CODEWITHSUNDEEP
matlabsolver
StockB
StockB

Reputation: 774

Why does using `solve` with a multivariate system of equations error unexpectedly?

While trying to solve a system of equations with 2 variables and 2 unknowns (Izhikevich nullclines), I encountered an unexpected error: Warning: 4 equations in 2 variables. and Warning: Explicit solution could not be found.

This is unexpected because as I stated, I was providing only 2 equations with the 2 variables, which should be a well-formed system of equations.

My relevant lines of code are as follows:

syms uu vv [solvv, soluu] = solve([0.04*vv^2 + 5*vv + 140 - uu + I(t) == 0, a(t)*(b(t)*vv - uu) == 0], [vv, uu]);

The complete error trace is:

Warning: 4 equations in 2 variables. \> In C:\Program Files\MATLAB\R2012b\toolbox\symbolic\symbolic\symengine.p>symengine at 54 In mupadengine.mupadengine>mupadengine.evalin at 97 In mupadengine.mupadengine>mupadengine.feval at 150 In solve at 160 In Q3_new at 37 In run at 64 Warning: Explicit solution could not be found. \> In solve at 169 In Q3_new at 37 In run at 64

Confused, I went to MATLAB's documentation for solve and tried using the example snippet for solving a multivariate system of equations:

syms u v [solv, solu] = solve([2*u^2 + v^2 == 0, u - v == 1], [v, u])

The expected output of this snippet, according to the documentation, is:

solv = - (2^(1/2)*1i)/3 - 2/3 (2^(1/2)*1i)/3 - 2/3 solu = 1/3 - (2^(1/2)*1i)/3 (2^(1/2)*1i)/3 + 1/3

but the snippit instead returns:

Warning: 4 equations in 2 variables. \> In C:\Program Files\MATLAB\R2012b\toolbox\symbolic\symbolic\symengine.p>symengine at 54 In mupadengine.mupadengine>mupadengine.evalin at 97 In mupadengine.mupadengine>mupadengine.feval at 150 In solve at 160 Warning: Explicit solution could not be found. \> In solve at 169

solv =

[ empty sym ]

solu =

[]

as before.

Now I know I'm not making some beginner's mistake with my code because even the example code errors in the same way. Calling the singlevariate example snippit works as expected. I have tried this with MATLAB 2012a and MATLAB 2014a.

What could explain this unusual behaviour?

Upvotes: 1

Views: 2336

Answers (1)

Rollen
Rollen

Reputation: 1210

Can duplicate this on MATLAB 2014a. I found that if I already defined the variables using syms you can let solve resolve the variables automatically.

syms u v
[sv, su] = solve([2*u^2 + v^2 == 0, u - v == 1], [v, u]) % Doesn't work

% works but order-unspecified so this is not desirable
[su, sv] = solve([2*u^2 + v^2 == 0, u - v == 1])

Another user points out a mistake in using the incorrect documentation. MATLAB 2014a uses the following notation instead for re-ordered solutions. The other form seems to be for 2015. You should probably verify this holds true in 2012a but it seems to do so

syms u v
[sv, su] = solve([2*u^2 + v^2 == 0, u - v == 1], v, u)

Upvotes: 3

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