Calculating and printing uncertainties of fits after the "normal" display of fit-parameters

Hello,

I am storing multiple fits in a cell array "fits". Currently I am just using celldisp to obtain f.e. the following:

>> celldisp(fit)
 
fit{1} =
 
     Linear model Poly1:
     y(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =     0.00226  (0.002015, 0.002506)
       p2 =    0.004049  (0.003472, 0.004627)
 
 
fit{2} =
 
     Linear model Poly1:
     y(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =    0.004422  (0.004302, 0.004542)
       p2 =    0.003982  (0.0037, 0.004264)
       
       

Now I am trying to print the following instead to the command window:

Fit{1} = % What I would like to print instead
 
     Linear model Poly1:
     y(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =     0.00226  (0.002015, 0.002506) +- 0.000246 % (values obtained by calculating upper bound - value outside brackets)
       p2 =    0.004049  (0.003472, 0.004627) +- 0.000578 % (i.e 0.004627-0.004049=0.000578 and so on)
       
       
Fit{2} =
 
     Linear model Poly1:
     y(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =    0.004422  (0.004302, 0.004542) +- 0.00012
       p2 =    0.003982  (0.0037, 0.004264)   +- 0.000282  
       

My first idea was to then extract the values from the different fits:

for j=1:1:numel(fit)
    % Extract All Data:
    Coeffvalues{j}=coeffvalues(fit{j});      % get the p1 and p2 values
    Confintvalues{j}=confint(fit{j});        % get the corresponding confidence bounds
end
for j=1:1:numel(Coeffvalues)
    Confintcalcvals=Confintvalues{j}(2,:)';
    for k=1:1:length(Coeffvalues{1,1})
        Difference(j,k)= Confintcalcvals(k)-Coeffvalues{1,j}(k); % Row j contains the diffs for fit j, position k is for the respective value
    end
end
Difference % contains the differences to be inserted into the displayed fit messages, one row per fit

Now I should have all data I need in nice sorted columns, one per parameter.

My problem now is that I have no clue whatsoever how to emulate the message given when fits are displayed, and then add these values at the correct positions. For instance, I couldn't figure out how to access the string of the cfit-object containing the fit equation, since I assume I would have to rebuild the entire message string by string, which I only now realise could become a pain in the ass if we have a differing number of Coefficients. No clue how to do that automatically aside from coding it for the first X possibilities and just hope you won't encounter a fit with more than X parameters. I assume this is not the best way.

This gets worse since I have to make the entire process loopable so it repeats for whatever number of fits I end up having.

Thank you & stay save.

C.A.

Answer 1

[Uday Pradhan]

Hi Claudius,

I would suggest to create a custom display function for this task. I have created a function that I describe below. You may refer and use this or create your own if this gives you a better and/or efficient idea.

function celldispForFits(someCell) %someCell is the cell of fits

s = inputname(1);

for i = 1:numel(someCell)
    modelDetails=evalc('disp(someCell{i})'); %get the display message as a char array
    strMessage = editMessage(modelDetails,someCell{i}); %get the updated message
    fprintf('\n');
    disp([s subs(i,size(someCell)) ' =']) %taken this from the original celldisp function
    fprintf('\n');
    disp(strMessage);
end

function s = subs(i,siz)
%SUBS Display subscripts
if length(siz)==2 && any(any(siz==1))
  v = cell(1,1);
else
  v = cell(size(siz));
end
[v{1:end}] = ind2sub(siz,i);
s = ['{' int2str(v{1})];
for i=2:length(v)
  s = [s ',' int2str(v{i})];
end
s = [s '}'];
end
end

In a separate file, I created the function "editMessage" which edits the original message and applies the changes that you have mentioned in your question.

function s = editMessage(modelDetails,f) %f = fit Object, modelDetails the original displayed message

displayStr = split(modelDetails,newline); %split the message with respect to newline delimiter
displayStr = displayStr(~cellfun('isempty',displayStr)); %remove the empty arrays that may occur
var = 4; %line number in the message from which editing is required

for i = 1 : numel(displayStr) %loop through each line in the message
    k = 1;
    while displayStr{i}(k) == ' '
        k = k + 1; %for each line search for the first word
    end
    str = "";
    while displayStr{i}(k) ~= ' '
        str = str + displayStr{i}(k);
        k = k + 1;  %get the first word in the line
    end
    if str == "Coefficients"
        var = i + 1; %if the word is Coefficients store the next line number
        break; %this is the line number from which we need to start editing the message
    end
end

coeffVals = coeffvalues(f);
confidenceInt = confint(f);
toAdd = [""]; %new edits to be inserted

for i = 1:numel(coeffVals)
    toAdd(i) = num2str(confidenceInt(2,i) - coeffVals(i));
    %upper bound  - value
end

idx = 1;

for i = var : numel(displayStr) %from the line number in var till the end
    displayStr{i} = displayStr{i} + "  +-  " +  toAdd(idx); %make the required edits
    idx = idx + 1;
end

finalStr = "";

for i = 1:numel(displayStr)
    finalStr = finalStr + displayStr(i) + newline; %create the new message to display
end

s = finalStr;

end

These functions make the assumption that the lines that need editing occur after the line "Coefficients (with ...) :" and are not context - aware. I have tested these on some fits that I created and seems to work well on those examples. Hope this will help you.

[Claudius Simon Appel]

Thank you.

That works perfectly.

As far as I am aware, I wouldn't need it to be context aware - as long as TMW doesn't change the way fits are displayed, that is.

I'll incorporate this into my code now. I assume a link to your answer under credits is sufficient?

C.A.

Okay, I have found one question:

Would it be possible to set the format of the added values? I tend to get either big values or very small values, which is why I usually output in scientific notation. This is already done for the default fit displayed by your solution, but not for the added values.

An example:

Fit {1} =

     Linear model Poly1:
     y(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =   1.591e+11  (1.569e+11, 1.613e+11)  +-  2191097475.9686 % <- this would be more fitting as 2.2e9 or 2.19e9
       p2 =   2.393e+04  (1.614e+04, 3.172e+04)  +-  7789.0385
       

[Uday Pradhan]

You can use "precision" argument of the "num2str" function to display numbers in the exponential function. For example you may use :

toAdd(i) = num2str(confidenceInt(2,i) - coeffVals(i),'%10.2e');
%this stores each value in exponential format with two decimal places

A caveat to this approach is that every number will be displayed in the exponential format. You may use an "if" statement to deal with only larger numbers to be displayed in this form.

if confidenceInt(2,i) - coeffVals(i) > 1e5
    toAdd(i) = num2str(confidenceInt(2,i) - coeffVals(i),'%10.2e');
else
    toAdd(i) = num2str(confidenceInt(2,i) - coeffVals(i));
end

This is extra work but that's all I can think of right now. You are free to make changes and include my code in yours but do accept my answer so that other community members may benefit from it when they come across similar doubts.

[Claudius Simon Appel]

Thank you.