1SGELQ2(1)                LAPACK routine (version 3.1)                SGELQ2(1)
2
3
4

NAME

6       SGELQ2 - an LQ factorization of a real m by n matrix A
7

SYNOPSIS

9       SUBROUTINE SGELQ2( M, N, A, LDA, TAU, WORK, INFO )
10
11           INTEGER        INFO, LDA, M, N
12
13           REAL           A( LDA, * ), TAU( * ), WORK( * )
14

PURPOSE

16       SGELQ2  computes an LQ factorization of a real m by n matrix A: A = L *
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) REAL array, dimension (LDA,N)
28               On entry, the m by n matrix A.  On exit, the  elements  on  and
29               below the diagonal of the array contain the m by min(m,n) lower
30               trapezoidal matrix L (L is lower triangular if  m  <=  n);  the
31               elements  above the diagonal, with the array TAU, represent the
32               orthogonal matrix Q as a product of elementary reflectors  (see
33               Further  Details).   LDA     (input) INTEGER The leading dimen‐
34               sion of the array A.  LDA >= max(1,M).
35
36       TAU     (output) REAL array, dimension (min(M,N))
37               The scalar factors of the elementary  reflectors  (see  Further
38               Details).
39
40       WORK    (workspace) REAL array, dimension (M)
41
42       INFO    (output) INTEGER
43               = 0: successful exit
44               < 0: if INFO = -i, the i-th argument had an illegal value
45

FURTHER DETAILS

47       The matrix Q is represented as a product of elementary reflectors
48
49          Q = H(k) . . . H(2) H(1), where k = min(m,n).
50
51       Each H(i) has the form
52
53          H(i) = I - tau * v * v'
54
55       where tau is a real scalar, and v is a real vector with
56       v(1:i-1)  =  0  and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
57       and tau in TAU(i).
58
59
60
61
62 LAPACK routine (version 3.1)    November 2006                       SGELQ2(1)
Impressum