Function Name: uniqueBestFit % Inputs (2): - (double) x-data % - (double) y-data

Question

Function Name: uniqueBestFit

% Inputs (2): - (double) x-data

% - (double) y-data

% Outputs (0): - None

% Output Plots (1): Plot of the different subplots leading to a unique fit

%

% Function Description:

% Write a function called "uniqueBestFit" that takes in x and y data and

% creates a plot of all of the polynomial fits until the average absolute

% difference between the input data and the fit is less than 0.75.

% Each unique fit will be its own subplot, with two subplots per row. If

% you do not already know curve fitting, you can get more information in

% this article:

% http://en.wikipedia.org/wiki/Curve_fitting

%

% Specifics:

% - For each fit, you should calculate the average absolute difference

% (AAD) between the y-values obtained from evaluating the fitted curve

% at the original x-values and the original y values.

% - Plot all the original points in each subplot with red "x"s.

% - If the average absolute difference (mean absolute difference)

% is less than 0.75, plot it in blue, otherwise, plot it in black.

% - Use 100 linearly spaced points between the smallest and largest x

% value for new x values when you are plotting the polynomial fit

% curves.

% - The title of the fitted plots should read '__ Order Fit', where the

% blank is the ordinal number of the fit. Example, a first order fit

% should read '1st Order Fit', while second order fit will read '2nd

% Order Fit' and so on.

% - x-values are not guaranteed to be in any particular order, but the

% 1st x-value will correspond to the 1st y-value and so on.

% - There is not guaranteed to be a fit with average absolute difference

% strictly less than 0.75.

% - You should continue plotting until you have reached the last *UNIQUE*

% polynomial, even after you have found the first polynomial with AAD

% less than 0.75.

%

% Constraints:

% - You may assume that you are to begin with a 1st order fit, i.e. that

% the input vector is a length of at least 2. Note that even though

% only one plot will exist when the input vector is of length 2, you

% must still adhere to the rule that there are to be enough space for

% two subplots per row.

% - You may assume that the input vectors are the same size.

%

% Test Cases:

% uniqueBestFit(1:5,[5 1 15 9 8])

% => should look like UBF_Solution1.png

%

% uniqueBestFit([1 6 2 4 9 8 5 3], [0.5 0.9 1.5 2.0 0.1 0.1 1.3 0.2])

% => should look like UBF_Solution2.png

%

% uniqueBestFit([0.2 0.5 1.2 1.6 2.6 9.6],[1 3 1 6 7 0.1])

% => should look like UBF_Solution3.png

Explanation / Answer

function uniqueBestFit(x,y)

len=length(y);

label={'1st','2nd','3rd'};

r=floor(len/2);

found=false;

for k=1:(len-1)

subplot(r,2,k), plot(y,'rx');

hold on;

if k<4

title(strcat(label{k},' Order Fit'));

else

title(strcat(num2str(k),'th Order Fit'));

end

p=polyfit(x,y,k);

ynew=polyval(p,x);

AAD=sum(abs(ynew-y))/len;

xplot=min(x):((max(x)-min(x))/100):max(x);

yplot=polyval(p,xplot);

if AAD<0.75 && found==false

plot(xplot,yplot,'b');

found=true;

else

plot(xplot,yplot,'k');

end

end

end

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