large symbolic matrix substitution

Hi,

I am trying to find a way to efficiently substitute a large symbolic Jacobian matrix with the corresponding numerical values, but all at once. As long as "subs" command becomes extremely slow and the PC becomes idle with no output, I am urgently looking for alternative faster ways. The problem with "matlabFunction" is that it accepts the elements of the "guess matrix" one by one and I don't know how to pass the numerical matrix values all at once to it.

As an example , if

R=sym('R',[1000 1])

RV=matlabFunction (R)

T=ones(1000,1)

then, how to pass "T" into "RV", as a whole?

Any other effective solutions are appreciated, as well. (MATLAB R2012b)

Thanks.

Answer 1

[Star Strider]

I am not certain what you are actually doing, but this works for this example:

syms x y z
f(x,y,z) = 3*x*y + 5*x*z + 7*y*z + 13*x*z;
JF = jacobian(f, [x y z]);
MJF = matlabFunction(JF);
[VX,VY,VZ] = deal(ones(5,1));
JN = MJF(VX, VY, VZ);

The deal function simply takes the single (5x1) column vector created by the ones function and distributes it to [VX,VY,VZ] that are then arguments to the Jacobian anonymous function ‘MJF’.

One item of possible relevance is that ‘R’ should probably be a row vector rather than a column vector.

[Parmida Boroumand]

Thanks for your answer. It was good to learn about the "deal" function. However, it is not solving my problem :(

In the real program, I am currently trying to do the following,

Jac_Subs=subs(Jac,Def_Mat,Def_Mat0);

Eq_Subs=-subs(Equ,Def_Mat,Def_Mat0);

where "Jac" is the square Jacobian matrix, a function of the sybmolic elements of "Def_Mat" to be substituted by "Def_Mat0" and "Equ" is the symbolic vector of equations to be solved.

Since the program becomes idle at this point, I just put it in a loop as below which works for less numbers of the unknowns, but again freezes for the actual size.

Jac_Subs(i,j)=subs(Jac(i,j),Def_Mat,Def_Mat0);

Eq_Subs(i,1)=-subs(Equ(i,1),Def_Mat,Def_Mat0);

And application of the "fsolve" command to just grab the set of equations does not do a great job in this case, either! (Too slow)

Anything alternatives for "subs" to accept "Def_Mat" and "Def_Mat0", in this format and not element wise? Or any hints on the limitations associated with "subs"?

tnx.

[Star Strider]

My pleasure!

It seems that your system is freezing because of the size of the matrices involved. I don’t understand what ‘Def_Mat’, ‘Def_Mat0’, and ‘Equ’ are. It might be best at this point to use matlabFunction to convert everything to numeric and go from there.