Compute first partial derivatives for a recursive function.
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I would like to ask if there is a way to compute the first derivatives of a recursive function.
For example, let say that we have a function f_{i} = w + a * f_{i-1} and we want to compute the first partial derivatives of a function f_{i} with respect to the variables w and a.
It is a simple example and it is cumputed easily. But I would like to know if there is a method when I have a more complicated example.
Thank you in advance.
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Answers (1)
Roger Stafford
on 1 Jan 2014
I don't see any particular difficulty here. By taking the derivatives of each f_(i) with respect to a or w you obtain another recursive formula. In your particular example you get
df_(i)/da = f_(i-1)+a*df_(i-1)/da
and
df_(i)/dw = 1 + a*df_(i-1)/dw
Each of these can be evaluated by a recursive procedure, (preferably using ordinary for-loops.) Presumably the initial values of df_(1)/da and df_(1)/dw are regarded as zero. If not, you will need to know what they are.
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