dimforge / dimforge/nalgebra

QR decomposition could computes the full QR factorization

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Description

QR decomposition is a useful mathematical tool to represent a matrix into a product A = QR.

By using _nalgebra::linalg::QR;_ interfaces, we could obtain both matrices Q and R only as a _reduced decomposition_ but _not_ as the **full decomposition**.

The full decomposition allows to obtain moreinformation about a system of equation, and thus open the door to the resolution of optimization problems. For example, users of MATLAB could be interested to use the optimization alogirthm with constraint described into this following link https://www.mathworks.com/help/optim/ug/fmincon.html and transpose it in Rust with ospq ( https://crates.io/crates/osqp/0.6.2 ).

To solve optimization problem expressed in the MATLAB interface, we need to work with the Q_1 and Q_2 matrices with the ospq Rust crate.

The goal here would be to express a given matrix A into its product QR as a full decomposition format.

The following link describes the differences: https://en.wikipedia.org/wiki/QR_decomposition

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