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1. lucamagher
   

   Member
   Joined: May '13
   Posts: 2

   Hi guys
   I am sure I am being stupid with this question. My apologies in advance.

   I have an unequal spacing grid of points, say, size(grid) = [100 200].
   I want to evaluate the gradient of a function f(grid) along both dimensions of the grid.
   How can I do this?

   Just to play around with function gradientFD, I coded :
   x = 0:0.01:10;
   y = 0:0.01:5;

   [X,Y] = meshgrid(x,y);
   f = cos(2*pi*X).*Y;

   dfx = gradientFD(f,x,2);
   dfy = gradientFD(f,y,1);

   dfx is evaluated correctly, whereas dfy is not.
   What is wrong with my understanding of gradientFD function ?
   Thanks much

   Posted 10 years ago #

2. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,640

   Hi lucamagher,

   The second input to the gradientFD function should be the grid-point spacing, rather than an array of the grid coordinates, i.e.,

   dfx = gradientFD(f, dx, 2);
   dfy = gradientFD(f, dy, 1);

   where dx and dy are 0.01 in your example.

   Brad.

   Posted 10 years ago #

3. lucamagher
   

   Member
   Joined: May '13
   Posts: 2

   Thank you very much Brad.
   How can I handle non-evenly spaced grid points?

   My actual problem is that dx and dy are not constant, as in the preceding example.
   So, my problem is akin to this:

   dx = sort(rand(100,1));
   dy = sort(rand(50,1));

   x = 10*dx;
   y = 5*dy;

   [X,Y] = meshgrid(x,y);
   f = cos(2*pi*X).*Y;

   dfx = gradientFD(f,dx,2);
   dfy = gradientFD(f,dy,1);

   subplot(2,1,1)
   pcolor(X,Y,dfx), shading interp
   subplot(2,1,2)
   pcolor(X,Y,dfy), shading interp

   Where am I doing wrong here?
   Thank you very much for your assistance.

   Luca

   Posted 10 years ago #

4. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,640

   Hi Luca,

   The k-Wave functions gradientFD and getFDMatrix require the grid points to be evenly spaced. If your grid points are not evenly spaced, you will have to generate the finite difference coefficients at each position manually. This is not difficult, just fiddly. See for example:

   B. Fornberg, “Generation of finite difference formulas on arbitrarily spaced grids,” Math. Comput, vol. 51, no. 184, pp. 699–706, 1988.

   You could also see if there is anything on the MATLAB file exchange, e.g., here.

   Brad.

   Posted 10 years ago #

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