1 SUBROUTINE SGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
2 $ RWORK, RESID )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER TRANS
10 INTEGER LDB, LDX, N, NRHS
11 REAL RESID
12 * ..
13 * .. Array Arguments ..
14 REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
15 $ RWORK( * ), X( LDX, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * SGTT02 computes the residual for the solution to a tridiagonal
22 * system of equations:
23 * RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
24 * where EPS is the machine epsilon.
25 *
26 * Arguments
27 * =========
28 *
29 * TRANS (input) CHARACTER
30 * Specifies the form of the residual.
31 * = 'N': B - A * X (No transpose)
32 * = 'T': B - A'* X (Transpose)
33 * = 'C': B - A'* X (Conjugate transpose = Transpose)
34 *
35 * N (input) INTEGTER
36 * The order of the matrix A. N >= 0.
37 *
38 * NRHS (input) INTEGER
39 * The number of right hand sides, i.e., the number of columns
40 * of the matrices B and X. NRHS >= 0.
41 *
42 * DL (input) REAL array, dimension (N-1)
43 * The (n-1) sub-diagonal elements of A.
44 *
45 * D (input) REAL array, dimension (N)
46 * The diagonal elements of A.
47 *
48 * DU (input) REAL array, dimension (N-1)
49 * The (n-1) super-diagonal elements of A.
50 *
51 * X (input) REAL array, dimension (LDX,NRHS)
52 * The computed solution vectors X.
53 *
54 * LDX (input) INTEGER
55 * The leading dimension of the array X. LDX >= max(1,N).
56 *
57 * B (input/output) REAL array, dimension (LDB,NRHS)
58 * On entry, the right hand side vectors for the system of
59 * linear equations.
60 * On exit, B is overwritten with the difference B - op(A)*X.
61 *
62 * LDB (input) INTEGER
63 * The leading dimension of the array B. LDB >= max(1,N).
64 *
65 * RWORK (workspace) REAL array, dimension (N)
66 *
67 * RESID (output) REAL
68 * norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 REAL ONE, ZERO
74 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
75 * ..
76 * .. Local Scalars ..
77 INTEGER J
78 REAL ANORM, BNORM, EPS, XNORM
79 * ..
80 * .. External Functions ..
81 LOGICAL LSAME
82 REAL SASUM, SLAMCH, SLANGT
83 EXTERNAL LSAME, SASUM, SLAMCH, SLANGT
84 * ..
85 * .. External Subroutines ..
86 EXTERNAL SLAGTM
87 * ..
88 * .. Intrinsic Functions ..
89 INTRINSIC MAX
90 * ..
91 * .. Executable Statements ..
92 *
93 * Quick exit if N = 0 or NRHS = 0
94 *
95 RESID = ZERO
96 IF( N.LE.0 .OR. NRHS.EQ.0 )
97 $ RETURN
98 *
99 * Compute the maximum over the number of right hand sides of
100 * norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ).
101 *
102 IF( LSAME( TRANS, 'N' ) ) THEN
103 ANORM = SLANGT( '1', N, DL, D, DU )
104 ELSE
105 ANORM = SLANGT( 'I', N, DL, D, DU )
106 END IF
107 *
108 * Exit with RESID = 1/EPS if ANORM = 0.
109 *
110 EPS = SLAMCH( 'Epsilon' )
111 IF( ANORM.LE.ZERO ) THEN
112 RESID = ONE / EPS
113 RETURN
114 END IF
115 *
116 * Compute B - op(A)*X.
117 *
118 CALL SLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
119 $ LDB )
120 *
121 DO 10 J = 1, NRHS
122 BNORM = SASUM( N, B( 1, J ), 1 )
123 XNORM = SASUM( N, X( 1, J ), 1 )
124 IF( XNORM.LE.ZERO ) THEN
125 RESID = ONE / EPS
126 ELSE
127 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
128 END IF
129 10 CONTINUE
130 *
131 RETURN
132 *
133 * End of SGTT02
134 *
135 END
2 $ RWORK, RESID )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER TRANS
10 INTEGER LDB, LDX, N, NRHS
11 REAL RESID
12 * ..
13 * .. Array Arguments ..
14 REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
15 $ RWORK( * ), X( LDX, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * SGTT02 computes the residual for the solution to a tridiagonal
22 * system of equations:
23 * RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
24 * where EPS is the machine epsilon.
25 *
26 * Arguments
27 * =========
28 *
29 * TRANS (input) CHARACTER
30 * Specifies the form of the residual.
31 * = 'N': B - A * X (No transpose)
32 * = 'T': B - A'* X (Transpose)
33 * = 'C': B - A'* X (Conjugate transpose = Transpose)
34 *
35 * N (input) INTEGTER
36 * The order of the matrix A. N >= 0.
37 *
38 * NRHS (input) INTEGER
39 * The number of right hand sides, i.e., the number of columns
40 * of the matrices B and X. NRHS >= 0.
41 *
42 * DL (input) REAL array, dimension (N-1)
43 * The (n-1) sub-diagonal elements of A.
44 *
45 * D (input) REAL array, dimension (N)
46 * The diagonal elements of A.
47 *
48 * DU (input) REAL array, dimension (N-1)
49 * The (n-1) super-diagonal elements of A.
50 *
51 * X (input) REAL array, dimension (LDX,NRHS)
52 * The computed solution vectors X.
53 *
54 * LDX (input) INTEGER
55 * The leading dimension of the array X. LDX >= max(1,N).
56 *
57 * B (input/output) REAL array, dimension (LDB,NRHS)
58 * On entry, the right hand side vectors for the system of
59 * linear equations.
60 * On exit, B is overwritten with the difference B - op(A)*X.
61 *
62 * LDB (input) INTEGER
63 * The leading dimension of the array B. LDB >= max(1,N).
64 *
65 * RWORK (workspace) REAL array, dimension (N)
66 *
67 * RESID (output) REAL
68 * norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 REAL ONE, ZERO
74 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
75 * ..
76 * .. Local Scalars ..
77 INTEGER J
78 REAL ANORM, BNORM, EPS, XNORM
79 * ..
80 * .. External Functions ..
81 LOGICAL LSAME
82 REAL SASUM, SLAMCH, SLANGT
83 EXTERNAL LSAME, SASUM, SLAMCH, SLANGT
84 * ..
85 * .. External Subroutines ..
86 EXTERNAL SLAGTM
87 * ..
88 * .. Intrinsic Functions ..
89 INTRINSIC MAX
90 * ..
91 * .. Executable Statements ..
92 *
93 * Quick exit if N = 0 or NRHS = 0
94 *
95 RESID = ZERO
96 IF( N.LE.0 .OR. NRHS.EQ.0 )
97 $ RETURN
98 *
99 * Compute the maximum over the number of right hand sides of
100 * norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ).
101 *
102 IF( LSAME( TRANS, 'N' ) ) THEN
103 ANORM = SLANGT( '1', N, DL, D, DU )
104 ELSE
105 ANORM = SLANGT( 'I', N, DL, D, DU )
106 END IF
107 *
108 * Exit with RESID = 1/EPS if ANORM = 0.
109 *
110 EPS = SLAMCH( 'Epsilon' )
111 IF( ANORM.LE.ZERO ) THEN
112 RESID = ONE / EPS
113 RETURN
114 END IF
115 *
116 * Compute B - op(A)*X.
117 *
118 CALL SLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
119 $ LDB )
120 *
121 DO 10 J = 1, NRHS
122 BNORM = SASUM( N, B( 1, J ), 1 )
123 XNORM = SASUM( N, X( 1, J ), 1 )
124 IF( XNORM.LE.ZERO ) THEN
125 RESID = ONE / EPS
126 ELSE
127 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
128 END IF
129 10 CONTINUE
130 *
131 RETURN
132 *
133 * End of SGTT02
134 *
135 END