linpack_d, a MATLAB code which solves systems of linear equations for a variety of matrix types and storage modes, by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. The matrix and vector data is presumed to be real.

MATLAB already provides a wide set of linear equation solvers. This (partial) set of LINPACK routines is provided just for testing and comparison.

LINPACK has officially been superseded by the LAPACK library. The LAPACK library uses more modern algorithms and code structure. However, the LAPACK library can be extraordinarily complex; what is done in a single LINPACK routine may correspond to 10 or 20 utility routines in LAPACK. This is fine if you treat LAPACK as a black box. But if you wish to learn how the algorithm works, or to adapt it, or to convert the code to another language, this is a real drawback. This is one reason I still keep a copy of LINPACK around.

Versions of LINPACK in various arithmetic precisions are available through the NETLIB web site.


The information on this web page is distributed under the MIT license.


linpack_d is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:


BLAS1_D, a MATLAB code which contains basic linear algebra routines for vector-vector operations, using double precision real arithmetic.

CONDITION, a MATLAB code which implements methods of computing or estimating the condition number of a matrix.

lapack_test, a FORTRAN90 code which demonstrates the use of the LAPACK linear algebra library.

LINPACK_C, a MATLAB code which solves linear systems using single precision complex arithmetic;

LINPACK_S, a MATLAB code which solves linear systems using single precision real arithmetic;

LINPACK_Z, a MATLAB code which solves linear systems using double precision complex arithmetic;

TEMPLATES, a MATLAB code which carries out simple versions of various iterative solvers.

test_matrix, a MATLAB code which defines test matrices.

TOEPLITZ_CHOLESKY, a MATLAB code which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.

wathen_matrix, a MATLAB code which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, Linpack, conjugate gradient) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).


Original FORTRAN77 version by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. This version by John Burkardt.


  1. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
    LINPACK User's Guide,
    SIAM, 1979,
    ISBN13: 978-0-898711-72-1,
    LC: QA214.L56.
  2. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
    Algorithm 539, Basic Linear Algebra Subprograms for Fortran Usage,
    ACM Transactions on Mathematical Software,
    Volume 5, Number 3, September 1979, pages 308-323.

Source Code:


Last revised on 04 June 2024.