Annotation of rpl/lapack/lapack/zgeqr2.f, revision 1.17
1.13 bertrand 1: *> \brief \b ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
1.10 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.17 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.10 bertrand 7: *
8: *> \htmlonly
1.17 ! bertrand 9: *> Download ZGEQR2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqr2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqr2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqr2.f">
1.10 bertrand 15: *> [TXT]</a>
1.17 ! bertrand 16: *> \endhtmlonly
1.10 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
1.17 ! bertrand 22: *
1.10 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, M, N
25: * ..
26: * .. Array Arguments ..
27: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
28: * ..
1.17 ! bertrand 29: *
1.10 bertrand 30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> ZGEQR2 computes a QR factorization of a complex m by n matrix A:
37: *> A = Q * R.
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 elements below the diagonal,
62: *> with the array TAU, represent the unitary matrix Q as a
63: *> product of elementary reflectors (see Further Details).
64: *> \endverbatim
65: *>
66: *> \param[in] LDA
67: *> \verbatim
68: *> LDA is INTEGER
69: *> The leading dimension of the array A. LDA >= max(1,M).
70: *> \endverbatim
71: *>
72: *> \param[out] TAU
73: *> \verbatim
74: *> TAU is COMPLEX*16 array, dimension (min(M,N))
75: *> The scalar factors of the elementary reflectors (see Further
76: *> Details).
77: *> \endverbatim
78: *>
79: *> \param[out] WORK
80: *> \verbatim
81: *> WORK is COMPLEX*16 array, dimension (N)
82: *> \endverbatim
83: *>
84: *> \param[out] INFO
85: *> \verbatim
86: *> INFO is INTEGER
87: *> = 0: successful exit
88: *> < 0: if INFO = -i, the i-th argument had an illegal value
89: *> \endverbatim
90: *
91: * Authors:
92: * ========
93: *
1.17 ! bertrand 94: *> \author Univ. of Tennessee
! 95: *> \author Univ. of California Berkeley
! 96: *> \author Univ. of Colorado Denver
! 97: *> \author NAG Ltd.
1.10 bertrand 98: *
1.17 ! bertrand 99: *> \date December 2016
1.10 bertrand 100: *
101: *> \ingroup complex16GEcomputational
102: *
103: *> \par Further Details:
104: * =====================
105: *>
106: *> \verbatim
107: *>
108: *> The matrix Q is represented as a product of elementary reflectors
109: *>
110: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
111: *>
112: *> Each H(i) has the form
113: *>
114: *> H(i) = I - tau * v * v**H
115: *>
116: *> where tau is a complex scalar, and v is a complex vector with
117: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
118: *> and tau in TAU(i).
119: *> \endverbatim
120: *>
121: * =====================================================================
1.1 bertrand 122: SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
123: *
1.17 ! bertrand 124: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.17 ! bertrand 127: * December 2016
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: INTEGER INFO, LDA, M, N
131: * ..
132: * .. Array Arguments ..
133: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
134: * ..
135: *
136: * =====================================================================
137: *
138: * .. Parameters ..
139: COMPLEX*16 ONE
140: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
141: * ..
142: * .. Local Scalars ..
143: INTEGER I, K
144: COMPLEX*16 ALPHA
145: * ..
146: * .. External Subroutines ..
1.5 bertrand 147: EXTERNAL XERBLA, ZLARF, ZLARFG
1.1 bertrand 148: * ..
149: * .. Intrinsic Functions ..
150: INTRINSIC DCONJG, MAX, MIN
151: * ..
152: * .. Executable Statements ..
153: *
154: * Test the input arguments
155: *
156: INFO = 0
157: IF( M.LT.0 ) THEN
158: INFO = -1
159: ELSE IF( N.LT.0 ) THEN
160: INFO = -2
161: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
162: INFO = -4
163: END IF
164: IF( INFO.NE.0 ) THEN
165: CALL XERBLA( 'ZGEQR2', -INFO )
166: RETURN
167: END IF
168: *
169: K = MIN( M, N )
170: *
171: DO 10 I = 1, K
172: *
173: * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
174: *
1.5 bertrand 175: CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
1.1 bertrand 176: $ TAU( I ) )
177: IF( I.LT.N ) THEN
178: *
1.9 bertrand 179: * Apply H(i)**H to A(i:m,i+1:n) from the left
1.1 bertrand 180: *
181: ALPHA = A( I, I )
182: A( I, I ) = ONE
183: CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
184: $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
185: A( I, I ) = ALPHA
186: END IF
187: 10 CONTINUE
188: RETURN
189: *
190: * End of ZGEQR2
191: *
192: END
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