Thread Subject:

Using max when there is symbolic variable

Hi,

I am trying to solve this problem:
p_i=max(0,(-1+sqrt(1-4*c_i*d_i+4*(c_i-d_i)*c_i*d_i/(x*a_i))/2*c_i*d_i) if c_i>d_i
and p_i=0 otherwise. p_i, c_i,d_i are diagonal elements of matrices P, C, D and A. I need to find x and after that to calculate p_i, but I do not know how to implement max because at first x is a symbolic variable.

I would appreciate if anyone could help me.
Maya

"Maya" wrote in message <kqmght$e9p$1@newscl01ah.mathworks.com>...
> Hi,
>
> I am trying to solve this problem:
> p_i=max(0,(-1+sqrt(1-4*c_i*d_i+4*(c_i-d_i)*c_i*d_i/(x*a_i))/2*c_i*d_i) if c_i>d_i
> and p_i=0 otherwise. p_i, c_i,d_i are diagonal elements of matrices P, C, D and A. I need to find x and after that to calculate p_i, but I do not know how to implement max because at first x is a symbolic variable.
>
> I would appreciate if anyone could help me.
> Maya

I missed this: x>0 is chosen to satisfy the constraint Tr(A*P)>=Pt.

On Saturday, June 29, 2013 5:01:09 PM UTC+5:30, Maya wrote:
> Hi,
>
>
>
> I am trying to solve this problem:
>
> p_i=max(0,(-1+sqrt(1-4*c_i*d_i+4*(c_i-d_i)*c_i*d_i/(x*a_i))/2*c_i*d_i) if c_i>d_i
>
> and p_i=0 otherwise. p_i, c_i,d_i are diagonal elements of matrices P, C, D and A. I need to find x and after that to calculate p_i, but I do not know how to implement max because at first x is a symbolic variable.
>
>
>
> I would appreciate if anyone could help me.
>
> Maya

syms c_i d_i a_i x
>> expand(-1+sqrt(1-4*c_i*d_i+4*(c_i-d_i)*c_i*d_i/(x*a_i))/2*c_i*d_i)
 
ans =
 
(c_i*d_i*((4*c_i^2*d_i)/(a_i*x) - (4*c_i*d_i^2)/(a_i*x) - 4*c_i*d_i + 1)^(1/2))/2 - 1


solve(-1+sqrt(1-4*c_i*d_i+4*(c_i-d_i)*c_i*d_i/(x*a_i))/2*c_i*d_i)
 
ans =
 
(c_i*d_i*(4*c_i - 4*d_i))/(a_i*(4*c_i*d_i + 4/(c_i^2*d_i^2) - 1))

this the value of x if p_i=0

i dont understand your problem exactly....

you want to find max(0,somenumber). is it?

here somenumber is a variable.... is it?

"Maya " <sanja_angelova@hotmail.com> wrote in message
news:kqmght$e9p$1@newscl01ah.mathworks.com...
> Hi,
>
> I am trying to solve this problem:
> p_i=max(0,(-1+sqrt(1-4*c_i*d_i+4*(c_i-d_i)*c_i*d_i/(x*a_i))/2*c_i*d_i) if
> c_i>d_i
> and p_i=0 otherwise. p_i, c_i,d_i are diagonal elements of matrices P, C,
> D and A. I need to find x and after that to calculate p_i, but I do not
> know how to implement max because at first x is a symbolic variable.

You will need to substitute numeric values into that expression before
calling MAX, since in general it is impossible to say what this function
call should return if MAX were defined for symbolic variables:

syms x y
max(x, y)

--
Steve Lord
slord@mathworks.com
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