Annotation of rpl/lapack/lapack/dgeqr2.f, revision 1.20
1.13 bertrand 1: *> \brief \b DGEQR2 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 DGEQR2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2.f">
1.10 bertrand 15: *> [TXT]</a>
1.17 bertrand 16: *> \endhtmlonly
1.10 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGEQR2( 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: * DOUBLE PRECISION 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: *> DGEQR2 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;
! 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 DOUBLE PRECISION 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 orthogonal 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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: *
1.20 ! bertrand 108: *> \date November 2019
1.10 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).
128: *> \endverbatim
129: *>
130: * =====================================================================
1.1 bertrand 131: SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
132: *
1.20 ! bertrand 133: * -- LAPACK computational routine (version 3.9.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.20 ! bertrand 136: * November 2019
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: INTEGER INFO, LDA, M, N
140: * ..
141: * .. Array Arguments ..
142: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
143: * ..
144: *
145: * =====================================================================
146: *
147: * .. Parameters ..
148: DOUBLE PRECISION ONE
149: PARAMETER ( ONE = 1.0D+0 )
150: * ..
151: * .. Local Scalars ..
152: INTEGER I, K
153: DOUBLE PRECISION AII
154: * ..
155: * .. External Subroutines ..
1.5 bertrand 156: EXTERNAL DLARF, DLARFG, XERBLA
1.1 bertrand 157: * ..
158: * .. Intrinsic Functions ..
159: INTRINSIC MAX, MIN
160: * ..
161: * .. Executable Statements ..
162: *
163: * Test the input arguments
164: *
165: INFO = 0
166: IF( M.LT.0 ) THEN
167: INFO = -1
168: ELSE IF( N.LT.0 ) THEN
169: INFO = -2
170: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
171: INFO = -4
172: END IF
173: IF( INFO.NE.0 ) THEN
174: CALL XERBLA( 'DGEQR2', -INFO )
175: RETURN
176: END IF
177: *
178: K = MIN( M, N )
179: *
180: DO 10 I = 1, K
181: *
182: * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
183: *
1.5 bertrand 184: CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
1.1 bertrand 185: $ TAU( I ) )
186: IF( I.LT.N ) THEN
187: *
188: * Apply H(i) to A(i:m,i+1:n) from the left
189: *
190: AII = A( I, I )
191: A( I, I ) = ONE
192: CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
193: $ A( I, I+1 ), LDA, WORK )
194: A( I, I ) = AII
195: END IF
196: 10 CONTINUE
197: RETURN
198: *
199: * End of DGEQR2
200: *
201: END
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