CGEQRF(l) ) CGEQRF(l)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( * )
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 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 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).
LAPACK version 3.0 15 June 2000 CGEQRF(l)
