How to choose a value from the plot?

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Priya 2014-5-23

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编辑： Priya 2014-8-6

采纳的回答： Star Strider

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plot(contact_geometry.y-d,contact_geometry.r_L)

Could someone please tell me, is it possible to do coding in such a way that one random value of Y is chosen for each iteration automatically.

For eg, when I run the program for the first time, R should be 0.4494, next time 0.4657. And this should rely on the above plot command. Please help.

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Star Strider 2014-5-23

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Not certain what you want, so here are two possibilities:

For any y on the domain (-0.03, 0.01):

f = @(x)  1./(1-75*x);          % Substitute your function
x = 0.04*rand-0.03;             % Define domain
y = f(x);                       % Calculate ‘y’

For your particular three values:

v = [0.4494  0.4542  0.4657];
y = v(randi(3));                % Randomly choose one

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Star Strider 2014-5-24

编辑：Star Strider 2014-5-24

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contact_geom_poly.mat

This polynomial approximation gives a good fit to your data:

load('wheel_rail_AW.mat')
S = contact_geometry
d = 0.01;
x = linspace(min(S.y-d), max(S.y-d),size(S.y-d,2));
[p,ps,smu] = polyfit(S.y-d, S.r_L, 8);      % Fit polynomial
v = polyval(p, x, ps, smu);                 % Calculate values of fit for a given s
figure(1)
plot(S.y-d, S.r_L, '.-')
hold on
plot(x, v, '-r', 'LineWidth', 1.5)
hold off
grid

I kept the plot block in so you can see the effectiveness of the fit.

I saved the [p,ps,smu] information in ‘contact_geom_poly.mat’ that I’ve attached here. All you need to do is load it, then provide an x value for this line:

y = polyval(p, x, ps, smu);

and get the y value. If you give it any value of x in the interval (-0.03,0.01), it should give you reasonably accurate values for y.

There are other approaches for this of course, one being interpolation, but that is significantly more complicated.

EDIT —

This is the easiest way to use the polynomial I fit to your data:

load('contact_geom_poly.mat')  
f = @(x) polyval(p, x, ps, smu);
y1 = f(-0.018)                      % Scalar argument
y2 = f([-0.0021  0.0067])           % Vector argument

yields:

y1 =
     449.4902e-003
y2 =
     454.3047e-003   465.7238e-003

These compare almost exactly to the data on the plot in your Question.

Star Strider 2014-5-25

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My pleasure!

I actually demonstrated that in my comment headed: ‘Star Strider on 24 May 2014 at 13:02’ about 7-8 comments above this one.

Here is some revised code to make it as easy as possible for you to calculate your regression coefficients and structures for various dependent variables. The routine does its best to fit your data, then creates ‘.mat’ files for the polynomial fit output so you can easily use them in your application:

datamatfile = 'wheel_rail_AW.mat';
dirmats = which(datamatfile);           % Find directory for input data file
dirsep = strfind(dirmats, '\');         % Get path to ‘datamatfile’
pathname = dirmats(1:max(dirsep));      % Create path (‘fileparts’ returns an empty string for some reason)
load(datamatfile)                       % Load data
S = contact_geometry;                   % Create data structure
d = 0.01;                               % Define ‘d’
SNames = fieldnames(S)                  % Variable names in ‘datamatfile’
% ———————— Prompt for dependent variable for polynomial regression ————————
vblnr = listdlg('PromptString', {'Select a dependent variable' 'for polynomial regression:'}, 'ListString', SNames, 'SelectionMode','single')
vbl = char(SNames(vblnr));              % Variable to be regressed
x = linspace(min(S.y-d), max(S.y-d),size(S.y-d,2));
[p,ps,smu] = polyfit(S.y-d, eval(['S.' vbl]), 51);      % Fit polynomial
v = polyval(p, x, ps, smu);              % Calculate values of fit for a given s
figure(1)
plot(S.y-d, eval(['S.' vbl]), '.-')
hold on
plot(x, v, '-r', 'LineWidth', 1.5)
hold off
xlabel('y-d')
ylabel('Amplitude')
title(sprintf('Plot of ‘%s’ as a function of [y-d]', vbl))
grid
% ———————————————— Save regression information and notify ————————————————
save([pathname 'contact_geom_poly_' vbl '.mat'], 'p', 'ps', 'smu')
h1 = msgbox({'Polynomial regression structures saved as' ['contact_geom_poly_' vbl '.mat']});

Your data have some significant discontinuities, so to be as robust as possible with this, I am using an excessively high-degree polynomial. It fits most of your data reasonably well, but ‘rings’ at the discontinuities. There is no way to avoid that, because ‘ringing’ will occur at the ends if it fits the discontinuities without ringing. This way, it ‘rings’ a bit at the discontinuities and at the ends, but minimally at both. This is about the best you can expect from it.

The routine searches for the directory ‘wheel_rail_AW.mat’ is in and stores the ‘.mat’ files it creates in the same directory.

-------------------------------------------------------------------------------------------------------------------------------------

NOTE — I will hear quite justifiable screams in my direction at my using a 51-degree polynomial. The purpose here is to provide a reasonable approximation of data with some saturation discontinuities over a narrow domain to make the interpolation as easy as possible in the intended application. Reading the entire thread provides the necessary context.

Star Strider 2014-5-25

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Not a problem. I just wanted to be sure you know that I’m not leaving you stranded.

You don’t need to assign the values for the regression coefficients. The polyfit function does that for you. All you have to do is choose the variable you want polyfit to provide the polynomial fit for. The code I posted in my previous comment will do everything for you.

Run the entire code in my previous comment. (You may want to make a separate script file for it.) You will see that it offers you a menu of variables to regress against (y-d), does the regression, plots it, stores the estimated parameters and structures in a ‘.mat’ file that incorporates the name of the variable at the end of the ‘.mat’ file name, and tells you what it did.

All you have to do then is run these lines in your code:

load('contact_geom_poly_r_L.mat')  
f = @(x) polyval(p, x, ps, smu);
x = 0.04*rand-0.03;             % Define domain
y = f(x);

to use the fit for ‘r_L’. Substitute the ‘.mat’ file name of your choice in the load statement for the other variables.

It will do its best to produce the y values you want for the ‘.mat’ file you choose.

Priya 2014-6-6

Perfect! Thanks once again.

Star Strider 2014-6-6

Again, my pleasure!

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