Vectorization of this loop

Question

Dilunath Hareendranath 2012-4-18

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The following loop calculates the distance and angle values of every location from a point and stores in arrays named Radius and theta. This loop is called nearly 3600 times in the code. This loop is effecting the performance of the code. Please suggest some ways to vectorise this loop.

xwidth and ywidth varies from 500 to 750. So, memory needed is also very high. Please suggest ways to decrease the memory needed.

x1=0;
y1=1;
inj_x=round(xwidth/2.0);
inj_y=round(ywidth/2.0);
Radius=zeros(ywidth,xwidth);
theta=zeros(ywidth,xwidth);
for r=1:ywidth
for c=1:xwidth
  x2=r-inj_y;
  y2=c-inj_x;
  Radius(r,c)=(x2^2+y2^2)^.5;
  theta(r,c)=mod(atan2(x1*y2-x2*y1,x1*x2+y1*y2),2*pi);
end
end

Thanks in advance

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Answer 1

Andrei Bobrov 2012-4-18

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in your case

r = (1:ywidth).' - round(ywidth/2);
c = (1:xwidth) - round(xwidth/2); 
Radius = bsxfun(@hypot,r,c);
theta = mod(bsxfun(@atan2,-r,c),2*pi);

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Dilunath Hareendranath 2012-4-18

Thanks andrei.. This code is taking only 0.09 seconds to process.. whereas previous code was taking 2.8 seconds.

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Answer 2

Honglei Chen 2012-4-18

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x1=0;
y1=1;
inj_x=round(xwidth/2.0);
inj_y=round(ywidth/2.0);
[x2,y2] = ndgrid((1:ywidth)'-inj_y,(1:xwidth)'-inj_x);
Radius=(x2.^2+y2.^2).^.5;
theta=mod(atan2(x1.*y2-x2.*y1,x1.*x2+y1.*y2),2*pi);

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Dilunath Hareendranath 2012-4-18

Thanks Honglei Chen for answering. This code is also taking less time.

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Answer 3

Jan 2012-4-18

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For a fair speed comparison cleanup the loops:

move all repeated calculation outside
SSQRT() is faster than ^0.5

twoPi = 2 * pi;
for r = 1:ywidth
  x2   = r - inj_y;
  x2_2 = x2 * x2;
  x1x2 = x1 * x2;
  y1x2 = y1 * x2;
  for c = 1:xwidth
    y2 = c-inj_x;
    Radius(r,c) = sqrt(x2_2 + y2^2);
    theta(r,c)  = mod(atan2(x1*y2 - y1x2, x1x2 + y1*y2), twoPi);
  end
end

Perhaps a partial vectorization is fastest:

twoPi = 2*pi;
for c = 1:xwidth
  y2 = c-inj_x;
  x2 = transpose(1-inj_y:ywidth - inj_y);
  Radius(:,c) = sqrt(x2.^2 + y2^2);
  theta(:,c)  = mod(atan2(x1*y2-x2*y1, x1*x2+y1*y2), twoPi);
end

And fully vectorized:

x2 = transpose(1 - inj_y:ywidth - inj_y);
y2 = 1 - inj_x:xwidth  - inj_x;
Radius = sqrt(bsxfun(@plus, x2 .^ 2 + y2 .^ 2);
k1     = bsxfun(@minus, x1 * y2, y1 * x2);
k2     = bsxfun(@plus, x1 * x2, y1 * y2);
theta  = mod(bsxfun(@atan, k1, k2), 2*pi);

And if x1 and y1 are really fixed to 0 and 1 this can be simplified.