2329
|
1 SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO ) |
|
2 * |
3333
|
3 * -- LAPACK routine (version 3.0) -- |
2329
|
4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
|
5 * Courant Institute, Argonne National Lab, and Rice University |
|
6 * September 30, 1994 |
|
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 * ZUNG2R generates an m by n complex 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 ZGEQRF. |
|
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) COMPLEX*16 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 ZGEQRF 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) COMPLEX*16 array, dimension (K) |
|
50 * TAU(i) must contain the scalar factor of the elementary |
|
51 * reflector H(i), as returned by ZGEQRF. |
|
52 * |
|
53 * WORK (workspace) COMPLEX*16 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 COMPLEX*16 ONE, ZERO |
|
63 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), |
|
64 $ ZERO = ( 0.0D+0, 0.0D+0 ) ) |
|
65 * .. |
|
66 * .. Local Scalars .. |
|
67 INTEGER I, J, L |
|
68 * .. |
|
69 * .. External Subroutines .. |
|
70 EXTERNAL XERBLA, ZLARF, ZSCAL |
|
71 * .. |
|
72 * .. Intrinsic Functions .. |
|
73 INTRINSIC MAX |
|
74 * .. |
|
75 * .. Executable Statements .. |
|
76 * |
|
77 * Test the input arguments |
|
78 * |
|
79 INFO = 0 |
|
80 IF( M.LT.0 ) THEN |
|
81 INFO = -1 |
|
82 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN |
|
83 INFO = -2 |
|
84 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN |
|
85 INFO = -3 |
|
86 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
|
87 INFO = -5 |
|
88 END IF |
|
89 IF( INFO.NE.0 ) THEN |
|
90 CALL XERBLA( 'ZUNG2R', -INFO ) |
|
91 RETURN |
|
92 END IF |
|
93 * |
|
94 * Quick return if possible |
|
95 * |
|
96 IF( N.LE.0 ) |
|
97 $ RETURN |
|
98 * |
|
99 * Initialise columns k+1:n to columns of the unit matrix |
|
100 * |
|
101 DO 20 J = K + 1, N |
|
102 DO 10 L = 1, M |
|
103 A( L, J ) = ZERO |
|
104 10 CONTINUE |
|
105 A( J, J ) = ONE |
|
106 20 CONTINUE |
|
107 * |
|
108 DO 40 I = K, 1, -1 |
|
109 * |
|
110 * Apply H(i) to A(i:m,i:n) from the left |
|
111 * |
|
112 IF( I.LT.N ) THEN |
|
113 A( I, I ) = ONE |
|
114 CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), |
|
115 $ A( I, I+1 ), LDA, WORK ) |
|
116 END IF |
|
117 IF( I.LT.M ) |
|
118 $ CALL ZSCAL( M-I, -TAU( I ), A( I+1, I ), 1 ) |
|
119 A( I, I ) = ONE - TAU( I ) |
|
120 * |
|
121 * Set A(1:i-1,i) to zero |
|
122 * |
|
123 DO 30 L = 1, I - 1 |
|
124 A( L, I ) = ZERO |
|
125 30 CONTINUE |
|
126 40 CONTINUE |
|
127 RETURN |
|
128 * |
|
129 * End of ZUNG2R |
|
130 * |
|
131 END |