Solving an eq. using a large table by vpasolve is to slow

Hi,

I'm trying to use the solve function of MATLAB using a relatively large table of data (~30000 rows).

My eq. uses some of the variables from the table to predict and compare to a known sampled variable.

Yet, the running time for solving the eq. by using a loop yields such large running time.

I imagine that their some easier and faster way to solve this eq, and I hope I reached the right place.

First, I used the next code:

syms X
for i = 1:height(a)
    Equation = ((a.var1(i) -c1*(X)^4)- (c2*a.var2(i)*(6.105.*exp((c3*X)./(x+c4)) -a.var3(i)))  - (c5*(x-a.var4(i)))) = 0;
    solution(i) = double(vpasolve(eqn(i),Tw));
end

where

c1,c2,c3,c4 and c5 are constants

and a.var1 to a.var 4 are the variables from the table

Later, I saw some further solutions online, that convert the code to:

ThemeCopy

syms a.var1 a.var2 a.var3 a.var4 i X
Equation = ((a.var1(i) -c1*(X)^4)- (c2*a.var2(i)*(6.105.*exp((c3*X)./(x+c4)) -a.var3(i)))  - (c5*(x-a.var4(i)))) = 0;
tsym = solve(simplify(Equation), X);
tfun = matlabFunction(tsym, 'vars', {'a.var1', 'a.var2', 'a.var3', 'a.var4','i'});
for i = 1:height(a)
    t(i) = tfun(a.var1,a.var2,a.var3,a.var4, i);
end

Unfortunately, I got the following error back

Error using sym/subsindex

Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be symbolic variables, and function body must be sym expression.

Error in indexing (line 1075)

R_tilde = builtin('subsref',L_tilde,Idx);

Related documentation

I assume the problem is related to the index table, but i'm struggling to find the solution

If other solution pop's to your mind that will be great as well.

Tnx in advance.

[Torsten]

Please supply the equation(s) you are trying to solve and the variable(s) you are trying to solve for in a mathematical notation.

I cannot recover this information from your code.

[guy tau]

The eq. takes the following form

Where the a's are values with know data from the table (i.e., along the loop, =##).

and the c's are constant (i.e., remain as is with each loop).

and the X represent the value I wish to solve at each iteration.

Hope it is clearer now

Answer 1

[Torsten]

syms A.var1 A.var2 A.var3 A.var4 X
Equation = ((A.var1 -c1*X^4)- (c2*A.var2*(6.105.*exp((c3*X)./(X+c4)) -A.var3))  - (c5*(X-A.var4))) == 0;

for i = 1:height(a)
    X_num(i) = double(vpasolve(subs(Equation,[A.var1 A.var2 A.var3 A.var4],[a.var1(i) a.var2(i) a.var3(i) a.var4(i)]),X))
end

[Walter Roberson]

I recommend assigning the result of vpasolve to a temporary variable, and if the variable is empty assign NaN as the result. vpasolve() is not guaranteed to be able to find a solution.

[guy tau]

Tnx, I tried the code and it work's!

Is their anything else that can be made to improve the speed? The running time is still quite low...

I assume that the loops create the problem here. Can it also be related to the eq.?

Also interesting, I can see that as the iteration progress’s, the time to solve each iteration increases, which makes wonder on the reason behind it.

[Walter Roberson]

On thing that can help is to feed the previous result as the initial guess. vpasolve(expression, guess) in the single variable case. This assumes that the solution for this new case is probably "close" to the previous one. The performance difference can be a lot.

[Walter Roberson]

syms A.var1 A.var2 A.var3 A.var4 X

You cannot 'syms' a dot-indexed variable. The closest you can get would be

A.var1 = sym('var1'); A.var2 = sym('var2'); A.var3 = sym('var3');

But I think you would be better off using

syms var [1 4]
syms X


    X_num(i) = double(vpasolve(subs(Equation, var, [a.var1(i) a.var2(i) a.var3(i) a.var4(i)]),X))