LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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sgerq2.f
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1*> \brief \b SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgerq2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, 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*> SGERQ2 computes an RQ factorization of a real m by n matrix A:
37*> A = R * Q.
38*> \endverbatim
39*
40* Arguments:
41* ==========
42*
43*> \param[in] M
44*> \verbatim
45*> M is INTEGER
46*> The number of rows of the matrix A. M >= 0.
47*> \endverbatim
48*>
49*> \param[in] N
50*> \verbatim
51*> N is INTEGER
52*> The number of columns of the matrix A. N >= 0.
53*> \endverbatim
54*>
55*> \param[in,out] A
56*> \verbatim
57*> A is REAL array, dimension (LDA,N)
58*> On entry, the m by n matrix A.
59*> On exit, if m <= n, the upper triangle of the subarray
60*> A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
61*> if m >= n, the elements on and above the (m-n)-th subdiagonal
62*> contain the m by n upper trapezoidal matrix R; the remaining
63*> elements, with the array TAU, represent the orthogonal matrix
64*> Q as a product of elementary reflectors (see Further
65*> Details).
66*> \endverbatim
67*>
68*> \param[in] LDA
69*> \verbatim
70*> LDA is INTEGER
71*> The leading dimension of the array A. LDA >= max(1,M).
72*> \endverbatim
73*>
74*> \param[out] TAU
75*> \verbatim
76*> TAU is REAL array, dimension (min(M,N))
77*> The scalar factors of the elementary reflectors (see Further
78*> Details).
79*> \endverbatim
80*>
81*> \param[out] WORK
82*> \verbatim
83*> WORK is REAL array, dimension (M)
84*> \endverbatim
85*>
86*> \param[out] INFO
87*> \verbatim
88*> INFO is INTEGER
89*> = 0: successful exit
90*> < 0: if INFO = -i, the i-th argument had an illegal value
91*> \endverbatim
92*
93* Authors:
94* ========
95*
96*> \author Univ. of Tennessee
97*> \author Univ. of California Berkeley
98*> \author Univ. of Colorado Denver
99*> \author NAG Ltd.
100*
101*> \ingroup realGEcomputational
102*
103*> \par Further Details:
104* =====================
105*>
106*> \verbatim
107*>
108*> The matrix Q is represented as a product of elementary reflectors
109*>
110*> Q = H(1) H(2) . . . H(k), where k = min(m,n).
111*>
112*> Each H(i) has the form
113*>
114*> H(i) = I - tau * v * v**T
115*>
116*> where tau is a real scalar, and v is a real vector with
117*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
118*> A(m-k+i,1:n-k+i-1), and tau in TAU(i).
119*> \endverbatim
120*>
121* =====================================================================
122 SUBROUTINE sgerq2( M, N, A, LDA, TAU, WORK, INFO )
123*
124* -- LAPACK computational routine --
125* -- LAPACK is a software package provided by Univ. of Tennessee, --
126* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127*
128* .. Scalar Arguments ..
129 INTEGER INFO, LDA, M, N
130* ..
131* .. Array Arguments ..
132 REAL A( LDA, * ), TAU( * ), WORK( * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 REAL ONE
139 parameter( one = 1.0e+0 )
140* ..
141* .. Local Scalars ..
142 INTEGER I, K
143 REAL AII
144* ..
145* .. External Subroutines ..
146 EXTERNAL slarf, slarfg, xerbla
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC max, min
150* ..
151* .. Executable Statements ..
152*
153* Test the input arguments
154*
155 info = 0
156 IF( m.LT.0 ) THEN
157 info = -1
158 ELSE IF( n.LT.0 ) THEN
159 info = -2
160 ELSE IF( lda.LT.max( 1, m ) ) THEN
161 info = -4
162 END IF
163 IF( info.NE.0 ) THEN
164 CALL xerbla( 'SGERQ2', -info )
165 RETURN
166 END IF
167*
168 k = min( m, n )
169*
170 DO 10 i = k, 1, -1
171*
172* Generate elementary reflector H(i) to annihilate
173* A(m-k+i,1:n-k+i-1)
174*
175 CALL slarfg( n-k+i, a( m-k+i, n-k+i ), a( m-k+i, 1 ), lda,
176 \$ tau( i ) )
177*
178* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
179*
180 aii = a( m-k+i, n-k+i )
181 a( m-k+i, n-k+i ) = one
182 CALL slarf( 'Right', m-k+i-1, n-k+i, a( m-k+i, 1 ), lda,
183 \$ tau( i ), a, lda, work )
184 a( m-k+i, n-k+i ) = aii
185 10 CONTINUE
186 RETURN
187*
188* End of SGERQ2
189*
190 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sgerq2(M, N, A, LDA, TAU, WORK, INFO)
SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
Definition: sgerq2.f:123
subroutine slarfg(N, ALPHA, X, INCX, TAU)
SLARFG generates an elementary reflector (Householder matrix).
Definition: slarfg.f:106
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