
SGEQRF(l) ) SGEQRF(l)
NAME
SGEQRF  compute a QR factorization of a real MbyN matrix A
SYNOPSIS
SUBROUTINE SGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
REAL A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
SGEQRF computes a QR factorization of a real MbyN matrix A: A = Q * R.
ARGUMENTS
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the MbyN matrix A. On exit, the elements on and above the diagonal of
the array contain the min(M,N)byN upper trapezoidal matrix R (R is upper trian
gular if m >= n); the elements below the diagonal, with the array TAU, represent
the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Fur
ther Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further Details).
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N). For optimum performance
LWORK >= N*NB, where NB is the optimal blocksize.
If LWORK = 1, then a workspace query is assumed; the routine only calculates the
optimal size of the WORK array, returns this value as the first entry of the WORK
array, and no error message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I  tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
LAPACK version 3.0 15 June 2000 SGEQRF(l) 
