1 REAL FUNCTION CTZT01( M, N, A, 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 A( LDA, * ), AF( LDA, * ), TAU( * ),
13 $ WORK( LWORK )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * CTZT01 returns
20 * || A - R*Q || / ( M * eps * ||A|| )
21 * for an upper trapezoidal A that was factored with CTZRQF.
22 *
23 * Arguments
24 * =========
25 *
26 * M (input) INTEGER
27 * The number of rows of the matrices A and AF.
28 *
29 * N (input) INTEGER
30 * The number of columns of the matrices A and AF.
31 *
32 * A (input) COMPLEX array, dimension (LDA,N)
33 * The original upper trapezoidal M by N matrix A.
34 *
35 * AF (input) COMPLEX array, dimension (LDA,N)
36 * The output of CTZRQF for input matrix A.
37 * The lower triangle is not referenced.
38 *
39 * LDA (input) INTEGER
40 * The leading dimension of the arrays A and AF.
41 *
42 * TAU (input) COMPLEX array, dimension (M)
43 * Details of the Householder transformations as returned by
44 * CTZRQF.
45 *
46 * WORK (workspace) COMPLEX array, dimension (LWORK)
47 *
48 * LWORK (input) INTEGER
49 * The length of the array WORK. LWORK >= m*n + m.
50 *
51 * =====================================================================
52 *
53 * .. Parameters ..
54 REAL ZERO, ONE
55 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
56 * ..
57 * .. Local Scalars ..
58 INTEGER I, J
59 REAL NORMA
60 * ..
61 * .. Local Arrays ..
62 REAL RWORK( 1 )
63 * ..
64 * .. External Functions ..
65 REAL CLANGE, SLAMCH
66 EXTERNAL CLANGE, SLAMCH
67 * ..
68 * .. External Subroutines ..
69 EXTERNAL CAXPY, CLATZM, CLASET, XERBLA
70 * ..
71 * .. Intrinsic Functions ..
72 INTRINSIC CMPLX, MAX, REAL
73 * ..
74 * .. Executable Statements ..
75 *
76 CTZT01 = ZERO
77 *
78 IF( LWORK.LT.M*N+M ) THEN
79 CALL XERBLA( 'CTZT01', 8 )
80 RETURN
81 END IF
82 *
83 * Quick return if possible
84 *
85 IF( M.LE.0 .OR. N.LE.0 )
86 $ RETURN
87 *
88 NORMA = CLANGE( 'One-norm', M, N, A, LDA, RWORK )
89 *
90 * Copy upper triangle R
91 *
92 CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( ZERO ), WORK, M )
93 DO 20 J = 1, M
94 DO 10 I = 1, J
95 WORK( ( J-1 )*M+I ) = AF( I, J )
96 10 CONTINUE
97 20 CONTINUE
98 *
99 * R = R * P(1) * ... *P(m)
100 *
101 DO 30 I = 1, M
102 CALL CLATZM( 'Right', I, N-M+1, AF( I, M+1 ), LDA, TAU( I ),
103 $ WORK( ( I-1 )*M+1 ), WORK( M*M+1 ), M,
104 $ WORK( M*N+1 ) )
105 30 CONTINUE
106 *
107 * R = R - A
108 *
109 DO 40 I = 1, N
110 CALL CAXPY( M, CMPLX( -ONE ), A( 1, I ), 1,
111 $ WORK( ( I-1 )*M+1 ), 1 )
112 40 CONTINUE
113 *
114 CTZT01 = CLANGE( 'One-norm', M, N, WORK, M, RWORK )
115 *
116 CTZT01 = CTZT01 / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
117 IF( NORMA.NE.ZERO )
118 $ CTZT01 = CTZT01 / NORMA
119 *
120 RETURN
121 *
122 * End of CTZT01
123 *
124 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 A( LDA, * ), AF( LDA, * ), TAU( * ),
13 $ WORK( LWORK )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * CTZT01 returns
20 * || A - R*Q || / ( M * eps * ||A|| )
21 * for an upper trapezoidal A that was factored with CTZRQF.
22 *
23 * Arguments
24 * =========
25 *
26 * M (input) INTEGER
27 * The number of rows of the matrices A and AF.
28 *
29 * N (input) INTEGER
30 * The number of columns of the matrices A and AF.
31 *
32 * A (input) COMPLEX array, dimension (LDA,N)
33 * The original upper trapezoidal M by N matrix A.
34 *
35 * AF (input) COMPLEX array, dimension (LDA,N)
36 * The output of CTZRQF for input matrix A.
37 * The lower triangle is not referenced.
38 *
39 * LDA (input) INTEGER
40 * The leading dimension of the arrays A and AF.
41 *
42 * TAU (input) COMPLEX array, dimension (M)
43 * Details of the Householder transformations as returned by
44 * CTZRQF.
45 *
46 * WORK (workspace) COMPLEX array, dimension (LWORK)
47 *
48 * LWORK (input) INTEGER
49 * The length of the array WORK. LWORK >= m*n + m.
50 *
51 * =====================================================================
52 *
53 * .. Parameters ..
54 REAL ZERO, ONE
55 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
56 * ..
57 * .. Local Scalars ..
58 INTEGER I, J
59 REAL NORMA
60 * ..
61 * .. Local Arrays ..
62 REAL RWORK( 1 )
63 * ..
64 * .. External Functions ..
65 REAL CLANGE, SLAMCH
66 EXTERNAL CLANGE, SLAMCH
67 * ..
68 * .. External Subroutines ..
69 EXTERNAL CAXPY, CLATZM, CLASET, XERBLA
70 * ..
71 * .. Intrinsic Functions ..
72 INTRINSIC CMPLX, MAX, REAL
73 * ..
74 * .. Executable Statements ..
75 *
76 CTZT01 = ZERO
77 *
78 IF( LWORK.LT.M*N+M ) THEN
79 CALL XERBLA( 'CTZT01', 8 )
80 RETURN
81 END IF
82 *
83 * Quick return if possible
84 *
85 IF( M.LE.0 .OR. N.LE.0 )
86 $ RETURN
87 *
88 NORMA = CLANGE( 'One-norm', M, N, A, LDA, RWORK )
89 *
90 * Copy upper triangle R
91 *
92 CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( ZERO ), WORK, M )
93 DO 20 J = 1, M
94 DO 10 I = 1, J
95 WORK( ( J-1 )*M+I ) = AF( I, J )
96 10 CONTINUE
97 20 CONTINUE
98 *
99 * R = R * P(1) * ... *P(m)
100 *
101 DO 30 I = 1, M
102 CALL CLATZM( 'Right', I, N-M+1, AF( I, M+1 ), LDA, TAU( I ),
103 $ WORK( ( I-1 )*M+1 ), WORK( M*M+1 ), M,
104 $ WORK( M*N+1 ) )
105 30 CONTINUE
106 *
107 * R = R - A
108 *
109 DO 40 I = 1, N
110 CALL CAXPY( M, CMPLX( -ONE ), A( 1, I ), 1,
111 $ WORK( ( I-1 )*M+1 ), 1 )
112 40 CONTINUE
113 *
114 CTZT01 = CLANGE( 'One-norm', M, N, WORK, M, RWORK )
115 *
116 CTZT01 = CTZT01 / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
117 IF( NORMA.NE.ZERO )
118 $ CTZT01 = CTZT01 / NORMA
119 *
120 RETURN
121 *
122 * End of CTZT01
123 *
124 END