1: SUBROUTINE DORG2L( 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: * DORG2L generates an m by n real matrix Q with orthonormal columns,
19: * which is defined as the last n columns of a product of k elementary
20: * reflectors of order m
21: *
22: * Q = H(k) . . . H(2) H(1)
23: *
24: * as returned by DGEQLF.
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. M >= N >= 0.
34: *
35: * K (input) INTEGER
36: * The number of elementary reflectors whose product defines the
37: * matrix Q. N >= K >= 0.
38: *
39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40: * On entry, the (n-k+i)-th column must contain the vector which
41: * defines the elementary reflector H(i), for i = 1,2,...,k, as
42: * returned by DGEQLF in the last k columns of its array
43: * argument A.
44: * On exit, the m by n matrix Q.
45: *
46: * LDA (input) INTEGER
47: * The first dimension of the array A. LDA >= max(1,M).
48: *
49: * TAU (input) DOUBLE PRECISION array, dimension (K)
50: * TAU(i) must contain the scalar factor of the elementary
51: * reflector H(i), as returned by DGEQLF.
52: *
53: * WORK (workspace) DOUBLE PRECISION array, dimension (N)
54: *
55: * INFO (output) INTEGER
56: * = 0: successful exit
57: * < 0: if INFO = -i, the i-th argument has an illegal value
58: *
59: * =====================================================================
60: *
61: * .. Parameters ..
62: DOUBLE PRECISION ONE, ZERO
63: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
64: * ..
65: * .. Local Scalars ..
66: INTEGER I, II, J, L
67: * ..
68: * .. External Subroutines ..
69: EXTERNAL DLARF, DSCAL, XERBLA
70: * ..
71: * .. Intrinsic Functions ..
72: INTRINSIC MAX
73: * ..
74: * .. Executable Statements ..
75: *
76: * Test the input arguments
77: *
78: INFO = 0
79: IF( M.LT.0 ) THEN
80: INFO = -1
81: ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
82: INFO = -2
83: ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
84: INFO = -3
85: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
86: INFO = -5
87: END IF
88: IF( INFO.NE.0 ) THEN
89: CALL XERBLA( 'DORG2L', -INFO )
90: RETURN
91: END IF
92: *
93: * Quick return if possible
94: *
95: IF( N.LE.0 )
96: $ RETURN
97: *
98: * Initialise columns 1:n-k to columns of the unit matrix
99: *
100: DO 20 J = 1, N - K
101: DO 10 L = 1, M
102: A( L, J ) = ZERO
103: 10 CONTINUE
104: A( M-N+J, J ) = ONE
105: 20 CONTINUE
106: *
107: DO 40 I = 1, K
108: II = N - K + I
109: *
110: * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
111: *
112: A( M-N+II, II ) = ONE
113: CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
114: $ LDA, WORK )
115: CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
116: A( M-N+II, II ) = ONE - TAU( I )
117: *
118: * Set A(m-k+i+1:m,n-k+i) to zero
119: *
120: DO 30 L = M - N + II + 1, M
121: A( L, II ) = ZERO
122: 30 CONTINUE
123: 40 CONTINUE
124: RETURN
125: *
126: * End of DORG2L
127: *
128: END
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