# mx.symbol.linalg_gelqf¶

## Description¶

LQ factorization for general matrix. Input is a tensor A of dimension n >= 2.

If n=2, we compute the LQ factorization (LAPACK gelqf, followed by orglq). A must have shape (x, y) with x <= y, and must have full rank =x. The LQ factorization consists of L with shape (x, x) and Q with shape (x, y), so that:

A = L * Q

Here, L is lower triangular (upper triangle equal to zero) with nonzero diagonal, and Q is row-orthonormal, meaning that

Q * QT

is equal to the identity matrix of shape (x, x).

If n>2, gelqf is performed separately on the trailing two dimensions for all inputs (batch mode).

Note

The operator supports float32 and float64 data types only.

Example:

Single LQ factorization
A = [[1., 2., 3.], [4., 5., 6.]]
Q, L = gelqf(A)
Q = [[-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578]]
L = [[-3.74165739, 0.],
[-8.55235974, 1.96396101]]

Batch LQ factorization
A = [[[1., 2., 3.], [4., 5., 6.]],
[[7., 8., 9.], [10., 11., 12.]]]
Q, L = gelqf(A)
Q = [[[-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578]],
[[-0.50257071, -0.57436653, -0.64616234],
[0.7620735, 0.05862104, -0.64483142]]]
L = [[[-3.74165739, 0.],
[-8.55235974, 1.96396101]],
[[-13.92838828, 0.],
[-19.09768702, 0.52758934]]]


## Usage¶

mx.symbol.linalg_gelqf(...)


## Arguments¶

Argument

Description

A

NDArray-or-Symbol.

Tensor of input matrices to be factorized

name

string, optional.

Name of the resulting symbol.

## Value¶

out The result mx.symbol