linsolve time-consuming

Hello all,

Here is my code and it is running more than 2 days. Z1, Z2, A, B, D and E are known 1 X 1.000.000 vector and C and F are constant values 1X1. I am trying to estimate X and Y but the program is still working. Is there any chance to find when will it finish with these matrices? Any help will be great. Thanx all.

syms X Y

Z1=X.*A-Y.*B*C;

Z2=X.*D-Y.*E*F;

[A,B]=equationsToMatrix([Z1,Z2], [X,Y]);

X = linsolve(A,B);

Answer 1

[Stephan]

Get rid of symbolic calculation - this makes code very slow and solve numeric:

clear X Y
% This works if your values are of size 1 x 1.000.000
X = linsolve([A', (-B.*C)'; D.' (-E.*F)'],[Z1'; Z2'])

[Fikret Dogru]

Thanks for your help but I got an error. "Requested 2317620x1158810 (10004.9GB) array exceeds maximum array size preference. Creation of arrays greater than this limit may take a long time and cause MATLAB to become unresponsive. See array size limit or preference panel for more information." Do you have any idea to solve this?

[Torsten]

Y = (Z1.*D - Z2.*A) ./ (A.*E*F - B.*D*C);
X = (Z1.*E*F - Z2.*B*C) ./ (A.*E*F - B.*D*C);

if the denominator is different from zero.

[Fikret Dogru]

Thanks Stephan,

it helped but which method is this? It is the first time I have seen solving problem like that.

Fikret

[Stephan]

You should thank Torsten - but here is an explaination of what he did:

syms X Y A B C D E F Z1 Z2
eq(1) = Z1==X.*A-Y.*B*C;
eq(2) = Z2==X.*D-Y.*E*F;
sol = solve(eq,[X,Y]);
sol.X
sol.Y

[Torsten]

@ Fikret Dogru:

The method is called "Cramer's rule".