ), B( LDB, * ), X( LDX, * )
* ..
*
* Purpose
* =======
*
* ZSPT02 computes the residual in the solution of a complex symmetric
* system of linear equations A*x = b when packed storage is used for
* the coefficient matrix. The ratio computed is
*
* RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
*
* where EPS is the machine precision.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* complex symmetric matrix A is stored:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The number of rows and columns of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of columns of B, the matrix of right hand sides.
* NRHS >= 0.
*
* A (input) COMPLEX*16 array, dimension (N*(N+1)/2)
* The original complex symmetric matrix A, stored as a packed
* triangular matrix.
*
* X (input) COMPLEX*16 array, dimension (LDX,NRHS)
* The computed solution vectors for the system of linear
* equations.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* B (input/output) COMPLEX*16 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 - A*X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* RESID (output) DOUBLE PRECISION
* The maximum over the number of right hand sides of
* norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 CONE
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER J
DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DZASUM, ZLANSP
EXTERNAL DLAMCH, DZASUM, ZLANSP
* ..
* .. External Subroutines ..
EXTERNAL ZSPMV
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0
*
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = ZLANSP( '1', UPLO, N, A, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute B - A*X for the matrix of right hand sides B.
*
DO 10 J = 1, NRHS
CALL ZSPMV( UPLO, N, -CONE, A, X( 1, J ), 1, CONE, B( 1, J ),
$ 1 )
10 CONTINUE
*
* Compute the maximum over the number of right hand sides of
* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
*
RESID = ZERO
DO 20 J = 1, NRHS
BNORM = DZASUM( N, B( 1, J ), 1 )
XNORM = DZASUM( N, X( 1, J ), 1 )
IF( XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
END IF
20 CONTINUE
*
RETURN
*
* End of ZSPT02
*
END
|
