LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
srzt01.f
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1 *> \brief \b SRZT01
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 SRZT01( M, N, A, AF, LDA, TAU, WORK,
12 * LWORK )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
19 * $ WORK( LWORK )
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> SRZT01 returns
29 *> || A - R*Q || / ( M * eps * ||A|| )
30 *> for an upper trapezoidal A that was factored with 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 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 REAL 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 REAL array, dimension (LDA,N)
57 *> The output of STZRZF 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 REAL array, dimension (M)
70 *> Details of the Householder transformations as returned by
71 *> STZRZF.
72 *> \endverbatim
73 *>
74 *> \param[out] WORK
75 *> \verbatim
76 *> WORK is REAL 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*nb.
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 single_lin
94 *
95 * =====================================================================
96  REAL function srzt01( 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  REAL a( lda, * ), af( lda, * ), tau( * ),
108  $ work( lwork )
109 * ..
110 *
111 * =====================================================================
112 *
113 * .. Parameters ..
114  REAL zero, one
115  parameter( zero = 0.0e+0, one = 1.0e+0 )
116 * ..
117 * .. Local Scalars ..
118  INTEGER i, info, j
119  REAL norma
120 * ..
121 * .. Local Arrays ..
122  REAL rwork( 1 )
123 * ..
124 * .. External Functions ..
125  REAL slamch, slange
126  EXTERNAL slamch, slange
127 * ..
128 * .. External Subroutines ..
129  EXTERNAL saxpy, slaset, sormrz, xerbla
130 * ..
131 * .. Intrinsic Functions ..
132  INTRINSIC max, real
133 * ..
134 * .. Executable Statements ..
135 *
136  srzt01 = zero
137 *
138  IF( lwork.LT.m*n+m ) THEN
139  CALL xerbla( 'SRZT01', 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 = slange( 'One-norm', m, n, a, lda, rwork )
149 *
150 * Copy upper triangle R
151 *
152  CALL slaset( 'Full', m, n, zero, zero, work, m )
153  DO 20 j = 1, m
154  DO 10 i = 1, j
155  work( ( j-1 )*m+i ) = af( i, j )
156  10 CONTINUE
157  20 CONTINUE
158 *
159 * R = R * P(1) * ... *P(m)
160 *
161  CALL sormrz( 'Right', 'No tranpose', m, n, m, n-m, af, lda, tau,
162  $ work, m, work( m*n+1 ), lwork-m*n, info )
163 *
164 * R = R - A
165 *
166  DO 30 i = 1, n
167  CALL saxpy( m, -one, a( 1, i ), 1, work( ( i-1 )*m+1 ), 1 )
168  30 CONTINUE
169 *
170  srzt01 = slange( 'One-norm', m, n, work, m, rwork )
171 *
172  srzt01 = srzt01 / ( slamch( 'Epsilon' )*real( max( m, n ) ) )
173  IF( norma.NE.zero )
174  $ srzt01 = srzt01 / norma
175 *
176  RETURN
177 *
178 * End of SRZT01
179 *
180  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
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
real function srzt01(M, N, A, AF, LDA, TAU, WORK, LWORK)
SRZT01
Definition: srzt01.f:98
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68