1 SUBROUTINE DGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
2 $ RCOND, 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 INTEGER LDA, LDAINV, LDWORK, N
10 DOUBLE PRECISION RCOND, RESID
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
14 $ WORK( LDWORK, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DGET03 computes the residual for a general matrix times its inverse:
21 * norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
22 * where EPS is the machine epsilon.
23 *
24 * Arguments
25 * ==========
26 *
27 * N (input) INTEGER
28 * The number of rows and columns of the matrix A. N >= 0.
29 *
30 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
31 * The original N x N matrix A.
32 *
33 * LDA (input) INTEGER
34 * The leading dimension of the array A. LDA >= max(1,N).
35 *
36 * AINV (input) DOUBLE PRECISION array, dimension (LDAINV,N)
37 * The inverse of the matrix A.
38 *
39 * LDAINV (input) INTEGER
40 * The leading dimension of the array AINV. LDAINV >= max(1,N).
41 *
42 * WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,N)
43 *
44 * LDWORK (input) INTEGER
45 * The leading dimension of the array WORK. LDWORK >= max(1,N).
46 *
47 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
48 *
49 * RCOND (output) DOUBLE PRECISION
50 * The reciprocal of the condition number of A, computed as
51 * ( 1/norm(A) ) / norm(AINV).
52 *
53 * RESID (output) DOUBLE PRECISION
54 * norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
55 *
56 * =====================================================================
57 *
58 * .. Parameters ..
59 DOUBLE PRECISION ZERO, ONE
60 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
61 * ..
62 * .. Local Scalars ..
63 INTEGER I
64 DOUBLE PRECISION AINVNM, ANORM, EPS
65 * ..
66 * .. External Functions ..
67 DOUBLE PRECISION DLAMCH, DLANGE
68 EXTERNAL DLAMCH, DLANGE
69 * ..
70 * .. External Subroutines ..
71 EXTERNAL DGEMM
72 * ..
73 * .. Intrinsic Functions ..
74 INTRINSIC DBLE
75 * ..
76 * .. Executable Statements ..
77 *
78 * Quick exit if N = 0.
79 *
80 IF( N.LE.0 ) THEN
81 RCOND = ONE
82 RESID = ZERO
83 RETURN
84 END IF
85 *
86 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
87 *
88 EPS = DLAMCH( 'Epsilon' )
89 ANORM = DLANGE( '1', N, N, A, LDA, RWORK )
90 AINVNM = DLANGE( '1', N, N, AINV, LDAINV, RWORK )
91 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
92 RCOND = ZERO
93 RESID = ONE / EPS
94 RETURN
95 END IF
96 RCOND = ( ONE / ANORM ) / AINVNM
97 *
98 * Compute I - A * AINV
99 *
100 CALL DGEMM( 'No transpose', 'No transpose', N, N, N, -ONE, AINV,
101 $ LDAINV, A, LDA, ZERO, WORK, LDWORK )
102 DO 10 I = 1, N
103 WORK( I, I ) = ONE + WORK( I, I )
104 10 CONTINUE
105 *
106 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
107 *
108 RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK )
109 *
110 RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
111 *
112 RETURN
113 *
114 * End of DGET03
115 *
116 END
2 $ RCOND, 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 INTEGER LDA, LDAINV, LDWORK, N
10 DOUBLE PRECISION RCOND, RESID
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
14 $ WORK( LDWORK, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DGET03 computes the residual for a general matrix times its inverse:
21 * norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
22 * where EPS is the machine epsilon.
23 *
24 * Arguments
25 * ==========
26 *
27 * N (input) INTEGER
28 * The number of rows and columns of the matrix A. N >= 0.
29 *
30 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
31 * The original N x N matrix A.
32 *
33 * LDA (input) INTEGER
34 * The leading dimension of the array A. LDA >= max(1,N).
35 *
36 * AINV (input) DOUBLE PRECISION array, dimension (LDAINV,N)
37 * The inverse of the matrix A.
38 *
39 * LDAINV (input) INTEGER
40 * The leading dimension of the array AINV. LDAINV >= max(1,N).
41 *
42 * WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,N)
43 *
44 * LDWORK (input) INTEGER
45 * The leading dimension of the array WORK. LDWORK >= max(1,N).
46 *
47 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
48 *
49 * RCOND (output) DOUBLE PRECISION
50 * The reciprocal of the condition number of A, computed as
51 * ( 1/norm(A) ) / norm(AINV).
52 *
53 * RESID (output) DOUBLE PRECISION
54 * norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
55 *
56 * =====================================================================
57 *
58 * .. Parameters ..
59 DOUBLE PRECISION ZERO, ONE
60 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
61 * ..
62 * .. Local Scalars ..
63 INTEGER I
64 DOUBLE PRECISION AINVNM, ANORM, EPS
65 * ..
66 * .. External Functions ..
67 DOUBLE PRECISION DLAMCH, DLANGE
68 EXTERNAL DLAMCH, DLANGE
69 * ..
70 * .. External Subroutines ..
71 EXTERNAL DGEMM
72 * ..
73 * .. Intrinsic Functions ..
74 INTRINSIC DBLE
75 * ..
76 * .. Executable Statements ..
77 *
78 * Quick exit if N = 0.
79 *
80 IF( N.LE.0 ) THEN
81 RCOND = ONE
82 RESID = ZERO
83 RETURN
84 END IF
85 *
86 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
87 *
88 EPS = DLAMCH( 'Epsilon' )
89 ANORM = DLANGE( '1', N, N, A, LDA, RWORK )
90 AINVNM = DLANGE( '1', N, N, AINV, LDAINV, RWORK )
91 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
92 RCOND = ZERO
93 RESID = ONE / EPS
94 RETURN
95 END IF
96 RCOND = ( ONE / ANORM ) / AINVNM
97 *
98 * Compute I - A * AINV
99 *
100 CALL DGEMM( 'No transpose', 'No transpose', N, N, N, -ONE, AINV,
101 $ LDAINV, A, LDA, ZERO, WORK, LDWORK )
102 DO 10 I = 1, N
103 WORK( I, I ) = ONE + WORK( I, I )
104 10 CONTINUE
105 *
106 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
107 *
108 RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK )
109 *
110 RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
111 *
112 RETURN
113 *
114 * End of DGET03
115 *
116 END