?gelq2

Syntax

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

Description

The routine computes an LQ factorization of a real/complex m-by-n matrix A as A = L*Q.

The routine does not form the matrix Q explicitly. Instead, Q is represented as a product of min(m, n) elementary reflectors :

Q = H(k) ... H(2) H(1) (or Q = H(k)' ... H(2)' H(1)' for complex flavors), where k = min(m, n)

Each H(i) has the form

H(i) = I - tau*v*v'

where tau is a real/complex scalar stored in tau(i), and v is a real/complex vector with v(1:i-1) = 0 and v(i) = 1.

On exit, v(i+1:n) (for real functions) and conjgv(i+1:n) (for complex functions) are stored in a(i, i+1:n).

Input Parameters

m

INTEGER. The number of rows in the matrix A (m ≥ 0).

n

INTEGER. The number of columns in A (n ≥ 0).

a, work

REAL for sgelq2

DOUBLE PRECISION for dgelq2

COMPLEX for cgelq2

COMPLEX*16 for zgelq2.

Arrays: a(lda,*) contains the m-by-n matrix A. The second dimension of a must be at least max(1, n).

work(m) is a workspace array.

lda

INTEGER. The first dimension of a; at least max(1, m).

Output Parameters

a

Overwritten by the factorization data as follows:

on exit, the elements on and below the diagonal of the array a contain the m-by-min(n,m) lower trapezoidal matrix L (L is lower triangular if n ≥ m); the elements above the diagonal, with the array tau, represent the orthogonal/unitary matrix Q as a product of min(n,m) elementary reflectors.

tau

REAL for sgelq2

DOUBLE PRECISION for dgelq2

COMPLEX for cgelq2

COMPLEX*16 for zgelq2.

Array, DIMENSION at least max(1, min(m, n)).

Contains scalar factors of the elementary reflectors.

info

INTEGER.

If info = 0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.