Effacer les filtres
Effacer les filtres

How to fit a curve using "power" fitting or "custom fitting"?

6 vues (au cours des 30 derniers jours)
ishita agrawal
ishita agrawal le 16 Sep 2017
Commenté : ishita agrawal le 22 Sep 2017
I have data which I need to fit using following equation:
y= f(x)= a*x^b+c.
r.MarkerEdgeColor = 'r';
r.MarkerFaceColor = [0.9 0.9 0.9];
hold on
% Power fit - %y=f(x)=a*x^b+c
x = data(:);
y = a*x^b+c;
%f = fit(x,y);
p = plot(x,y)
p(1).LineWidth = 2;
c = p.Color;
p.Color = 'r';
It shows: Error using ^ One argument must be a square matrix and the other must be a scalar. Use POWER (.^) for elementwise power.
But if I use(.^), it shows multiple fit lines as shown in attached figure. I want just one fit line for same equation.

Réponse acceptée

Image Analyst
Image Analyst le 16 Sep 2017
I attach a demo to do an exponential fit. Adapt as needed.
  3 commentaires
Image Analyst
Image Analyst le 16 Sep 2017
Modifié(e) : Image Analyst le 16 Sep 2017
Below is the full demo:
% Uses fitnlm() to fit a non-linear model (a power law curve) through noisy data.
% Requires the Statistics and Machine Learning Toolbox, which is where fitnlm() is contained.
% Initialization steps.
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
% Create the X coordinates: 30 points from 0.01 to 20, inclusive.
X = linspace(0.01, 20, 30);
% Define function that the X values obey.
a = 10 % Arbitrary sample values I picked.
b = 0.4
c = 2
Y = a * X .^ b + c; % Get a vector. No noise in this Y yet.
% Add noise to Y.
Y = Y + 0.8 * randn(1, length(Y));
% Now we have noisy training data that we can send to fitnlm().
% Plot the noisy initial data.
plot(X, Y, 'b*', 'LineWidth', 2, 'MarkerSize', 15);
grid on;
% Convert X and Y into a table, which is the form fitnlm() likes the input data to be in.
tbl = table(X', Y');
% Define the model as Y = a * (x .^ b) + c
% Note how this "x" of modelfun is related to big X and big Y.
% x((:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table.
modelfun = @(b,x) b(1) * x(:, 1) .^ + b(2) + b(3);
beta0 = [10, .4, 2]; % Guess values to start with. Just make your best guess.
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, modelfun, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!
% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
% Create smoothed/regressed data using the model:
yFitted = coefficients(1) * X .^ coefficients(2) + coefficients(3);
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(X, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('Power Law Regression with fitnlm()', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legendHandle = legend('Noisy Y', 'Fitted Y', 'Location', 'north');
legendHandle.FontSize = 25;
message = sprintf('Coefficients for Y = a * X ^ b + c:\n a = %8.5f\n b = %8.5f\n c = %8.5f',...
coefficients(1), coefficients(2), coefficients(3));
text(8, 15, message, 'FontSize', 23, 'Color', 'r', 'FontWeight', 'bold', 'Interpreter', 'none');
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')
If you need more help, attach npp7 and lk_2k1.
ishita agrawal
ishita agrawal le 22 Sep 2017
This is good enough. Thank you so much.

Connectez-vous pour commenter.

Plus de réponses (0)


En savoir plus sur Linear and Nonlinear Regression dans Help Center et File Exchange

Community Treasure Hunt

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

Start Hunting!

Translated by