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: *> A = Q * R. The diagonal entries of R are real and nonnegative.
38: *> \endverbatim
39: *
40: * Arguments:
41: * ==========
42: *
43: *> \param[in] M
44: *> \verbatim
45: *> M is INTEGER
46: *> The number of rows of the matrix A. M >= 0.
47: *> \endverbatim
48: *>
49: *> \param[in] N
50: *> \verbatim
51: *> N is INTEGER
52: *> The number of columns of the matrix A. N >= 0.
53: *> \endverbatim
54: *>
55: *> \param[in,out] A
56: *> \verbatim
57: *> A is COMPLEX*16 array, dimension (LDA,N)
58: *> On entry, the m by n matrix A.
59: *> On exit, the elements on and above the diagonal of the array
60: *> contain the min(m,n) by n upper trapezoidal matrix R (R is
61: *> upper triangular if m >= n). The diagonal entries of R
62: *> are real and nonnegative; the elements below the diagonal,
63: *> with the array TAU, represent the unitary matrix Q as a
64: *> product of elementary reflectors (see Further Details).
65: *> \endverbatim
66: *>
67: *> \param[in] LDA
68: *> \verbatim
69: *> LDA is INTEGER
70: *> The leading dimension of the array A. LDA >= max(1,M).
71: *> \endverbatim
72: *>
73: *> \param[out] TAU
74: *> \verbatim
75: *> TAU is COMPLEX*16 array, dimension (min(M,N))
76: *> The scalar factors of the elementary reflectors (see Further
77: *> Details).
78: *> \endverbatim
79: *>
80: *> \param[out] WORK
81: *> \verbatim
82: *> WORK is COMPLEX*16 array, dimension (N)
83: *> \endverbatim
84: *>
85: *> \param[out] INFO
86: *> \verbatim
87: *> INFO is INTEGER
88: *> = 0: successful exit
89: *> < 0: if INFO = -i, the i-th argument had an illegal value
90: *> \endverbatim
91: *
92: * Authors:
93: * ========
94: *
95: *> \author Univ. of Tennessee
96: *> \author Univ. of California Berkeley
97: *> \author Univ. of Colorado Denver
98: *> \author NAG Ltd.
99: *
100: *> \date December 2016
101: *
102: *> \ingroup complex16GEcomputational
103: *
104: *> \par Further Details:
105: * =====================
106: *>
107: *> \verbatim
108: *>
109: *> The matrix Q is represented as a product of elementary reflectors
110: *>
111: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
112: *>
113: *> Each H(i) has the form
114: *>
115: *> H(i) = I - tau * v * v**H
116: *>
117: *> where tau is a complex scalar, and v is a complex vector with
118: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
119: *> and tau in TAU(i).
120: *>
121: *> See Lapack Working Note 203 for details
122: *> \endverbatim
123: *>
124: * =====================================================================
125: SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
126: *
127: * -- LAPACK computational routine (version 3.7.0) --
128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130: * December 2016
131: *
132: * .. Scalar Arguments ..
133: INTEGER INFO, LDA, M, N
134: * ..
135: * .. Array Arguments ..
136: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: COMPLEX*16 ONE
143: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
144: * ..
145: * .. Local Scalars ..
146: INTEGER I, K
147: COMPLEX*16 ALPHA
148: * ..
149: * .. External Subroutines ..
150: EXTERNAL XERBLA, ZLARF, ZLARFGP
151: * ..
152: * .. Intrinsic Functions ..
153: INTRINSIC DCONJG, MAX, MIN
154: * ..
155: * .. Executable Statements ..
156: *
157: * Test the input arguments
158: *
159: INFO = 0
160: IF( M.LT.0 ) THEN
161: INFO = -1
162: ELSE IF( N.LT.0 ) THEN
163: INFO = -2
164: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
165: INFO = -4
166: END IF
167: IF( INFO.NE.0 ) THEN
168: CALL XERBLA( 'ZGEQR2P', -INFO )
169: RETURN
170: END IF
171: *
172: K = MIN( M, N )
173: *
174: DO 10 I = 1, K
175: *
176: * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
177: *
178: CALL ZLARFGP( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
179: $ TAU( I ) )
180: IF( I.LT.N ) THEN
181: *
182: * Apply H(i)**H to A(i:m,i+1:n) from the left
183: *
184: ALPHA = A( I, I )
185: A( I, I ) = ONE
186: CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
187: $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
188: A( I, I ) = ALPHA
189: END IF
190: 10 CONTINUE
191: RETURN
192: *
193: * End of ZGEQR2P
194: *
195: END
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