1 SUBROUTINE DPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
2 $ RWORK, 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 CHARACTER UPLO
10 INTEGER LDA, LDAINV, LDWORK, N
11 DOUBLE PRECISION RCOND, RESID
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
15 $ WORK( LDWORK, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * DPOT03 computes the residual for a symmetric matrix times its
22 * inverse:
23 * norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * 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 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
39 * The original symmetric matrix A.
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= max(1,N)
43 *
44 * AINV (input/output) DOUBLE PRECISION array, dimension (LDAINV,N)
45 * On entry, the inverse of the matrix A, stored as a symmetric
46 * matrix in the same format as A.
47 * In this version, AINV is expanded into a full matrix and
48 * multiplied by A, so the opposing triangle of AINV will be
49 * changed; i.e., if the upper triangular part of AINV is
50 * stored, the lower triangular part will be used as work space.
51 *
52 * LDAINV (input) INTEGER
53 * The leading dimension of the array AINV. LDAINV >= max(1,N).
54 *
55 * WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,N)
56 *
57 * LDWORK (input) INTEGER
58 * The leading dimension of the array WORK. LDWORK >= max(1,N).
59 *
60 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
61 *
62 * RCOND (output) DOUBLE PRECISION
63 * The reciprocal of the condition number of A, computed as
64 * ( 1/norm(A) ) / norm(AINV).
65 *
66 * RESID (output) DOUBLE PRECISION
67 * norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
68 *
69 * =====================================================================
70 *
71 * .. Parameters ..
72 DOUBLE PRECISION ZERO, ONE
73 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
74 * ..
75 * .. Local Scalars ..
76 INTEGER I, J
77 DOUBLE PRECISION AINVNM, ANORM, EPS
78 * ..
79 * .. External Functions ..
80 LOGICAL LSAME
81 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
82 EXTERNAL LSAME, DLAMCH, DLANGE, DLANSY
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL DSYMM
86 * ..
87 * .. Intrinsic Functions ..
88 INTRINSIC DBLE
89 * ..
90 * .. Executable Statements ..
91 *
92 * Quick exit if N = 0.
93 *
94 IF( N.LE.0 ) THEN
95 RCOND = ONE
96 RESID = ZERO
97 RETURN
98 END IF
99 *
100 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
101 *
102 EPS = DLAMCH( 'Epsilon' )
103 ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
104 AINVNM = DLANSY( '1', UPLO, N, AINV, LDAINV, RWORK )
105 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
106 RCOND = ZERO
107 RESID = ONE / EPS
108 RETURN
109 END IF
110 RCOND = ( ONE / ANORM ) / AINVNM
111 *
112 * Expand AINV into a full matrix and call DSYMM to multiply
113 * AINV on the left by A.
114 *
115 IF( LSAME( UPLO, 'U' ) ) THEN
116 DO 20 J = 1, N
117 DO 10 I = 1, J - 1
118 AINV( J, I ) = AINV( I, J )
119 10 CONTINUE
120 20 CONTINUE
121 ELSE
122 DO 40 J = 1, N
123 DO 30 I = J + 1, N
124 AINV( J, I ) = AINV( I, J )
125 30 CONTINUE
126 40 CONTINUE
127 END IF
128 CALL DSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO,
129 $ WORK, LDWORK )
130 *
131 * Add the identity matrix to WORK .
132 *
133 DO 50 I = 1, N
134 WORK( I, I ) = WORK( I, I ) + ONE
135 50 CONTINUE
136 *
137 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
138 *
139 RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK )
140 *
141 RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
142 *
143 RETURN
144 *
145 * End of DPOT03
146 *
147 END
2 $ RWORK, 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 CHARACTER UPLO
10 INTEGER LDA, LDAINV, LDWORK, N
11 DOUBLE PRECISION RCOND, RESID
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
15 $ WORK( LDWORK, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * DPOT03 computes the residual for a symmetric matrix times its
22 * inverse:
23 * norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * 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 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
39 * The original symmetric matrix A.
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= max(1,N)
43 *
44 * AINV (input/output) DOUBLE PRECISION array, dimension (LDAINV,N)
45 * On entry, the inverse of the matrix A, stored as a symmetric
46 * matrix in the same format as A.
47 * In this version, AINV is expanded into a full matrix and
48 * multiplied by A, so the opposing triangle of AINV will be
49 * changed; i.e., if the upper triangular part of AINV is
50 * stored, the lower triangular part will be used as work space.
51 *
52 * LDAINV (input) INTEGER
53 * The leading dimension of the array AINV. LDAINV >= max(1,N).
54 *
55 * WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,N)
56 *
57 * LDWORK (input) INTEGER
58 * The leading dimension of the array WORK. LDWORK >= max(1,N).
59 *
60 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
61 *
62 * RCOND (output) DOUBLE PRECISION
63 * The reciprocal of the condition number of A, computed as
64 * ( 1/norm(A) ) / norm(AINV).
65 *
66 * RESID (output) DOUBLE PRECISION
67 * norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
68 *
69 * =====================================================================
70 *
71 * .. Parameters ..
72 DOUBLE PRECISION ZERO, ONE
73 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
74 * ..
75 * .. Local Scalars ..
76 INTEGER I, J
77 DOUBLE PRECISION AINVNM, ANORM, EPS
78 * ..
79 * .. External Functions ..
80 LOGICAL LSAME
81 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
82 EXTERNAL LSAME, DLAMCH, DLANGE, DLANSY
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL DSYMM
86 * ..
87 * .. Intrinsic Functions ..
88 INTRINSIC DBLE
89 * ..
90 * .. Executable Statements ..
91 *
92 * Quick exit if N = 0.
93 *
94 IF( N.LE.0 ) THEN
95 RCOND = ONE
96 RESID = ZERO
97 RETURN
98 END IF
99 *
100 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
101 *
102 EPS = DLAMCH( 'Epsilon' )
103 ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
104 AINVNM = DLANSY( '1', UPLO, N, AINV, LDAINV, RWORK )
105 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
106 RCOND = ZERO
107 RESID = ONE / EPS
108 RETURN
109 END IF
110 RCOND = ( ONE / ANORM ) / AINVNM
111 *
112 * Expand AINV into a full matrix and call DSYMM to multiply
113 * AINV on the left by A.
114 *
115 IF( LSAME( UPLO, 'U' ) ) THEN
116 DO 20 J = 1, N
117 DO 10 I = 1, J - 1
118 AINV( J, I ) = AINV( I, J )
119 10 CONTINUE
120 20 CONTINUE
121 ELSE
122 DO 40 J = 1, N
123 DO 30 I = J + 1, N
124 AINV( J, I ) = AINV( I, J )
125 30 CONTINUE
126 40 CONTINUE
127 END IF
128 CALL DSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO,
129 $ WORK, LDWORK )
130 *
131 * Add the identity matrix to WORK .
132 *
133 DO 50 I = 1, N
134 WORK( I, I ) = WORK( I, I ) + ONE
135 50 CONTINUE
136 *
137 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
138 *
139 RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK )
140 *
141 RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
142 *
143 RETURN
144 *
145 * End of DPOT03
146 *
147 END