MATLAB: Writing the own polyfit function

help meleastsquarespolyfitregression

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.

Best Answer

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)'

Related Solutions

MATLAB: Is left divison faster than polyfit(x, y, 1)

There is some overhead in polyfit due to the error handling. Checking the inputs is a really good idea, but if you are absolutely sure that the inputs are correct, this can save some time:

function p = fPolyFit(x, y, n)
x = x(:);
V = ones(length(x), n + 1);   % Vandermonde matrix
for j = n:-1:1
   V(:, j) = V(:, j + 1) .* x;
end
[Q, R] = qr(V, 0);            % Solve least squares problem
p      = transpose(R \ (transpose(Q) * y(:)));

And if you have to solve this with the same x and different y, storing the Vandermonde matrix can accelerate the code again.

MATLAB: Iterating over a vector to create a cell array without for loop

Most likely this cannot be vectorized. By why do you ask for it? Do you want to accelerate the code? This is possible:

Avoid repeated work. E.g.

date1{i}=datenum(datos.Date(index(i):end));

Convetry many date repeatedly. So move this befor the loop to convert the dates once only:

date1V = datenum(datos.Date);
% and inside the loop:
  date1{i} = date1V(index(i):end);

regress() is a very powerful function. All you want to do is a polynomial fit. Then this is probably faster:

function p = TinyPolyFit(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(:)));
end

Best Answer

Related Solutions

MATLAB: Is left divison faster than polyfit(x, y, 1)

MATLAB: Iterating over a vector to create a cell array without for loop

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