1DGERQ2(1)                LAPACK routine (version 3.1)                DGERQ2(1)
2
3
4

NAME

6       DGERQ2 - an RQ factorization of a real m by n matrix A
7

SYNOPSIS

9       SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
10
11           INTEGER        INFO, LDA, M, N
12
13           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )
14

PURPOSE

16       DGERQ2  computes an RQ factorization of a real m by n matrix A: A = R *
17       Q.
18
19

ARGUMENTS

21       M       (input) INTEGER
22               The number of rows of the matrix A.  M >= 0.
23
24       N       (input) INTEGER
25               The number of columns of the matrix A.  N >= 0.
26
27       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
28               On entry, the m by n matrix A.  On exit, if m <= n,  the  upper
29               triangle  of  the  subarray  A(1:m,n-m+1:n) contains the m by m
30               upper triangular matrix R; if m >= n, the elements on and above
31               the  (m-n)-th  subdiagonal contain the m by n upper trapezoidal
32               matrix R; the remaining elements, with the array TAU, represent
33               the  orthogonal  matrix Q as a product of elementary reflectors
34               (see Further Details).
35
36       LDA     (input) INTEGER
37               The leading dimension of the array A.  LDA >= max(1,M).
38
39       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
40               The scalar factors of the elementary  reflectors  (see  Further
41               Details).
42
43       WORK    (workspace) DOUBLE PRECISION array, dimension (M)
44
45       INFO    (output) INTEGER
46               = 0: successful exit
47               < 0: if INFO = -i, the i-th argument had an illegal value
48

FURTHER DETAILS

50       The matrix Q is represented as a product of elementary reflectors
51
52          Q = H(1) H(2) . . . H(k), where k = min(m,n).
53
54       Each H(i) has the form
55
56          H(i) = I - tau * v * v'
57
58       where tau is a real scalar, and v is a real vector with
59       v(n-k+i+1:n)  =  0  and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
60       A(m-k+i,1:n-k+i-1), and tau in TAU(i).
61
62
63
64
65 LAPACK routine (version 3.1)    November 2006                       DGERQ2(1)