Minimize Number By Changing Another Number

[erhan34]

Hi everyone,

I used excel's solver for this problem. It works. But now I need to use SAS. I am kind of new to SAS. So, any help would be appreciated. And Here is my problem.

I have 3 matrices(or data set).

1. and 3. are Constant.  2. matrix changes with an index value(I need to find this value by changing until  sum of percentage error of matrix 2 and matrix 3 becomes less than 0.0001. Here are the example matrices.

1. Matrix Z values of normal dist.(example)                

t1	t2	t3	t4	t5
-1.34	0.45	-1.22	0.11	0.99
-1.1	0.2	0.3	0.23	0.99
...	...	...	...	...
...	...	...	...	...

2. Matrix( Depends on First Matrix and Index Value).

At the beginning second matrix is empty.

We calculate     2. Matrix Cell[1,1] = probit(1. matrix[1,1] - Index Value)

If sum of squared per. error is not small enough. We should apply new index and This matrix will change again.

t1	t2	t3	t4	t5
.	.	.	.	.
.	.	.	.	.
...	...	...	...	...
...	...	...	...	...

3. Matrix is always constant as the 1. matrix

t1	t2	t3	t4	t5
0.89	0.45	0.22	0.11	0
0.2	0.7	0.5	0.23	0.1
...	...	...	...	...
...	...	...	...	...

And Then We calculate percentage error between 2. and 3. matrix for every cell.  ( ( 3.Matrix[1,1] - 2. Matrix[1,1])/ 3Matrix[1,1]) ^2   then sum all of them.

So Sum of these numbers should be less than 0.0001 and I should do this  by changing index value. If sum of percentage errors are small enough. Then that is the index value that i am looking for.

Even simple examples would help. Maybe I can try to apply them by myself. There are some examples online. I couldnt find way to apply to this situation. Thanks in advance to everyone.

[Ksharp]

You are operating a Matrix , you'd better post it at

• SAS/IML and SAS/IML Studio

and there is a problem. probit(p)  should be 0<p<1 . but in your sample data they can't be true in sometime .

Anyway, here is some data step code you can refer to , But I suggest you post it at IML forum.

data one;
input t1-t5;
cards;
-1.34     0.45     -1.22     0.11     0.99
-1.1     0.2     0.3     0.23     0.99
;
run;
%let index=0.5;
data two(keep=_t:);
set one;
array one{*} t1-t5;
array two{*} _t1-_t5;
do i=1 to dim(one);
 two{i}=probit(one{i}-&index );
end;
run;
data three;
input t1-t5;
cards;
0.89     0.45     0.22     0.11     0
0.2     0.7     0.5     0.23     0.1
;
run;
data error(keep=e:);
 merge three two;
 array three{*} t1-t5;
 array two{*} _t1-_t5;
 array error{*} e1-e5;
 do i=1 to dim(error);
  error{i}= (divide((three{i}-two{i}),three{i}))**2;
 end;
run;

Xia Keshan

[RobPratt]

Here's one way to use PROC OPTMODEL to solve this optimization problem with one decision variable:

proc optmodel;
   set ISET;
   set JSET = 1..5;
   num one {ISET, JSET};
   num three {ISET, JSET};
   read data one into ISET=[_N_] {j in JSET} <one[_N_,j]=col('t'||j)>;
   read data three into [_N_] {j in JSET} <three[_N_,j]=col('t'||j)>;

   var Index;
   impvar Two {i in ISET, j in JSET} = probit(one[i,j] - Index);
   min TotalError = sum {i in ISET, j in JSET} ((three[i,j]-Two[i,j])/three[i,j])^2;

   solve;
   print Two;
   print Index;
quit;

But you need to clean up the data before you can use PROBIT.