How to interpolate the given plot?

I plot speed vs. width (the first three columns are the velocity components and the last the width, please see first file here https://drive.google.com/drive/folders/1CgeDuCahVZvLXXkNkGWlPg8lSGyurmI3) using the following code

clc
close all
clear all
warning('OFF', 'MATLAB:table:ModifiedAndSavedVarnames')
%step 0
Qi = readmatrix("004timestepN2Void30mm.csv");
[v,w] = size(Qi);

%step 1
fCom_004 = Qi(:,1);
sCom_004 = Qi(:,2); 
tCom_004 = Qi(:,3); 
width_004 = [0;Qi(:,w)+0.0075]; 
U_004 = sqrt(fCom_004.^2 + sCom_004.^2 + tCom_004.^2);
refined_U_004 = [0;U_004];

%step 3
figure
plot(width_004,refined_U_004)
legend('0.004 timestep','Location','bestoutside')
xlabel('width [m] | 30mm profile')
ylabel('U magnitude [m/s]')
axis square;
grid on;

You'll see that the peak is far from being smooth. To fix the issue I am trying to use interpolation. To do so I modified step 3

newX = linspace (0, 0.015,3e3);
newY = interp1(width_0002,refined_U_0002,newX);
figure
plot(newX,newY)
legend('0.004 timestep','Location','bestoutside')
xlabel('width [m] | 30mm profile')
ylabel('U magnitude [m/s]')
axis square;
grid on;

But the following error pops up "Sample points must be unique."

I think I know why this is happening.

By default, Matlab seems to only read the first four decimals of a given number. Notice that in the last column many numbers only differ from the fifth number; that's why Matlab sees them as equal.

Assuming that I am right, how to make Matlab read the full given numbers of a file?

Thanks in advance! :)

Answer 1

[Star Strider]

MATLAB reads what it is given.

%step 0
Qi = readmatrix("JD_PM sampleData30mm.csv");
[v,w] = size(Qi);
%step 1
fCom_004 = Qi(:,1);
sCom_004 = Qi(:,2); 
tCom_004 = Qi(:,3); 
width_004 = [0;Qi(:,w)+0.0075]; 
U_004 = sqrt(fCom_004.^2 + sCom_004.^2 + tCom_004.^2);
refined_U_004 = [0;U_004];
%step 3
figure
plot(width_004,refined_U_004)
legend('0.004 timestep','Location','bestoutside')
xlabel('width [m] | 30mm profile')
ylabel('U magnitude [m/s]')
axis square;
grid on;

% % You'll see that the peak is far from being smooth. To fix the issue I am trying to use interpolation. To do so I modified step 3 
newX = linspace (0, 0.015,3e3);
[width_004,idx] = unique(width_004, 'stable');                          % Eliminate Duplicates 
newY = interp1(width_004,refined_U_004(idx),newX);
figure
plot(newX,newY)
legend('0.004 timestep','Location','bestoutside')
xlabel('width [m] | 30mm profile')
ylabel('U magnitude [m/s]')
axis square;
grid on;

I tried different interpolation methods ('pchip', 'spline') and do not see a difference.

.

[JD_PM]

Thank you Star Strider. As interpolation seems to not help to get a smoother peak, do you know of an alternative method to do so?

[Star Strider]

My pleasure!

One option is to develop a nonlinear model for that and fit the data to it.

Another option is to use the Signal Processing Toolbox sgolayfilt funciton —

%step 0
Qi = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/982200/JD_PM%20sampleData30mm.csv');
[v,w] = size(Qi);
%step 1
fCom_004 = Qi(:,1);
sCom_004 = Qi(:,2); 
tCom_004 = Qi(:,3); 
width_004 = [0;Qi(:,w)+0.0075]; 
U_004 = sqrt(fCom_004.^2 + sCom_004.^2 + tCom_004.^2);
refined_U_004 = [0;U_004];
%step 3
figure
plot(width_004,refined_U_004)
legend('0.004 timestep','Location','bestoutside')
xlabel('width [m] | 30mm profile')
ylabel('U magnitude [m/s]')
axis square;
grid on;

% % You'll see that the peak is far from being smooth. To fix the issue I am trying to use interpolation. To do so I modified step 3 
newX = linspace (0, 0.015,3e3);
[width_004,idx] = unique(width_004, 'stable');                          % Eliminate Duplicates 
newY = sgolayfilt(refined_U_004(idx), 3, 81);                           % Use 'sgolayfilt'
figure
plot(width_004,newY)
legend('0.004 timestep','Location','bestoutside')
xlabel('width [m] | 30mm profile')
ylabel('U magnitude [m/s]')
axis square;
grid on;

Change the ‘framelen’ value to get the desired result.

The smoothdata function has an ‘sgolay’ option, however I do not know if that requires the Signal Processing Toolbox as well.

.