Michael
Posts:
4
Registered:
3/26/12
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Speeding up calculation of matrix
Posted:
Mar 26, 2012 3:09 PM
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Hi,
I am calculating a matrix M from two column vectors and two coefficients, calculated like so:
%%%%%%%%%%%%%
x=rand(10,1);
y=rand(10,1);
fit_x = 2;
fit_y = 3;
% initialize M
nRows = length(x);
nCols = (fit_x+1)*(fit_y+1);
M=ones(nRows,nCols);
% build each column of M
iCol = 1;
for px=0:fit_x
for py=0:fit_y
M(:,iCol)=x.^px .* y.^py;
iCol=iCol+1;
end
end
%%%%%%%%%%%%%
where x and y are normally input vectors, and fit_x and fit_y are input scalars. This function is called many times by my code, and after profiling, a significant portion of time is spent generating this M matrix.
Is there a better way to do this? I feel like I am overlooking a one-line vectorized solution to this, replacing the loop. I have tried:
%%%%%%%%%%%%
x_power = kron(0:fit_x,ones(nRows,fit_y+1));
y_power = repmat(0:fit_y,nRows,fit_x+1);
x2 = repmat(x,1,nCols);
y2 = repmat(y,1,nCols);
M2 = x2.^x_power .* y2.^y_power;
%%%%%%%%%%%%
to compute the matrix in one shot, but it takes significantly longer - in fact, each call to repmat in the second method takes about as long as generating the matrix using the double loop. Any suggestions?
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