Annotation of rpl/lapack/lapack/dorg2r.f, revision 1.4
1.1 bertrand 1: SUBROUTINE DORG2R( 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: * DORG2R generates an m by n real matrix Q with orthonormal columns,
19: * which is defined as the first n columns of a product of k elementary
20: * reflectors of order m
21: *
22: * Q = H(1) H(2) . . . H(k)
23: *
24: * as returned by DGEQRF.
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 i-th column must contain the vector which
41: * defines the elementary reflector H(i), for i = 1,2,...,k, as
42: * returned by DGEQRF in the first 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 DGEQRF.
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, 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( 'DORG2R', -INFO )
90: RETURN
91: END IF
92: *
93: * Quick return if possible
94: *
95: IF( N.LE.0 )
96: $ RETURN
97: *
98: * Initialise columns k+1:n to columns of the unit matrix
99: *
100: DO 20 J = K + 1, N
101: DO 10 L = 1, M
102: A( L, J ) = ZERO
103: 10 CONTINUE
104: A( J, J ) = ONE
105: 20 CONTINUE
106: *
107: DO 40 I = K, 1, -1
108: *
109: * Apply H(i) to A(i:m,i:n) from the left
110: *
111: IF( I.LT.N ) THEN
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: END IF
116: IF( I.LT.M )
117: $ CALL DSCAL( M-I, -TAU( I ), A( I+1, I ), 1 )
118: A( I, I ) = ONE - TAU( I )
119: *
120: * Set A(1:i-1,i) to zero
121: *
122: DO 30 L = 1, I - 1
123: A( L, I ) = ZERO
124: 30 CONTINUE
125: 40 CONTINUE
126: RETURN
127: *
128: * End of DORG2R
129: *
130: END
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