Annotation of rpl/lapack/lapack/zgeql2.f, revision 1.4
1.1 bertrand 1: SUBROUTINE ZGEQL2( M, N, 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, 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'
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, ZLARFP
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 ZLARFP( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) )
110: *
111: * Apply H(i)' 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
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