/*----A FEW IML COMMANDS-------*
reset spaces=5 fuzz=.000001;  <-- space between matrices, round to 0 ;
* multiply       ` transpose (BACK quote)   <---  X`*X
X = {1 2, 3 4};   <-- create matrix, first row 1 2, second is 3 4
A[2,3]  <-- subscripts    A[2,3] = 4 replaces,  ELT = A[2,3] gives element
A[1:3,1:3]  <--- upper left 3x3 submatrix
A[5, ]  A[1:3, ]  <-- 5th row and 3xn submatrix
A[ ,2] <-- column 2        _ _
|| <-- join horizontally  |_|_|    _
// <--------- join vertically     |_|
C=A//B; D=A||B;                   |_|
                   FUNCTIONS
NROW(A) number of rows in A   N=NROW(A);
NCOL(A)
VECDIAG(A) vector equals diagonal of A
     V=VECDIAG(X) is {1 4} for our X above
L=DIAG(V) <-- makes diagonal matrix with V
elts on diagonal    1 0
                    0 4
L=DIAG(X) <-- replaces off diagonals with 0 (X square)
B=INV(X) <--- B is inverse of X
G=GINV(A)  <-- a generalized inverse
D=DET(A)  <--- determinant
T = TRACE(A) <--- trace = sum of diagonal
                   SUBROUTINE
CALL SVD(U,L,Z,X) <-- given X, find U L Z
              so that X = ULZ', Z'Z=I, U'U=I

*/

PROC IML;
reset spaces=5 fuzz=.0001;
A = {1 3, 2 4, 3 3, 5 2}; B = A*{4,-2};
C = A||B;
print A[format=2.0]  B  C[format=2.0];
G = GINV(C); CGC = C*G*C; rank = TRACE(G*C);
text= {"Rank can","be computed",
"from","generalized","inverse"};
print text G[format=5.2] CGC[format=2.0] rank;


%let dsn=A; 
proc iml; reset fw=4 spaces=5; 
D = {1.008 2 3, 4 5 6, 7 8 9};
start data_a(D);
L=diag(D);  
names = {X1, x2, X3}; mixedcase = {"X1","x2","X3"};
print D L names mixedcase;
create &dsn from L[colname=names]; 
append from L;    
finish data_a;

G={10.08 8 9, 10 11 12, 13 14 15}; 
call data_a(G); 
%let dsn=b; 
call data_a(D) ; 
   ** store module=data_a;
proc print data=a; title "A";
proc print data=b; title "B"; 

proc iml; C={9 8 7, 6 5 4, 3 2 1};
   ** load module=data_a;
call data_a(C); 
proc print data=b; title "new B";  ** check the log !!! ***;
run; 


data study; 
input subject wt ht age char $; 
cards; 
1  150 70 33  John
2  160 72 50  Bill
3  180 68 21  Dave
4  106 62 38  Mary
 ; 
 proc iml; 
 names = {subject age wt ht}; 
 use study; 
 read all var names into dat;
 read point {2 4} var {wt age} into small ; 
 read all var names into fancy [colname = names  rowname=char];
print dat small fancy;  
reset noname; print ,,, "Reset to noname option" ,;
  ** comma -> skip line,  slash-> new page **;
print dat small ,, fancy;
quit;