cgelqf.f (3) Linux Manual Page
cgelqf.f –
Synopsis
Functions/Subroutines
subroutine cgelqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)CGELQF
Function/Subroutine Documentation
subroutine cgelqf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerLWORK, integerINFO)
CGELQF Purpose:
CGELQF computes an LQ factorization of a complex M-by-N matrix A:
A = L * Q.
Parameters:
- M
M is INTEGER
N
The number of rows of the matrix A. M >= 0.N is INTEGER
A
The number of columns of the matrix A. N >= 0.A is COMPLEX array, dimension (LDA,N)
LDA
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors (see Further Details).LDA is INTEGER
TAU
The leading dimension of the array A. LDA >= max(1,M).TAU is COMPLEX array, dimension (min(M,N))
WORK
The scalar factors of the elementary reflectors (see Further
Details).WORK is COMPLEX array, dimension (MAX(1,LWORK))
LWORK
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LWORK is INTEGER
INFO
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*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.INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
- Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
- November 2011
Further Details:
The matrix Q is represented as a product of elementary reflectors
Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
Each H(i) has the form
H(i) = I – tau * v * v**H
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).
Definition at line 136 of file cgelqf.f.