Can we do polyfit on matrix?

Hi,

I have two matrix, A and B, each of 1000 rows and 100 columns. I need to do 100 polyfit on the columns. I can loop through the columns. But I am just wondering if there is any simple way to plug in A, B without the loop and return the result in an other matrix C.

Thanks,

Jennifer

Answer 1

[Jan]

As far as I understand all columns are processed by polyfit independently. So you can at least omit the expensive checking of the inputs:

A = rand(1000, 100);
B = rand(1000, 100);
n = 3;

V = ones(1000, n + 1);
for k = 1:100
  x = A(:, k);
  y = B(:, k);

    % Vandermonde matrix:
    V(:, n+1) = 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

I fyou need further outputs of polyfit and e.g. a normalization of the input values, explain this explicitly here. Posting your existing code is always a good idea to reduce the need to guess, what you exactly need.

[JFz]

Thank you!

let me try this with my numbers.....

[donald adams]

Great solution! Thanks

[Sarah]

what if these two matrices were not of the same size? ohw would the solution change then?

Answer 2

[Jos (10584)]

A loop is the most obvious choice. You can hide the loop using arrayfun

FitFH = @(k) polyfit(X(:,k), Y(:,k), 1)
P = arrayfun(FitFH, 1:size(X,2), 'un',0)

P{X} will hold the fit for the X-th columns.

[JFz]

This is cool. Thank you! Let me try it too.

[JFz]

What do the 'un' and 0) do in the 2nd line?

[Jos (10584)]

help arrayfun

will give you the answer. The output is non-uniform.

[Jos (10584)]

And by the way, you can write your own (anonymous) polyfit function that skips the input checks as Jan suggested, but this might be over your head right now.

Answer 3

[Namrata Badiger]

A = rand(1000, 100);

B = rand(1000, 100);

n = 3;

V = ones(1000, n + 1);

for k = 1:100

x = A(:, k);

y = B(:, k);

% Vandermonde matrix:

V(:, n+1) = 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(:)));

...

endB = rand(1000, 100);n = 3;V = ones(1000, n + 1);for k = 1:100 x = A(:, k); y = B(:, k); % Vandermonde matrix: V(:, n+1) = 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