LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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sorg2r.f
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1*> \brief \b SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
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/sorg2r.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorg2r.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorg2r.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SORG2R( M, N, K, A, LDA, TAU, WORK, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, K, LDA, M, N
25* ..
26* .. Array Arguments ..
27* REAL A( LDA, * ), TAU( * ), WORK( * )
28* ..
29*
30*
31*> \par Purpose:
32* =============
33*>
34*> \verbatim
35*>
36*> SORG2R generates an m by n real matrix Q with orthonormal columns,
37*> which is defined as the first n columns of a product of k elementary
38*> reflectors of order m
39*>
40*> Q = H(1) H(2) . . . H(k)
41*>
42*> as returned by SGEQRF.
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 REAL array, dimension (LDA,N)
70*> On entry, the i-th column must contain the vector which
71*> defines the elementary reflector H(i), for i = 1,2,...,k, as
72*> returned by SGEQRF in the first 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 REAL array, dimension (K)
86*> TAU(i) must contain the scalar factor of the elementary
87*> reflector H(i), as returned by SGEQRF.
88*> \endverbatim
89*>
90*> \param[out] WORK
91*> \verbatim
92*> WORK is REAL 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*> \ingroup realOTHERcomputational
111*
112* =====================================================================
113 SUBROUTINE sorg2r( M, N, K, A, LDA, TAU, WORK, INFO )
114*
115* -- LAPACK computational routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 INTEGER INFO, K, LDA, M, N
121* ..
122* .. Array Arguments ..
123 REAL A( LDA, * ), TAU( * ), WORK( * )
124* ..
125*
126* =====================================================================
127*
128* .. Parameters ..
129 REAL ONE, ZERO
130 parameter( one = 1.0e+0, zero = 0.0e+0 )
131* ..
132* .. Local Scalars ..
133 INTEGER I, J, L
134* ..
135* .. External Subroutines ..
136 EXTERNAL slarf, sscal, xerbla
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC max
140* ..
141* .. Executable Statements ..
142*
143* Test the input arguments
144*
145 info = 0
146 IF( m.LT.0 ) THEN
147 info = -1
148 ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
149 info = -2
150 ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
151 info = -3
152 ELSE IF( lda.LT.max( 1, m ) ) THEN
153 info = -5
154 END IF
155 IF( info.NE.0 ) THEN
156 CALL xerbla( 'SORG2R', -info )
157 RETURN
158 END IF
159*
160* Quick return if possible
161*
162 IF( n.LE.0 )
163 \$ RETURN
164*
165* Initialise columns k+1:n to columns of the unit matrix
166*
167 DO 20 j = k + 1, n
168 DO 10 l = 1, m
169 a( l, j ) = zero
170 10 CONTINUE
171 a( j, j ) = one
172 20 CONTINUE
173*
174 DO 40 i = k, 1, -1
175*
176* Apply H(i) to A(i:m,i:n) from the left
177*
178 IF( i.LT.n ) THEN
179 a( i, i ) = one
180 CALL slarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
181 \$ a( i, i+1 ), lda, work )
182 END IF
183 IF( i.LT.m )
184 \$ CALL sscal( m-i, -tau( i ), a( i+1, i ), 1 )
185 a( i, i ) = one - tau( i )
186*
187* Set A(1:i-1,i) to zero
188*
189 DO 30 l = 1, i - 1
190 a( l, i ) = zero
191 30 CONTINUE
192 40 CONTINUE
193 RETURN
194*
195* End of SORG2R
196*
197 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:124
subroutine sorg2r(M, N, K, A, LDA, TAU, WORK, INFO)
SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf ...
Definition: sorg2r.f:114
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79