1 SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, LDA, M, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZGEQR2 computes a QR factorization of a complex m by n matrix A:
19 * A = Q * R.
20 *
21 * Arguments
22 * =========
23 *
24 * M (input) INTEGER
25 * The number of rows of the matrix A. M >= 0.
26 *
27 * N (input) INTEGER
28 * The number of columns of the matrix A. N >= 0.
29 *
30 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
31 * On entry, the m by n matrix A.
32 * On exit, the elements on and above the diagonal of the array
33 * contain the min(m,n) by n upper trapezoidal matrix R (R is
34 * upper triangular if m >= n); the elements below the diagonal,
35 * with the array TAU, represent the unitary matrix Q as a
36 * product of elementary reflectors (see Further Details).
37 *
38 * LDA (input) INTEGER
39 * The leading dimension of the array A. LDA >= max(1,M).
40 *
41 * TAU (output) COMPLEX*16 array, dimension (min(M,N))
42 * The scalar factors of the elementary reflectors (see Further
43 * Details).
44 *
45 * WORK (workspace) COMPLEX*16 array, dimension (N)
46 *
47 * INFO (output) INTEGER
48 * = 0: successful exit
49 * < 0: if INFO = -i, the i-th argument had an illegal value
50 *
51 * Further Details
52 * ===============
53 *
54 * The matrix Q is represented as a product of elementary reflectors
55 *
56 * Q = H(1) H(2) . . . H(k), where k = min(m,n).
57 *
58 * Each H(i) has the form
59 *
60 * H(i) = I - tau * v * v**H
61 *
62 * where tau is a complex scalar, and v is a complex vector with
63 * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
64 * and tau in TAU(i).
65 *
66 * =====================================================================
67 *
68 * .. Parameters ..
69 COMPLEX*16 ONE
70 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
71 * ..
72 * .. Local Scalars ..
73 INTEGER I, K
74 COMPLEX*16 ALPHA
75 * ..
76 * .. External Subroutines ..
77 EXTERNAL XERBLA, ZLARF, ZLARFG
78 * ..
79 * .. Intrinsic Functions ..
80 INTRINSIC DCONJG, MAX, MIN
81 * ..
82 * .. Executable Statements ..
83 *
84 * Test the input arguments
85 *
86 INFO = 0
87 IF( M.LT.0 ) THEN
88 INFO = -1
89 ELSE IF( N.LT.0 ) THEN
90 INFO = -2
91 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
92 INFO = -4
93 END IF
94 IF( INFO.NE.0 ) THEN
95 CALL XERBLA( 'ZGEQR2', -INFO )
96 RETURN
97 END IF
98 *
99 K = MIN( M, N )
100 *
101 DO 10 I = 1, K
102 *
103 * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
104 *
105 CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
106 $ TAU( I ) )
107 IF( I.LT.N ) THEN
108 *
109 * Apply H(i)**H to A(i:m,i+1:n) from the left
110 *
111 ALPHA = A( I, I )
112 A( I, I ) = ONE
113 CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
114 $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
115 A( I, I ) = ALPHA
116 END IF
117 10 CONTINUE
118 RETURN
119 *
120 * End of ZGEQR2
121 *
122 END
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, LDA, M, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZGEQR2 computes a QR factorization of a complex m by n matrix A:
19 * A = Q * R.
20 *
21 * Arguments
22 * =========
23 *
24 * M (input) INTEGER
25 * The number of rows of the matrix A. M >= 0.
26 *
27 * N (input) INTEGER
28 * The number of columns of the matrix A. N >= 0.
29 *
30 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
31 * On entry, the m by n matrix A.
32 * On exit, the elements on and above the diagonal of the array
33 * contain the min(m,n) by n upper trapezoidal matrix R (R is
34 * upper triangular if m >= n); the elements below the diagonal,
35 * with the array TAU, represent the unitary matrix Q as a
36 * product of elementary reflectors (see Further Details).
37 *
38 * LDA (input) INTEGER
39 * The leading dimension of the array A. LDA >= max(1,M).
40 *
41 * TAU (output) COMPLEX*16 array, dimension (min(M,N))
42 * The scalar factors of the elementary reflectors (see Further
43 * Details).
44 *
45 * WORK (workspace) COMPLEX*16 array, dimension (N)
46 *
47 * INFO (output) INTEGER
48 * = 0: successful exit
49 * < 0: if INFO = -i, the i-th argument had an illegal value
50 *
51 * Further Details
52 * ===============
53 *
54 * The matrix Q is represented as a product of elementary reflectors
55 *
56 * Q = H(1) H(2) . . . H(k), where k = min(m,n).
57 *
58 * Each H(i) has the form
59 *
60 * H(i) = I - tau * v * v**H
61 *
62 * where tau is a complex scalar, and v is a complex vector with
63 * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
64 * and tau in TAU(i).
65 *
66 * =====================================================================
67 *
68 * .. Parameters ..
69 COMPLEX*16 ONE
70 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
71 * ..
72 * .. Local Scalars ..
73 INTEGER I, K
74 COMPLEX*16 ALPHA
75 * ..
76 * .. External Subroutines ..
77 EXTERNAL XERBLA, ZLARF, ZLARFG
78 * ..
79 * .. Intrinsic Functions ..
80 INTRINSIC DCONJG, MAX, MIN
81 * ..
82 * .. Executable Statements ..
83 *
84 * Test the input arguments
85 *
86 INFO = 0
87 IF( M.LT.0 ) THEN
88 INFO = -1
89 ELSE IF( N.LT.0 ) THEN
90 INFO = -2
91 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
92 INFO = -4
93 END IF
94 IF( INFO.NE.0 ) THEN
95 CALL XERBLA( 'ZGEQR2', -INFO )
96 RETURN
97 END IF
98 *
99 K = MIN( M, N )
100 *
101 DO 10 I = 1, K
102 *
103 * Generate elementary reflector H(i) to annihilate A(i+1:m,i)
104 *
105 CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
106 $ TAU( I ) )
107 IF( I.LT.N ) THEN
108 *
109 * Apply H(i)**H to A(i:m,i+1:n) from the left
110 *
111 ALPHA = A( I, I )
112 A( I, I ) = ONE
113 CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
114 $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
115 A( I, I ) = ALPHA
116 END IF
117 10 CONTINUE
118 RETURN
119 *
120 * End of ZGEQR2
121 *
122 END