zgelqf (l) - Linux Manuals

zgelqf: computes an LQ factorization of a complex M-by-N matrix A

Command to display zgelqf manual in Linux: $ man l zgelqf

NAME

ZGELQF - computes an LQ factorization of a complex M-by-N matrix A

SYNOPSIS

SUBROUTINE ZGELQF(: M, N, A, LDA, TAU, WORK, LWORK, INFO )
: INTEGER INFO, LDA, LWORK, M, N
: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.

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*16 array, dimension (LDA,N): 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 (input) INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N)): The scalar factors of the elementary reflectors (see Further Details).
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)): On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER: 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 (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(k)aq . . . H(2)aq H(1)aq, where k = min(m,n).
Each H(i) has the form

H(i) = I - tau * v * vaq
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).