LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
dorg2l.f
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1 *> \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DORG2L( 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 *> DORG2L generates an m by n real matrix Q with orthonormal columns,
37 *> which is defined as the last n columns of a product of k elementary
38 *> reflectors of order m
39 *>
40 *> Q = H(k) . . . H(2) H(1)
41 *>
42 *> as returned by DGEQLF.
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. M >= N >= 0.
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. N >= 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 (n-k+i)-th column must contain the vector which
71 *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72 *> returned by DGEQLF in the last k columns of its array
73 *> argument A.
74 *> On exit, the m by n matrix Q.
75 *> \endverbatim
76 *>
77 *> \param[in] LDA
78 *> \verbatim
79 *> LDA is INTEGER
80 *> The first dimension of the array A. LDA >= max(1,M).
81 *> \endverbatim
82 *>
83 *> \param[in] TAU
84 *> \verbatim
85 *> TAU is DOUBLE PRECISION array, dimension (K)
86 *> TAU(i) must contain the scalar factor of the elementary
87 *> reflector H(i), as returned by DGEQLF.
88 *> \endverbatim
89 *>
90 *> \param[out] WORK
91 *> \verbatim
92 *> WORK is DOUBLE PRECISION array, dimension (N)
93 *> \endverbatim
94 *>
95 *> \param[out] INFO
96 *> \verbatim
97 *> INFO is INTEGER
98 *> = 0: successful exit
99 *> < 0: if INFO = -i, the i-th argument has an illegal value
100 *> \endverbatim
101 *
102 * Authors:
103 * ========
104 *
105 *> \author Univ. of Tennessee
106 *> \author Univ. of California Berkeley
107 *> \author Univ. of Colorado Denver
108 *> \author NAG Ltd.
109 *
110 *> \date December 2016
111 *
112 *> \ingroup doubleOTHERcomputational
113 *
114 * =====================================================================
115  SUBROUTINE dorg2l( M, N, K, A, LDA, TAU, WORK, INFO )
116 *
117 * -- LAPACK computational routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  INTEGER INFO, K, LDA, M, N
124 * ..
125 * .. Array Arguments ..
126  DOUBLE PRECISION A( lda, * ), TAU( * ), WORK( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  DOUBLE PRECISION ONE, ZERO
133  parameter( one = 1.0d+0, zero = 0.0d+0 )
134 * ..
135 * .. Local Scalars ..
136  INTEGER I, II, J, L
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL dlarf, dscal, xerbla
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC max
143 * ..
144 * .. Executable Statements ..
145 *
146 * Test the input arguments
147 *
148  info = 0
149  IF( m.LT.0 ) THEN
150  info = -1
151  ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
152  info = -2
153  ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
154  info = -3
155  ELSE IF( lda.LT.max( 1, m ) ) THEN
156  info = -5
157  END IF
158  IF( info.NE.0 ) THEN
159  CALL xerbla( 'DORG2L', -info )
160  RETURN
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( n.LE.0 )
166  \$ RETURN
167 *
168 * Initialise columns 1:n-k to columns of the unit matrix
169 *
170  DO 20 j = 1, n - k
171  DO 10 l = 1, m
172  a( l, j ) = zero
173  10 CONTINUE
174  a( m-n+j, j ) = one
175  20 CONTINUE
176 *
177  DO 40 i = 1, k
178  ii = n - k + i
179 *
180 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
181 *
182  a( m-n+ii, ii ) = one
183  CALL dlarf( 'Left', m-n+ii, ii-1, a( 1, ii ), 1, tau( i ), a,
184  \$ lda, work )
185  CALL dscal( m-n+ii-1, -tau( i ), a( 1, ii ), 1 )
186  a( m-n+ii, ii ) = one - tau( i )
187 *
188 * Set A(m-k+i+1:m,n-k+i) to zero
189 *
190  DO 30 l = m - n + ii + 1, m
191  a( l, ii ) = zero
192  30 CONTINUE
193  40 CONTINUE
194  RETURN
195 *
196 * End of DORG2L
197 *
198  END
subroutine dorg2l(M, N, K, A, LDA, TAU, WORK, INFO)
DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf ...
Definition: dorg2l.f:116
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:81
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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