LAPACK  3.10.1
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 *> \ingroup complex16_lin
94 *
95 * =====================================================================
96  DOUBLE PRECISION FUNCTION zrzt01( M, N, A, AF, LDA, TAU, WORK,
97  $ LWORK )
98 *
99 * -- LAPACK test routine --
100 * -- LAPACK is a software package provided by Univ. of Tennessee, --
101 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
102 *
103 * .. Scalar Arguments ..
104  INTEGER lda, lwork, m, n
105 * ..
106 * .. Array Arguments ..
107  COMPLEX*16 a( lda, * ), af( lda, * ), tau( * ),
108  $ work( lwork )
109 * ..
110 *
111 * =====================================================================
112 *
113 * .. Parameters ..
114  DOUBLE PRECISION zero, one
115  parameter( zero = 0.0d0, one = 1.0d0 )
116 * ..
117 * .. Local Scalars ..
118  INTEGER i, info, j
119  DOUBLE PRECISION norma
120 * ..
121 * .. Local Arrays ..
122  DOUBLE PRECISION rwork( 1 )
123 * ..
124 * .. External Functions ..
125  DOUBLE PRECISION dlamch, zlange
126  EXTERNAL dlamch, zlange
127 * ..
128 * .. External Subroutines ..
129  EXTERNAL xerbla, zaxpy, zlaset, zunmrz
130 * ..
131 * .. Intrinsic Functions ..
132  INTRINSIC dble, dcmplx, max
133 * ..
134 * .. Executable Statements ..
135 *
136  zrzt01 = zero
137 *
138  IF( lwork.LT.m*n+m ) THEN
139  CALL xerbla( 'ZRZT01', 8 )
140  RETURN
141  END IF
142 *
143 * Quick return if possible
144 *
145  IF( m.LE.0 .OR. n.LE.0 )
146  $ RETURN
147 *
148  norma = zlange( 'One-norm', m, n, a, lda, rwork )
149 *
150 * Copy upper triangle R
151 *
152  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), work,
153  $ m )
154  DO 20 j = 1, m
155  DO 10 i = 1, j
156  work( ( j-1 )*m+i ) = af( i, j )
157  10 CONTINUE
158  20 CONTINUE
159 *
160 * R = R * P(1) * ... *P(m)
161 *
162  CALL zunmrz( 'Right', 'No tranpose', m, n, m, n-m, af, lda, tau,
163  $ work, m, work( m*n+1 ), lwork-m*n, info )
164 *
165 * R = R - A
166 *
167  DO 30 i = 1, n
168  CALL zaxpy( m, dcmplx( -one ), a( 1, i ), 1,
169  $ work( ( i-1 )*m+1 ), 1 )
170  30 CONTINUE
171 *
172  zrzt01 = zlange( 'One-norm', m, n, work, m, rwork )
173 *
174  zrzt01 = zrzt01 / ( dlamch( 'Epsilon' )*dble( max( m, n ) ) )
175  IF( norma.NE.zero )
176  $ zrzt01 = zrzt01 / norma
177 *
178  RETURN
179 *
180 * End of ZRZT01
181 *
182  END
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
double precision function zrzt01(M, N, A, AF, LDA, TAU, WORK, LWORK)
ZRZT01
Definition: zrzt01.f:98
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:115
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:106
subroutine zunmrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRZ
Definition: zunmrz.f:187