Scripting Guide - SAS

Chapter 7 Data Structures 157
Matrices
Find the solution to this system using the following script:
A=[1 2 2, 2 4 4, 1 1 1];
B=[6,12,1];
Show(GInverse(A)*B);
G Inverse(A)*B=[-4,2.5,2.5]
Solve
The Solve() function solves a system of linear equations. Solve() finds the vector x so that x = A – 1 b
where A equals a square, nonsingular matrix and b is a vector. The matrix A and the vector b must have the
same number of rows. Solve(A,b) is the same as Inverse(A)*b.
A=[1 -4 2, 3 3 2, 0 4 -1];
b=[1, 2, 1];
x=solve(A,b);
[-16.9999999999999, 4.99999999999998, 18.9999999999999]
A*x;
[1, 2, 0.999999999999997]
Note: There can be small discrepancies in the results due to floating point limitations, as illustrated in the
example.
Sweep
The Sweep() function inverts parts (or pivots) of a square matrix. If you sequence through all of the pivots,
you are left with the matrix inverse. Normally the matrix must be positive definite (or negative definite) so
that the diagonal pivots never go to zero. Sweep() does not check whether the matrix is positive definite. If
the matrix is not positive definite, then it still works, as long as no zero pivot diagonals are encountered. If
zero (or near-zero) pivot diagonals are encountered on a full sweep, then the result is a g2 generalized inverse
if the zero pivot row and column are zeroed.
About the Sweep Function
Suppose matrix E consists of smaller matrix partitions, A, B, C, and D:
E
=
AB
CD
The syntax for Sweep() appears as follows:
Sweep(E, [...]); // where [...] indicates partition A
This produces the matrix result equivalent to the following:
A 1 A 1 B
– CA 1 D – CA 1 B