Yesterday Rick showed how to use Cholesky decomposition to transform data by the ROOT function of SAS/IML. Cholesky decomposition is so important in simulation. For those DATA STEP programmers who are not very familiar with SAS/IML, PROC FCMP in SAS may be another option, since it has an equivalent routine CALL CHOL.

To replicate Rick’s example of general Cholesky transformation for correlates variables, I randomly chose three variables from a SASHELP dataset SASHELP.CARS and created a simulated dataset which shares the identical variance-covariance structure. A simulated dataset can be viewed as an “expanded’ version of the original data set.

Conclusion:

In PROC FCMP, for memory's sake, don’t allocate many matrices (or arrays). A better way is to use CALL DYNAMIC_ARRAY routine to resize a used matrix, which is similar to the ReDim statement in VBA. A VBA programmer can easily migrate to SAS through PROC FCMP.

proc corr data=sashelp.cars cov outp=corr_cov plots=scatter;

var weight length mpg_city;

run;

data cov;

set corr_cov;

where _type_ = 'COV';

drop _:;

run;

proc fcmp;

/* Allocate space for matrices*/

array a1[3, 3] / nosymbols;

array a2[3, 3] / nosymbols;

array b1[3, 1000] / nosymbols;

array b2[3, 1000] / nosymbols;

/* Simulate a matrix by normal distribution*/

do i = 1 to 3;

do j = 1 to 1000;

b1[i, j] = rannor(12345);

end;

end;

/* Read the covariance matrix*/

rc1 = read_array('cov', a1);

call chol(a1, a2);

put a2;

call mult(a2, b1, b2);

/* Output the result matrix*/

call dynamic_array(b1, 1000, 3);

call transpose(b2, b1);

rc2 = write_array('result', b1);

quit;

proc corr data=result cov plots=scatter;

run;