1 SUBROUTINE DPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID )
2 *
3 * -- LAPACK test routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER LDB, LDX, N, NRHS
9 DOUBLE PRECISION RESID
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DPTT02 computes the residual for the solution to a symmetric
19 * tridiagonal system of equations:
20 * RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
21 * where EPS is the machine epsilon.
22 *
23 * Arguments
24 * =========
25 *
26 * N (input) INTEGTER
27 * The order of the matrix A.
28 *
29 * NRHS (input) INTEGER
30 * The number of right hand sides, i.e., the number of columns
31 * of the matrices B and X. NRHS >= 0.
32 *
33 * D (input) DOUBLE PRECISION array, dimension (N)
34 * The n diagonal elements of the tridiagonal matrix A.
35 *
36 * E (input) DOUBLE PRECISION array, dimension (N-1)
37 * The (n-1) subdiagonal elements of the tridiagonal matrix A.
38 *
39 * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
40 * The n by nrhs matrix of solution vectors X.
41 *
42 * LDX (input) INTEGER
43 * The leading dimension of the array X. LDX >= max(1,N).
44 *
45 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
46 * On entry, the n by nrhs matrix of right hand side vectors B.
47 * On exit, B is overwritten with the difference B - A*X.
48 *
49 * LDB (input) INTEGER
50 * The leading dimension of the array B. LDB >= max(1,N).
51 *
52 * RESID (output) DOUBLE PRECISION
53 * norm(B - A*X) / (norm(A) * norm(X) * EPS)
54 *
55 * =====================================================================
56 *
57 * .. Parameters ..
58 DOUBLE PRECISION ONE, ZERO
59 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
60 * ..
61 * .. Local Scalars ..
62 INTEGER J
63 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
64 * ..
65 * .. External Functions ..
66 DOUBLE PRECISION DASUM, DLAMCH, DLANST
67 EXTERNAL DASUM, DLAMCH, DLANST
68 * ..
69 * .. Intrinsic Functions ..
70 INTRINSIC MAX
71 * ..
72 * .. External Subroutines ..
73 EXTERNAL DLAPTM
74 * ..
75 * .. Executable Statements ..
76 *
77 * Quick return if possible
78 *
79 IF( N.LE.0 ) THEN
80 RESID = ZERO
81 RETURN
82 END IF
83 *
84 * Compute the 1-norm of the tridiagonal matrix A.
85 *
86 ANORM = DLANST( '1', N, D, E )
87 *
88 * Exit with RESID = 1/EPS if ANORM = 0.
89 *
90 EPS = DLAMCH( 'Epsilon' )
91 IF( ANORM.LE.ZERO ) THEN
92 RESID = ONE / EPS
93 RETURN
94 END IF
95 *
96 * Compute B - A*X.
97 *
98 CALL DLAPTM( N, NRHS, -ONE, D, E, X, LDX, ONE, B, LDB )
99 *
100 * Compute the maximum over the number of right hand sides of
101 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
102 *
103 RESID = ZERO
104 DO 10 J = 1, NRHS
105 BNORM = DASUM( N, B( 1, J ), 1 )
106 XNORM = DASUM( N, X( 1, J ), 1 )
107 IF( XNORM.LE.ZERO ) THEN
108 RESID = ONE / EPS
109 ELSE
110 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
111 END IF
112 10 CONTINUE
113 *
114 RETURN
115 *
116 * End of DPTT02
117 *
118 END
2 *
3 * -- LAPACK test routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER LDB, LDX, N, NRHS
9 DOUBLE PRECISION RESID
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DPTT02 computes the residual for the solution to a symmetric
19 * tridiagonal system of equations:
20 * RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
21 * where EPS is the machine epsilon.
22 *
23 * Arguments
24 * =========
25 *
26 * N (input) INTEGTER
27 * The order of the matrix A.
28 *
29 * NRHS (input) INTEGER
30 * The number of right hand sides, i.e., the number of columns
31 * of the matrices B and X. NRHS >= 0.
32 *
33 * D (input) DOUBLE PRECISION array, dimension (N)
34 * The n diagonal elements of the tridiagonal matrix A.
35 *
36 * E (input) DOUBLE PRECISION array, dimension (N-1)
37 * The (n-1) subdiagonal elements of the tridiagonal matrix A.
38 *
39 * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
40 * The n by nrhs matrix of solution vectors X.
41 *
42 * LDX (input) INTEGER
43 * The leading dimension of the array X. LDX >= max(1,N).
44 *
45 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
46 * On entry, the n by nrhs matrix of right hand side vectors B.
47 * On exit, B is overwritten with the difference B - A*X.
48 *
49 * LDB (input) INTEGER
50 * The leading dimension of the array B. LDB >= max(1,N).
51 *
52 * RESID (output) DOUBLE PRECISION
53 * norm(B - A*X) / (norm(A) * norm(X) * EPS)
54 *
55 * =====================================================================
56 *
57 * .. Parameters ..
58 DOUBLE PRECISION ONE, ZERO
59 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
60 * ..
61 * .. Local Scalars ..
62 INTEGER J
63 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
64 * ..
65 * .. External Functions ..
66 DOUBLE PRECISION DASUM, DLAMCH, DLANST
67 EXTERNAL DASUM, DLAMCH, DLANST
68 * ..
69 * .. Intrinsic Functions ..
70 INTRINSIC MAX
71 * ..
72 * .. External Subroutines ..
73 EXTERNAL DLAPTM
74 * ..
75 * .. Executable Statements ..
76 *
77 * Quick return if possible
78 *
79 IF( N.LE.0 ) THEN
80 RESID = ZERO
81 RETURN
82 END IF
83 *
84 * Compute the 1-norm of the tridiagonal matrix A.
85 *
86 ANORM = DLANST( '1', N, D, E )
87 *
88 * Exit with RESID = 1/EPS if ANORM = 0.
89 *
90 EPS = DLAMCH( 'Epsilon' )
91 IF( ANORM.LE.ZERO ) THEN
92 RESID = ONE / EPS
93 RETURN
94 END IF
95 *
96 * Compute B - A*X.
97 *
98 CALL DLAPTM( N, NRHS, -ONE, D, E, X, LDX, ONE, B, LDB )
99 *
100 * Compute the maximum over the number of right hand sides of
101 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
102 *
103 RESID = ZERO
104 DO 10 J = 1, NRHS
105 BNORM = DASUM( N, B( 1, J ), 1 )
106 XNORM = DASUM( N, X( 1, J ), 1 )
107 IF( XNORM.LE.ZERO ) THEN
108 RESID = ONE / EPS
109 ELSE
110 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
111 END IF
112 10 CONTINUE
113 *
114 RETURN
115 *
116 * End of DPTT02
117 *
118 END