LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zrzt02.f
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1*> \brief \b ZRZT02
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 ZRZT02( M, N, AF, LDA, TAU, WORK,
12* LWORK )
13*
14* .. Scalar Arguments ..
15* INTEGER LDA, LWORK, M, N
16* ..
17* .. Array Arguments ..
18* COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK )
19* ..
20*
21*
22*> \par Purpose:
23* =============
24*>
25*> \verbatim
26*>
27*> ZRZT02 returns
28*> || I - Q'*Q || / ( M * eps)
29*> where the matrix Q is defined by the Householder transformations
30*> generated by 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 matrix AF.
40*> \endverbatim
41*>
42*> \param[in] N
43*> \verbatim
44*> N is INTEGER
45*> The number of columns of the matrix AF.
46*> \endverbatim
47*>
48*> \param[in] AF
49*> \verbatim
50*> AF is COMPLEX*16 array, dimension (LDA,N)
51*> The output of ZTZRZF.
52*> \endverbatim
53*>
54*> \param[in] LDA
55*> \verbatim
56*> LDA is INTEGER
57*> The leading dimension of the array AF.
58*> \endverbatim
59*>
60*> \param[in] TAU
61*> \verbatim
62*> TAU is COMPLEX*16 array, dimension (M)
63*> Details of the Householder transformations as returned by
64*> ZTZRZF.
65*> \endverbatim
66*>
67*> \param[out] WORK
68*> \verbatim
69*> WORK is COMPLEX*16 array, dimension (LWORK)
70*> \endverbatim
71*>
72*> \param[in] LWORK
73*> \verbatim
74*> LWORK is INTEGER
75*> Length of WORK array. LWORK >= N*N+N.
76*> \endverbatim
77*
78* Authors:
79* ========
80*
81*> \author Univ. of Tennessee
82*> \author Univ. of California Berkeley
83*> \author Univ. of Colorado Denver
84*> \author NAG Ltd.
85*
86*> \ingroup complex16_lin
87*
88* =====================================================================
89 DOUBLE PRECISION FUNCTION zrzt02( M, N, AF, LDA, TAU, WORK,
90 \$ LWORK )
91*
92* -- LAPACK test routine --
93* -- LAPACK is a software package provided by Univ. of Tennessee, --
94* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
95*
96* .. Scalar Arguments ..
97 INTEGER lda, lwork, m, n
98* ..
99* .. Array Arguments ..
100 COMPLEX*16 af( lda, * ), tau( * ), work( lwork )
101* ..
102*
103* =====================================================================
104*
105* .. Parameters ..
106 DOUBLE PRECISION zero, one
107 parameter( zero = 0.0d0, one = 1.0d0 )
108* ..
109* .. Local Scalars ..
110 INTEGER i, info
111* ..
112* .. Local Arrays ..
113 DOUBLE PRECISION rwork( 1 )
114* ..
115* .. External Functions ..
116 DOUBLE PRECISION dlamch, zlange
117 EXTERNAL dlamch, zlange
118* ..
119* .. External Subroutines ..
120 EXTERNAL xerbla, zlaset, zunmrz
121* ..
122* .. Intrinsic Functions ..
123 INTRINSIC dble, dcmplx, max
124* ..
125* .. Executable Statements ..
126*
127 zrzt02 = zero
128*
129 IF( lwork.LT.n*n+n ) THEN
130 CALL xerbla( 'ZRZT02', 7 )
131 RETURN
132 END IF
133*
134* Quick return if possible
135*
136 IF( m.LE.0 .OR. n.LE.0 )
137 \$ RETURN
138*
139* Q := I
140*
141 CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), work,
142 \$ n )
143*
144* Q := P(1) * ... * P(m) * Q
145*
146 CALL zunmrz( 'Left', 'No transpose', n, n, m, n-m, af, lda, tau,
147 \$ work, n, work( n*n+1 ), lwork-n*n, info )
148*
149* Q := P(m)' * ... * P(1)' * Q
150*
151 CALL zunmrz( 'Left', 'Conjugate transpose', n, n, m, n-m, af, lda,
152 \$ tau, work, n, work( n*n+1 ), lwork-n*n, info )
153*
154* Q := Q - I
155*
156 DO 10 i = 1, n
157 work( ( i-1 )*n+i ) = work( ( i-1 )*n+i ) - one
158 10 CONTINUE
159*
160 zrzt02 = zlange( 'One-norm', n, n, work, n, rwork ) /
161 \$ ( dlamch( 'Epsilon' )*dble( max( m, n ) ) )
162 RETURN
163*
164* End of ZRZT02
165*
166 END
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
double precision function zrzt02(M, N, AF, LDA, TAU, WORK, LWORK)
ZRZT02
Definition: zrzt02.f:91
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