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

## Syntax

lapack_int LAPACKE_sgelq2 (int matrix_layout, lapack_int m, lapack_int n, float* a, lapack_int lda, float* tau);

lapack_int LAPACKE_dgelq2 (int matrix_layout, lapack_int m, lapack_int n, double* a, lapack_int lda, double * tau);

lapack_int LAPACKE_cgelq2 (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_float* a, lapack_int lda, lapack_complex_float* tau);

lapack_int LAPACKE_zgelq2 (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda, lapack_complex_double* tau);

• mkl.h

## 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, the j-th (i+1 jn) component of vector v (for real functions) or its conjugate (for complex functions) is stored in a[i - 1 + lda*(j - 1)] for column major layout or in a[j - 1 + lda*(i - 1)] for row major layout.

## Input Parameters

A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

m

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

n

The number of columns in A (n 0).

a

Array, size at least max(1, lda*n) for column major and max(1, lda*m) for row major layout. Array a contains the m-by-n matrix A.

lda

The leading dimension of a; at least max(1, m) for column major layout and max(1,n) for row major layout.

## 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 nm); 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

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

Contains scalar factors of the elementary reflectors.

## Return Values

This function returns a value info.

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.

For more complete information about compiler optimizations, see our Optimization Notice.