how can write this in matlab ?

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.

Answer 1

[Star Strider]

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)

[Kadri Qevani]

M is one file?? and con you wite in matlab??

[Star Strider]

I do not understand ‘M is one file’.

If you want to save the function as a file, you will save it with the filename P.m.

If you are reading ‘M’ in as a matrix, use one of the file reading functions, such as textscan. I cannot write code to read it into your MATLAB workspace without knowing what it is, and the format it is written in.

[Kadri Qevani]

You can use the method of least squares?

[Image Analyst]

Do you have the 2D data P, and need to find coefficients A and M? And what does "tabular shape" mean? You mean rectangular, like a 2D matrix?

[Kadri Qevani]

Yes tabular shape is rectangula like a 2D matrix. M is one function

Ln P(x)= ln Ae^Mx
ln P(x)=ln A+ ln e^Mx

A is coefficients

[Star Strider]

I do not understand ‘M is one function’. Can you give a small example of what ‘M’ is?

[Kadri Qevani]

% clear
clear all
close all
clc
% Simple example
x = [  0.0 2.0 2.7 3.0 4.0] ;  
y = [1.5 2.5 3.5 5.0 7.5] ;  
Y = log(y);
X = x ;

s_X = sum(X);
s_Y = sum(Y);

s_X_2 = sum(X.^2);
s_XY = sum(X.*Y);

N = length(X) ;
B = (s_XY-(s_X_2*(s_Y/s_X)))/(s_X-(s_X_2*N/s_X)) ;
A = (s_Y - N*B)/s_X;
C = exp(B);

xx = zeros(1,100) ;
yy = zeros(1,100) ;
jj=1;
span = (max(X)-min(X))/100;
for x_i = 0:span:max(X)
xx(jj) = x_i;
yy(jj) = C*exp(A*x_i);
jj=jj+1;
end

hold on
plot(x,y,'kh')
plot(xx,yy)
legend('exemple', 'graph ') 
hold off

something like this??

[Star Strider]

Actually, I believe this is what you want to do:

x = [  0.0 2.0 2.7 3.0 4.0];  
y = [1.5 2.5 3.5 5.0 7.5]; 

P = @(b,x) b(1).*exp(b(2).*x);              % Regression Model

SSECF = @(b) sum((y - P(b,x)).^2);          % Sum-Squared-Error Cost Function

B0 = rand(2,1);                             % Initial Paremeter Estimates
[B, SSE] = fminsearch(SSECF, B0);           % Estimate Parameter Vector ‘B’

xplt = linspace(min(x), max(x));            % Vector Of ‘x’ To plot
figure(1)
plot(x, y, 'bp')                            % Plot Data (Blue Stars)
hold on
plot(xplt, P(B,xplt), '-r')                 % Plot Function Fit (Red Line)
grid
text(0.6, 6.5, sprintf('P(x) = %.4f\\cdote^{%.4f\\cdotx}', B))

It uses the fminsearch function and the sum-squared-error cost function, ‘SSECF’ with your ‘P’ function (where ‘A’ = ‘b(1)’ and ‘M’ = ‘b(2)’) to perform a nonlinear regression, and produces this plot:

Note that with the text call, the plot displays the function and the values of the estimated parameters as well.