How to treat missing data in AMPL

[jacob....@gmail.com]

To Whom It May Concern,

My objective function is trying to minimize the sum of a set of covariance values. As a result, I have a decision variable indexed in two dimensions. However, the covariance matrix is relatively sparse, and so includes a lot of "." values. When I try to solve the problem with these "." values, I get an error saying that the value doesn't exist, and so the model will not run. Is there any way I can limit the decision variable so that it only looks at cells in the covariance table that are populated (i.e., not equal to ".")?

Thanks!

Jake

[Robert Fourer]

You can model your covariance matrix as a sparse matrix in AMPL. As a small example, in the model you could write

param m integer > 0;
set C within {1..m,1..m};
param cov {C};

Then in an AMPL data file, the covariance matrix could be given by

param m := 4;
param: C: cov: 1 2 3 4 :=
1 36 . . -2
2 . 7 3 .
3 . . -8 16
4 12 3 . 77 ;

The second param statement defines both C and cov, as you can see by displaying them after reading above statements:

ampl: option display_1col 0;
ampl: display C, cov;
set C := (1,1) (1,4) (2,2) (2,3) (3,3) (3,4) (4,1) (4,2) (4,4);

cov [*,*]
: 1 2 3 4 :=
1 36 . . -2
2 . 7 3 .
3 . . -8 16
4 12 3 . 77 ;

Then in your model, instead of indexing over {i in 1..m, j in 1..m} you would index over {(i,j) in C} so that you refer only to the nonzero elements of cov.

Alternatively you can define the covariances as, say,

param cov {1..m,1..m} default 0.0;

so that cov[i,j] gets a value of zero (or some other number you choose) wherever there is a . in the data. Then you can write indexing expressions like {i in 1..m, j in 1..m: cov[i,j] <> 0} to index over only the significant values. For large problems this can become inefficient, however.

Bob Fourer
am...@googlegroups.com

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