Define function with nonlinear equation system vercat error

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weggee
weggee 2022-1-23
评论： Walter Roberson 2022-1-24
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]

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回答（2 个）

Matt J
Matt J 2022-1-23
编辑：Matt J 2022-1-23
Ran in:
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
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Torsten
Torsten 2022-1-24
@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
Matt J 2022-1-24
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] );

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Walter Roberson
Walter Roberson 2022-1-24
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.
  1 个评论
Walter Roberson
Walter Roberson 2022-1-24
Ran in:
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

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