Linear Least Squares Test Problems

TEST_LLS is a C++ library which implements linear least squares (LLS) test problems which seek a vector x which minimizes the error in the rectangular linear system A*x=b.

Some linear least squares problems include constraints on the data, such as requiring that every entry of X be positive. This library only contains unconstrained problems. For such problems, the task is typically to find a vector X which minimizes the Euclidean norm of the residual r=Ax-b, or, in cases where multiple minimizers exist, to find the minimizer of minimal Euclidean norm.

TEST_LLS requires access to a compiled copy of the R8LIB library.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


TEST_LLS is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

LLSQ, a C++ library which solves the simple linear least squares problem of finding the formula of a straight line y=a*x+b which minimizes the root-mean-square error to a set of N data points.

MINPACK, a C++ library which solves systems of nonlinear equations, or the least squares minimization of the residual of a set of linear or nonlinear equations.

QR_SOLVE, a C++ library which computes the least squares solution of a linear system A*x=b.

R8LIB, a C++ library which contains many utility routines using double precision real (R8) arithmetic.


  1. Cleve Moler,
    Numerical Computing with MATLAB,
    SIAM, 2004,
    ISBN13: 978-0-898716-60-3,
    LC: QA297.M625,
    ebook: http://www.mathworks.com/moler/chapters.html

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 04 October 2012.