Error using integral; First input argument must be a function handle.

I am trying to fit my equation using the modelE which is the sum of two functions exciton and continum. Continum is the integral of function cont. I am having error while using matlab inbuilt integral function. Can someone guide me where I am messing up on this code?

A=xlsread('Data');
xdata=1240./A(:,1);
ydata=A(:,2);
plot(xdata,ydata,'r.','markersize',30)
box on
energy=xdata;
Absorption=ydata;

options =optimoptions(@lsqcurvefit,'Algorithm','trust-region-reflective',...
    'StepTolerance',1e-19,'MaxFunctionEvaluations',1e10, ... 
    'MaxIterations',1e3)

options = 
  lsqcurvefit options:

   Options used by current Algorithm ('trust-region-reflective'):
   (Other available algorithms: 'levenberg-marquardt')

   Set properties:
                   Algorithm: 'trust-region-reflective'
      MaxFunctionEvaluations: 1.0000e+10
               MaxIterations: 1000
               StepTolerance: 1.0000e-19

   Default properties:
              CheckGradients: 0
                     Display: 'final'
    FiniteDifferenceStepSize: 'sqrt(eps)'
        FiniteDifferenceType: 'forward'
           FunctionTolerance: 1.0000e-06
         JacobianMultiplyFcn: []
         OptimalityTolerance: 1.0000e-06
                   OutputFcn: []
                     PlotFcn: []
    SpecifyObjectiveGradient: 0
         SubproblemAlgorithm: 'factorization'
                    TypicalX: 'ones(numberOfVariables,1)'
                 UseParallel: 0

var=[0.0529 2.3926 0.0307 1.002];
MI=lsqcurvefit(@modelE,var,energy,Absorption,[],[],options);

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

fitdata=modelE(MI,energy);

hold on

plot(energy,modelE(var,energy),'co')

Warning: Imaginary parts of complex X and/or Y arguments ignored.

plot(energy,exciton(var,energy),'m.','markersize',30)

plot(energy, continum(var,energy),'k.')

Error using integral
First input argument must be a function handle.

Error in solution>continum (line 40)
z = integral(cont(var,energy),2.39,inf);

function alpha = modelE(var,energy)
alpha = cont(var,energy) +var(2).* exciton(var,energy);
end


function x= exciton(var,energy)
 x= 2.*var(1).*sech((energy-var(2)+var(1))./var(3))+...
    0.125.*var(1).*sech((energy-var(2)+(var(1)./8))./var(3))+...
    (2/27).*var(1).*sech((energy-var(2)+(var(1)./27))./var(3));
    
end

function y= cont(var,energy)
y=(sech((energy-var(2))./var(3))).*(1./(1-exp(-2.*pi.*sqrt(var(1)./(energy-var(2)))))).*(1./(1-(var(4).*energy-var(2))));
end

function z= continum(var,energy)
z = integral(cont(var,energy),2.39,inf);
end

[Bibek Dhami]

@Torsten I had typo in my integral, so I was getting the constant value. Actually the integral should be not over energy.

But now I am having some issue with the curve fitting. I am using lower and upper bound to restrict the values but I am getting following error.

Lower and upper bounds not supported with complex-valued initial

A=xlsread('Data');
xdata=1240./A(:,1);
ydata=A(:,2);
plot(xdata,ydata,'r.','markersize',30)
box on
energy=xdata;
Absorption=ydata;

options =optimoptions(@lsqcurvefit,'Algorithm','levenberg-marquardt',...
    'StepTolerance',1e-19,'MaxFunctionEvaluations',1e10, ... 
    'MaxIterations',1e3);
lb=[0.03, 2.35, 0.02, 2];
ub=[0.09, 2.40, 0.05, 5];

var=[0.0429 2.3776 0.0207 2.902];
MI=lsqcurvefit(@modelE,var,energy,Absorption,lb,ub,options);
fitdata=modelE(MI,energy);

hold on

% plot(energy,modelE(var,energy),'co')
% plot(energy,exciton(var,energy),'m.','markersize',30)
% plot(energy, continum(var,energy),'k.')

plot(energy,fitdata,'ro')
plot(energy,exciton(MI,energy),'g.','markersize',30)
plot(energy, continum(MI,energy),'b.')


function alpha = modelE(var,energy)
alpha = continum(var,energy) + exciton(var,energy);
end


function x= exciton(var,energy)
 x= 2.*var(1).*sech((energy-var(2)+var(1))./var(3))+...
    0.125.*var(1).*sech((energy-var(2)+(var(1)./8))./var(3))+...
    (2/27).*var(1).*sech((energy-var(2)+(var(1)./27))./var(3));
    
end

function y= cont(var,energy,x)
y=(sech((energy-x)./var(3))).*(1./(1-exp(-2.*pi.*sqrt(var(1)./(x-var(2)))))).*(1./(1-(var(4).*(x-var(2)))));
end


function z= continum(var,energy)
  z = integral(@(x)cont(var,energy,x),2.25,200,'ArrayValued',true);
end

[Torsten]

During the integration in "continuum", the expression

var(1)./(x-var(2))

becomes or is negative and thus

sqrt(var(1)./(x-var(2)))

becomes complex-valued.

This makes MATLAB's "lsqcurvefit" throw an error and stop.

Answer 1

[Torsten]

function z= continum(var,energy)
  z = integral(@(x)cont(var,x),2.39,inf);
end

[Bibek Dhami]

@Torsten Thank you so much it works. But I am having another issue. The plot of this function should give us something like this but it is just giving a line parallel to x axis.

[Torsten]

An integral gives a single scalar value, not a curve.