lmcurvefit

版本 2.0.0 (4.3 KB) 作者: Lateef Adewale Kareem
curve fitting using Levenberg Marquardt algorithm
2.0
(1)
11.0 次下载
更新时间 2024/9/17

查看许可证

% the following examples are available here
% https://www.mathworks.com/help/optim/ug/lsqcurvefit.html
% you can compare to the result from lmcurvefit to that of inbuilt matlab
% function lsqcurvefit
%% Example 1 (Unconstrained Curve Fitting)
close all
xdata = [0.9 1.5 13.8 19.8 24.1 28.2 35.2 60.3 74.6 81.3]';
ydata = [455.2 428.6 124.1 67.3 43.2 28.1 13.1 -0.4 -1.3 -1.5]';
x0 = [100;-1];
times = linspace(xdata(1),xdata(end))';
scatter(xdata, ydata, 'o'); hold on;
plt = plot(times, myfun1(x0, times), 'r');
model = @(x,xdata) myfun1(x, xdata, times, plt);
[x_lm, ~, ~, ~, output] = lmcurvefit(model, x0, xdata, ydata,[],[],[],[])
%% Example 2 (Box Constrained Curve Fitting)
close all
xdata = linspace(0, 3)';
ydata = exp(-1.3*xdata)+0.05*rand(size(xdata));
lb = [0;-2];
ub = [3/4; -1];
x0 = [1/2;-2];
scatter(xdata, ydata, 'o'); hold on;
plt = plot(xdata, myfun2(x0, xdata), 'r');
model = @(x,xdata) myfun2(x, xdata, xdata, plt);
[x_lm, ~, resnorm_lm, residual_lm, output] = ...
lmcurvefit(model, x0, xdata, ydata, [], [], lb, ub);
%% Example 3 (Linear InEquality Constraint)
close all; clc
rng default
xdata = linspace(2,7)';
ydata = myfun3([2,4,5,0.5]',xdata) + 0.1*randn(size(xdata));
lb = zeros(4,1);
ub = 7*ones(4,1);
A = [-1 -1 1 1];
b = 0;
startpt = [1 2 3 1]';
options = optimoptions(@lsqcurvefit, Display='iter');
scatter(xdata, ydata, 'o'); hold on;
plt = plot(xdata, myfun3(startpt,xdata), 'r');
fineq = @(x)A*x - b;
fun = @(x, xdat) myfun3(x,xdat, plt);
[x_lm, ~, resnorm_lm, residual_lm, output_lm] = ...
lmcurvefit(fun, startpt, xdata, ydata, fineq, [], lb, ub);
%% Example 4 (Nonlinear InEquality Constraint)
close all; clc
rng default
xdata = linspace(2,7)';
ydata = myfun3([2,4,5,0.5]',xdata) + 0.1*randn(size(xdata));
lb = zeros(4,1);
ub = 7*ones(4,1);
startpt = [1 2 3 1]';
options = optimoptions(@lsqcurvefit, Display='iter');
scatter(xdata, ydata, 'o'); hold on;
plt = plot(xdata, myfun3(startpt,xdata), 'r');
fineq = @(x)x(1)^2 + x(2)^2 - 4^2;
fun = @(x, xdat) myfun3(x,xdat, plt);
[x_lm, ~, resnorm_lm, residual_lm, output_lm] = ...
lmcurvefit(fun, startpt, xdata, ydata, fineq, [], lb, ub);
%% model functions
function F = myfun1(x,xdata, times, plt)
F = x(1)*exp(x(2)*xdata);
if(nargin > 2)
plt.YData = x(1)*exp(x(2)*times);
drawnow; pause(0.01);
end
end
function F = myfun2(x,xdata, times, plt)
F = x(1)*exp(x(2)*xdata);
if(nargin >2)
plt.YData = x(1)*exp(x(2)*times);
drawnow; pause(0.01);
end
end
function F = myfun3(x,xdata, plt)
a = x(1); b = x(2); t0 = x(3); c = x(4);
F = a + b*atan(xdata - t0) + c*xdata;
if(nargin>2)
plt.YData = F;
drawnow; pause(0.01);
end
end

引用格式

Lateef Adewale Kareem (2024). lmcurvefit (https://www.mathworks.com/matlabcentral/fileexchange/172344-lmcurvefit), MATLAB Central File Exchange. 检索时间: .

MATLAB 版本兼容性
创建方式 R2024a
兼容任何版本
平台兼容性
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

版本 已发布 发行说明
2.0.0

Algorithm is improved with back tracking. function handle for the updating the figure has been removed. But the example still shows how to achieve that by updating the plot inside the objective function.

1.0.25

corrected second example
1.0.2

Added functionality for bound and constraints. added jacobian file too.
1.0.1

improved stopping criteria
1.0.0