Annotation of rpl/lapack/lapack/zungl2.f, revision 1.10
1.9 bertrand 1: *> \brief \b ZUNGL2
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZUNGL2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zungl2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zungl2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zungl2.f">
15: *> [TXT]</a>
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: *> \date November 2011
110: *
111: *> \ingroup complex16OTHERcomputational
112: *
113: * =====================================================================
1.1 bertrand 114: SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO )
115: *
1.9 bertrand 116: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 117: * -- LAPACK is a software package provided by Univ. of Tennessee, --
118: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 119: * November 2011
1.1 bertrand 120: *
121: * .. Scalar Arguments ..
122: INTEGER INFO, K, LDA, M, N
123: * ..
124: * .. Array Arguments ..
125: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
126: * ..
127: *
128: * =====================================================================
129: *
130: * .. Parameters ..
131: COMPLEX*16 ONE, ZERO
132: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
133: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
134: * ..
135: * .. Local Scalars ..
136: INTEGER I, J, L
137: * ..
138: * .. External Subroutines ..
139: EXTERNAL XERBLA, ZLACGV, ZLARF, ZSCAL
140: * ..
141: * .. Intrinsic Functions ..
142: INTRINSIC DCONJG, MAX
143: * ..
144: * .. Executable Statements ..
145: *
146: * Test the input arguments
147: *
148: INFO = 0
149: IF( M.LT.0 ) THEN
150: INFO = -1
151: ELSE IF( N.LT.M ) THEN
152: INFO = -2
153: ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
154: INFO = -3
155: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
156: INFO = -5
157: END IF
158: IF( INFO.NE.0 ) THEN
159: CALL XERBLA( 'ZUNGL2', -INFO )
160: RETURN
161: END IF
162: *
163: * Quick return if possible
164: *
165: IF( M.LE.0 )
166: $ RETURN
167: *
168: IF( K.LT.M ) THEN
169: *
170: * Initialise rows k+1:m to rows of the unit matrix
171: *
172: DO 20 J = 1, N
173: DO 10 L = K + 1, M
174: A( L, J ) = ZERO
175: 10 CONTINUE
176: IF( J.GT.K .AND. J.LE.M )
177: $ A( J, J ) = ONE
178: 20 CONTINUE
179: END IF
180: *
181: DO 40 I = K, 1, -1
182: *
1.8 bertrand 183: * Apply H(i)**H to A(i:m,i:n) from the right
1.1 bertrand 184: *
185: IF( I.LT.N ) THEN
186: CALL ZLACGV( N-I, A( I, I+1 ), LDA )
187: IF( I.LT.M ) THEN
188: A( I, I ) = ONE
189: CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
190: $ DCONJG( TAU( I ) ), A( I+1, I ), LDA, WORK )
191: END IF
192: CALL ZSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
193: CALL ZLACGV( N-I, A( I, I+1 ), LDA )
194: END IF
195: A( I, I ) = ONE - DCONJG( TAU( I ) )
196: *
197: * Set A(i,1:i-1) to zero
198: *
199: DO 30 L = 1, I - 1
200: A( I, L ) = ZERO
201: 30 CONTINUE
202: 40 CONTINUE
203: RETURN
204: *
205: * End of ZUNGL2
206: *
207: END
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