LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dqpt01.f
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1 *> \brief \b DQPT01
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 DQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
12 * WORK, LWORK )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER K, LDA, LWORK, M, N
16 * ..
17 * .. Array Arguments ..
18 * INTEGER JPVT( * )
19 * DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), TAU( * ),
20 * $ WORK( LWORK )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DQPT01 tests the QR-factorization with pivoting of a matrix A. The
30 *> array AF contains the (possibly partial) QR-factorization of A, where
31 *> the upper triangle of AF(1:k,1:k) is a partial triangular factor,
32 *> the entries below the diagonal in the first k columns are the
33 *> Householder vectors, and the rest of AF contains a partially updated
34 *> matrix.
35 *>
36 *> This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] M
43 *> \verbatim
44 *> M is INTEGER
45 *> The number of rows of the matrices A and AF.
46 *> \endverbatim
47 *>
48 *> \param[in] N
49 *> \verbatim
50 *> N is INTEGER
51 *> The number of columns of the matrices A and AF.
52 *> \endverbatim
53 *>
54 *> \param[in] K
55 *> \verbatim
56 *> K is INTEGER
57 *> The number of columns of AF that have been reduced
58 *> to upper triangular form.
59 *> \endverbatim
60 *>
61 *> \param[in] A
62 *> \verbatim
63 *> A is DOUBLE PRECISION array, dimension (LDA, N)
64 *> The original matrix A.
65 *> \endverbatim
66 *>
67 *> \param[in] AF
68 *> \verbatim
69 *> AF is DOUBLE PRECISION array, dimension (LDA,N)
70 *> The (possibly partial) output of DGEQPF. The upper triangle
71 *> of AF(1:k,1:k) is a partial triangular factor, the entries
72 *> below the diagonal in the first k columns are the Householder
73 *> vectors, and the rest of AF contains a partially updated
74 *> matrix.
75 *> \endverbatim
76 *>
77 *> \param[in] LDA
78 *> \verbatim
79 *> LDA is INTEGER
80 *> The leading dimension of the arrays A and AF.
81 *> \endverbatim
82 *>
83 *> \param[in] TAU
84 *> \verbatim
85 *> TAU is DOUBLE PRECISION array, dimension (K)
86 *> Details of the Householder transformations as returned by
87 *> DGEQPF.
88 *> \endverbatim
89 *>
90 *> \param[in] JPVT
91 *> \verbatim
92 *> JPVT is INTEGER array, dimension (N)
93 *> Pivot information as returned by DGEQPF.
94 *> \endverbatim
95 *>
96 *> \param[out] WORK
97 *> \verbatim
98 *> WORK is DOUBLE PRECISION array, dimension (LWORK)
99 *> \endverbatim
100 *>
101 *> \param[in] LWORK
102 *> \verbatim
103 *> LWORK is INTEGER
104 *> The length of the array WORK. LWORK >= M*N+N.
105 *> \endverbatim
106 *
107 * Authors:
108 * ========
109 *
110 *> \author Univ. of Tennessee
111 *> \author Univ. of California Berkeley
112 *> \author Univ. of Colorado Denver
113 *> \author NAG Ltd.
114 *
115 *> \date December 2016
116 *
117 *> \ingroup double_lin
118 *
119 * =====================================================================
120  DOUBLE PRECISION FUNCTION dqpt01( M, N, K, A, AF, LDA, TAU, JPVT,
121  $ WORK, LWORK )
122 *
123 * -- LAPACK test routine (version 3.7.0) --
124 * -- LAPACK is a software package provided by Univ. of Tennessee, --
125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 * December 2016
127 *
128 * .. Scalar Arguments ..
129  INTEGER K, LDA, LWORK, M, N
130 * ..
131 * .. Array Arguments ..
132  INTEGER JPVT( * )
133  DOUBLE PRECISION A( lda, * ), AF( lda, * ), TAU( * ),
134  $ work( lwork )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Parameters ..
140  DOUBLE PRECISION ZERO, ONE
141  parameter( zero = 0.0d0, one = 1.0d0 )
142 * ..
143 * .. Local Scalars ..
144  INTEGER I, INFO, J
145  DOUBLE PRECISION NORMA
146 * ..
147 * .. Local Arrays ..
148  DOUBLE PRECISION RWORK( 1 )
149 * ..
150 * .. External Functions ..
151  DOUBLE PRECISION DLAMCH, DLANGE
152  EXTERNAL dlamch, dlange
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL daxpy, dcopy, dormqr, xerbla
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC dble, max, min
159 * ..
160 * .. Executable Statements ..
161 *
162  dqpt01 = zero
163 *
164 * Test if there is enough workspace
165 *
166  IF( lwork.LT.m*n+n ) THEN
167  CALL xerbla( 'DQPT01', 10 )
168  RETURN
169  END IF
170 *
171 * Quick return if possible
172 *
173  IF( m.LE.0 .OR. n.LE.0 )
174  $ RETURN
175 *
176  norma = dlange( 'One-norm', m, n, a, lda, rwork )
177 *
178  DO 30 j = 1, k
179  DO 10 i = 1, min( j, m )
180  work( ( j-1 )*m+i ) = af( i, j )
181  10 CONTINUE
182  DO 20 i = j + 1, m
183  work( ( j-1 )*m+i ) = zero
184  20 CONTINUE
185  30 CONTINUE
186  DO 40 j = k + 1, n
187  CALL dcopy( m, af( 1, j ), 1, work( ( j-1 )*m+1 ), 1 )
188  40 CONTINUE
189 *
190  CALL dormqr( 'Left', 'No transpose', m, n, k, af, lda, tau, work,
191  $ m, work( m*n+1 ), lwork-m*n, info )
192 *
193  DO 50 j = 1, n
194 *
195 * Compare i-th column of QR and jpvt(i)-th column of A
196 *
197  CALL daxpy( m, -one, a( 1, jpvt( j ) ), 1, work( ( j-1 )*m+1 ),
198  $ 1 )
199  50 CONTINUE
200 *
201  dqpt01 = dlange( 'One-norm', m, n, work, m, rwork ) /
202  $ ( dble( max( m, n ) )*dlamch( 'Epsilon' ) )
203  IF( norma.NE.zero )
204  $ dqpt01 = dqpt01 / norma
205 *
206  RETURN
207 *
208 * End of DQPT01
209 *
210  END
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:84
double precision function dqpt01(M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK)
DQPT01
Definition: dqpt01.f:122
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:91
subroutine dormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQR
Definition: dormqr.f:169
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62