DGEQRF(3F)DGEQRF(3F)NAME
DGEQRF - compute a QR factorization of a real M-by-N matrix A
SYNOPSIS
SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
PURPOSE
DGEQRF 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) DOUBLE PRECISION 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
reflectors (see Further Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) DOUBLE PRECISION 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.
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).
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DGEQRF(3F)DGEQRF(3F)
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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