Define function with nonlinear equation system vercat error

Hi,

I am trying to define a nonlinear equation system in a function in order to solve it using fsolve.

Already calling the function it self raises the error

"Error using vertcat

Dimensions of arrays being concatenated are not consistent."

running fminunc results in

Error in fminunc (line 307)

f = feval(funfcn{3},x,varargin{:});

Error in GPS_Calculation (line 49)

sol = fminunc(f,[6 6 6 6])

Caused by:

Failure in initial objective function evaluation. FMINUNC cannot continue.

How can I fix this?

f = @(x)[sqrt( (101 - x(1)).^2 + (16 - x(2)).^2 + (207 - x(3)).^2 ) + x(4) - 310.5685; 
    sqrt( (52 - x(1)).^2 + (21 - x(2)).^2 + (302 - x(3)).^2 ) + x(4) - 387.5097; 
    sqrt( (17 - x(1)).^2 + (53 - x(2)).^2 + (350 - x(3)).^2 ) + x(4) -434.7066; 
    sqrt( (-15 - x(1)).^2 + (159 - x(2)).^2 + (208 - x(3)).^2 ) + x(4) - 341.25730]

f([6 6 6 6])

sol = fminsearch(f,[6 6 6 6])
sol = fminunc(f,[6 6 6 6])
sol = fsolve(F,[6 6 6 6]

Answer 1

[Matt J]

F = @(x)[sqrt( (101 - x(1)).^2 + (16 - x(2)).^2 + (207 - x(3)).^2 )+ x(4)- 310.5685; 
    sqrt( (52 - x(1)).^2 + (21 - x(2)).^2 + (302 - x(3)).^2 )+x(4)-387.5097; 
    sqrt( (17 - x(1)).^2 + (53 - x(2)).^2 + (350 - x(3)).^2 )+x(4)-434.7066; 
    sqrt( (-15 - x(1)).^2 + (159 - x(2)).^2 + (208 - x(3)).^2 )+x(4)-341.25730];


f=@(x) norm(F(x))^2;



[sol,fval] = fminsearch(f,[6 6 6 6],optimset('TolFun',1e-12','MaxIter',1e5,'MaxFunEvals',inf))

sol = 1×4

5.1967 7.5954 8.4908 89.9902

fval = 2.7201e-14

opts=optimoptions('fminunc','StepTol',1e-12,'OptimalityTol',1e-12,'FunctionTol',1e-12,'Display','none');
[sol, fval] = fminunc(f,[6 6 6 6],opts)

sol = 1×4

5.1283 7.4954 8.2884 89.7746

fval = 6.2284e-07

opts=optimoptions('fsolve','StepTol',1e-12,'OptimalityTol',1e-12,'FunctionTol',1e-12,'Display','none');
[sol,fval] = fsolve(F,[6 6 6 6],opts)

sol = 1×4

5.1967 7.5954 8.4908 89.9902

fval = 4×1

1.0e+-12 * 0.1137 -0.1705 -0.1137 0

[weggee]

Thank you! Can you elaborate why calling norm() is necessary?

[Matt J]

Thank you!

You're welcome, but please Accept-click the answer if your question is settled.

Can you elaborate why calling norm() is necessary?

fminsearch and fminunc are function minimizers. It is not possible to minimize a vector-valued quantity. You can only do a comparison a>b when a and b are scalars.

[Torsten]

@Nico Weckardt

Alternatively, you can use "fsolve" to solve 4 equations in 4 unknowns:

f = @(x)[sqrt( (101 - x(1)).^2 + (16 - x(2)).^2 + (207 - x(3)).^2 ) + x(4) - 310.5685; 
         sqrt( (52 - x(1)).^2 + (21 - x(2)).^2 + (302 - x(3)).^2 ) + x(4) - 387.5097; 
         sqrt( (17 - x(1)).^2 + (53 - x(2)).^2 + (350 - x(3)).^2 ) + x(4) - 434.7066; 
         sqrt( (-15 - x(1)).^2 + (159 - x(2)).^2 + (208 - x(3)).^2 ) + x(4) - 341.25730]
xsol = fsolve(f,[6 6 6 6])

[weggee]

@Matt J

fminsearch and fminunc are function minimizers. It is not possible to minimize a vector-valued quantity. You can only do a comparison a>b when a and b are scalars.

Thank you for your answer. Is there also a way to define the equations system as a scalar right away? That would avoid the problem

[Walter Roberson]

You have four independent goals, and it might not be possible to satisfy all four of them simultaneously.

There is no way to put them all together into one equation without deciding how you want to weight the relative importance of each of them being satisfied.

[Torsten]

@weggee

Is there also a way to define the equations system as a scalar right away? That would avoid the problem

That's what taking the norm of the equations and using a minimizer to solve does.

[Matt J]

You caould have done

f = @(x)norm( [sqrt( (101 - x(1)).^2 + (16 - x(2)).^2 + (207 - x(3)).^2 )+ x(4)- 310.5685; 
    sqrt( (52 - x(1)).^2 + (21 - x(2)).^2 + (302 - x(3)).^2 )+x(4)-387.5097; 
    sqrt( (17 - x(1)).^2 + (53 - x(2)).^2 + (350 - x(3)).^2 )+x(4)-434.7066; 
    sqrt( (-15 - x(1)).^2 + (159 - x(2)).^2 + (208 - x(3)).^2 )+x(4)-341.25730] );

Answer 2

[Walter Roberson]

You have a multi objective search, trying to simultaneously minimize four different objectives. fmincon is only able to minimize a single objective. You need to switch to a Pareto search using gamultiobj() or paretosearch()

Remember that Pareto searches are not global minima searches: they correspond to finding local minima such that moving the point in any direction makes at least one of the objectives worse.

[Walter Roberson]

There happens to be a unique solution. But notice that I did not use fmincon()

syms x [1 4]
eqn = [sqrt( (101 - x(1)).^2 + (16 - x(2)).^2 + (207 - x(3)).^2 ) + x(4) - 310.5685; 
    sqrt( (52 - x(1)).^2 + (21 - x(2)).^2 + (302 - x(3)).^2 ) + x(4) - 387.5097; 
    sqrt( (17 - x(1)).^2 + (53 - x(2)).^2 + (350 - x(3)).^2 ) + x(4) - 434.7066; 
    sqrt( (-15 - x(1)).^2 + (159 - x(2)).^2 + (208 - x(3)).^2 ) + x(4) - 341.25730]

eqn = 

sol = solve(eqn)

sol = struct with fields:
    x1: 103822410932647867988108939361258584970909255712767107632984851/1956912675242977971478733823948770948256077913556186906492928 - (129051806647358847*2106559777848689611763319847455226230701878591815072007499937183516353063743909708404663119^(1/…
    x2: 426905901714079451496930566148879909559098800764964499621325585/3913825350485955942957467647897541896512155827112373812985856 - (136826147043425299*2106559777848689611763319847455226230701878591815072007499937183516353063743909708404663119^(1/…
    x3: 265396183855587512112924351704545980843661454136842211566905355/978456337621488985739366911974385474128038956778093453246464 - (88565665080818287*2106559777848689611763319847455226230701878591815072007499937183516353063743909708404663119^(1/2)…
    x4: 173764389483007670549038691540576895965144260875517/444950427491443854587199399236117403292173074432 - (46067*2106559777848689611763319847455226230701878591815072007499937183516353063743909708404663119^(1/2))/2224752137457219272935996996180587…

format long g
X1 = double(sol.x1)

X1 = 
          5.19673845646778

X2 = double(sol.x2)

X2 = 
          7.59542522463441

X3 = double(sol.x3)

X3 = 
          8.49082794634566

X4 = double(sol.x4)

X4 = 
          89.9901846810174