Annotation of rpl/lapack/lapack/dgeqr2p.f, revision 1.18
1.9 bertrand 1: *> \brief \b DGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
1.6 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.6 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 9: *> Download DGEQR2P + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2p.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2p.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2p.f">
1.6 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.6 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
1.14 bertrand 22: *
1.6 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, M, N
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
28: * ..
1.14 bertrand 29: *
1.6 bertrand 30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
1.17 bertrand 36: *> DGEQR2P computes a QR factorization of a real 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: *>
1.6 bertrand 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 DOUBLE PRECISION 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
1.12 bertrand 71: *> upper triangular if m >= n). The diagonal entries of R are
72: *> nonnegative; the elements below the diagonal,
1.6 bertrand 73: *> with the array TAU, represent the orthogonal 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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: *
1.14 bertrand 105: *> \author Univ. of Tennessee
106: *> \author Univ. of California Berkeley
107: *> \author Univ. of Colorado Denver
108: *> \author NAG Ltd.
1.6 bertrand 109: *
110: *> \ingroup doubleGEcomputational
111: *
112: *> \par Further Details:
113: * =====================
114: *>
115: *> \verbatim
116: *>
117: *> The matrix Q is represented as a product of elementary reflectors
118: *>
119: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
120: *>
121: *> Each H(i) has the form
122: *>
123: *> H(i) = I - tau * v * v**T
124: *>
125: *> where tau is a real scalar, and v is a real vector with
126: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
127: *> and tau in TAU(i).
1.12 bertrand 128: *>
129: *> See Lapack Working Note 203 for details
1.6 bertrand 130: *> \endverbatim
131: *>
132: * =====================================================================
1.1 bertrand 133: SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
134: *
1.18 ! bertrand 135: * -- LAPACK computational routine --
1.1 bertrand 136: * -- LAPACK is a software package provided by Univ. of Tennessee, --
137: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138: *
139: * .. Scalar Arguments ..
140: INTEGER INFO, LDA, M, N
141: * ..
142: * .. Array Arguments ..
143: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
144: * ..
145: *
146: * =====================================================================
147: *
148: * .. Parameters ..
149: DOUBLE PRECISION ONE
150: PARAMETER ( ONE = 1.0D+0 )
151: * ..
152: * .. Local Scalars ..
153: INTEGER I, K
154: DOUBLE PRECISION AII
155: * ..
156: * .. External Subroutines ..
157: EXTERNAL DLARF, DLARFGP, XERBLA
158: * ..
159: * .. Intrinsic Functions ..
160: INTRINSIC MAX, MIN
161: * ..
162: * .. Executable Statements ..
163: *
164: * Test the input arguments
165: *
166: INFO = 0
167: IF( M.LT.0 ) THEN
168: INFO = -1
169: ELSE IF( N.LT.0 ) THEN
170: INFO = -2
171: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
172: INFO = -4
173: END IF
174: IF( INFO.NE.0 ) THEN
175: CALL XERBLA( 'DGEQR2P', -INFO )
176: RETURN
177: END IF
178: *
179: K = MIN( M, N )
180: *
181: DO 10 I = 1, K
182: *
183: * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
184: *
185: CALL DLARFGP( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
186: $ TAU( I ) )
187: IF( I.LT.N ) THEN
188: *
189: * Apply H(i) to A(i:m,i+1:n) from the left
190: *
191: AII = A( I, I )
192: A( I, I ) = ONE
193: CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
194: $ A( I, I+1 ), LDA, WORK )
195: A( I, I ) = AII
196: END IF
197: 10 CONTINUE
198: RETURN
199: *
200: * End of DGEQR2P
201: *
202: END
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