1 SUBROUTINE ZGET03( 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 RWORK( * )
14 COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
15 $ WORK( LDWORK, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZGET03 computes the residual for a general matrix times its inverse:
22 * norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
23 * where EPS is the machine epsilon.
24 *
25 * Arguments
26 * ==========
27 *
28 * N (input) INTEGER
29 * The number of rows and columns of the matrix A. N >= 0.
30 *
31 * A (input) COMPLEX*16 array, dimension (LDA,N)
32 * The original N x N matrix A.
33 *
34 * LDA (input) INTEGER
35 * The leading dimension of the array A. LDA >= max(1,N).
36 *
37 * AINV (input) COMPLEX*16 array, dimension (LDAINV,N)
38 * The inverse of the matrix A.
39 *
40 * LDAINV (input) INTEGER
41 * The leading dimension of the array AINV. LDAINV >= max(1,N).
42 *
43 * WORK (workspace) COMPLEX*16 array, dimension (LDWORK,N)
44 *
45 * LDWORK (input) INTEGER
46 * The leading dimension of the array WORK. LDWORK >= max(1,N).
47 *
48 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
49 *
50 * RCOND (output) DOUBLE PRECISION
51 * The reciprocal of the condition number of A, computed as
52 * ( 1/norm(A) ) / norm(AINV).
53 *
54 * RESID (output) DOUBLE PRECISION
55 * norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
56 *
57 * =====================================================================
58 *
59 * .. Parameters ..
60 DOUBLE PRECISION ZERO, ONE
61 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
62 COMPLEX*16 CZERO, CONE
63 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
64 $ CONE = ( 1.0D+0, 0.0D+0 ) )
65 * ..
66 * .. Local Scalars ..
67 INTEGER I
68 DOUBLE PRECISION AINVNM, ANORM, EPS
69 * ..
70 * .. External Functions ..
71 DOUBLE PRECISION DLAMCH, ZLANGE
72 EXTERNAL DLAMCH, ZLANGE
73 * ..
74 * .. External Subroutines ..
75 EXTERNAL ZGEMM
76 * ..
77 * .. Intrinsic Functions ..
78 INTRINSIC DBLE
79 * ..
80 * .. Executable Statements ..
81 *
82 * Quick exit if N = 0.
83 *
84 IF( N.LE.0 ) THEN
85 RCOND = ONE
86 RESID = ZERO
87 RETURN
88 END IF
89 *
90 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
91 *
92 EPS = DLAMCH( 'Epsilon' )
93 ANORM = ZLANGE( '1', N, N, A, LDA, RWORK )
94 AINVNM = ZLANGE( '1', N, N, AINV, LDAINV, RWORK )
95 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
96 RCOND = ZERO
97 RESID = ONE / EPS
98 RETURN
99 END IF
100 RCOND = ( ONE / ANORM ) / AINVNM
101 *
102 * Compute I - A * AINV
103 *
104 CALL ZGEMM( 'No transpose', 'No transpose', N, N, N, -CONE, AINV,
105 $ LDAINV, A, LDA, CZERO, WORK, LDWORK )
106 DO 10 I = 1, N
107 WORK( I, I ) = CONE + WORK( I, I )
108 10 CONTINUE
109 *
110 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
111 *
112 RESID = ZLANGE( '1', N, N, WORK, LDWORK, RWORK )
113 *
114 RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
115 *
116 RETURN
117 *
118 * End of ZGET03
119 *
120 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 RWORK( * )
14 COMPLEX*16 A( LDA, * ), AINV( LDAINV, * ),
15 $ WORK( LDWORK, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * ZGET03 computes the residual for a general matrix times its inverse:
22 * norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
23 * where EPS is the machine epsilon.
24 *
25 * Arguments
26 * ==========
27 *
28 * N (input) INTEGER
29 * The number of rows and columns of the matrix A. N >= 0.
30 *
31 * A (input) COMPLEX*16 array, dimension (LDA,N)
32 * The original N x N matrix A.
33 *
34 * LDA (input) INTEGER
35 * The leading dimension of the array A. LDA >= max(1,N).
36 *
37 * AINV (input) COMPLEX*16 array, dimension (LDAINV,N)
38 * The inverse of the matrix A.
39 *
40 * LDAINV (input) INTEGER
41 * The leading dimension of the array AINV. LDAINV >= max(1,N).
42 *
43 * WORK (workspace) COMPLEX*16 array, dimension (LDWORK,N)
44 *
45 * LDWORK (input) INTEGER
46 * The leading dimension of the array WORK. LDWORK >= max(1,N).
47 *
48 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
49 *
50 * RCOND (output) DOUBLE PRECISION
51 * The reciprocal of the condition number of A, computed as
52 * ( 1/norm(A) ) / norm(AINV).
53 *
54 * RESID (output) DOUBLE PRECISION
55 * norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
56 *
57 * =====================================================================
58 *
59 * .. Parameters ..
60 DOUBLE PRECISION ZERO, ONE
61 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
62 COMPLEX*16 CZERO, CONE
63 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
64 $ CONE = ( 1.0D+0, 0.0D+0 ) )
65 * ..
66 * .. Local Scalars ..
67 INTEGER I
68 DOUBLE PRECISION AINVNM, ANORM, EPS
69 * ..
70 * .. External Functions ..
71 DOUBLE PRECISION DLAMCH, ZLANGE
72 EXTERNAL DLAMCH, ZLANGE
73 * ..
74 * .. External Subroutines ..
75 EXTERNAL ZGEMM
76 * ..
77 * .. Intrinsic Functions ..
78 INTRINSIC DBLE
79 * ..
80 * .. Executable Statements ..
81 *
82 * Quick exit if N = 0.
83 *
84 IF( N.LE.0 ) THEN
85 RCOND = ONE
86 RESID = ZERO
87 RETURN
88 END IF
89 *
90 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
91 *
92 EPS = DLAMCH( 'Epsilon' )
93 ANORM = ZLANGE( '1', N, N, A, LDA, RWORK )
94 AINVNM = ZLANGE( '1', N, N, AINV, LDAINV, RWORK )
95 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
96 RCOND = ZERO
97 RESID = ONE / EPS
98 RETURN
99 END IF
100 RCOND = ( ONE / ANORM ) / AINVNM
101 *
102 * Compute I - A * AINV
103 *
104 CALL ZGEMM( 'No transpose', 'No transpose', N, N, N, -CONE, AINV,
105 $ LDAINV, A, LDA, CZERO, WORK, LDWORK )
106 DO 10 I = 1, N
107 WORK( I, I ) = CONE + WORK( I, I )
108 10 CONTINUE
109 *
110 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
111 *
112 RESID = ZLANGE( '1', N, N, WORK, LDWORK, RWORK )
113 *
114 RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
115 *
116 RETURN
117 *
118 * End of ZGET03
119 *
120 END