LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zungl2.f
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1 *> \brief \b ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, K, LDA, M, N
25 * ..
26 * .. Array Arguments ..
27 * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> ZUNGL2 generates an m-by-n complex 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 . . . H(2)**H H(1)**H
41 *>
42 *> as returned by ZGELQF.
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 COMPLEX*16 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 ZGELQF 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 COMPLEX*16 array, dimension (K)
85 *> TAU(i) must contain the scalar factor of the elementary
86 *> reflector H(i), as returned by ZGELQF.
87 *> \endverbatim
88 *>
89 *> \param[out] WORK
90 *> \verbatim
91 *> WORK is COMPLEX*16 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 complex16OTHERcomputational
110 *
111 * =====================================================================
112  SUBROUTINE zungl2( 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  COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  COMPLEX*16 ONE, ZERO
129  parameter( one = ( 1.0d+0, 0.0d+0 ),
130  \$ zero = ( 0.0d+0, 0.0d+0 ) )
131 * ..
132 * .. Local Scalars ..
133  INTEGER I, J, L
134 * ..
135 * .. External Subroutines ..
136  EXTERNAL xerbla, zlacgv, zlarf, zscal
137 * ..
138 * .. Intrinsic Functions ..
139  INTRINSIC dconjg, 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.m ) THEN
149  info = -2
150  ELSE IF( k.LT.0 .OR. k.GT.m ) 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( 'ZUNGL2', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( m.LE.0 )
163  \$ RETURN
164 *
165  IF( k.LT.m ) THEN
166 *
167 * Initialise rows k+1:m to rows of the unit matrix
168 *
169  DO 20 j = 1, n
170  DO 10 l = k + 1, m
171  a( l, j ) = zero
172  10 CONTINUE
173  IF( j.GT.k .AND. j.LE.m )
174  \$ a( j, j ) = one
175  20 CONTINUE
176  END IF
177 *
178  DO 40 i = k, 1, -1
179 *
180 * Apply H(i)**H to A(i:m,i:n) from the right
181 *
182  IF( i.LT.n ) THEN
183  CALL zlacgv( n-i, a( i, i+1 ), lda )
184  IF( i.LT.m ) THEN
185  a( i, i ) = one
186  CALL zlarf( 'Right', m-i, n-i+1, a( i, i ), lda,
187  \$ dconjg( tau( i ) ), a( i+1, i ), lda, work )
188  END IF
189  CALL zscal( n-i, -tau( i ), a( i, i+1 ), lda )
190  CALL zlacgv( n-i, a( i, i+1 ), lda )
191  END IF
192  a( i, i ) = one - dconjg( tau( i ) )
193 *
194 * Set A(i,1:i-1) to zero
195 *
196  DO 30 l = 1, i - 1
197  a( i, l ) = zero
198  30 CONTINUE
199  40 CONTINUE
200  RETURN
201 *
202 * End of ZUNGL2
203 *
204  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
subroutine zlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition: zlarf.f:128
subroutine zungl2(M, N, K, A, LDA, TAU, WORK, INFO)
ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (u...
Definition: zungl2.f:113