1 SUBROUTINE DPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
2 $ RWORK, RESID )
3 *
4 * -- LAPACK test routine (version 3.1.2) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * April 2007
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER LDA, LDB, LDX, N, NRHS
11 DOUBLE PRECISION RESID
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
15 $ X( LDX, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * DPOT06 computes the residual for a solution of a system of linear
22 * equations A*x = b :
23 * RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
24 * where EPS is the machine epsilon.
25 *
26 * Arguments
27 * =========
28 *
29 * UPLO (input) CHARACTER*1
30 * Specifies whether the upper or lower triangular part of the
31 * symmetric matrix A is stored:
32 * = 'U': Upper triangular
33 * = 'L': Lower triangular
34 *
35 * N (input) INTEGER
36 * The number of rows and columns of the matrix A. N >= 0.
37 *
38 * NRHS (input) INTEGER
39 * The number of columns of B, the matrix of right hand sides.
40 * NRHS >= 0.
41 *
42 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
43 * The original M x N matrix A.
44 *
45 * LDA (input) INTEGER
46 * The leading dimension of the array A. LDA >= max(1,N).
47 *
48 * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
49 * The computed solution vectors for the system of linear
50 * equations.
51 *
52 * LDX (input) INTEGER
53 * The leading dimension of the array X. If TRANS = 'N',
54 * LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
55 *
56 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
57 * On entry, the right hand side vectors for the system of
58 * linear equations.
59 * On exit, B is overwritten with the difference B - A*X.
60 *
61 * LDB (input) INTEGER
62 * The leading dimension of the array B. IF TRANS = 'N',
63 * LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
64 *
65 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
66 *
67 * RESID (output) DOUBLE PRECISION
68 * The maximum over the number of right hand sides of
69 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
70 *
71 * =====================================================================
72 *
73 * .. Parameters ..
74 DOUBLE PRECISION ZERO, ONE, NEGONE
75 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
76 PARAMETER ( NEGONE = -1.0D+0 )
77 * ..
78 * .. Local Scalars ..
79 INTEGER IFAIL, J
80 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
81 * ..
82 * .. External Functions ..
83 LOGICAL LSAME
84 INTEGER IDAMAX
85 DOUBLE PRECISION DLAMCH, DLANSY
86 EXTERNAL LSAME, IDAMAX, DLAMCH, DLANSY
87 * ..
88 * .. External Subroutines ..
89 EXTERNAL DSYMM
90 * ..
91 * .. Intrinsic Functions ..
92 INTRINSIC MAX, ABS
93 * ..
94 * .. Executable Statements ..
95 *
96 * Quick exit if N = 0 or NRHS = 0
97 *
98 IF( N.LE.0 .OR. NRHS.EQ.0 ) THEN
99 RESID = ZERO
100 RETURN
101 END IF
102 *
103 * Exit with RESID = 1/EPS if ANORM = 0.
104 *
105 EPS = DLAMCH( 'Epsilon' )
106 ANORM = DLANSY( 'I', UPLO, N, A, LDA, RWORK )
107 IF( ANORM.LE.ZERO ) THEN
108 RESID = ONE / EPS
109 RETURN
110 END IF
111 *
112 * Compute B - A*X and store in B.
113 IFAIL=0
114 *
115 CALL DSYMM( 'Left', UPLO, N, NRHS, NEGONE, A, LDA, X,
116 $ LDX, ONE, B, LDB )
117 *
118 * Compute the maximum over the number of right hand sides of
119 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
120 *
121 RESID = ZERO
122 DO 10 J = 1, NRHS
123 BNORM = ABS(B(IDAMAX( N, B( 1, J ), 1 ),J))
124 XNORM = ABS(X(IDAMAX( N, X( 1, J ), 1 ),J))
125 IF( XNORM.LE.ZERO ) THEN
126 RESID = ONE / EPS
127 ELSE
128 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
129 END IF
130 10 CONTINUE
131 *
132 RETURN
133 *
134 * End of DPOT06
135 *
136 END
2 $ RWORK, RESID )
3 *
4 * -- LAPACK test routine (version 3.1.2) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * April 2007
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER LDA, LDB, LDX, N, NRHS
11 DOUBLE PRECISION RESID
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
15 $ X( LDX, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * DPOT06 computes the residual for a solution of a system of linear
22 * equations A*x = b :
23 * RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
24 * where EPS is the machine epsilon.
25 *
26 * Arguments
27 * =========
28 *
29 * UPLO (input) CHARACTER*1
30 * Specifies whether the upper or lower triangular part of the
31 * symmetric matrix A is stored:
32 * = 'U': Upper triangular
33 * = 'L': Lower triangular
34 *
35 * N (input) INTEGER
36 * The number of rows and columns of the matrix A. N >= 0.
37 *
38 * NRHS (input) INTEGER
39 * The number of columns of B, the matrix of right hand sides.
40 * NRHS >= 0.
41 *
42 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
43 * The original M x N matrix A.
44 *
45 * LDA (input) INTEGER
46 * The leading dimension of the array A. LDA >= max(1,N).
47 *
48 * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
49 * The computed solution vectors for the system of linear
50 * equations.
51 *
52 * LDX (input) INTEGER
53 * The leading dimension of the array X. If TRANS = 'N',
54 * LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
55 *
56 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
57 * On entry, the right hand side vectors for the system of
58 * linear equations.
59 * On exit, B is overwritten with the difference B - A*X.
60 *
61 * LDB (input) INTEGER
62 * The leading dimension of the array B. IF TRANS = 'N',
63 * LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
64 *
65 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
66 *
67 * RESID (output) DOUBLE PRECISION
68 * The maximum over the number of right hand sides of
69 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
70 *
71 * =====================================================================
72 *
73 * .. Parameters ..
74 DOUBLE PRECISION ZERO, ONE, NEGONE
75 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
76 PARAMETER ( NEGONE = -1.0D+0 )
77 * ..
78 * .. Local Scalars ..
79 INTEGER IFAIL, J
80 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
81 * ..
82 * .. External Functions ..
83 LOGICAL LSAME
84 INTEGER IDAMAX
85 DOUBLE PRECISION DLAMCH, DLANSY
86 EXTERNAL LSAME, IDAMAX, DLAMCH, DLANSY
87 * ..
88 * .. External Subroutines ..
89 EXTERNAL DSYMM
90 * ..
91 * .. Intrinsic Functions ..
92 INTRINSIC MAX, ABS
93 * ..
94 * .. Executable Statements ..
95 *
96 * Quick exit if N = 0 or NRHS = 0
97 *
98 IF( N.LE.0 .OR. NRHS.EQ.0 ) THEN
99 RESID = ZERO
100 RETURN
101 END IF
102 *
103 * Exit with RESID = 1/EPS if ANORM = 0.
104 *
105 EPS = DLAMCH( 'Epsilon' )
106 ANORM = DLANSY( 'I', UPLO, N, A, LDA, RWORK )
107 IF( ANORM.LE.ZERO ) THEN
108 RESID = ONE / EPS
109 RETURN
110 END IF
111 *
112 * Compute B - A*X and store in B.
113 IFAIL=0
114 *
115 CALL DSYMM( 'Left', UPLO, N, NRHS, NEGONE, A, LDA, X,
116 $ LDX, ONE, B, LDB )
117 *
118 * Compute the maximum over the number of right hand sides of
119 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
120 *
121 RESID = ZERO
122 DO 10 J = 1, NRHS
123 BNORM = ABS(B(IDAMAX( N, B( 1, J ), 1 ),J))
124 XNORM = ABS(X(IDAMAX( N, X( 1, J ), 1 ),J))
125 IF( XNORM.LE.ZERO ) THEN
126 RESID = ONE / EPS
127 ELSE
128 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
129 END IF
130 10 CONTINUE
131 *
132 RETURN
133 *
134 * End of DPOT06
135 *
136 END