1: *> \brief \b ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZUNG2L + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zung2l.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zung2l.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zung2l.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZUNG2L( 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: *> ZUNG2L generates an m by n complex matrix Q with orthonormal columns,
37: *> which is defined as the last n columns of a product of k elementary
38: *> reflectors of order m
39: *>
40: *> Q = H(k) . . . H(2) H(1)
41: *>
42: *> as returned by ZGEQLF.
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. M >= N >= 0.
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. N >= 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 (n-k+i)-th column must contain the vector which
71: *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72: *> returned by ZGEQLF in the last k columns of its array
73: *> argument A.
74: *> On exit, the m-by-n matrix Q.
75: *> \endverbatim
76: *>
77: *> \param[in] LDA
78: *> \verbatim
79: *> LDA is INTEGER
80: *> The first dimension of the array A. LDA >= max(1,M).
81: *> \endverbatim
82: *>
83: *> \param[in] TAU
84: *> \verbatim
85: *> TAU is COMPLEX*16 array, dimension (K)
86: *> TAU(i) must contain the scalar factor of the elementary
87: *> reflector H(i), as returned by ZGEQLF.
88: *> \endverbatim
89: *>
90: *> \param[out] WORK
91: *> \verbatim
92: *> WORK is COMPLEX*16 array, dimension (N)
93: *> \endverbatim
94: *>
95: *> \param[out] INFO
96: *> \verbatim
97: *> INFO is INTEGER
98: *> = 0: successful exit
99: *> < 0: if INFO = -i, the i-th argument has an illegal value
100: *> \endverbatim
101: *
102: * Authors:
103: * ========
104: *
105: *> \author Univ. of Tennessee
106: *> \author Univ. of California Berkeley
107: *> \author Univ. of Colorado Denver
108: *> \author NAG Ltd.
109: *
110: *> \ingroup complex16OTHERcomputational
111: *
112: * =====================================================================
113: SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO )
114: *
115: * -- LAPACK computational routine --
116: * -- LAPACK is a software package provided by Univ. of Tennessee, --
117: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118: *
119: * .. Scalar Arguments ..
120: INTEGER INFO, K, LDA, M, N
121: * ..
122: * .. Array Arguments ..
123: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
124: * ..
125: *
126: * =====================================================================
127: *
128: * .. Parameters ..
129: COMPLEX*16 ONE, ZERO
130: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
131: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
132: * ..
133: * .. Local Scalars ..
134: INTEGER I, II, J, L
135: * ..
136: * .. External Subroutines ..
137: EXTERNAL XERBLA, ZLARF, ZSCAL
138: * ..
139: * .. Intrinsic Functions ..
140: INTRINSIC MAX
141: * ..
142: * .. Executable Statements ..
143: *
144: * Test the input arguments
145: *
146: INFO = 0
147: IF( M.LT.0 ) THEN
148: INFO = -1
149: ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
150: INFO = -2
151: ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
152: INFO = -3
153: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
154: INFO = -5
155: END IF
156: IF( INFO.NE.0 ) THEN
157: CALL XERBLA( 'ZUNG2L', -INFO )
158: RETURN
159: END IF
160: *
161: * Quick return if possible
162: *
163: IF( N.LE.0 )
164: $ RETURN
165: *
166: * Initialise columns 1:n-k to columns of the unit matrix
167: *
168: DO 20 J = 1, N - K
169: DO 10 L = 1, M
170: A( L, J ) = ZERO
171: 10 CONTINUE
172: A( M-N+J, J ) = ONE
173: 20 CONTINUE
174: *
175: DO 40 I = 1, K
176: II = N - K + I
177: *
178: * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
179: *
180: A( M-N+II, II ) = ONE
181: CALL ZLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
182: $ LDA, WORK )
183: CALL ZSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
184: A( M-N+II, II ) = ONE - TAU( I )
185: *
186: * Set A(m-k+i+1:m,n-k+i) to zero
187: *
188: DO 30 L = M - N + II + 1, M
189: A( L, II ) = ZERO
190: 30 CONTINUE
191: 40 CONTINUE
192: RETURN
193: *
194: * End of ZUNG2L
195: *
196: END
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