CGEQRF(l) — LAPACK routine (version 2.0)

NAME

CGEQRF - compute a QR factorization of a complex M-by-N matrix A

SYNOPSIS

SUBROUTINE CGEQRF(
M, N, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER INFO, LDA, LWORK, M, N

COMPLEX A( LDA, ∗ ), TAU( ∗ ), WORK( LWORK )

PURPOSE

CGEQRF computes a QR factorization of a complex 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) COMPLEX 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 unitary 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) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further Details).

WORK (workspace/output) COMPLEX 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 complex scalar, and v is a complex 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).