# ?gelq2

Computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

## Syntax

call sgelq2( m, n, a, lda, tau, work, info )

call dgelq2( m, n, a, lda, tau, work, info )

call cgelq2( m, n, a, lda, tau, work, info )

call zgelq2( m, n, a, lda, tau, work, info )

• mkl.fi

## 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 ... H(2)HH(1)H` for complex flavors), where `k = min(m, n)`

Each H(i) has the form

`H(i) = I - tau*v*vT` for real flavors, or

`H(i) = I - tau*v*vH` for complex flavors,

where tau is a real/complex scalar stored in tau(i), and v is a real/complex vector with `v1:i-1 = 0` and `vi = 1`.

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

## Input Parameters

The data types are given for the Fortran interface.

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

DOUBLE COMPLEX 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 leading 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

DOUBLE COMPLEX for zgelq2.

Array, size 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.

`If info = -1011`, memory allocation error occurred.

Para obtener información más completa sobre las optimizaciones del compilador, consulte nuestro Aviso de optimización.