LAPACK  3.9.0 LAPACK: Linear Algebra PACKage
zrzt01.f
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1 *> \brief \b ZRZT01
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * DOUBLE PRECISION FUNCTION ZRZT01( M, N, A, AF, LDA, TAU, WORK,
12 * LWORK )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * COMPLEX*16 A( LDA, * ), AF( LDA, * ), TAU( * ),
19 * \$ WORK( LWORK )
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> ZRZT01 returns
29 *> || A - R*Q || / ( M * eps * ||A|| )
30 *> for an upper trapezoidal A that was factored with ZTZRZF.
31 *> \endverbatim
32 *
33 * Arguments:
34 * ==========
35 *
36 *> \param[in] M
37 *> \verbatim
38 *> M is INTEGER
39 *> The number of rows of the matrices A and AF.
40 *> \endverbatim
41 *>
42 *> \param[in] N
43 *> \verbatim
44 *> N is INTEGER
45 *> The number of columns of the matrices A and AF.
46 *> \endverbatim
47 *>
48 *> \param[in] A
49 *> \verbatim
50 *> A is COMPLEX*16 array, dimension (LDA,N)
51 *> The original upper trapezoidal M by N matrix A.
52 *> \endverbatim
53 *>
54 *> \param[in] AF
55 *> \verbatim
56 *> AF is COMPLEX*16 array, dimension (LDA,N)
57 *> The output of ZTZRZF for input matrix A.
58 *> The lower triangle is not referenced.
59 *> \endverbatim
60 *>
61 *> \param[in] LDA
62 *> \verbatim
63 *> LDA is INTEGER
64 *> The leading dimension of the arrays A and AF.
65 *> \endverbatim
66 *>
67 *> \param[in] TAU
68 *> \verbatim
69 *> TAU is COMPLEX*16 array, dimension (M)
70 *> Details of the Householder transformations as returned by
71 *> ZTZRZF.
72 *> \endverbatim
73 *>
74 *> \param[out] WORK
75 *> \verbatim
76 *> WORK is COMPLEX*16 array, dimension (LWORK)
77 *> \endverbatim
78 *>
79 *> \param[in] LWORK
80 *> \verbatim
81 *> LWORK is INTEGER
82 *> The length of the array WORK. LWORK >= m*n + m.
83 *> \endverbatim
84 *
85 * Authors:
86 * ========
87 *
88 *> \author Univ. of Tennessee
89 *> \author Univ. of California Berkeley
90 *> \author Univ. of Colorado Denver
91 *> \author NAG Ltd.
92 *
93 *> \date December 2016
94 *
95 *> \ingroup complex16_lin
96 *
97 * =====================================================================
98  DOUBLE PRECISION FUNCTION zrzt01( M, N, A, AF, LDA, TAU, WORK,
99  \$ LWORK )
100 *
101 * -- LAPACK test routine (version 3.7.0) --
102 * -- LAPACK is a software package provided by Univ. of Tennessee, --
103 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
104 * December 2016
105 *
106 * .. Scalar Arguments ..
107  INTEGER lda, lwork, m, n
108 * ..
109 * .. Array Arguments ..
110  COMPLEX*16 a( lda, * ), af( lda, * ), tau( * ),
111  \$ work( lwork )
112 * ..
113 *
114 * =====================================================================
115 *
116 * .. Parameters ..
117  DOUBLE PRECISION zero, one
118  parameter( zero = 0.0d0, one = 1.0d0 )
119 * ..
120 * .. Local Scalars ..
121  INTEGER i, info, j
122  DOUBLE PRECISION norma
123 * ..
124 * .. Local Arrays ..
125  DOUBLE PRECISION rwork( 1 )
126 * ..
127 * .. External Functions ..
128  DOUBLE PRECISION dlamch, zlange
129  EXTERNAL dlamch, zlange
130 * ..
131 * .. External Subroutines ..
132  EXTERNAL xerbla, zaxpy, zlaset, zunmrz
133 * ..
134 * .. Intrinsic Functions ..
135  INTRINSIC dble, dcmplx, max
136 * ..
137 * .. Executable Statements ..
138 *
139  zrzt01 = zero
140 *
141  IF( lwork.LT.m*n+m ) THEN
142  CALL xerbla( 'ZRZT01', 8 )
143  RETURN
144  END IF
145 *
146 * Quick return if possible
147 *
148  IF( m.LE.0 .OR. n.LE.0 )
149  \$ RETURN
150 *
151  norma = zlange( 'One-norm', m, n, a, lda, rwork )
152 *
153 * Copy upper triangle R
154 *
155  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), work,
156  \$ m )
157  DO 20 j = 1, m
158  DO 10 i = 1, j
159  work( ( j-1 )*m+i ) = af( i, j )
160  10 CONTINUE
161  20 CONTINUE
162 *
163 * R = R * P(1) * ... *P(m)
164 *
165  CALL zunmrz( 'Right', 'No tranpose', m, n, m, n-m, af, lda, tau,
166  \$ work, m, work( m*n+1 ), lwork-m*n, info )
167 *
168 * R = R - A
169 *
170  DO 30 i = 1, n
171  CALL zaxpy( m, dcmplx( -one ), a( 1, i ), 1,
172  \$ work( ( i-1 )*m+1 ), 1 )
173  30 CONTINUE
174 *
175  zrzt01 = zlange( 'One-norm', m, n, work, m, rwork )
176 *
177  zrzt01 = zrzt01 / ( dlamch( 'Epsilon' )*dble( max( m, n ) ) )
178  IF( norma.NE.zero )
179  \$ zrzt01 = zrzt01 / norma
180 *
181  RETURN
182 *
183 * End of ZRZT01
184 *
185  END
zaxpy
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:90
zlange
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:117
zrzt01
double precision function zrzt01(M, N, A, AF, LDA, TAU, WORK, LWORK)
ZRZT01
Definition: zrzt01.f:100
zlaset
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:108
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
zunmrz
subroutine zunmrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRZ
Definition: zunmrz.f:189
dlamch
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:70