SGEQRF - compute 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 ele
ments on and above the diagonal of the array con
tain 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 reflectors (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 (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.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal 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).
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