1 DOUBLE PRECISION FUNCTION ZRZT01( 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*16 A( LDA, * ), AF( LDA, * ), TAU( * ),
13 $ WORK( LWORK )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZRZT01 returns
20 * || A - R*Q || / ( M * eps * ||A|| )
21 * for an upper trapezoidal A that was factored with ZTZRZF.
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*16 array, dimension (LDA,N)
33 * The original upper trapezoidal M by N matrix A.
34 *
35 * AF (input) COMPLEX*16 array, dimension (LDA,N)
36 * The output of ZTZRZF 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*16 array, dimension (M)
43 * Details of the Householder transformations as returned by
44 * ZTZRZF.
45 *
46 * WORK (workspace) COMPLEX*16 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 DOUBLE PRECISION ZERO, ONE
55 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
56 * ..
57 * .. Local Scalars ..
58 INTEGER I, INFO, J
59 DOUBLE PRECISION NORMA
60 * ..
61 * .. Local Arrays ..
62 DOUBLE PRECISION RWORK( 1 )
63 * ..
64 * .. External Functions ..
65 DOUBLE PRECISION DLAMCH, ZLANGE
66 EXTERNAL DLAMCH, ZLANGE
67 * ..
68 * .. External Subroutines ..
69 EXTERNAL XERBLA, ZAXPY, ZLASET, ZUNMRZ
70 * ..
71 * .. Intrinsic Functions ..
72 INTRINSIC DBLE, DCMPLX, MAX
73 * ..
74 * .. Executable Statements ..
75 *
76 ZRZT01 = ZERO
77 *
78 IF( LWORK.LT.M*N+M ) THEN
79 CALL XERBLA( 'ZRZT01', 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 = ZLANGE( 'One-norm', M, N, A, LDA, RWORK )
89 *
90 * Copy upper triangle R
91 *
92 CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), WORK,
93 $ M )
94 DO 20 J = 1, M
95 DO 10 I = 1, J
96 WORK( ( J-1 )*M+I ) = AF( I, J )
97 10 CONTINUE
98 20 CONTINUE
99 *
100 * R = R * P(1) * ... *P(m)
101 *
102 CALL ZUNMRZ( 'Right', 'No tranpose', M, N, M, N-M, AF, LDA, TAU,
103 $ WORK, M, WORK( M*N+1 ), LWORK-M*N, INFO )
104 *
105 * R = R - A
106 *
107 DO 30 I = 1, N
108 CALL ZAXPY( M, DCMPLX( -ONE ), A( 1, I ), 1,
109 $ WORK( ( I-1 )*M+1 ), 1 )
110 30 CONTINUE
111 *
112 ZRZT01 = ZLANGE( 'One-norm', M, N, WORK, M, RWORK )
113 *
114 ZRZT01 = ZRZT01 / ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
115 IF( NORMA.NE.ZERO )
116 $ ZRZT01 = ZRZT01 / NORMA
117 *
118 RETURN
119 *
120 * End of ZRZT01
121 *
122 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 A( LDA, * ), AF( LDA, * ), TAU( * ),
13 $ WORK( LWORK )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZRZT01 returns
20 * || A - R*Q || / ( M * eps * ||A|| )
21 * for an upper trapezoidal A that was factored with ZTZRZF.
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*16 array, dimension (LDA,N)
33 * The original upper trapezoidal M by N matrix A.
34 *
35 * AF (input) COMPLEX*16 array, dimension (LDA,N)
36 * The output of ZTZRZF 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*16 array, dimension (M)
43 * Details of the Householder transformations as returned by
44 * ZTZRZF.
45 *
46 * WORK (workspace) COMPLEX*16 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 DOUBLE PRECISION ZERO, ONE
55 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
56 * ..
57 * .. Local Scalars ..
58 INTEGER I, INFO, J
59 DOUBLE PRECISION NORMA
60 * ..
61 * .. Local Arrays ..
62 DOUBLE PRECISION RWORK( 1 )
63 * ..
64 * .. External Functions ..
65 DOUBLE PRECISION DLAMCH, ZLANGE
66 EXTERNAL DLAMCH, ZLANGE
67 * ..
68 * .. External Subroutines ..
69 EXTERNAL XERBLA, ZAXPY, ZLASET, ZUNMRZ
70 * ..
71 * .. Intrinsic Functions ..
72 INTRINSIC DBLE, DCMPLX, MAX
73 * ..
74 * .. Executable Statements ..
75 *
76 ZRZT01 = ZERO
77 *
78 IF( LWORK.LT.M*N+M ) THEN
79 CALL XERBLA( 'ZRZT01', 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 = ZLANGE( 'One-norm', M, N, A, LDA, RWORK )
89 *
90 * Copy upper triangle R
91 *
92 CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), WORK,
93 $ M )
94 DO 20 J = 1, M
95 DO 10 I = 1, J
96 WORK( ( J-1 )*M+I ) = AF( I, J )
97 10 CONTINUE
98 20 CONTINUE
99 *
100 * R = R * P(1) * ... *P(m)
101 *
102 CALL ZUNMRZ( 'Right', 'No tranpose', M, N, M, N-M, AF, LDA, TAU,
103 $ WORK, M, WORK( M*N+1 ), LWORK-M*N, INFO )
104 *
105 * R = R - A
106 *
107 DO 30 I = 1, N
108 CALL ZAXPY( M, DCMPLX( -ONE ), A( 1, I ), 1,
109 $ WORK( ( I-1 )*M+1 ), 1 )
110 30 CONTINUE
111 *
112 ZRZT01 = ZLANGE( 'One-norm', M, N, WORK, M, RWORK )
113 *
114 ZRZT01 = ZRZT01 / ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
115 IF( NORMA.NE.ZERO )
116 $ ZRZT01 = ZRZT01 / NORMA
117 *
118 RETURN
119 *
120 * End of ZRZT01
121 *
122 END