Hi,
I have this Cost Function H = 1/(deltaX)2 [(A2 - A1)2 + (A3 - A2)2 + (A4 - A3)2]
I'd like to minimize this cost function by forming the derivatives of our function's variable. then we have :
dH/dA1 = 2/(deltaX)2 ( - A2 + A1)
dH/dA2 = 2/(deltaX)2 (-A1 + 2A2 - A3)
dH/dA3 = 2/(deltaX)2 (-A2 + 2A3 - A4)
dH/dA4 = 2/(deltaX)2 (A4 - A3)
first I need to write the MATLAB code for above example and the next step is , every where which there is A2, instead of that I would like to put (A1 + A3 + A4)
so eventually my function should be like this:
H = 1/(deltaX)2 [((A1 + A3 + A4 ) - A1)2 + (A3 - (A1 + A3 + A4 ))2 + (A4 - A3)2]
and then forming the partial derivatives of our function's variables the same as above mentioned.
Thank you
Please see my paper, "Monte Carlo Marching", to see how you can minimize your cost function without calculating derivatives. The given computer code stands alone so you don't have to interface with another program.
Easiest way is to use the symbolic toolbox;
syms deltaX A1 A2 A3 A4 %declare variables
H = (1/(deltaX^2))*((A2 - A1)^2 + (A3 - A2)^2 + (A4 - A3)^2); %define H
dhdA1 = diff(H,A1);
dhdA2 = diff(H,A2);
dhdA3 = diff(H,A3);
dhdA4 = diff(H,A4);
This will give you the requisite equations.
Thanks David, Your are right.
In my calculation I didn't take into account power of 2 (^2) . that's why I could reach what I wanted.
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