[SciPy-User] Functional nonlinear equation

josef.pktd@gmai... josef.pktd@gmai...
Sun Dec 27 08:58:10 CST 2009

```On Sun, Dec 27, 2009 at 9:35 AM, Dorian <wizzard028wise@gmail.com> wrote:
> Is there any way to solve it in the functional form ?
> I do not have "mathematica" to do it.
> Thanks for the plot suggestion.
>
> Dorian
>
> On Sun, Dec 27, 2009 at 3:00 PM, Richard <reg8@cornell.edu> wrote:
>>
>> I assume , x,y,a are real variables.  I would try using a contour plotting
>> program. There is probably something like that already available in
>> matplotlib. You would evaluate f(x,y) on a grid of (x,y) values and the
>> contouring program will perform an efficient search for the points in the
>> x,y plane where f = <any constant>.
>>
>> Richard
>>
>>
>> On Dec 27, 2009, at 7:42 AM, Dorian wrote:
>>
>> Hi  all,
>>
>> How do I solve  the following functional nonlinear equation
>>
>> f(x,y)= (-1/a^2)*(x*y)^(1/a-1)+(1/a)*x^(1/a-1)+(1/a)*y^(1/a-1) =0
>>
>> where  "a"  is positive parameter.
>>
>> If there is a way to plot  f(x,y) for different values of "a"
>> it will be very appreciated.
>>
>>
>> Dorian

for
y(x) st. f(x,y) =0

I would loop over x in linspace(xl, xh)
and use scipy.optimize.fsolve or any other root finder to find y given x (and a)

The only problem is if y(x) is not a function, e.g. if f(x,y)=0
describes a circle. Maybe local starting values help tracing the
different arms.

There might be other parameterizations, to get the full contour, e.g.
use the same trick as matplotlib or interpolation on a grid.   The
only cases I did, had a unique y given x.

Josef

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```