# initlalize several variables at once

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I currently have a code where I am initializing many parameters, that will be solved for later.

I do this by:

C1=params(1);

C2=params(2);

C3=params(3);

C4=params(4);

C5=params(5);

C6=params(6);

C7=params(7);

C8=params(8);

C9=params(9);

C10=params(10);

C11=params(11);

C12=params(12);

C13=params(13);

There's got to be an easier way...

Additionally, I set my intial guesses like:

params0=[0.1,0.1,0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1];

Is there a way to more easily set this, assuming they all have the same initial guess? Typing them all out that way is tedious, and my code is constantly changing. How can I automate it?

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### More Answers (3)

Matt J
on 19 Mar 2019

Edited: Matt J
on 19 Mar 2019

Is there a way to more easily set this, assuming they all have the same initial guess?

One way:

params0=linspace(0.1,0.1,13)

Another is:

params0=repelem(0.1,1,13);

There's got to be an easier way...

If you have a very large vector of variables, it does not make sense to assign them to separate variables. You should probably be manipulating them as a vector. But if you must index the variables individually, I would just rename params to something shorter,

C=params;

and then refer to the variables via indexing C(1), C(2),..C(13) throughout the code. Although, it is then unclear why you chose to name the vector params in the first place...

##### 4 Comments

Matt J
on 19 Mar 2019

Edited: Matt J
on 19 Mar 2019

Perhaps instead of zeroth, first,etc... you generate a cell array called "orders" like so:

T=[0 0; 1 0; 0 1]; %table of exponent combinations

[orders{1:max(d)+1}]=deal(0); %initialize

for k=1:numel(C)

i=T(k,1); j=T(k,2);

orders{i+j+1}=orders{i+j+1} + C(k) * X.^i .* Y.^j ;

end

Matt J
on 20 Mar 2019

Edited: Matt J
on 20 Mar 2019

One other thing I would point out is the model function you have shown us here is linear in the coefficients. This means that it can be represented as a matrix multiplication and the entire fit can be done with simple linear algebra instead of an iterative solver like lsqcurvefit.

A=func2mat(@(p) modelfun(p,xdata), params0);

coefficients =A\g(:);

That's it!

##### 4 Comments

Matt J
on 20 Mar 2019

Matt J
on 20 Mar 2019

Just to sum things up here, below is my implementation of the fit, combining all my various recommendations. Both the algebraic method that I proposed and the method using lsqcurvefit are implemented and compared. You will see that the algebraic method is both faster and more accurate (gives a lower resnorm) than lsqcurvefit.

%% Data Set-up

num=xlsread('example.xlsx',1,'A2:F18110');

Np=4; %polynomial order

g = num(:,6);

otherStuff.r = num(:,4);

otherStuff.eta = num(:,3);

otherStuff.g = g;

otherStuff.eta_c = 0.6452;

otherStuff.Np=Np;

otherStuff.A1 = -0.4194;

otherStuff.A2 = 0.5812;

otherStuff.A3 = 0.6439;

otherStuff.A4 = 0.4730;

%% Fitting (2 methods)

%fit using matrix algebra

tic;

A=func2mat(@(p) modelfun(p,otherStuff), ones(Np+1,Np+1));

Cfit1 =A\g(:);

resnorm1=norm(A*Cfit1-g(:));

toc %Elapsed time is 0.124593 seconds.

%fit iteratively with lsqcurvefit

tic;

options=optimoptions(@lsqcurvefit,'MaxFunctionEvaluations',10000);

Cinitial(1:Np+1,1:Np+1)=0.1;

[Cfit2, resnorm2]=lsqcurvefit(@modelfun,Cinitial,otherStuff,g,[],[],options);

toc %Elapsed time is 1.687990 seconds.

%% Display

figure(1); showFit(Cfit1,otherStuff);

figure(2); showFit(Cfit2,otherStuff);

resnorm1,resnorm2,

function ghat=modelfun(C,otherStuff)

r = otherStuff.r;

eta = otherStuff.eta;

eta_c = otherStuff.eta_c;

Np = otherStuff.Np;

A1 = otherStuff.A1;

A2 = otherStuff.A2;

A3 = otherStuff.A3;

A4 = otherStuff.A4;

PV = 1 + 3*eta./(eta_c-eta)+ A1*(eta./eta_c) + 2*A2*(eta./eta_c).^2 +...

3*A3*(eta./eta_c).^3 + 4*A4*(eta./eta_c).^4;

rdf_contact = (PV - 1)./(4*eta);

Cflip=rot90(reshape(C,Np+1,Np+1),2);

poly_guess = polyVal2D(Cflip,r-1,eta/eta_c,Np,Np);

ghat = (poly_guess.*rdf_contact);

end

function showFit(Cfit,otherStuff)

r = otherStuff.r(:);

eta = otherStuff.eta(:);

g = otherStuff.g(:);

ghat=modelfun(Cfit,otherStuff);

tri = delaunay(r,eta);

%% Plot it with TRISURF

h=trisurf(tri, r, eta, ghat);

h.EdgeColor='b';

h.FaceColor='b';

axis vis3d

hold on;

scatter3(r,eta,g,'MarkerEdgeColor','none',...

'MarkerFaceColor','r','MarkerFaceAlpha',.05);

xlabel 'r', ylabel '\eta', zlabel 'g(r,\eta)'

hold off

end

Both methods give a similar looking surface plot:

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