# 15.1.237. tablet_qt/maths/dqrls.h¶

```/*
Copyright (C) 2012, University of Cambridge, Department of Psychiatry.
Created by Rudolf Cardinal (rnc1001@cam.ac.uk).

This file is part of CamCOPS.

CamCOPS is free software: you can redistribute it and/or modify
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

CamCOPS is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with CamCOPS. If not, see <https://www.gnu.org/licenses/>.
*/

#pragma once

#include <QStringList>
#include "maths/include_eigen_dense.h"  // IWYU pragma: keep

// See:
// - R's lm.c

namespace dqrls {

// Represents the result of Cdqrls()
struct DqrlsResult {
bool success = false;  // did we succeed?
Eigen::FullPivHouseholderQR<Eigen::MatrixXd> qr;  // QR decomposition
Eigen::MatrixXd coefficients;  // the results; B in "XB = Y"; see below
// Eigen::ArrayXXd residuals;
// Eigen::ArrayXXd effects;
Eigen::Index rank;  // rank of the QR decomposition
// Eigen::ArrayXi pivot;  // INDICES, 0-based here, 1-based in R
// Eigen::ArrayXd qraux;
double tol;  // tolerance
bool pivoted;  // did the QR decomposition have nonzero pivots?
// ... I have no idea what that means.
QStringList errors;
};

// Solves XB = Y, for B.
//
// Provides the C++ equivalent of the Fortran dqrls code.
// Calculates a least-squares solution to this matrix equation.
//
// - X has size (n, p)
// - Y has size (n, ny)
// - n: number of observations
// - p: number of predictors
// - ny: number of dependent variables
//
// - B will have size (p, ny).
//
// Returns a DqrlsResult object in which B is called "coefficients".
DqrlsResult Cdqrls(const Eigen::MatrixXd& x,  // size (n, p)
const Eigen::MatrixXd& y,  // size (n, ny)
double tol,  // tolerance
bool check = true);  // check dimensions of result are right

}  // namespace dqrls
```