fsolve

Hi,

I'm solving a system of two non linear equations involving the same number of variables. I'm using the command fsolve, so before I've defined my functions:

function F = eqns(x)
F = [x(1).*A + (1-x(1)).*x(2).*B + (1-x(1)).*(1-x(2)).*C - b1;
      x(1).*D + (1-x(1)).*x(2).*E + (1-x(1)).*(1-x(2)).*F - b2]

and save it as nle.m. A,B,C,D,E,F are constant values and b1 and b2 are my own data stored in two vectors in the workspace.

The command

x0 = [0 0];
[x,toll] = fsolve(@nle,x0)

solve my system only if I write the values of b1 and b2 in the equations defined into the m-file. Since I've thousand of b1 and b2 pairs, I would that fsolve find the zero capturing the current values of b1 and b2 from the workspace. How can I do this?

Thanks for the help

Answer 1

[Titus Edelhofer]

Hi,

add the b1, b2 to the function as variables:

function F = eqns(x, b1, b2)
F = ...

and call pass your b1, b2 to the call for fsolve:

b1 = 42;
b2 = 1;
fun = @(x) nle(x, b1, b2);
[x,toll] = fsolve(fun, x0);

Titus

[gianluca]

Hi Titus,

I added the b1 and b2 to the function as variables and this is a essential step and I thank you.

But when I pass b1 and b2 to the call for fsolve, I think fsolve searches the zero for all the values of b1 and b2 simultaneously and gives me the message:

Warning: Default trust-region dogleg method of FSOLVE cannot

handle non-square systems; switching to Gauss-Newton method.

> In fsolve at 232

Optimizer appears to be converging to a minimum that is not a root:

Sum of squares of the function values is > sqrt(options.TolFun).

The b1 and b2 are vectors of size (2000x1) but I would find the m-solutions for each pair of b1-b2. Do you have some ideas?

[Sean de Wolski]

Can you paste the code you used to run this? b1 =42,b2=1; were just for example and should not be copied to your code.

[Titus Edelhofer]

That's exactly right. You will need to loop over b1 and b2, e.g.

b1 = ...; b2 = ...;

result = zeros(size(b1));

for i=1:length(b1)

fun = @(x) nle(x, b1(i), b2(i));

result(i) = fsolve(fun, x0);

end

[gianluca]

Hi,

this is the nle.m file:

function F = eqns(x,b1,b2)

F = [x(1).*0+(1-x(1)).*x(2).*30+(1-x(1)).*(1-x(2)).*150-b1;

x(1).*189+(1-x(1)).*x(2).*55.5+(1-x(1)).*(1-x(2)).*89.9-b2];

In the command windows:

b1 = CGR1;

b2 = S;

fun = @(x) nle(x, b1, b2);

[x,toll] = fsolve(fun, x0);

where CGR1 and S are the vector of size (28721 x 1).

I attach yuo a little part of the CGR1 and S vectors (e.g. 10 rows):

CGR1 = [37.6 38.6 39.7 40.7 41.8 42.8 43.9 44.9 46.0 47.1]

S = [67.4 67.7 67.9 68.1 68.3 68.5 68.7 69.0 69.2 77.3]

[Titus Edelhofer]

Hi,

you need to put the call to fsolve into the loop as I did above.

Titus