# ASA159 Random generation of a table.

ASA159 is a MATLAB library which constructs a table having given row and column sums, by Michael Patefield;

ASA159 is Applied Statistics Algorithm 159. Source code for many Applied Statistics Algorithms is available through STATLIB.

ASA159 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
```
and
```        3  0  3
0  4  1
```

### Languages:

ASA159 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:

ASA144, a MATLAB library which randomly generates an RxC contingency table.

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

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

### Author:

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

### Reference:

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.

### Examples and Tests:

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

Last revised on 10 March 2009.