# TEST_LLS 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.

### Licensing:

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

### Languages:

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.

### 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.

### 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

### List of Routines:

• 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 07 September 2012.