How can I better control bestfit lines

I have a piece of code that generates a best fit line alongside error bars. As well as a best fit for a scatter graph.

I am trying to be able to adjust the best fit line.

The data is in tabular for as follows

Strength_MPa = [       
20  2880
20  3280
20  3990
1200  2000
1200  2990
1200  3500
1300  2200
1300  2700
1300  3280
1400  1390
1400  1770
1400  2150 ];

Grainsize_nm = [
25  90  
1200  120
1300  150
1350  310
1400  450
1500  790 ];
% Nextel 610
figure1 = figure;
% 
y = reshape(Strength_MPa,3,[]);
% 
x = y(1,1:end/2);
%
% 
y_min = y(1,end/2+1:end);
% 
y_mid = y(2,end/2+1:end);
% 
y_max = y(3,end/2+1:end);
% 
%% Fit: 'untitled fit 1'.
[xData, yData] = prepareCurveData( x, y_mid );
% 
% 
% Set up fittype and options.
ft = fittype( 'power2' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [2450.16071129496 -0.0464507882616668 0.160697077002396];
% 
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% 
% Plot fit with data.
% figure( 'Name', 'untitled fit 1' );

h = plot(fitresult, xData, yData);
% h.Color = 'b';
% h.LineStyle = '-';
% h.Marker = 'none';
% legend( h, 'y_mid vs. x', 'untitled fit 1', 'Location', 'NorthEast', 'Interpreter', 'none' );
% Label axes
xlabel( 'x', 'Interpreter', 'none' );
ylabel( 'y_mid', 'Interpreter', 'none' );
grid off
% 
hold on
%% 
yyaxis left
% 
errorbar(x,y_mid,y_mid-y_min,y_max-y_mid,'LineStyle','none')
% 
ylim([0 4500])
% 
ylabel('Strength [MPa]','Color',[ 0 0 0 ])
% 
ax = gca;
% 
ax.YColor = 'k';
% 
% 
yyaxis right
% 
x = (Grainsize_nm(:,1));
y = (Grainsize_nm(:,2));
%% Fit: 'untitled fit 1'.
[xData, yData] = prepareCurveData( x, y );

% Set up fittype and options.
ft = fittype( 'exp1' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [58.0338200304954 0.00142172529592695];
% opts.StartPoint = [25 90];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% 
% Plot fit with data.
h = plot( fitresult, xData, yData );
% legend( h, 'y vs. x', 'untitled fit 1', 'Location', 'NorthEast', 'Interpreter', 'none' );
% Label axes
xlabel( 'x', 'Interpreter', 'none' );
ylabel( 'y', 'Interpreter', 'none' );
% grid off
plot(Grainsize_nm(:,1),Grainsize_nm(:,2),'-ro','MarkerFaceColor','r','LineStyle','none')
% 
ylim([0 900])
% 
ylabel('Grainsize [nm]','Color',[ 0 0 0 ])
% 
xlim([0 1600])
% 
ax = gca;
% 
ax.YColor = 'k';

% 
% 

There are some issues I have with the code.

Firstly I confess I have used the curve fittter app as I am quite a rookie on MatLab, I have also leaned heavily on the community to get the plots lookig as they are so far, which is greatly appreciated.

Despite me commenting out the legend command a legend appears. I want the fit curve and the error bars or the fit curve and the marker plots to both be included as one item in the legend

I would like to get the curves to fit better and remove the markers from withing the error bars. So in the case of the error bars start much closer to y_mid and then run closer to the y_mid on all the other points. In the case of the scatter plot start much closer to [25 500].and the run closer to all the other scatter points. I would also like the best fit curves to extend past the last point if possible. It would be good to change the line style of each curve fit too.

Many thanks

Alex

Answer 1

[Voss]

"I would like to ... remove the markers from within the error bars ... I would also like the best fit curves to extend past the last point if possible. It would be good to change the line style of each curve fit too."

• One way to do all of those things is not to plot the fitobject returned from fit, but instead use its coefficients to calculate your own fit curve and plot that. See x_fit and y_fit in the code below.

"Despite me commenting out the legend command a legend appears."

• Plotting the fitobject creates a legend. Another advantage of creating your own lines is that you can easily control what goes into the legend (to a degree, see the next item).

"I want the fit curve and the error bars or the fit curve and the marker plots to both be included as one item in the legend"

• I'm not sure of a way to do that - at least not if you want the data and fit line to be two different colors.

"I would like to get the curves to fit better"

• Try changing the fit type and/or fit method and/or other fit options.

Strength_MPa = [       
20  2880
20  3280
20  3990
1200  2000
1200  2990
1200  3500
1300  2200
1300  2700
1300  3280
1400  1390
1400  1770
1400  2150 ];

Grainsize_nm = [
25  90  
1200  120
1300  150
1350  310
1400  450
1500  790 ];

figure1 = figure;


y = reshape(Strength_MPa,3,[]);
x = y(1,1:end/2);
y_min = y(1,end/2+1:end);
y_mid = y(2,end/2+1:end);
y_max = y(3,end/2+1:end);

% Fit: 'untitled fit 1'.
[xData, yData] = prepareCurveData( x, y_mid );

% Set up fittype and options.
ft = fittype( 'power2' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [2450.16071129496 -0.0464507882616668 0.160697077002396];

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% plot fit:
x_fit = linspace(1,1600,100);
y_fit = fitresult(x_fit);
plot(x_fit,y_fit,'--r','DisplayName','Strength Fit')

% Label axes
xlabel( 'x', 'Interpreter', 'none' );
ylabel( 'y_mid', 'Interpreter', 'none' );
grid off
hold on

% plot errorbar:
yyaxis left
errorbar(x,y_mid,y_mid-y_min,y_max-y_mid, ...
    'LineStyle','none', ...
    'DisplayName','Strength')
ylim([0 4500])
ylabel('Strength [MPa]','Color',[ 0 0 0 ])
ax = gca;
ax.YColor = 'k';


% Fit: 'untitled fit 1'.
x = (Grainsize_nm(:,1));
y = (Grainsize_nm(:,2));
[xData, yData] = prepareCurveData( x, y );

% Set up fittype and options.
ft = fittype( 'exp1' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [58.0338200304954 0.00142172529592695];
% opts.StartPoint = [25 90];

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% plot fit:
yyaxis right
x_fit = linspace(1,1600,100);
y_fit = fitresult(x_fit);
plot(x_fit,y_fit,':b','DisplayName','Grain Size Fit')

% Label axes
xlabel( 'x', 'Interpreter', 'none' );
ylabel( 'y', 'Interpreter', 'none' );

plot(Grainsize_nm(:,1),Grainsize_nm(:,2),'-ro', ...
    'MarkerFaceColor','r', ...
    'LineStyle','none', ...
    'DisplayName','Grain Size')
ylim([0 900])
ylabel('Grainsize [nm]','Color',[ 0 0 0 ])
xlim([0 1600])
ax = gca;
ax.YColor = 'k';

legend

[A Poyser]

That is brilliant. Thanks so much

In response to

• I'm not sure of a way to do that - at least not if you want the data and fit line to be two different colors.

They can indeed be the same colour.

One thing that is not clear to me is what the line say opts.Startpoint actually does

opts.StartPoint = [58.0338200304954 0.00142172529592695];

[Voss]

You're welcome!

Since they can be the same color, what you can do is to create some additional lines (actually one errorbar and one line) which don't show up on the plot but are shown in the legend. See the last few lines of code below.

I'm not familiar enough with fit to say what StartPoint really does, but maybe this helps:

https://www.mathworks.com/matlabcentral/answers/476729-what-exactly-is-a-startpoint-for-a-curve-fitting-tool-its-significance-and-how-it-works

Strength_MPa = [       
20  2880
20  3280
20  3990
1200  2000
1200  2990
1200  3500
1300  2200
1300  2700
1300  3280
1400  1390
1400  1770
1400  2150 ];

Grainsize_nm = [
25  90  
1200  120
1300  150
1350  310
1400  450
1500  790 ];

figure1 = figure;


y = reshape(Strength_MPa,3,[]);
x = y(1,1:end/2);
y_min = y(1,end/2+1:end);
y_mid = y(2,end/2+1:end);
y_max = y(3,end/2+1:end);

% Fit: 'untitled fit 1'.
[xData, yData] = prepareCurveData( x, y_mid );

% Set up fittype and options.
ft = fittype( 'power2' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [2450.16071129496 -0.0464507882616668 0.160697077002396];

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% plot fit:
x_fit = linspace(1,1600,100);
y_fit = fitresult(x_fit);
plot(x_fit,y_fit,'--r')

% Label axes
xlabel( 'x', 'Interpreter', 'none' );
ylabel( 'y_mid', 'Interpreter', 'none' );
grid off
hold on

% plot errorbar:
yyaxis left
errorbar(x,y_mid,y_mid-y_min,y_max-y_mid, ...
    'LineStyle','none', ...
    'Color','r')
ylim([0 4500])
ylabel('Strength [MPa]','Color',[ 0 0 0 ])
ax = gca;
ax.YColor = 'k';


% Fit: 'untitled fit 1'.
x = (Grainsize_nm(:,1));
y = (Grainsize_nm(:,2));
[xData, yData] = prepareCurveData( x, y );

% Set up fittype and options.
ft = fittype( 'exp1' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [58.0338200304954 0.00142172529592695];
% opts.StartPoint = [25 90];

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% plot fit:
yyaxis right
x_fit = linspace(1,1600,100);
y_fit = fitresult(x_fit);
plot(x_fit,y_fit,':b')

% Label axes
xlabel( 'x', 'Interpreter', 'none' );
ylabel( 'y', 'Interpreter', 'none' );

plot(Grainsize_nm(:,1),Grainsize_nm(:,2),'bo', ...
    'MarkerFaceColor','b')
ylim([0 900])
ylabel('Grainsize [nm]','Color',[ 0 0 0 ])
xlim([0 1600])
ax = gca;
ax.YColor = 'k';

% "dummy" lines for the legend:
h_eb = errorbar(-100,-1,1, ...
    'Color','r', ...
    'LineStyle','--', ...
    'DisplayName','Strength');
h_sc = plot(NaN,NaN,':bo', ...
    'MarkerFaceColor','b', ...
    'DisplayName','Grain Size');
legend([h_eb h_sc])

[A Poyser]

amazing, thanks. Still need to figure out how to control the curve without using the curve fitting tool