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*****************************************************************************************/
SAS/IML software gives you access to a powerful and flexible programming language 
*(Interactive Matrix Language) in a dynamic, interactive environment. 
*
*The fundamental object of the language is a data matrix. 
*You can use SAS/IML software interactively (at the statement level) to see results immediately,
*or you can store statements in a module and execute them later. 

*The programming is dynamic because necessary activities such as memory allocation and 
*dimensioning of matrices are performed automatically. 
/******************************************************************************************;
******************************************************************************************;
* Reading Matrix A;
*********************;
proc IML;
A={1 2 3,4 5 6,7 5 9}; *THE MATRIX A IS 3*3. USE COMMA TO SPECIFY THE COLUMN. 
	                   *USING SPACE TO SPERATE THE CLOUMN ELEMENT ;
PRINT A;               *PRINT OUT THE MATRIX.;
/****************************************
*TRANSPOSE  OF A MATRIX & PRINTING THIS;
****************************************/
A_TRANSPOSE=A`; 
PRINT A_TRANSPOSE;
/********************************************************** 
*THIS COMPUTES the eigenvalues & EIGENVECTORS of MATRIX A;
**********************************************************/

CALL EIGEN( EVALUE,EVECTOR,A);   

PRINT EVALUE;     		* Prints out a vector of eigenvalues;
PRINT EVECTOR;          * Prints out a matrix whose columns are EIGENVECTORS 
						( NORMALIZED, unit length);
/********************************************************** 
*FINDING THE INVERSE OF THE MATRIX A;
**********************************************************/

INV_A=INV(A);           
PRINT INV_A;             *Prints out the INVERSE*;

  C = {1 2 3,4 5 6};       PRINT C;             *makes a 2x3 matrix;

  C1=C[+,];                PRINT C1;            *makes a 1x3 matrix by summing the columns;

  C2=C[,+];                PRINT C2;            *makes a 2x1 matrix by summing the rows;

  F = C[,2];               PRINT F;             *makes a matrix out of second column of C;

  D = DIAG( C[,2] );       PRINT D;             *puts second column of c on diagonal;

  CC= VECDIAG(D);          PRINT CC;            *makes a vector out of the diagonal;

  DD = EXP(D);             PRINT DD;            *exponentiates each entry;

  E = C || C;              PRINT E;             *puts c next to itself;

  K = REPEAT(C,3,2);       PRINT K;             *creates a 3x2 matrix with matrix entry C;

  G = 3+3*(C[,2:3]##3);    PRINT G;             *raises each entry of columns 2 & 3 of C
                                                to the third power then multiples
                                                by 3 and adds 3;

  H = C ## C;              PRINT H;             *raises each entry of C to itself;

  J = C # C;               PRINT J;             *multiplies each entry of C by itself;

RUN;
quit;
/********************************************************** 
* ANOTHER WAY OF READING MATRIX;
**********************************************************/
DATA TEST; 
      INFILE cards; 
      INPUT v1 v2 v3; 
cards; 
3  1  2 
4  1  2 
3  0  0 
1  0  7 
; 
RUN; 
/******************************************************************************* 
*Read all data into an IML matrix X. FOR THIS USE the statements USE and READ.; 
*******************************************************************************/
PROC IML; 
USE TEST; 
READ all var{v1 v2 v3} into X; 
n=nrow(X);					*n is the number of observations, i.e. number of rows in X matrix;
	one=J(N,1,1); 		    *12 x 1 vector of containing ones: UNIT VECTOR;
	df=n-1;
	mean=(one`*X)/n; 		*mean vector contains the means;
	xm=x-one*mean; 		    *contains the mean corrected (X-1'*MEAN);
	sscpm=xm`*xm; 
	************************************;
	* SAMPLE VARIANCE-COVARIANCE MATRIX;
	************************************;
	s=sscpm/df; 			

	d=diag(S);		        * CREATING A DIAGONAL MATRIX FROM THE DIAGONAL 
	                          ELEMENTS OF S;
	***************************************************
	*STANDARDIZED MATRIX: THAT IS, (X-1'*MEAN)/SQRT(D);
	*YOU NEED THIS MATRIX FOR FINDING CORRELATION MATRIX
	*************************************************** ;
	xs=xm*sqrt(inv(d));		
	***************************************************
	*CORRELATION MATRIX;
	***************************************************;
	r=xs`*xs/(n-1);
    ***************************************************
	*DETERMINANT OF S: GENERALIZED VARIANCE
	***************************************************;	
	gv=det(s);
    ***************************************************
	*PRINTING ALL RESULTS;
	***************************************************; 
    print mean,xm,sscpm,s,xs,r,gv;
    print X; 
    RUN;