Excessive Run Time For back solve of 'huge' symbolic matrices.

I am calculating a left matrix division A\b on MatLab 2009b and it has taken more than a week now. I admit that the matrix A is huge and it contains some symbols. Is there any way to speed up this calculation, or will I ever get some results? Thanks a lot!

[Oleg Komarov]

Quantify huge and by symbols you mean symbolic variables?

[Walter Roberson]

Does mldivide even work with symbolic arrays??

[Jan]

@Walter: J wrote, that it runs since a week now. This seems to imply, that it runs at all. But who knows...

[Sean de Wolski]

@Walter, it appears to:

syms a c

a\c

ans =

c/a

[Walter Roberson]

Let's see... shouldn't it be c' / a' ? c/a would be the equivalent answer if one assumed scalars, but the question was about arrays. (I would have to have a closer look at the definitions to determine whether the transpose should be plain transpose or conjugate transpose.)

[Doug Hull]

Does the same code work for normal sized matrices, say 10x10?

What is huge?

[J]

Matrix A is a weighting matrix. Dimension: 24*24; Storage space: 4 mb; symbolic variables contained: 6.

Actually, following Windmeijer 2005, I am correcting the undersized error terms in my GMM estimation. The code and data are both available for email.

Thank you very much!

[J]

Theoretically, the code should work (Please try the following)

%%%%%%%%%%%%%%%%%%%

syms x y;

A= [2*x x; x x/3];

b=eye(2)*y;

C= A\b;

C

%%%%%%%%%%%%%%%%%%%

But the division takes so long that I start wondering ...

Anybody got any ideas?

Thanks a lot!

[Andrew Newell]

The calculation takes about a second on my computer, which is pretty slow for a 2x2 problem!

[J]

The trial calculation does take less than 1 second (please see the following), and it makes me believe that the code is executable.

%%%%%%%%%%%%%%%%%%%%%%%

syms x y;

A= [2*x x; x x/3];

b=eye(2)*y;

tic, C= A\b, toc;

%%%%%%%%%%%%%%%%%%%%%%%

Elapsed time is 0.023101 seconds.

%%%%%%%%%%%%%%%%%%%%%%%

However, the real calculation takes more than a week and I wonder if anything is wrong (Please see the original question and comment #7).

Thank you very much!

Answer 1

[Andrew Newell]

Do you really need the symbolic answer? It's probably very complicated, and not very edifying. You could create a function that inputs numerical values for your six variables and calculates A\b numerically. It would be orders of magnitude faster.

[J]

As I state in comment # 7, "following Windmeijer 2005, I am correcting the undersized error terms in my GMM estimation."

The left matrix division A\b is a middle step for a term that I need to calculate partial derivatives [Jacobian matrix on those 6 variables].

I really wish there is a way to get rid off the symbles early and still be able to calculate the derivatives later.

Thank you very much!

[Andrew Newell]

You could calculate numerical partial derivatives. A package such as John d'Errico's (http://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation) can be very accurate.