LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches
zrzt01.f
Go to the documentation of this file.
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