1 SUBROUTINE DPTT01( N, D, E, DF, EF, WORK, 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 N
9 DOUBLE PRECISION RESID
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION D( * ), DF( * ), E( * ), EF( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
19 * factorization and computes the residual
20 * norm(L*D*L' - A) / ( n * norm(A) * 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 * D (input) DOUBLE PRECISION array, dimension (N)
30 * The n diagonal elements of the tridiagonal matrix A.
31 *
32 * E (input) DOUBLE PRECISION array, dimension (N-1)
33 * The (n-1) subdiagonal elements of the tridiagonal matrix A.
34 *
35 * DF (input) DOUBLE PRECISION array, dimension (N)
36 * The n diagonal elements of the factor L from the L*D*L'
37 * factorization of A.
38 *
39 * EF (input) DOUBLE PRECISION array, dimension (N-1)
40 * The (n-1) subdiagonal elements of the factor L from the
41 * L*D*L' factorization of A.
42 *
43 * WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
44 *
45 * RESID (output) DOUBLE PRECISION
46 * norm(L*D*L' - A) / (n * norm(A) * EPS)
47 *
48 * =====================================================================
49 *
50 * .. Parameters ..
51 DOUBLE PRECISION ONE, ZERO
52 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
53 * ..
54 * .. Local Scalars ..
55 INTEGER I
56 DOUBLE PRECISION ANORM, DE, EPS
57 * ..
58 * .. External Functions ..
59 DOUBLE PRECISION DLAMCH
60 EXTERNAL DLAMCH
61 * ..
62 * .. Intrinsic Functions ..
63 INTRINSIC ABS, DBLE, MAX
64 * ..
65 * .. Executable Statements ..
66 *
67 * Quick return if possible
68 *
69 IF( N.LE.0 ) THEN
70 RESID = ZERO
71 RETURN
72 END IF
73 *
74 EPS = DLAMCH( 'Epsilon' )
75 *
76 * Construct the difference L*D*L' - A.
77 *
78 WORK( 1 ) = DF( 1 ) - D( 1 )
79 DO 10 I = 1, N - 1
80 DE = DF( I )*EF( I )
81 WORK( N+I ) = DE - E( I )
82 WORK( 1+I ) = DE*EF( I ) + DF( I+1 ) - D( I+1 )
83 10 CONTINUE
84 *
85 * Compute the 1-norms of the tridiagonal matrices A and WORK.
86 *
87 IF( N.EQ.1 ) THEN
88 ANORM = D( 1 )
89 RESID = ABS( WORK( 1 ) )
90 ELSE
91 ANORM = MAX( D( 1 )+ABS( E( 1 ) ), D( N )+ABS( E( N-1 ) ) )
92 RESID = MAX( ABS( WORK( 1 ) )+ABS( WORK( N+1 ) ),
93 $ ABS( WORK( N ) )+ABS( WORK( 2*N-1 ) ) )
94 DO 20 I = 2, N - 1
95 ANORM = MAX( ANORM, D( I )+ABS( E( I ) )+ABS( E( I-1 ) ) )
96 RESID = MAX( RESID, ABS( WORK( I ) )+ABS( WORK( N+I-1 ) )+
97 $ ABS( WORK( N+I ) ) )
98 20 CONTINUE
99 END IF
100 *
101 * Compute norm(L*D*L' - A) / (n * norm(A) * EPS)
102 *
103 IF( ANORM.LE.ZERO ) THEN
104 IF( RESID.NE.ZERO )
105 $ RESID = ONE / EPS
106 ELSE
107 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
108 END IF
109 *
110 RETURN
111 *
112 * End of DPTT01
113 *
114 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 N
9 DOUBLE PRECISION RESID
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION D( * ), DF( * ), E( * ), EF( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
19 * factorization and computes the residual
20 * norm(L*D*L' - A) / ( n * norm(A) * 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 * D (input) DOUBLE PRECISION array, dimension (N)
30 * The n diagonal elements of the tridiagonal matrix A.
31 *
32 * E (input) DOUBLE PRECISION array, dimension (N-1)
33 * The (n-1) subdiagonal elements of the tridiagonal matrix A.
34 *
35 * DF (input) DOUBLE PRECISION array, dimension (N)
36 * The n diagonal elements of the factor L from the L*D*L'
37 * factorization of A.
38 *
39 * EF (input) DOUBLE PRECISION array, dimension (N-1)
40 * The (n-1) subdiagonal elements of the factor L from the
41 * L*D*L' factorization of A.
42 *
43 * WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
44 *
45 * RESID (output) DOUBLE PRECISION
46 * norm(L*D*L' - A) / (n * norm(A) * EPS)
47 *
48 * =====================================================================
49 *
50 * .. Parameters ..
51 DOUBLE PRECISION ONE, ZERO
52 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
53 * ..
54 * .. Local Scalars ..
55 INTEGER I
56 DOUBLE PRECISION ANORM, DE, EPS
57 * ..
58 * .. External Functions ..
59 DOUBLE PRECISION DLAMCH
60 EXTERNAL DLAMCH
61 * ..
62 * .. Intrinsic Functions ..
63 INTRINSIC ABS, DBLE, MAX
64 * ..
65 * .. Executable Statements ..
66 *
67 * Quick return if possible
68 *
69 IF( N.LE.0 ) THEN
70 RESID = ZERO
71 RETURN
72 END IF
73 *
74 EPS = DLAMCH( 'Epsilon' )
75 *
76 * Construct the difference L*D*L' - A.
77 *
78 WORK( 1 ) = DF( 1 ) - D( 1 )
79 DO 10 I = 1, N - 1
80 DE = DF( I )*EF( I )
81 WORK( N+I ) = DE - E( I )
82 WORK( 1+I ) = DE*EF( I ) + DF( I+1 ) - D( I+1 )
83 10 CONTINUE
84 *
85 * Compute the 1-norms of the tridiagonal matrices A and WORK.
86 *
87 IF( N.EQ.1 ) THEN
88 ANORM = D( 1 )
89 RESID = ABS( WORK( 1 ) )
90 ELSE
91 ANORM = MAX( D( 1 )+ABS( E( 1 ) ), D( N )+ABS( E( N-1 ) ) )
92 RESID = MAX( ABS( WORK( 1 ) )+ABS( WORK( N+1 ) ),
93 $ ABS( WORK( N ) )+ABS( WORK( 2*N-1 ) ) )
94 DO 20 I = 2, N - 1
95 ANORM = MAX( ANORM, D( I )+ABS( E( I ) )+ABS( E( I-1 ) ) )
96 RESID = MAX( RESID, ABS( WORK( I ) )+ABS( WORK( N+I-1 ) )+
97 $ ABS( WORK( N+I ) ) )
98 20 CONTINUE
99 END IF
100 *
101 * Compute norm(L*D*L' - A) / (n * norm(A) * EPS)
102 *
103 IF( ANORM.LE.ZERO ) THEN
104 IF( RESID.NE.ZERO )
105 $ RESID = ONE / EPS
106 ELSE
107 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
108 END IF
109 *
110 RETURN
111 *
112 * End of DPTT01
113 *
114 END