On Sun, 9 Aug 2015, Shachar Shemesh wrote:
I should point out that the simplified matrix I was using to prove to
myself that the idea has merit is 20x20 (inversed using state of the
art in the vi text editing front). The code I'll actually have to run
will be 273x273. The Matrix itself is sparsish, so it's really not
that bad. Still, to prove things are working I'll have to (probably
pre-calculate) several thousand such matrices.
Actually, for this specific problem, implementing Gaussian elimination
is much better than looking for a library or a tool, and interfacing
with it.
Untested C-Pseudo code:
Input: A,B: nxn matrices, B=I_n
Output: det(A), B=A^{-1} if A det=1
for(i=0;i<n;i++) {
for(j=i;j<n;j++) if(A[j][i]==1) {
ExchangeLines(A,i,j);
ExchangeLines(B,i,j);
break;
}
if(j==n) return 0;
for(k=1;k<n;k++) if(A[k][i]==1 && k!=j) {
AddLines(A,k,j);
AddLines(B,k,j);
}
}
return 1;
--
Matan.
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