Assume and find different possible unknown variables of inequalities , Need help please

Hi All,

I have inequalities, with two unkonwn variables, So How could I assume one variables with different numbers, and get the others?

I mean:

-15<10*x+2*y<20

How could I assume for example x=2, 3, and so on, and then find answer of (y) depends on the value of (x)

I have been trying to apply assume, and find commands, but unfortunaley, I could not So I hope anyone could help me

Please

Looking to hearing from you

Thank you,

Answer 1

[John D'Errico]

First, you cannot write a pair of inequalities that way in MATLAB. It works as a conventional form, because people know what you intended. But MATLAB will misinterpret things.

Next, computers don't deal well with strict inequalities, because of floating point problems.

You have

-15 < 10*x+2*y

AND

10*x+2*y < 20

If we solve for y that just meets the requirements in those two cases, we would see this:

syms x y

solve(-15 == 10*x+2*y,y)
ans =
- 5*x - 13/2

solve(10*x+2*y == 20,y)
ans =
9 - 5*x

We can think f it as an interval for y, as a function of x.

yinterval = [ solve(-15 == 10*x+2*y,y),solve(10*x+2*y == 20,y)]
yinterval =
[ - 5*x - 15/2, 10 - 5*x]

yinterval = matlabFunction(yinterval)
yinterval =
  function_handle with value:
    @(x)[x.*-5.0-1.5e+1./2.0,x.*-5.0+1.0e+1]

So now for any specific x, we can produce an interval for y that satisfies the inequalities.

yinterval(2)
ans =
                     -17.5                         0
yinterval(3)
ans =
                     -22.5                        -5

[Ali Tawfik]

Hi John,

Thanks for your prompt reply.

I understood, your first part of the answer including the command lines unitl the second part (interval command lines ), would you mind explaining more, what the following lines mean ?

yinterval = matlabFunction(yinterval)

yinterval =

function_handle with value:

@(x)[x.*-5.0-1.5e+1./2.0,x.*-5.0+1.0e+1]

I need more explination please for function handle ?

Bear in mind I am using Matlab 2016a

Thanks,

[Ali Tawfik]

Also, I'd like to get y as a function of the value of x ?

I would appericate your help.

Thanks again!

[John D'Errico]

I gave you exactly that. But I'm not sure what is to be not understood. (You talked about the assume function, so this implies you have the symbolic toolbox.)

yinterval = [ solve(-15 == 10*x+2*y,y),solve(10*x+2*y == 20,y)]

When you don't understand something, look at the pieces. First, what do you think this means?

solve(-15 == 10*x+2*y,y)

If you don't understand solve, then you need to read the help docs for solve. It solves that expression for y, essentially as a function of x.

The second part does the same thing, but now for the upper end point of the interval.

solve(10*x+2*y == 20,y)

And in the end, I gave you a function that for any value of x, returns the bounds on y for that given x. That usd the matlabFunctino utility, which converts a symbolic expression into a function handle that you can use.

Any value of y between the returned limits will satisffy the inequalities, although at the ends of the interval stated, the inequality becomes a strict equality.

I'd suggest you spend some time reading the tutorials for tools like the symbolic toolbox if you will be using it. But also, if you were thinking about using find to solve this problem, that means you need to read the basic getting started tutorials, since you then have no clue what find does. Read the tutorials. Look at the examples.

[Ali Tawfik]

Hi again,

Thanks for your concern,

I totally understood what you have written. As well as, I understand that you create an interval depending on the results of y from inequalities,

but I am still confused, how could I use a function as you wrote before,

yinterval = matlabFunction(yinterval)

yinterval =

function_handle with value:

@(x)[x.*-5.0-1.5e+1./2.0,x.*-5.0+1.0e+1] ??

I do not usally use function, and I know I need to read about it, but I am kindly asking you, how could I use it here ?, especially in that problem ?

How Could I get y result depend on the input value of y

I am not talking about input () command,

I am talking about algorthim of yinterval = matlabFunction(yinterval)

yinterval =

function_handle with value:

@(x)[x.*-5.0-1.5e+1./2.0,x.*-5.0+1.0e+1]?

Thank you

[Ali Tawfik]

Hi Again,

Would you mind having a look for the final code after your suggestions,

clc;

syms x y real;

neg=solve(-15 == 10*x+2*y,y)

pos=solve(10*x+2*y == 20,y)

yinterval = [ neg,pos]

%% Add function

function myfunc(x)

neg=input('enter equation ') % I have written yinternal(1) %% (got error of undefined variable )

pos=input('enter equation ') %% (got error of undefined variable )

yin(:,1)=[cc,mm]

end

ANy help!

[Ali Tawfik]

Hi John,

I do not know, why you remove the question , as you do not have time to answer?

So I wish you could have time, to answer my question, or allow me to post the question, and allow others to see!

Thanks,