1: SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
2: *
3: * -- LAPACK routine (version 3.3.1) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * -- April 2011 --
7: *
8: * .. Scalar Arguments ..
9: INTEGER INFO, LDA, M, N
10: * ..
11: * .. Array Arguments ..
12: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13: * ..
14: *
15: * Purpose
16: * =======
17: *
18: * DGEQR2 computes a QR factorization of a real m by n matrix A:
19: * A = Q * R.
20: *
21: * Arguments
22: * =========
23: *
24: * M (input) INTEGER
25: * The number of rows of the matrix A. M >= 0.
26: *
27: * N (input) INTEGER
28: * The number of columns of the matrix A. N >= 0.
29: *
30: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
31: * On entry, the m by n matrix A.
32: * On exit, the elements on and above the diagonal of the array
33: * contain the min(m,n) by n upper trapezoidal matrix R (R is
34: * upper triangular if m >= n); the elements below the diagonal,
35: * with the array TAU, represent the orthogonal matrix Q as a
36: * product of elementary reflectors (see Further Details).
37: *
38: * LDA (input) INTEGER
39: * The leading dimension of the array A. LDA >= max(1,M).
40: *
41: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
42: * The scalar factors of the elementary reflectors (see Further
43: * Details).
44: *
45: * WORK (workspace) DOUBLE PRECISION array, dimension (N)
46: *
47: * INFO (output) INTEGER
48: * = 0: successful exit
49: * < 0: if INFO = -i, the i-th argument had an illegal value
50: *
51: * Further Details
52: * ===============
53: *
54: * The matrix Q is represented as a product of elementary reflectors
55: *
56: * Q = H(1) H(2) . . . H(k), where k = min(m,n).
57: *
58: * Each H(i) has the form
59: *
60: * H(i) = I - tau * v * v**T
61: *
62: * where tau is a real scalar, and v is a real vector with
63: * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
64: * and tau in TAU(i).
65: *
66: * =====================================================================
67: *
68: * .. Parameters ..
69: DOUBLE PRECISION ONE
70: PARAMETER ( ONE = 1.0D+0 )
71: * ..
72: * .. Local Scalars ..
73: INTEGER I, K
74: DOUBLE PRECISION AII
75: * ..
76: * .. External Subroutines ..
77: EXTERNAL DLARF, DLARFG, XERBLA
78: * ..
79: * .. Intrinsic Functions ..
80: INTRINSIC MAX, MIN
81: * ..
82: * .. Executable Statements ..
83: *
84: * Test the input arguments
85: *
86: INFO = 0
87: IF( M.LT.0 ) THEN
88: INFO = -1
89: ELSE IF( N.LT.0 ) THEN
90: INFO = -2
91: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
92: INFO = -4
93: END IF
94: IF( INFO.NE.0 ) THEN
95: CALL XERBLA( 'DGEQR2', -INFO )
96: RETURN
97: END IF
98: *
99: K = MIN( M, N )
100: *
101: DO 10 I = 1, K
102: *
103: * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
104: *
105: CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
106: $ TAU( I ) )
107: IF( I.LT.N ) THEN
108: *
109: * Apply H(i) to A(i:m,i+1:n) from the left
110: *
111: AII = A( I, I )
112: A( I, I ) = ONE
113: CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
114: $ A( I, I+1 ), LDA, WORK )
115: A( I, I ) = AII
116: END IF
117: 10 CONTINUE
118: RETURN
119: *
120: * End of DGEQR2
121: *
122: END
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