LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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drzt02.f
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1*> \brief \b DRZT02
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 DRZT02( M, N, AF, LDA, TAU, WORK,
12* LWORK )
13*
14* .. Scalar Arguments ..
15* INTEGER LDA, LWORK, M, N
16* ..
17* .. Array Arguments ..
18* DOUBLE PRECISION AF( LDA, * ), TAU( * ), WORK( LWORK )
19* ..
20*
21*
22*> \par Purpose:
23* =============
24*>
25*> \verbatim
26*>
27*> DRZT02 returns
28*> || I - Q'*Q || / ( M * eps)
29*> where the matrix Q is defined by the Householder transformations
30*> generated by DTZRZF.
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 DOUBLE PRECISION array, dimension (LDA,N)
51*> The output of DTZRZF.
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 DOUBLE PRECISION array, dimension (M)
63*> Details of the Householder transformations as returned by
64*> DTZRZF.
65*> \endverbatim
66*>
67*> \param[out] WORK
68*> \verbatim
69*> WORK is DOUBLE PRECISION 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*NB.
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 double_lin
87*
88* =====================================================================
89 DOUBLE PRECISION FUNCTION drzt02( 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 DOUBLE PRECISION af( lda, * ), tau( * ), work( lwork )
101* ..
102*
103* =====================================================================
104*
105* .. Parameters ..
106 DOUBLE PRECISION zero, one
107 parameter( zero = 0.0d+0, one = 1.0d+0 )
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, dlange
117 EXTERNAL dlamch, dlange
118* ..
119* .. External Subroutines ..
120 EXTERNAL dlaset, dormrz, xerbla
121* ..
122* .. Intrinsic Functions ..
123 INTRINSIC dble, max
124* ..
125* .. Executable Statements ..
126*
127 drzt02 = zero
128*
129 IF( lwork.LT.n*n+n ) THEN
130 CALL xerbla( 'DRZT02', 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 dlaset( 'Full', n, n, zero, one, work, n )
142*
143* Q := P(1) * ... * P(m) * Q
144*
145 CALL dormrz( 'Left', 'No transpose', n, n, m, n-m, af, lda, tau,
146 \$ work, n, work( n*n+1 ), lwork-n*n, info )
147*
148* Q := P(m) * ... * P(1) * Q
149*
150 CALL dormrz( 'Left', 'Transpose', n, n, m, n-m, af, lda, tau,
151 \$ work, n, work( n*n+1 ), lwork-n*n, info )
152*
153* Q := Q - I
154*
155 DO 10 i = 1, n
156 work( ( i-1 )*n+i ) = work( ( i-1 )*n+i ) - one
157 10 CONTINUE
158*
159 drzt02 = dlange( 'One-norm', n, n, work, n, rwork ) /
160 \$ ( dlamch( 'Epsilon' )*dble( max( m, n ) ) )
161 RETURN
162*
163* End of DRZT02
164*
165 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
double precision function drzt02(m, n, af, lda, tau, work, lwork)
DRZT02
Definition drzt02.f:91
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function dlange(norm, m, n, a, lda, work)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition dlange.f:114
subroutine dlaset(uplo, m, n, alpha, beta, a, lda)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition dlaset.f:110
subroutine dormrz(side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
DORMRZ
Definition dormrz.f:187