//
//Cholesky factarize command
//This command is used to Genaration normal distribution which has original covariance.
//


//Syntax
chole [variable];

//Syntax used options
prin [variables]/
[options]
;
//Option
input:corr   //calculate principal from correlation data(default).
input:cov    //calculate principal from covariance data.
input:direct //calculate principal from original data.

//
//Example 1 
//Multiply cholesky matorix and this tranpose one shows same with orignal correlation.
//
//Read bankers data.
get bankR.csv@;




//Get correlation of property of bankers.
corr salnow salbeg time work age;




get freq@ana;
//Execute cholesky factarizetion.
chole salnow salbeg time work age;




get freq@ana;
put chole;

//Transpose cholesky matrix.
transpose;
select col_1-5;
put trans;





get chole;
//Multiply cholesky matrix and transpose matrix.
mxmult salnow salbeg time work age by trans;



Multiplied matrix shows same with original correlation




//
//Example 2 
//Generate normal distribution which has same covariance with original data. 
//
//Read data as original covariance.
get school.csv@;




//Get correlation for input of cholesky factarization.
corr x1 x2 y;




//Get output corration and save tempolary file to check comparing with generated data.
get freq@ana;
put f_corr;

//Execution cholesky factarization by input of correlation.
chole x1 x2 y;




//Get output cholesky matrix and save tempolary file to use outlook function as below.
get freq@ana;
put f_chole;

//Get average and standard devietaion by statis command to use outlook function as below.
get school.csv@;
statis x1 x2 y;






//Save average and std. to tempolary file.
get freq@ana;
put f_stat;

// 
//Generate normal distibution which has same average and std,covariance of school.csv.
//
//Declare data clear and vector to use as below.
clear;
vector x[3];
vector ch[3][3];
vector sum[3];
//Generate 500 records which is normal distribution by loop.

for(i=1;i<=500;i++) {
  
  //Get average and std from file by outlook function.
  x1m=outlook(f_stat,"_items_","AVERAGE","x1");
  x1v=outlook(f_stat,"_items_","STD","x1");
  
  x2m=outlook(f_stat,"_items_","AVERAGE","x2");
  x2v=outlook(f_stat,"_items_","STD","x2");
 
  ym=outlook(f_stat,"_items_","AVERAGE","y");
  yv=outlook(f_stat,"_items_","STD","y");
 
  //Generate 3 normal distoribution.
  x[1]=ranstd(x1m,x1v);
  x[2]=ranstd(x2m,x2v);
  x[3]=ranstd(ym,yv);

  //Make cholesky matrix from file by outlook function.
  ch[1][1]=outlook(f_chole,"#",1,"x1");
  ch[1][2]=outlook(f_chole,"#",1,"x2");
  ch[1][3]=outlook(f_chole,"#",1,"y");
  ch[2][1]=outlook(f_chole,"#",2,"x1");
  ch[2][2]=outlook(f_chole,"#",2,"x2");
  ch[2][3]=outlook(f_chole,"#",2,"y");
  ch[3][1]=outlook(f_chole,"#",3,"x1");
  ch[3][2]=outlook(f_chole,"#",3,"x2");
  ch[3][3]=outlook(f_chole,"#",3,"y");  

  //Set covariance to normal distribution.
  for(j=1;j<=3;j++) {
    sum[j]=0;
    for(k=1;k<=3;k++) {
      sum[j]=sum[j]+ch[j][k]*x[k]; 
    }
  }
  x1r=sum[1];
  x2r=sum[2];
  yr =sum[3];
  
  //Output earch reacord. 
  outrec;
}




//View Genaration of normal distribution which may be same distoribution of school.csv.
plot scat x1r x2r yr;



//Check same correlation comparing generated data with original school.csv data 
corr x1r x2r yr;