1 DOUBLE PRECISION FUNCTION ZRZT02( 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 COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZRZT02 returns
19 * || I - Q'*Q || / ( M * eps)
20 * where the matrix Q is defined by the Householder transformations
21 * generated by ZTZRZF.
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) COMPLEX*16 array, dimension (LDA,N)
33 * The output of ZTZRZF.
34 *
35 * LDA (input) INTEGER
36 * The leading dimension of the array AF.
37 *
38 * TAU (input) COMPLEX*16 array, dimension (M)
39 * Details of the Householder transformations as returned by
40 * ZTZRZF.
41 *
42 * WORK (workspace) COMPLEX*16 array, dimension (LWORK)
43 *
44 * LWORK (input) INTEGER
45 * Length of WORK array. LWORK >= 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, INFO
55 * ..
56 * .. Local Arrays ..
57 DOUBLE PRECISION RWORK( 1 )
58 * ..
59 * .. External Functions ..
60 DOUBLE PRECISION DLAMCH, ZLANGE
61 EXTERNAL DLAMCH, ZLANGE
62 * ..
63 * .. External Subroutines ..
64 EXTERNAL XERBLA, ZLASET, ZUNMRZ
65 * ..
66 * .. Intrinsic Functions ..
67 INTRINSIC DBLE, DCMPLX, MAX
68 * ..
69 * .. Executable Statements ..
70 *
71 ZRZT02 = ZERO
72 *
73 IF( LWORK.LT.N*N+N ) THEN
74 CALL XERBLA( 'ZRZT02', 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 ZLASET( 'Full', N, N, DCMPLX( ZERO ), DCMPLX( ONE ), WORK,
86 $ N )
87 *
88 * Q := P(1) * ... * P(m) * Q
89 *
90 CALL ZUNMRZ( 'Left', 'No transpose', N, N, M, N-M, AF, LDA, TAU,
91 $ WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO )
92 *
93 * Q := P(m)' * ... * P(1)' * Q
94 *
95 CALL ZUNMRZ( 'Left', 'Conjugate transpose', N, N, M, N-M, AF, LDA,
96 $ TAU, WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO )
97 *
98 * Q := Q - I
99 *
100 DO 10 I = 1, N
101 WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE
102 10 CONTINUE
103 *
104 ZRZT02 = ZLANGE( 'One-norm', N, N, WORK, N, RWORK ) /
105 $ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
106 RETURN
107 *
108 * End of ZRZT02
109 *
110 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 COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZRZT02 returns
19 * || I - Q'*Q || / ( M * eps)
20 * where the matrix Q is defined by the Householder transformations
21 * generated by ZTZRZF.
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) COMPLEX*16 array, dimension (LDA,N)
33 * The output of ZTZRZF.
34 *
35 * LDA (input) INTEGER
36 * The leading dimension of the array AF.
37 *
38 * TAU (input) COMPLEX*16 array, dimension (M)
39 * Details of the Householder transformations as returned by
40 * ZTZRZF.
41 *
42 * WORK (workspace) COMPLEX*16 array, dimension (LWORK)
43 *
44 * LWORK (input) INTEGER
45 * Length of WORK array. LWORK >= 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, INFO
55 * ..
56 * .. Local Arrays ..
57 DOUBLE PRECISION RWORK( 1 )
58 * ..
59 * .. External Functions ..
60 DOUBLE PRECISION DLAMCH, ZLANGE
61 EXTERNAL DLAMCH, ZLANGE
62 * ..
63 * .. External Subroutines ..
64 EXTERNAL XERBLA, ZLASET, ZUNMRZ
65 * ..
66 * .. Intrinsic Functions ..
67 INTRINSIC DBLE, DCMPLX, MAX
68 * ..
69 * .. Executable Statements ..
70 *
71 ZRZT02 = ZERO
72 *
73 IF( LWORK.LT.N*N+N ) THEN
74 CALL XERBLA( 'ZRZT02', 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 ZLASET( 'Full', N, N, DCMPLX( ZERO ), DCMPLX( ONE ), WORK,
86 $ N )
87 *
88 * Q := P(1) * ... * P(m) * Q
89 *
90 CALL ZUNMRZ( 'Left', 'No transpose', N, N, M, N-M, AF, LDA, TAU,
91 $ WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO )
92 *
93 * Q := P(m)' * ... * P(1)' * Q
94 *
95 CALL ZUNMRZ( 'Left', 'Conjugate transpose', N, N, M, N-M, AF, LDA,
96 $ TAU, WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO )
97 *
98 * Q := Q - I
99 *
100 DO 10 I = 1, N
101 WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE
102 10 CONTINUE
103 *
104 ZRZT02 = ZLANGE( 'One-norm', N, N, WORK, N, RWORK ) /
105 $ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
106 RETURN
107 *
108 * End of ZRZT02
109 *
110 END