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1.1 bertrand 1: SUBROUTINE ZUNGL2( 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: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13: * ..
14: *
15: * Purpose
16: * =======
17: *
18: * ZUNGL2 generates an m-by-n complex 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 ZGELQF.
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) COMPLEX*16 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 ZGELQF 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) COMPLEX*16 array, dimension (K)
49: * TAU(i) must contain the scalar factor of the elementary
50: * reflector H(i), as returned by ZGELQF.
51: *
52: * WORK (workspace) COMPLEX*16 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: COMPLEX*16 ONE, ZERO
62: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
63: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
64: * ..
65: * .. Local Scalars ..
66: INTEGER I, J, L
67: * ..
68: * .. External Subroutines ..
69: EXTERNAL XERBLA, ZLACGV, ZLARF, ZSCAL
70: * ..
71: * .. Intrinsic Functions ..
72: INTRINSIC DCONJG, 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.M ) THEN
82: INFO = -2
83: ELSE IF( K.LT.0 .OR. K.GT.M ) 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( 'ZUNGL2', -INFO )
90: RETURN
91: END IF
92: *
93: * Quick return if possible
94: *
95: IF( M.LE.0 )
96: $ RETURN
97: *
98: IF( K.LT.M ) THEN
99: *
100: * Initialise rows k+1:m to rows of the unit matrix
101: *
102: DO 20 J = 1, N
103: DO 10 L = K + 1, M
104: A( L, J ) = ZERO
105: 10 CONTINUE
106: IF( J.GT.K .AND. J.LE.M )
107: $ A( J, J ) = ONE
108: 20 CONTINUE
109: END IF
110: *
111: DO 40 I = K, 1, -1
112: *
113: * Apply H(i)' to A(i:m,i:n) from the right
114: *
115: IF( I.LT.N ) THEN
116: CALL ZLACGV( N-I, A( I, I+1 ), LDA )
117: IF( I.LT.M ) THEN
118: A( I, I ) = ONE
119: CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
120: $ DCONJG( TAU( I ) ), A( I+1, I ), LDA, WORK )
121: END IF
122: CALL ZSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
123: CALL ZLACGV( N-I, A( I, I+1 ), LDA )
124: END IF
125: A( I, I ) = ONE - DCONJG( TAU( I ) )
126: *
127: * Set A(i,1:i-1) to zero
128: *
129: DO 30 L = 1, I - 1
130: A( I, L ) = ZERO
131: 30 CONTINUE
132: 40 CONTINUE
133: RETURN
134: *
135: * End of ZUNGL2
136: *
137: END