fid = fopen(\'testdata2.dat\'); if fid == -1 disp(\'File open not successful\')

Question

fid = fopen('testdata2.dat');

if fid == -1

disp('File open not successful')

else

   % Creates x and y vectors for the data points

   % Using fscanf

   matData = fscanf(fid,'%f %f ', [2 inf]);

   [fcurve, merror] = fLeastSquare(matData,1);

polycoef= double(coeffs(fcurve));

if polycoef(1)>0

   strlinefunc=[num2str(polycoef(2)),' x + ',num2str(polycoef(1))];

else

   strlinefunc=[num2str(polycoef(2)),' x - ',num2str((-1)*polycoef(1))];

end;

   strError=[' Error : ', num2str(merror)];

width=1;

vX=min(matData(1,:))-width:0.1:max(matData(1,:))+width;

plot(matData(1,:),matData(2,:),'ro',vX,fcurve(vX),'k-' );

title([strlinefunc,strError]);

   % Closing the file

   closeresult = fclose(fid);

   if closeresult == 0

   disp('File close successful')

   else

   disp('File close not successful')

   end

end

How could I modify this MATLAB code so is finds the line given by assuming that the x variable may contain the errors, and minimizing the sums of squares of the horizontal distances.

***Note fLeastSquare is defined by the following:

function [fcurve, merror] = fLeastSquare(data,degree)

%Data: matrix with two row of data(1,:) Xi and data(2,:) Yi list of points

%degree: degree of polynomial,the function we try to approximated.

numPts = length(data(1,:));

if numPts<degree

   error('You need input more data.');

end;

syms x fcurve;

a=sym('a',[1,degree+1]);

% calculate sum of(f(xi)-yi)^2

distance=0;

for i=1:numPts

   distexpr =0;

for j=1:degree+1

   distexpr=a(j)*data(1,i)^(j-1)+distexpr;

end

distance = distance+(distexpr-data(2,i))^2;

end

%take derivative of each ci, find the minimun distance

for k =1:degree+1

lstEqns(k) = diff(distance, a(k)) == 0 ;

end;

soln=solve(lstEqns,a)

csoln=struct2cell(soln);

for i =1:length(csoln)

matSoln(i,:)=double(csoln{i})';

end;

[row,col]=size(matSoln);

%build curve function:c(n)*x^(n-1)+c(n-1)*x^(n-2)+...+c2*x+c1

merror=Inf;

for j=1:col

expr = 0;

for i =1:row

expr=matSoln(i,j)*x^(i-1)+expr;

end

f=symfun(expr,x);

merr = double(sum((f(data(1,:))- data(2,:)).^2)/(((f(1)-f(0))^2+1)*numPts));

if merr < merror

   fcurve=f;

   merror = merr;

end

end;

end

Explanation / Answer

numPts = length(data(1,:));

if numPts<degree

   error('You need input more data.');

end;

syms x fcurve;

a=sym('a',[1,degree+1]);

% calculate sum of(f(xi)-yi)^2

distance=0;

for i=1:numPts

   distexpr =0;

for j=1:degree+1

   distexpr=a(j)*data(1,i)^(j-1)+distexpr;

end

distance = distance+(distexpr-data(2,i))^2;

end

%take derivative of each ci, find the minimun distance

for k =1:degree+1

lstEqns(k) = diff(distance, a(k)) == 0 ;

end;

soln=solve(lstEqns,a)

csoln=struct2cell(soln);

for i =1:length(csoln)

matSoln(i,:)=double(csoln{i})';

end;

[row,col]=size(matSoln);

%build curve function:c(n)*x^(n-1)+c(n-1)*x^(n-2)+...+c2*x+c1

merror=Inf;

for j=1:col

expr = 0;

for i =1:row

expr=matSoln(i,j)*x^(i-1)+expr;

end

f=symfun(expr,x);

merr = double(sum((f(data(1,:))- data(2,:)).^2)/(((f(1)-f(0))^2+1)*numPts));

if merr < merror

   fcurve=f;

   merror = merr;

end

end;

end

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