LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
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 *
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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