SGEQRF(1) LAPACK routine (version 3.2) SGEQRF(1)NAME
SGEQRF - computes a QR factorization of a real M-by-N 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 M-by-N 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 M-by-N matrix A. On exit, the elements on and
above the diagonal of the array contain the min(M,N)-by-N upper
trapezoidal matrix R (R is upper triangular 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 reflec‐
tors (see Further 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 (MAX(1,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 opti‐
mum performance LWORK >= N*NB, where NB is the optimal block‐
size. 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 i-th 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:i-1) = 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 routine (version 3.2) November 2008 SGEQRF(1)
