Annotation of rpl/lapack/lapack/zgerq2.f, revision 1.2
1.1 bertrand 1: SUBROUTINE ZGERQ2( 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: * ZGERQ2 computes an RQ factorization of a complex m by n matrix A:
19: * A = R * Q.
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 upper triangle of the subarray
33: * A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
34: * if m >= n, the elements on and above the (m-n)-th subdiagonal
35: * contain the m by n upper trapezoidal matrix R; the remaining
36: * elements, with the array TAU, represent the unitary matrix
37: * Q as a product of elementary reflectors (see Further
38: * 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 (M)
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(1)' H(2)' . . . H(k)', 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
66: * exit in A(m-k+i,1:n-k+i-1), 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, ZLACGV, ZLARF, ZLARFP
80: * ..
81: * .. Intrinsic Functions ..
82: INTRINSIC 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( 'ZGERQ2', -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(m-k+i,1:n-k+i-1)
107: *
108: CALL ZLACGV( N-K+I, A( M-K+I, 1 ), LDA )
109: ALPHA = A( M-K+I, N-K+I )
110: CALL ZLARFP( N-K+I, ALPHA, A( M-K+I, 1 ), LDA, TAU( I ) )
111: *
112: * Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
113: *
114: A( M-K+I, N-K+I ) = ONE
115: CALL ZLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA,
116: $ TAU( I ), A, LDA, WORK )
117: A( M-K+I, N-K+I ) = ALPHA
118: CALL ZLACGV( N-K+I-1, A( M-K+I, 1 ), LDA )
119: 10 CONTINUE
120: RETURN
121: *
122: * End of ZGERQ2
123: *
124: END
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