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@@ -0,0 +1,29 @@
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+-- Exercise 4.3
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+-- George C. Privon
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+-- 2023-12-22
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+type R = Double
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+type Derivative = (R -> R) -> R -> R
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+
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+-- a function to take the numerical derivative, approximated for some dt
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+derivative :: R -> Derivative
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+derivative dt x t = (x (t + dt/2) - x (t - dt/2)) / dt
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+
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+-- the function we want to take the derivative of
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+myfunc :: R -> R
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+myfunc x = x**4
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+
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+-- exact derivative of our function of interest
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+dmyfunc :: R -> R
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+dmyfunc x = 4 * x**3
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+
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+-- take the derivative with dt=1
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+dOne :: R -> R
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+dOne x = derivative 0.01 myfunc x
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+
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+-- compare the exact derivative with the numerical derivative using dt=1
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+relabserr :: R -> R
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+relabserr x = abs (dmyfunc x - dOne x) / dmyfunc x
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+
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+-- Solution
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+-- The derivative of f(x) = x**4, evaluated at x=0.01 with dt=0.01 produces a
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+-- relative error of 25%
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