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TEST_LLS\ Linear Least Squares Test Problems {#test_lls-linear-least-squares-test-problems align=”center”} ==================================

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.

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

TEST_LLS is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

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.

Reference: {#reference align=”center”}

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

Source Code: {#source-code align=”center”}

test_lls.cpp, the source code.
test_lls.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

test_lls_prb.cpp, a sample calling program.
test_lls_prb_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

P00_A returns the matrix A for any least squares problem.
P00_B returns the right hand side B for any least squares problem.
P00_M returns the number of equations M for any least squares problem.
P00_N returns the number of variables N for any least squares problem.
P00_PROB_NUM returns the number of least squares problems.
P00_X returns the least squares solution X for any least squares problem.
P01_A returns the matrix A for problem 1.
P01_B returns the right hand side B for problem 1.
P01_M returns the number of equations M for problem 1.
P01_N returns the number of variables N for problem 1.
P01_X returns the least squares solution X for problem 1.
P02_A returns the matrix A for problem 2.
P02_B returns the right hand side B for problem 2.
P02_M returns the number of equations M for problem 2.
P02_N returns the number of variables N for problem 2.
P02_X returns the least squares solution X for problem 2.
P03_A returns the matrix A for problem 3.
P03_B returns the right hand side B for problem 3.
P03_M returns the number of equations M for problem 3.
P03_N returns the number of variables N for problem 3.
P03_X returns the least squares solution X for problem 3.
P04_A returns the matrix A for problem 4.
P04_B returns the right hand side B for problem 4.
P04_M returns the number of equations M for problem 4.
P04_N returns the number of variables N for problem 4.
P04_X returns the least squares solution X for problem 4.
P05_A returns the matrix A for problem 5.
P05_B returns the right hand side B for problem 5.
P05_M returns the number of equations M for problem 5.
P05_N returns the number of variables N for problem 5.
P05_X returns the least squares solution X for problem 5.
P06_A returns the matrix A for problem 6.
P06_B returns the right hand side B for problem 6.
P06_M returns the number of equations M for problem 6.
P06_N returns the number of variables N for problem 6.
P06_X returns the least squares solution X for problem 6.

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

Last revised on 04 October 2012.