LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
srzt02.f
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1 *> \brief \b SRZT02
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * REAL FUNCTION SRZT02( M, N, AF, LDA, TAU, WORK,
12 * LWORK )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * REAL AF( LDA, * ), TAU( * ), WORK( LWORK )
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> SRZT02 returns
28 *> || I - Q'*Q || / ( M * eps)
29 *> where the matrix Q is defined by the Householder transformations
30 *> generated by STZRZF.
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 REAL array, dimension (LDA,N)
51 *> The output of STZRZF.
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 REAL array, dimension (M)
63 *> Details of the Householder transformations as returned by
64 *> STZRZF.
65 *> \endverbatim
66 *>
67 *> \param[out] WORK
68 *> \verbatim
69 *> WORK is REAL 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 single_lin
87 *
88 * =====================================================================
89  REAL function srzt02( 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  REAL af( lda, * ), tau( * ), work( lwork )
101 * ..
102 *
103 * =====================================================================
104 *
105 * .. Parameters ..
106  REAL zero, one
107  parameter( zero = 0.0e+0, one = 1.0e+0 )
108 * ..
109 * .. Local Scalars ..
110  INTEGER i, info
111 * ..
112 * .. Local Arrays ..
113  REAL rwork( 1 )
114 * ..
115 * .. External Functions ..
116  REAL slamch, slange
117  EXTERNAL slamch, slange
118 * ..
119 * .. External Subroutines ..
120  EXTERNAL slaset, sormrz, xerbla
121 * ..
122 * .. Intrinsic Functions ..
123  INTRINSIC max, real
124 * ..
125 * .. Executable Statements ..
126 *
127  srzt02 = zero
128 *
129  IF( lwork.LT.n*n+n ) THEN
130  CALL xerbla( 'SRZT02', 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 slaset( 'Full', n, n, zero, one, work, n )
142 *
143 * Q := P(1) * ... * P(m) * Q
144 *
145  CALL sormrz( '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 sormrz( '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  srzt02 = slange( 'One-norm', n, n, work, n, rwork ) /
160  \$ ( slamch( 'Epsilon' )*real( max( m, n ) ) )
161  RETURN
162 *
163 * End of SRZT02
164 *
165  END
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine sormrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMRZ
Definition: sormrz.f:187
real function srzt02(M, N, AF, LDA, TAU, WORK, LWORK)
SRZT02
Definition: srzt02.f:91
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68