Annotation of rpl/lapack/lapack/zgeqr2.f, revision 1.21
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: *>
1.20 bertrand 36: *> ZGEQR2 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;
45: *> 0 is a (m-n)-by-n zero matrix, if m > n.
46: *>
1.10 bertrand 47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] M
53: *> \verbatim
54: *> M is INTEGER
55: *> The number of rows of the matrix A. M >= 0.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The number of columns of the matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in,out] A
65: *> \verbatim
66: *> A is COMPLEX*16 array, dimension (LDA,N)
67: *> On entry, the m by n matrix A.
68: *> On exit, the elements on and above the diagonal of the array
69: *> contain the min(m,n) by n upper trapezoidal matrix R (R is
70: *> upper triangular if m >= n); the elements below the diagonal,
71: *> with the array TAU, represent the unitary matrix Q as a
72: *> product of elementary reflectors (see Further Details).
73: *> \endverbatim
74: *>
75: *> \param[in] LDA
76: *> \verbatim
77: *> LDA is INTEGER
78: *> The leading dimension of the array A. LDA >= max(1,M).
79: *> \endverbatim
80: *>
81: *> \param[out] TAU
82: *> \verbatim
83: *> TAU is COMPLEX*16 array, dimension (min(M,N))
84: *> The scalar factors of the elementary reflectors (see Further
85: *> Details).
86: *> \endverbatim
87: *>
88: *> \param[out] WORK
89: *> \verbatim
90: *> WORK is COMPLEX*16 array, dimension (N)
91: *> \endverbatim
92: *>
93: *> \param[out] INFO
94: *> \verbatim
95: *> INFO is INTEGER
96: *> = 0: successful exit
97: *> < 0: if INFO = -i, the i-th argument had an illegal value
98: *> \endverbatim
99: *
100: * Authors:
101: * ========
102: *
1.17 bertrand 103: *> \author Univ. of Tennessee
104: *> \author Univ. of California Berkeley
105: *> \author Univ. of Colorado Denver
106: *> \author NAG Ltd.
1.10 bertrand 107: *
108: *> \ingroup complex16GEcomputational
109: *
110: *> \par Further Details:
111: * =====================
112: *>
113: *> \verbatim
114: *>
115: *> The matrix Q is represented as a product of elementary reflectors
116: *>
117: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
118: *>
119: *> Each H(i) has the form
120: *>
121: *> H(i) = I - tau * v * v**H
122: *>
123: *> where tau is a complex scalar, and v is a complex vector with
124: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
125: *> and tau in TAU(i).
126: *> \endverbatim
127: *>
128: * =====================================================================
1.1 bertrand 129: SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
130: *
1.21 ! bertrand 131: * -- LAPACK computational routine --
1.1 bertrand 132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134: *
135: * .. Scalar Arguments ..
136: INTEGER INFO, LDA, M, N
137: * ..
138: * .. Array Arguments ..
139: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
140: * ..
141: *
142: * =====================================================================
143: *
144: * .. Parameters ..
145: COMPLEX*16 ONE
146: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
147: * ..
148: * .. Local Scalars ..
149: INTEGER I, K
150: COMPLEX*16 ALPHA
151: * ..
152: * .. External Subroutines ..
1.5 bertrand 153: EXTERNAL XERBLA, ZLARF, ZLARFG
1.1 bertrand 154: * ..
155: * .. Intrinsic Functions ..
156: INTRINSIC DCONJG, MAX, MIN
157: * ..
158: * .. Executable Statements ..
159: *
160: * Test the input arguments
161: *
162: INFO = 0
163: IF( M.LT.0 ) THEN
164: INFO = -1
165: ELSE IF( N.LT.0 ) THEN
166: INFO = -2
167: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
168: INFO = -4
169: END IF
170: IF( INFO.NE.0 ) THEN
171: CALL XERBLA( 'ZGEQR2', -INFO )
172: RETURN
173: END IF
174: *
175: K = MIN( M, N )
176: *
177: DO 10 I = 1, K
178: *
179: * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
180: *
1.5 bertrand 181: CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
1.1 bertrand 182: $ TAU( I ) )
183: IF( I.LT.N ) THEN
184: *
1.9 bertrand 185: * Apply H(i)**H to A(i:m,i+1:n) from the left
1.1 bertrand 186: *
187: ALPHA = A( I, I )
188: A( I, I ) = ONE
189: CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
190: $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
191: A( I, I ) = ALPHA
192: END IF
193: 10 CONTINUE
194: RETURN
195: *
196: * End of ZGEQR2
197: *
198: END
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