TEST_LS
Linear Least Squares Test Problems

TEST_LS is a MATLAB library which defines a number of linear least squares problems of the form A*x=b, where A is an M by N matrix.

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

Licensing:

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

Languages:

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

Related Data and Programs:

LLSQ, a MATLAB 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.

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

Reference:

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:

• p00_a.m returns the matrix A for any least squares problem.
• p00_b.m returns the right hand side B for any least squares problem.
• p00_m.m returns the number of equations M for any least squares problem.
• p00_n.m returns the number of variables N for any least squares problem.
• p00_prob_num.m returns the number of least squares problems.
• p00_x.m returns the least squares solution X for any least squares problem.
• p01_a.m returns the matrix A for problem 1.
• p01_b.m returns the right hand side B for problem 1.
• p01_m.m returns the number of equations M for problem 1.
• p01_n.m returns the number of variables N for problem 1.
• p01_x.m returns the least squares solution X for problem 1.
• p02_a.m returns the matrix A for problem 2.
• p02_b.m returns the right hand side B for problem 2.
• p02_m.m returns the number of equations M for problem 2.
• p02_n.m returns the number of variables N for problem 2.
• p02_x.m returns the least squares solution X for problem 2.
• p03_a.m returns the matrix A for problem 3.
• p03_b.m returns the right hand side B for problem 3.
• p03_m.m returns the number of equations M for problem 3.
• p03_n.m returns the number of variables N for problem 3.
• p03_x.m returns the least squares solution X for problem 3.
• p04_a.m returns the matrix A for problem 4.
• p04_b.m returns the right hand side B for problem 4.
• p04_m.m returns the number of equations M for problem 4.
• p04_n.m returns the number of variables N for problem 4.
• p04_x.m returns the least squares solution X for problem 4.
• p05_a.m returns the matrix A for problem 5.
• p05_b.m returns the right hand side B for problem 5.
• p05_m.m returns the number of equations M for problem 5.
• p05_n.m returns the number of variables N for problem 5.
• p05_x.m returns the least squares solution X for problem 5.
• p06_a.m returns the matrix A for problem 6.
• p06_b.m returns the right hand side B for problem 6.
• p06_m.m returns the number of equations M for problem 6.
• p06_n.m returns the number of variables N for problem 6.
• p06_x.m returns the least squares solution X for problem 6.

Examples and Tests:

• test_ls_test.m, a sample calling program.
• test_ls_test00.m, tries out MATLAB's A\b solver on the data.
• test_ls_test01.m, summarizes the test data.
• test_ls_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.