1 DOUBLE PRECISION FUNCTION DTZT02( M, N, AF, LDA, TAU, WORK,
2 $ LWORK )
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, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION AF( LDA, * ), TAU( * ), WORK( LWORK )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DTZT02 returns
19 * || I - Q'*Q || / ( M * eps)
20 * where the matrix Q is defined by the Householder transformations
21 * generated by DTZRQF.
22 *
23 * Arguments
24 * =========
25 *
26 * M (input) INTEGER
27 * The number of rows of the matrix AF.
28 *
29 * N (input) INTEGER
30 * The number of columns of the matrix AF.
31 *
32 * AF (input) DOUBLE PRECISION array, dimension (LDA,N)
33 * The output of DTZRQF.
34 *
35 * LDA (input) INTEGER
36 * The leading dimension of the array AF.
37 *
38 * TAU (input) DOUBLE PRECISION array, dimension (M)
39 * Details of the Householder transformations as returned by
40 * DTZRQF.
41 *
42 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK)
43 *
44 * LWORK (input) INTEGER
45 * length of WORK array. Must be >= N*N+N
46 *
47 * =====================================================================
48 *
49 * .. Parameters ..
50 DOUBLE PRECISION ZERO, ONE
51 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
52 * ..
53 * .. Local Scalars ..
54 INTEGER I
55 * ..
56 * .. Local Arrays ..
57 DOUBLE PRECISION RWORK( 1 )
58 * ..
59 * .. External Functions ..
60 DOUBLE PRECISION DLAMCH, DLANGE
61 EXTERNAL DLAMCH, DLANGE
62 * ..
63 * .. External Subroutines ..
64 EXTERNAL DLASET, DLATZM, XERBLA
65 * ..
66 * .. Intrinsic Functions ..
67 INTRINSIC DBLE, MAX
68 * ..
69 * .. Executable Statements ..
70 *
71 DTZT02 = ZERO
72 *
73 IF( LWORK.LT.N*N+N ) THEN
74 CALL XERBLA( 'DTZT02', 7 )
75 RETURN
76 END IF
77 *
78 * Quick return if possible
79 *
80 IF( M.LE.0 .OR. N.LE.0 )
81 $ RETURN
82 *
83 * Q := I
84 *
85 CALL DLASET( 'Full', N, N, ZERO, ONE, WORK, N )
86 *
87 * Q := P(1) * ... * P(m) * Q
88 *
89 DO 10 I = M, 1, -1
90 CALL DLATZM( 'Left', N-M+1, N, AF( I, M+1 ), LDA, TAU( I ),
91 $ WORK( I ), WORK( M+1 ), N, WORK( N*N+1 ) )
92 10 CONTINUE
93 *
94 * Q := P(m) * ... * P(1) * Q
95 *
96 DO 20 I = 1, M
97 CALL DLATZM( 'Left', N-M+1, N, AF( I, M+1 ), LDA, TAU( I ),
98 $ WORK( I ), WORK( M+1 ), N, WORK( N*N+1 ) )
99 20 CONTINUE
100 *
101 * Q := Q - I
102 *
103 DO 30 I = 1, N
104 WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE
105 30 CONTINUE
106 *
107 DTZT02 = DLANGE( 'One-norm', N, N, WORK, N, RWORK ) /
108 $ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
109 RETURN
110 *
111 * End of DTZT02
112 *
113 END
2 $ LWORK )
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, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION AF( LDA, * ), TAU( * ), WORK( LWORK )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DTZT02 returns
19 * || I - Q'*Q || / ( M * eps)
20 * where the matrix Q is defined by the Householder transformations
21 * generated by DTZRQF.
22 *
23 * Arguments
24 * =========
25 *
26 * M (input) INTEGER
27 * The number of rows of the matrix AF.
28 *
29 * N (input) INTEGER
30 * The number of columns of the matrix AF.
31 *
32 * AF (input) DOUBLE PRECISION array, dimension (LDA,N)
33 * The output of DTZRQF.
34 *
35 * LDA (input) INTEGER
36 * The leading dimension of the array AF.
37 *
38 * TAU (input) DOUBLE PRECISION array, dimension (M)
39 * Details of the Householder transformations as returned by
40 * DTZRQF.
41 *
42 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK)
43 *
44 * LWORK (input) INTEGER
45 * length of WORK array. Must be >= N*N+N
46 *
47 * =====================================================================
48 *
49 * .. Parameters ..
50 DOUBLE PRECISION ZERO, ONE
51 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
52 * ..
53 * .. Local Scalars ..
54 INTEGER I
55 * ..
56 * .. Local Arrays ..
57 DOUBLE PRECISION RWORK( 1 )
58 * ..
59 * .. External Functions ..
60 DOUBLE PRECISION DLAMCH, DLANGE
61 EXTERNAL DLAMCH, DLANGE
62 * ..
63 * .. External Subroutines ..
64 EXTERNAL DLASET, DLATZM, XERBLA
65 * ..
66 * .. Intrinsic Functions ..
67 INTRINSIC DBLE, MAX
68 * ..
69 * .. Executable Statements ..
70 *
71 DTZT02 = ZERO
72 *
73 IF( LWORK.LT.N*N+N ) THEN
74 CALL XERBLA( 'DTZT02', 7 )
75 RETURN
76 END IF
77 *
78 * Quick return if possible
79 *
80 IF( M.LE.0 .OR. N.LE.0 )
81 $ RETURN
82 *
83 * Q := I
84 *
85 CALL DLASET( 'Full', N, N, ZERO, ONE, WORK, N )
86 *
87 * Q := P(1) * ... * P(m) * Q
88 *
89 DO 10 I = M, 1, -1
90 CALL DLATZM( 'Left', N-M+1, N, AF( I, M+1 ), LDA, TAU( I ),
91 $ WORK( I ), WORK( M+1 ), N, WORK( N*N+1 ) )
92 10 CONTINUE
93 *
94 * Q := P(m) * ... * P(1) * Q
95 *
96 DO 20 I = 1, M
97 CALL DLATZM( 'Left', N-M+1, N, AF( I, M+1 ), LDA, TAU( I ),
98 $ WORK( I ), WORK( M+1 ), N, WORK( N*N+1 ) )
99 20 CONTINUE
100 *
101 * Q := Q - I
102 *
103 DO 30 I = 1, N
104 WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE
105 30 CONTINUE
106 *
107 DTZT02 = DLANGE( 'One-norm', N, N, WORK, N, RWORK ) /
108 $ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
109 RETURN
110 *
111 * End of DTZT02
112 *
113 END