LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dorgl2.f
Go to the documentation of this file.
1 *> \brief \b DORGL2
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgl2.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgl2.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgl2.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, K, LDA, M, N
25 * ..
26 * .. Array Arguments ..
27 * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> DORGL2 generates an m by n real matrix Q with orthonormal rows,
37 *> which is defined as the first m rows of a product of k elementary
38 *> reflectors of order n
39 *>
40 *> Q = H(k) . . . H(2) H(1)
41 *>
42 *> as returned by DGELQF.
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] M
49 *> \verbatim
50 *> M is INTEGER
51 *> The number of rows of the matrix Q. M >= 0.
52 *> \endverbatim
53 *>
54 *> \param[in] N
55 *> \verbatim
56 *> N is INTEGER
57 *> The number of columns of the matrix Q. N >= M.
58 *> \endverbatim
59 *>
60 *> \param[in] K
61 *> \verbatim
62 *> K is INTEGER
63 *> The number of elementary reflectors whose product defines the
64 *> matrix Q. M >= K >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in,out] A
68 *> \verbatim
69 *> A is DOUBLE PRECISION array, dimension (LDA,N)
70 *> On entry, the i-th row must contain the vector which defines
71 *> the elementary reflector H(i), for i = 1,2,...,k, as returned
72 *> by DGELQF in the first k rows of its array argument A.
73 *> On exit, the m-by-n matrix Q.
74 *> \endverbatim
75 *>
76 *> \param[in] LDA
77 *> \verbatim
78 *> LDA is INTEGER
79 *> The first dimension of the array A. LDA >= max(1,M).
80 *> \endverbatim
81 *>
82 *> \param[in] TAU
83 *> \verbatim
84 *> TAU is DOUBLE PRECISION array, dimension (K)
85 *> TAU(i) must contain the scalar factor of the elementary
86 *> reflector H(i), as returned by DGELQF.
87 *> \endverbatim
88 *>
89 *> \param[out] WORK
90 *> \verbatim
91 *> WORK is DOUBLE PRECISION array, dimension (M)
92 *> \endverbatim
93 *>
94 *> \param[out] INFO
95 *> \verbatim
96 *> INFO is INTEGER
97 *> = 0: successful exit
98 *> < 0: if INFO = -i, the i-th argument has an illegal value
99 *> \endverbatim
100 *
101 * Authors:
102 * ========
103 *
104 *> \author Univ. of Tennessee
105 *> \author Univ. of California Berkeley
106 *> \author Univ. of Colorado Denver
107 *> \author NAG Ltd.
108 *
109 *> \date November 2011
110 *
111 *> \ingroup doubleOTHERcomputational
112 *
113 * =====================================================================
114  SUBROUTINE dorgl2( M, N, K, A, LDA, TAU, WORK, INFO )
115 *
116 * -- LAPACK computational routine (version 3.4.0) --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 * November 2011
120 *
121 * .. Scalar Arguments ..
122  INTEGER INFO, K, LDA, M, N
123 * ..
124 * .. Array Arguments ..
125  DOUBLE PRECISION A( lda, * ), TAU( * ), WORK( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  DOUBLE PRECISION ONE, ZERO
132  parameter ( one = 1.0d+0, zero = 0.0d+0 )
133 * ..
134 * .. Local Scalars ..
135  INTEGER I, J, L
136 * ..
137 * .. External Subroutines ..
138  EXTERNAL dlarf, dscal, xerbla
139 * ..
140 * .. Intrinsic Functions ..
141  INTRINSIC max
142 * ..
143 * .. Executable Statements ..
144 *
145 * Test the input arguments
146 *
147  info = 0
148  IF( m.LT.0 ) THEN
149  info = -1
150  ELSE IF( n.LT.m ) THEN
151  info = -2
152  ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
153  info = -3
154  ELSE IF( lda.LT.max( 1, m ) ) THEN
155  info = -5
156  END IF
157  IF( info.NE.0 ) THEN
158  CALL xerbla( 'DORGL2', -info )
159  RETURN
160  END IF
161 *
162 * Quick return if possible
163 *
164  IF( m.LE.0 )
165  \$ RETURN
166 *
167  IF( k.LT.m ) THEN
168 *
169 * Initialise rows k+1:m to rows of the unit matrix
170 *
171  DO 20 j = 1, n
172  DO 10 l = k + 1, m
173  a( l, j ) = zero
174  10 CONTINUE
175  IF( j.GT.k .AND. j.LE.m )
176  \$ a( j, j ) = one
177  20 CONTINUE
178  END IF
179 *
180  DO 40 i = k, 1, -1
181 *
182 * Apply H(i) to A(i:m,i:n) from the right
183 *
184  IF( i.LT.n ) THEN
185  IF( i.LT.m ) THEN
186  a( i, i ) = one
187  CALL dlarf( 'Right', m-i, n-i+1, a( i, i ), lda,
188  \$ tau( i ), a( i+1, i ), lda, work )
189  END IF
190  CALL dscal( n-i, -tau( i ), a( i, i+1 ), lda )
191  END IF
192  a( i, i ) = one - tau( i )
193 *
194 * Set A(i,1:i-1) to zero
195 *
196  DO 30 l = 1, i - 1
197  a( i, l ) = zero
198  30 CONTINUE
199  40 CONTINUE
200  RETURN
201 *
202 * End of DORGL2
203 *
204  END
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:126
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:55
subroutine dorgl2(M, N, K, A, LDA, TAU, WORK, INFO)
DORGL2
Definition: dorgl2.f:115