Compute matrix product in base sas ( not using IML) - matrix

Question

In order to Compute the product of 2 matrices I am using this method:
First I put my matrices in the long format (col,row,value)
I use proc sql to compute the product of 2 matrices.
I use proc transpose to put the result of precedent step in the wide format.
My question is there is simpler method? Or at least how can I simplify my code?
here my code:
/* macro to put a matrix in the long format*/
%macro reshape(in_A = , ou_A= );
data &ou_A.;
set &in_A.;
array arr_A{*} _numeric_;
row = _n_;
do col = 1 to dim(arr_A);
value = arr_A{col};
output;
end;
keep row col value;
run;
%mend;
%macro prod_mat( in_A = , in_B= ,ou_AB =);
/* put the matrix in the long format */
%reshape(in_A=&in_A.,ou_A=lA);
%reshape(in_A=&in_B.,ou_A=lB);
/* compute product */
PROC SQL ;
CREATE TABLE PAB AS
SELECT lA.row, lB.col, SUM(lA.value * lB.value) as value
FROM lA JOIN lB ON lA.col = lB.row
GROUP BY lA.row, lB.col;
QUIT;
/* reshape the output to the wide format */
proc transpose data=PAB out=&ou_AB.(DROP=_name_) prefix=x;
by row ;
id col;
var value;
run;
%mend;
data A ;
input x1 x2 x3;
datalines ;
1 2 3
3 4 4
5 6 9
;
data B ;
input x1 x2;
datalines ;
1 2
3 4
4 5
;
%prod_mat(in_A =A,in_B=B,ou_AB=AB)

Answer 1

Well, here's my variant. It's not that the code itself is shorter then yours, but for big matrices it'll work faster because it avoids using SQL-join with cartesian product of all elements.
The main idea - full join (cartesian product) of rows of A and transposed B and then multiplying corresponding columns. E.g. in case of 3x3 and 3x2 matrices, we'll need to:
1) multiply and sum up in each row of the merged dataset column1*column4+column2*column5+column3*column6;
2) repeat it for the second row;
3) output the both values in one row.
%macro prod_mat_merge(in_A =,in_B=,ou_AB=);
/*determine number of rows and columns in the 2nd matrix*/
%let B_id=%sysfunc(open(&in_B));
%let B_rows=%sysfunc(attrn(&B_id,nobs));
%let B_cols=%sysfunc(attrn(&B_id,nvars));
%let rc=%sysfunc(close(&B_id));
/*transpose the 2nd matrix*/
proc transpose data=&in_B out=t&in_B(drop=_:);run;
/*making Cartesian product of the 1st and transposed 2nd matrices*/
data &ou_AB;
do until(eofA);
set &in_A end=eofA;
do i=1 to n;
set t&in_B nobs=n point=i;
output;
end;
end;
run;
/*multiplication*/
data &ou_AB;
/*new columns for products, equal to number of columns in the 2nd matrix*/
array p[&B_cols];
do j=1 to &B_cols;
p[j]=0;
set &ou_AB;
array col _ALL_;
/*multiply corresponding pairs of columns*/
do i=&B_cols+2 to &B_cols+1+&B_rows;
p[j]+col[i]*col[i+&B_rows];
end;
end;
output;
keep p:;
run;
%mend prod_mat_merge;
I've tested the both methods multiplying two random matrices 100x100 each. The method with reshaping and SQL-join takes ~1.5 sec, while the method with merging takes ~0.2 sec.