# fsolve with vectors x and y (not x(1) x(2))

4 views (last 30 days)
anto on 26 Dec 2022
Edited: Torsten on 26 Dec 2022
I'd like to use fsolve, to solve for the vectors x and y, this nonlinear system which i wrote in a function.
function F = EquationsList(x,y)
F(1) = -0.00011 + 2 * x(1) * (cos(y(1))+sin(y(1))) + 2 * x(2) * (cos(y(2))+sin(y(2))) + 2 * x(3) * (cos(y(3))+sin(y(3)));
F(2) = -0.00013 + 2 * x(1) * (cos(y(1))+sin(y(1))) + 2 * x(2) * (cos(y(2))+sin(y(2))) + 2 * x(3) * (cos(y(3))+sin(y(3)));
...
...
F(9) = -0.00015 + 2 * x(1) * (cos(y(1))+sin(y(1))) + 2 * x(2) * (cos(y(2))+sin(y(2))) + 2 * x(3) * (cos(y(3))+sin(y(3)));
end
in the code above I only reported the first 2 equations. It's a large system.
the equations derive from the development of the sum shown below: in which a,x,y are all scalars.
For using fsolve I coded this:
%defining constants:
N_mesh=3;
%define the problem for fsolve
problem.objective = @EquationsList;
%initial point
x0=zeros(N_mesh*N_mesh,1);
y0=zeros(N_mesh*N_mesh,1);
problem.x0 = x0;
problem.y0 = y0;
%solver
problem.solver = 'fsolve';
%set tolerances
problem.options = optimoptions('fsolve', ...
'MaxIter', 4000, ...
'MaxFunEvals',4000, ...
'StepTolerance',1e-16, ...
'FunctionTolerance',1e-16, ...
'OptimalityTolerance',1e-10,...
'Algorithm','levenberg-marquardt');
%solve
[x,y] = fsolve(problem);
But it gives me the error ' Not enough input arguments. '
Does anybody know how to use fsolve with these equations? I can't use only the vector x as the problem I'm trying to resolve requires two different output: x and y as vectors.
Thanks in advance for any replies.
Karim on 26 Dec 2022
well, what you show here has 4 unknowns for x and y, hence i would guess that you need to set the inital values accordingly. Why do you take the square of the number of variables?
% ...
N_mesh = 4;
% ...
x0 = zeros(N_mesh,1);
y0 = zeros(N_mesh,1);

Karim on 26 Dec 2022
Based on the comments, I would guess that you are looking for 8 parameters i.e.
syms x [1 4]; x
x = syms y [1 4]; y
y = can you try modifying your function "MyFun.m" such that:
function F = MyFun( input, numX )
% extract the variables from the input
x = input( 1:numX );
y = input( (numX+1):end );
% evaluate the equations
F(1) = -0.0001121770+2*x(1)*(cos(y(1))*cos(0.0000000000)+sin(y(1))*sin(0.0000000000))*((0.0021349691)^2)*(0.1666666667)...
+2*x(2)*(cos(y(2))*cos(0.0000000000)+sin(y(2))*sin(0.0000000000))*((0.0021349690)^2)*(0.1666666667)...
+2*x(3)*(cos(y(3))*cos(0.0000000000)+sin(y(3))*sin(0.0000000000))*((0.0021349690)^2)*(0.0000000000)...
+2*x(4)*(cos(y(4))*cos(0.0000000000)+sin(y(4))*sin(0.0000000000))*((0.0021349691)^2)*(0.0000000000);
F(2) = ...
end
and then you can call fsolve as:
% define the number of parameters
numX = 4;
numY = 4;
% define the problem for fsolve
problem.objective = @MyFun(x, numX);
% set the initial values
problem.x0 = zeros( numX+numY,1);
% set the solver
problem.solver = 'fsolve';
% set the options
problem.options = optimoptions('fsolve', ...
'MaxIter', 4000, ...
'MaxFunEvals',4000, ...
'StepTolerance',1e-16, ...
'FunctionTolerance',1e-16, ...
'OptimalityTolerance',1e-10,...
'Algorithm','levenberg-marquardt');
% solve the problem
solution = fsolve(problem);
% extract the variables
x = solution( 1:numX );
y = solution( (numX+1):end );
anto on 26 Dec 2022
Yes, that's what I've been thinking also just now:
fsolve wants only a vector of unknowns, so we just "assign" the first numX unknowns to the first vector (which i called x in the LATEX), and the following numY unknowns as the second vector (which I called y in the LATEX).
Thanks again Karim.

Torsten on 26 Dec 2022
Edited: Torsten on 26 Dec 2022
%defining constants:
N_mesh=3;
%define the problem for fsolve
problem.objective = @(z)EquationsList(z,Nmesh);
%initial point
x0=zeros(1,N_mesh*N_mesh);
y0=zeros(1,N_mesh*N_mesh);
problem.x0 = [x0,y0];
%solver
problem.solver = 'fsolve';
%set tolerances
problem.options = optimoptions('fsolve', ...
'MaxIter', 4000, ...
'MaxFunEvals',4000, ...
'StepTolerance',1e-16, ...
'FunctionTolerance',1e-16, ...
'OptimalityTolerance',1e-10,...
'Algorithm','levenberg-marquardt');
%solve
z = fsolve(problem);
x = z(1:Nmesh*Nmesh);
y = z(Nmesh*Nmesh+1:2*Nmesh*Nmesh);
function F = MyFun(z,Nmesh)
x = z(1:Nmesh*Nmesh);
y = z(Nmesh*Nmesh+1:2*Nmesh*Nmesh);
F(1) = -0.0001121770+2*x(1)*(cos(y(1))*cos(0.0000000000)+sin(y(1))*sin(0.0000000000))*((0.0021349691)^2)*(0.1666666667)...
+2*x(2)*(cos(y(2))*cos(0.0000000000)+sin(y(2))*sin(0.0000000000))*((0.0021349690)^2)*(0.1666666667)...
+2*x(3)*(cos(y(3))*cos(0.0000000000)+sin(y(3))*sin(0.0000000000))*((0.0021349690)^2)*(0.0000000000)...
+2*x(4)*(cos(y(4))*cos(0.0000000000)+sin(y(4))*sin(0.0000000000))*((0.0021349691)^2)*(0.0000000000);
F(2)= ....
...
...
end
anto on 26 Dec 2022
Perfect, thanks so much.

### Categories

Find more on Solver Outputs and Iterative Display in Help Center and File Exchange

R2022b

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!