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# dgeqrf

```
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 ele-
ments 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 orthogo-
nal 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) 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).

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).
```