1 SUBROUTINE ZGEQL2( 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 * ZGEQL2 computes a QL factorization of a complex m by n matrix A:
19 * A = Q * L.
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, if m >= n, the lower triangle of the subarray
33 * A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
34 * if m <= n, the elements on and below the (n-m)-th
35 * superdiagonal contain the m by n lower trapezoidal matrix L;
36 * the remaining elements, with the array TAU, represent the
37 * unitary matrix Q as a product of elementary reflectors
38 * (see Further Details).
39 *
40 * LDA (input) INTEGER
41 * The leading dimension of the array A. LDA >= max(1,M).
42 *
43 * TAU (output) COMPLEX*16 array, dimension (min(M,N))
44 * The scalar factors of the elementary reflectors (see Further
45 * Details).
46 *
47 * WORK (workspace) COMPLEX*16 array, dimension (N)
48 *
49 * INFO (output) INTEGER
50 * = 0: successful exit
51 * < 0: if INFO = -i, the i-th argument had an illegal value
52 *
53 * Further Details
54 * ===============
55 *
56 * The matrix Q is represented as a product of elementary reflectors
57 *
58 * Q = H(k) . . . H(2) H(1), where k = min(m,n).
59 *
60 * Each H(i) has the form
61 *
62 * H(i) = I - tau * v * v**H
63 *
64 * where tau is a complex scalar, and v is a complex vector with
65 * v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
66 * A(1:m-k+i-1,n-k+i), and tau in TAU(i).
67 *
68 * =====================================================================
69 *
70 * .. Parameters ..
71 COMPLEX*16 ONE
72 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
73 * ..
74 * .. Local Scalars ..
75 INTEGER I, K
76 COMPLEX*16 ALPHA
77 * ..
78 * .. External Subroutines ..
79 EXTERNAL XERBLA, ZLARF, ZLARFG
80 * ..
81 * .. Intrinsic Functions ..
82 INTRINSIC DCONJG, MAX, MIN
83 * ..
84 * .. Executable Statements ..
85 *
86 * Test the input arguments
87 *
88 INFO = 0
89 IF( M.LT.0 ) THEN
90 INFO = -1
91 ELSE IF( N.LT.0 ) THEN
92 INFO = -2
93 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
94 INFO = -4
95 END IF
96 IF( INFO.NE.0 ) THEN
97 CALL XERBLA( 'ZGEQL2', -INFO )
98 RETURN
99 END IF
100 *
101 K = MIN( M, N )
102 *
103 DO 10 I = K, 1, -1
104 *
105 * Generate elementary reflector H(i) to annihilate
106 * A(1:m-k+i-1,n-k+i)
107 *
108 ALPHA = A( M-K+I, N-K+I )
109 CALL ZLARFG( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) )
110 *
111 * Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left
112 *
113 A( M-K+I, N-K+I ) = ONE
114 CALL ZLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1,
115 $ DCONJG( TAU( I ) ), A, LDA, WORK )
116 A( M-K+I, N-K+I ) = ALPHA
117 10 CONTINUE
118 RETURN
119 *
120 * End of ZGEQL2
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 * ZGEQL2 computes a QL factorization of a complex m by n matrix A:
19 * A = Q * L.
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, if m >= n, the lower triangle of the subarray
33 * A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
34 * if m <= n, the elements on and below the (n-m)-th
35 * superdiagonal contain the m by n lower trapezoidal matrix L;
36 * the remaining elements, with the array TAU, represent the
37 * unitary matrix Q as a product of elementary reflectors
38 * (see Further Details).
39 *
40 * LDA (input) INTEGER
41 * The leading dimension of the array A. LDA >= max(1,M).
42 *
43 * TAU (output) COMPLEX*16 array, dimension (min(M,N))
44 * The scalar factors of the elementary reflectors (see Further
45 * Details).
46 *
47 * WORK (workspace) COMPLEX*16 array, dimension (N)
48 *
49 * INFO (output) INTEGER
50 * = 0: successful exit
51 * < 0: if INFO = -i, the i-th argument had an illegal value
52 *
53 * Further Details
54 * ===============
55 *
56 * The matrix Q is represented as a product of elementary reflectors
57 *
58 * Q = H(k) . . . H(2) H(1), where k = min(m,n).
59 *
60 * Each H(i) has the form
61 *
62 * H(i) = I - tau * v * v**H
63 *
64 * where tau is a complex scalar, and v is a complex vector with
65 * v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
66 * A(1:m-k+i-1,n-k+i), and tau in TAU(i).
67 *
68 * =====================================================================
69 *
70 * .. Parameters ..
71 COMPLEX*16 ONE
72 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
73 * ..
74 * .. Local Scalars ..
75 INTEGER I, K
76 COMPLEX*16 ALPHA
77 * ..
78 * .. External Subroutines ..
79 EXTERNAL XERBLA, ZLARF, ZLARFG
80 * ..
81 * .. Intrinsic Functions ..
82 INTRINSIC DCONJG, MAX, MIN
83 * ..
84 * .. Executable Statements ..
85 *
86 * Test the input arguments
87 *
88 INFO = 0
89 IF( M.LT.0 ) THEN
90 INFO = -1
91 ELSE IF( N.LT.0 ) THEN
92 INFO = -2
93 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
94 INFO = -4
95 END IF
96 IF( INFO.NE.0 ) THEN
97 CALL XERBLA( 'ZGEQL2', -INFO )
98 RETURN
99 END IF
100 *
101 K = MIN( M, N )
102 *
103 DO 10 I = K, 1, -1
104 *
105 * Generate elementary reflector H(i) to annihilate
106 * A(1:m-k+i-1,n-k+i)
107 *
108 ALPHA = A( M-K+I, N-K+I )
109 CALL ZLARFG( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) )
110 *
111 * Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left
112 *
113 A( M-K+I, N-K+I ) = ONE
114 CALL ZLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1,
115 $ DCONJG( TAU( I ) ), A, LDA, WORK )
116 A( M-K+I, N-K+I ) = ALPHA
117 10 CONTINUE
118 RETURN
119 *
120 * End of ZGEQL2
121 *
122 END