Writing my own polyfit function

How would one write their own polyfit function using only mldivide and for loops?

I have a basic idea:

function [A,e] = MyPolyRegressor(x, y, n)

c=ones(n,1);

    for i=1:n;

    c(:,i)=x.^(i-1);

    end

A=c\y

e=c*A-y

But it doesnt quite work.

[Jan]

Please explain what "doesn't quite work" mean explicitly. Do you get an error message or do the results differ from your expectations? This forum is fine for solving problem, but bad for guessing them.

Notes: The POWER operation is very expensive. Better multiply x cummulatively.

[SB]

Well, there's a dimension mismatch in line 4. Even when I switch c to c=ones(size(X)) to fix that issue, there are too many coefficients, none of which are correct.

[Jan]

Because you didn't format your code properly (please learn how to do this...), it is not possible to find out, which one is the "line 4".

But with some guessing: "ones(n,1)" and even "ones(size(x))" create vectors, while the required Vandermonde-matrix needs the dimensions [length(x), n+1].

Answer 1

[Jan]

function p = fPolyFit(x, y, n)

% Construct Vandermonde matrix:
x = x(:);
V = ones(length(x), n + 1);
for j = n:-1:1
   V(:, j) = V(:, j + 1) .* x;
end

% Solve least squares problem:
[Q, R] = qr(V, 0);
p      = transpose(R \ (transpose(Q) * y(:)));

% Equivalent: (V \ y)'

[SB]

For a weighted Least Squares problem, would you do function [A, e] = WeightedLeastSquares(X, Y, w,n)

X=diag(w)*X

Y=diag(w)*Y

X = X(:);

V = ones(length(X), n + 1);

for j = n:-1:1

   V(:, j) = V(:, j + 1) .* X;

end

[Q, R] = qr(V, 0);

A= (R \ (transpose(Q) * Y(:)));

e= V*A-Y;

?

Answer 2

[Vrushabh Bhangod]

function [p,mu,f] = plofit(x,y,n)
%  x = input samples
%  y  = output function,n = order
m = length(x); %number of rows in the Vandermonde Matrix
V = zeros(m,n);
a = n;
for i = 1:m
    v = zeros(1,n);
    for j = a:-1:1
      v(n+1-j) =  realpow(x(i),j);
    end
    V(i,:) = v;
end
V(:,n+1)=ones(m,1);% adding 1 column to ones to the vandermonde matrix
%%QR method to compute the least squares solution for the coefficients,'p'
[Q,R] = qr(V,0);
p = transpose(R \ (transpose(Q) * y'));
f = polyval(p,x);
%%to find mean
mean = sum(x)/length(x);
sq = 0;
for i =1:length(x)
    sq = sq + (x(i)-mean)^2;
end
sd = (sq/length(x))^0.5;
mu = [mean;sd];
end

[Max]

Works perfect, Thanks!