LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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sorgl2.f
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1*> \brief \b SORGL2
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/sorgl2.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorgl2.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorgl2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SORGL2( 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*> SORGL2 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 SGELQF.
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 REAL 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 SGELQF 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 REAL array, dimension (K)
85*> TAU(i) must contain the scalar factor of the elementary
86*> reflector H(i), as returned by SGELQF.
87*> \endverbatim
88*>
89*> \param[out] WORK
90*> \verbatim
91*> WORK is REAL 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*> \ingroup realOTHERcomputational
110*
111* =====================================================================
112 SUBROUTINE sorgl2( M, N, K, A, LDA, TAU, WORK, INFO )
113*
114* -- LAPACK computational routine --
115* -- LAPACK is a software package provided by Univ. of Tennessee, --
116* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117*
118* .. Scalar Arguments ..
119 INTEGER INFO, K, LDA, M, N
120* ..
121* .. Array Arguments ..
122 REAL A( LDA, * ), TAU( * ), WORK( * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 REAL ONE, ZERO
129 parameter( one = 1.0e+0, zero = 0.0e+0 )
130* ..
131* .. Local Scalars ..
132 INTEGER I, J, L
133* ..
134* .. External Subroutines ..
135 EXTERNAL slarf, sscal, xerbla
136* ..
137* .. Intrinsic Functions ..
138 INTRINSIC max
139* ..
140* .. Executable Statements ..
141*
142* Test the input arguments
143*
144 info = 0
145 IF( m.LT.0 ) THEN
146 info = -1
147 ELSE IF( n.LT.m ) THEN
148 info = -2
149 ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
150 info = -3
151 ELSE IF( lda.LT.max( 1, m ) ) THEN
152 info = -5
153 END IF
154 IF( info.NE.0 ) THEN
155 CALL xerbla( 'SORGL2', -info )
156 RETURN
157 END IF
158*
159* Quick return if possible
160*
161 IF( m.LE.0 )
162 \$ RETURN
163*
164 IF( k.LT.m ) THEN
165*
166* Initialise rows k+1:m to rows of the unit matrix
167*
168 DO 20 j = 1, n
169 DO 10 l = k + 1, m
170 a( l, j ) = zero
171 10 CONTINUE
172 IF( j.GT.k .AND. j.LE.m )
173 \$ a( j, j ) = one
174 20 CONTINUE
175 END IF
176*
177 DO 40 i = k, 1, -1
178*
179* Apply H(i) to A(i:m,i:n) from the right
180*
181 IF( i.LT.n ) THEN
182 IF( i.LT.m ) THEN
183 a( i, i ) = one
184 CALL slarf( 'Right', m-i, n-i+1, a( i, i ), lda,
185 \$ tau( i ), a( i+1, i ), lda, work )
186 END IF
187 CALL sscal( n-i, -tau( i ), a( i, i+1 ), lda )
188 END IF
189 a( i, i ) = one - tau( i )
190*
191* Set A(i,1:i-1) to zero
192*
193 DO 30 l = 1, i - 1
194 a( i, l ) = zero
195 30 CONTINUE
196 40 CONTINUE
197 RETURN
198*
199* End of SORGL2
200*
201 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 sorgl2(M, N, K, A, LDA, TAU, WORK, INFO)
SORGL2
Definition: sorgl2.f:113
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79