Oracle Data Mining and Analytics: Matrix Inversion Using PL/SQL

Recently someone asked me how to invert a matrix using the UTL_NLA PL/SQL package. This can be done by solving a system of linear equations AX = B like the ones I described in this post but setting B to the identity matrix. I thought that the question was interesting enough to deserve its own post. So I am replicating the answer here for those interested.

The UTL_NLA package has many different procedures for solving systems of linear equations. Most of them are designed to take advantage of special form matrices (e.g., triangular, banded, etc.). For the example below, I picked the procedure LAPACK_GELS. This procedure solves general systems of linear equations in a robust fashion. It uses QR or LQ decompositions as needed.

DECLARE
  A     utl_nla_array_dbl :=  utl_nla_array_dbl(
               5,   153,  352, 
               153, 5899, 9697,
               352, 9697, 26086);
  B     utl_nla_array_dbl := utl_nla_array_dbl( 
               1, 0, 0,
               0, 1, 0,               
               0, 0, 1);
  ipiv  utl_nla_array_int := utl_nla_array_int(0,0);
  info  integer;
  n     NUMBER := 3;
  i     NUMBER;
  j     NUMBER;
BEGIN

  UTL_NLA.LAPACK_GELS (
    trans  => 'N',  -- solve for A instead of A'
    m      => n,    -- A number of rows 
    n      => n,    -- A number of columns
    nrhs   => n,    -- B number of columns
    a      => A,    -- matrix A
    lda    => n,    -- max(1, m)
    b      => B,    -- matrix B
    ldb    => n,    -- ldb >= max(1, m, n)
    info   => info, -- operation status (0=sucess)
    pack   => 'R'   -- how the matrices are stored 
                    -- (C=column-wise)
  );

  dbms_output.put_line('inv(A)');
  dbms_output.put_line('-------------');
  dbms_output.put_line('info= '||info);
  IF info=0 THEN
    FOR l IN 1..B.count LOOP
      i := ceil(l/n);
      j := l-(i-1)*n;
      dbms_output.put_line('x[' || i ||']['||j||']= ' || 
                           TO_CHAR(B(l),'99.9999'));
    END LOOP;
  END IF;
END;
/

Here is the output for the above code:

inv(A)
-------------
info= 0
x[1][1]=  27.5307
x[1][2]=   -.2658
x[1][3]=   -.2727
x[2][1]=   -.2658
x[2][2]=    .0030
x[2][3]=    .0025
x[3][1]=   -.2727
x[3][2]=    .0025
x[3][3]=    .0028

Labels: Linear Algebra, UTL_NLA