vpasolve does not handle inequalities correctly

Hello MATLAB community,

I am currently experiencing a problem with vpasolve's handling of inequalities, mainly them not working. I am running the following on Windows 7:

MATLAB R2015a

v8.5.0.197613

Windows 64-bit

consider the following simple quadratic example

x^2-12.5*x+37==0

this has two solutions: x = 4.8138593383654928350373471329453 or x = 7.6861406616345071649626528670547

if we run vpasolve without an interval we get the two solutions: syms x

xx=vpasolve(x^2-12.5*x+37==0,x);

xx =

 4.8138593383654928350373471329453
 7.6861406616345071649626528670547

now, let's say we want to find the first solution, we know that it is lest than 5 so we bound our search between 0 and 5:

syms x

xx=vpasolve(x^2-12.5*x+37==0,x,[0,5]);

this gives us the solution

xx =

4.8138593383654928350373471329453

which is great but let's say we don't know the solution, just that it's less than five; we would use the inequality option:

syms x

xx=vpasolve([x^2-12.5*x+37==0,x<5],x);

but this returns

xx =

Empty sym: 0-by-1

which of course is not true. My particular problem is a more sophisticated multivariate problem but this example shows all the problems that I currently face. Any help would be greatly appreciated.

Cheers,

Jesse V

Answer 1

[Jesse]

I have worked out the solution to this problem, and hopefully it will help others.

First consider an (arbitrary) inequality

x - y < 5

we can rearrange this to be an inequality with some algebraic tricks, consider this rearranged to

 x - y - 5 < 0

then if the inequality holds true the left hand side must be negative, this can be made an inequality by use of the sign function:

 sign(x-y-5)==-1

now, MATLAB does not allow more constraints than parameters, so we just add a fake parameter!

For example, the solution to the previous code would be:

 syms x dummy
 [xx,~]=vpasolve([x^2-12.5*x+37==0,sign(x-5)==-1],[x,dummy])

where the tilde suppresses the output of the unneeded dummy variable. Now if the answer is less than five the equality is held.

Cheers,

Jesse

Answer 2

[Mischa Kim]

Jesse, according to the documentation

" vpasolve ignores assumptions set on variables. You can restrict the returned results to particular ranges by specifying appropriate search ranges using the argument init_guess."

In other words, you could use

 syms x
 xsol = vpasolve(x^2 - 12.5*x + 37 == 0, x, [-inf,5]);

if you don't know the solution, just that it's less than five

[Jesse]

Sorry, I guess my example was too simplistic then, the actual constraint is on a function of the variable and the variable example exhibited the same error. Consider instead something like cosh(x)*cos(y)<1, which is very similar to my true problem, when giving an equality like that it also returns a null result despite there really being a well defined answer in that region.