asa159, a FORTRAN90 code which constructs a table having given row and column sums, by Michael Patefield;

The code is Applied Statistics Algorithm 159.

The code accepts a table shape (the number of rows and columns), and two vectors, the lists of row and column sums. There may be 0, 1, or many tables with nonnegative, integral entries that have the given shape and sums. The routine will report the case if there are no candidates. If there is at least one candidate, then the routine will choose one, uniformly over the number of distinct candidates.

For example, suppose M = 2, N = 3, row sum = (/ 6, 5 /) and column sum = (/ 3, 4, 4 /), then here are two tables that satisfy the constraints:

        1  2  3
        2  2  1
        3  0  3
        0  4  1


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


asa159 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ASA144, a FORTRAN90 code which randomly generates an RxC contingency table.


ASA205, a FORTRAN90 code which generates all the contingency tables corresponding to a given set of row and column sums.

SUBSET, a FORTRAN90 code which includes a routine called I4MAT_01_ROWCOLSUM which generates a (0,1) matrix with given row and column sums.


Original FORTRAN77 version by Michael Patefield; Matlab version by John Burkardt.


  1. Michael Patefield,
    Algorithm AS 159: An Efficient Method of Generating RXC Tables with Given Row and Column Totals,
    Applied Statistics,
    Volume 30, Number 1, 1981, pages 91-97.

Source Code:

Last revised on 19 May 2020.