MATLAB: How can write this in matlab

fittingregression

I want to make one M-file that finds a function P(x)=A*e^M*x, which can approximate a function that is given in tabular shape.

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Assuming that ‘A’ and ‘M’ are matrices, and that ‘x’ is a vector:

function Z = P(A, M, x)
    for k1 = 1:length(x)
        P(:,:,k1) = A*expm(M*x(k1));       % Anonymous Function
    end
end

Call it as:

N = 3;                      % Matrix Size
A = rand(N);                % Create Random Matrix To Test Code

M = rand(N);                % Create Random Matrix To Test Code
x = linspace(0, 1, 10);     % Create ‘x’ Vector
Z = P(A, M, x);             % Z = A*expm(M*x)

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MATLAB: Curve fitting without the toolbox

There are the functions lsqcurvefit (Optimization Toolbox) and nlinfit (Statistics Toolbox) that will fit an objective function you provide. They each have their own advantages and disadvantages, depending upon what you want to do.

If you don’t have those, using the MATLAB core function fminsearch can do the nonlinear fit with an additional line of code (the OLS cost function). (See the fminsearch documentation for details on what it does and how it works.)

This works:

y = @(b,x) b(1).*exp(-b(2).*x);             % Objective function
p = [3; 5]*1E-1;                            % Create data
x  = linspace(1, 10);
yx = y(p,x) + 0.1*(rand(size(x))-0.5);
OLS = @(b) sum((y(b,x) - yx).^2);          % Ordinary Least Squares cost function
opts = optimset('MaxFunEvals',50000, 'MaxIter',10000);
B = fminsearch(OLS, rand(2,1), opts)       % Use ‘fminsearch’ to minimise the ‘OLS’ function
figure(1)
plot(x, yx, '*b')
hold on
plot(x, y(B,x), '-r')
hold off
grid

MATLAB: How to plot a function like this in matlab

x = 5 : 250;
y = exp(-a*x + b*x.^2);
plot(x, y)

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MATLAB: Curve fitting without the toolbox

MATLAB: How to plot a function like this in matlab

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