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1.1 bertrand 1: SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: INTEGER INFO, K, LDA, M, N
10: * ..
11: * .. Array Arguments ..
12: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13: * ..
14: *
15: * Purpose
16: * =======
17: *
18: * DORGL2 generates an m by n real matrix Q with orthonormal rows,
19: * which is defined as the first m rows of a product of k elementary
20: * reflectors of order n
21: *
22: * Q = H(k) . . . H(2) H(1)
23: *
24: * as returned by DGELQF.
25: *
26: * Arguments
27: * =========
28: *
29: * M (input) INTEGER
30: * The number of rows of the matrix Q. M >= 0.
31: *
32: * N (input) INTEGER
33: * The number of columns of the matrix Q. N >= M.
34: *
35: * K (input) INTEGER
36: * The number of elementary reflectors whose product defines the
37: * matrix Q. M >= K >= 0.
38: *
39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40: * On entry, the i-th row must contain the vector which defines
41: * the elementary reflector H(i), for i = 1,2,...,k, as returned
42: * by DGELQF in the first k rows of its array argument A.
43: * On exit, the m-by-n matrix Q.
44: *
45: * LDA (input) INTEGER
46: * The first dimension of the array A. LDA >= max(1,M).
47: *
48: * TAU (input) DOUBLE PRECISION array, dimension (K)
49: * TAU(i) must contain the scalar factor of the elementary
50: * reflector H(i), as returned by DGELQF.
51: *
52: * WORK (workspace) DOUBLE PRECISION array, dimension (M)
53: *
54: * INFO (output) INTEGER
55: * = 0: successful exit
56: * < 0: if INFO = -i, the i-th argument has an illegal value
57: *
58: * =====================================================================
59: *
60: * .. Parameters ..
61: DOUBLE PRECISION ONE, ZERO
62: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
63: * ..
64: * .. Local Scalars ..
65: INTEGER I, J, L
66: * ..
67: * .. External Subroutines ..
68: EXTERNAL DLARF, DSCAL, XERBLA
69: * ..
70: * .. Intrinsic Functions ..
71: INTRINSIC MAX
72: * ..
73: * .. Executable Statements ..
74: *
75: * Test the input arguments
76: *
77: INFO = 0
78: IF( M.LT.0 ) THEN
79: INFO = -1
80: ELSE IF( N.LT.M ) THEN
81: INFO = -2
82: ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
83: INFO = -3
84: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
85: INFO = -5
86: END IF
87: IF( INFO.NE.0 ) THEN
88: CALL XERBLA( 'DORGL2', -INFO )
89: RETURN
90: END IF
91: *
92: * Quick return if possible
93: *
94: IF( M.LE.0 )
95: $ RETURN
96: *
97: IF( K.LT.M ) THEN
98: *
99: * Initialise rows k+1:m to rows of the unit matrix
100: *
101: DO 20 J = 1, N
102: DO 10 L = K + 1, M
103: A( L, J ) = ZERO
104: 10 CONTINUE
105: IF( J.GT.K .AND. J.LE.M )
106: $ A( J, J ) = ONE
107: 20 CONTINUE
108: END IF
109: *
110: DO 40 I = K, 1, -1
111: *
112: * Apply H(i) to A(i:m,i:n) from the right
113: *
114: IF( I.LT.N ) THEN
115: IF( I.LT.M ) THEN
116: A( I, I ) = ONE
117: CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
118: $ TAU( I ), A( I+1, I ), LDA, WORK )
119: END IF
120: CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
121: END IF
122: A( I, I ) = ONE - TAU( I )
123: *
124: * Set A(i,1:i-1) to zero
125: *
126: DO 30 L = 1, I - 1
127: A( I, L ) = ZERO
128: 30 CONTINUE
129: 40 CONTINUE
130: RETURN
131: *
132: * End of DORGL2
133: *
134: END