1: *> \brief \b ZGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements 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
9: *> Download ZGEQR2P + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqr2p.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqr2p.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqr2p.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, 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: *> ZGEQR2P computes a QR factorization of a complex m-by-n matrix A:
37: *>
38: *> A = Q * ( R ),
39: *> ( 0 )
40: *>
41: *> where:
42: *>
43: *> Q is a m-by-m orthogonal matrix;
44: *> R is an upper-triangular n-by-n matrix with nonnegative diagonal
45: *> entries;
46: *> 0 is a (m-n)-by-n zero matrix, if m > n.
47: *>
48: *> \endverbatim
49: *
50: * Arguments:
51: * ==========
52: *
53: *> \param[in] M
54: *> \verbatim
55: *> M is INTEGER
56: *> The number of rows of the matrix A. M >= 0.
57: *> \endverbatim
58: *>
59: *> \param[in] N
60: *> \verbatim
61: *> N is INTEGER
62: *> The number of columns of the matrix A. N >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in,out] A
66: *> \verbatim
67: *> A is COMPLEX*16 array, dimension (LDA,N)
68: *> On entry, the m by n matrix A.
69: *> On exit, the elements on and above the diagonal of the array
70: *> contain the min(m,n) by n upper trapezoidal matrix R (R is
71: *> upper triangular if m >= n). The diagonal entries of R
72: *> are real and nonnegative; the elements below the diagonal,
73: *> with the array TAU, represent the unitary matrix Q as a
74: *> product of elementary reflectors (see Further Details).
75: *> \endverbatim
76: *>
77: *> \param[in] LDA
78: *> \verbatim
79: *> LDA is INTEGER
80: *> The leading dimension of the array A. LDA >= max(1,M).
81: *> \endverbatim
82: *>
83: *> \param[out] TAU
84: *> \verbatim
85: *> TAU is COMPLEX*16 array, dimension (min(M,N))
86: *> The scalar factors of the elementary reflectors (see Further
87: *> Details).
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 had 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: *> \date November 2019
111: *
112: *> \ingroup complex16GEcomputational
113: *
114: *> \par Further Details:
115: * =====================
116: *>
117: *> \verbatim
118: *>
119: *> The matrix Q is represented as a product of elementary reflectors
120: *>
121: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
122: *>
123: *> Each H(i) has the form
124: *>
125: *> H(i) = I - tau * v * v**H
126: *>
127: *> where tau is a complex scalar, and v is a complex vector with
128: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
129: *> and tau in TAU(i).
130: *>
131: *> See Lapack Working Note 203 for details
132: *> \endverbatim
133: *>
134: * =====================================================================
135: SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
136: *
137: * -- LAPACK computational routine (version 3.9.0) --
138: * -- LAPACK is a software package provided by Univ. of Tennessee, --
139: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140: * November 2019
141: *
142: * .. Scalar Arguments ..
143: INTEGER INFO, LDA, M, N
144: * ..
145: * .. Array Arguments ..
146: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
147: * ..
148: *
149: * =====================================================================
150: *
151: * .. Parameters ..
152: COMPLEX*16 ONE
153: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
154: * ..
155: * .. Local Scalars ..
156: INTEGER I, K
157: COMPLEX*16 ALPHA
158: * ..
159: * .. External Subroutines ..
160: EXTERNAL XERBLA, ZLARF, ZLARFGP
161: * ..
162: * .. Intrinsic Functions ..
163: INTRINSIC DCONJG, MAX, MIN
164: * ..
165: * .. Executable Statements ..
166: *
167: * Test the input arguments
168: *
169: INFO = 0
170: IF( M.LT.0 ) THEN
171: INFO = -1
172: ELSE IF( N.LT.0 ) THEN
173: INFO = -2
174: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
175: INFO = -4
176: END IF
177: IF( INFO.NE.0 ) THEN
178: CALL XERBLA( 'ZGEQR2P', -INFO )
179: RETURN
180: END IF
181: *
182: K = MIN( M, N )
183: *
184: DO 10 I = 1, K
185: *
186: * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
187: *
188: CALL ZLARFGP( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
189: $ TAU( I ) )
190: IF( I.LT.N ) THEN
191: *
192: * Apply H(i)**H to A(i:m,i+1:n) from the left
193: *
194: ALPHA = A( I, I )
195: A( I, I ) = ONE
196: CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
197: $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
198: A( I, I ) = ALPHA
199: END IF
200: 10 CONTINUE
201: RETURN
202: *
203: * End of ZGEQR2P
204: *
205: END
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