Usage

using NumFracDiff

Here we show a few brief examples for the usage of the library

First case

First, we define the input signal y (as a vector of floats) and the time step dt with respect to which we want to differentiate. We will plot the analytical function using the Plots.jl library.

using Plots
dt=0.001
x = collect(0:dt:10.0)
y = x.^2
plt = plot(size = (500, 500))
plot!(plt, x, y,
      linestyle=:dash,
      color=:blue,
      label="f(x)",

Next we instantiate the needed structures. NumDiffProblem defines the configuration of the derivative, while Workspace allocates the auxiliary vectors needed for the computation and stores the final result.

method = GL()
problem = NumDiffProblem(dt=dt,order=1.0,n=length(y),method=method)

NumDiffWorkspace{Float64}([1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0  …  -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])

To execute the computation, invoke the compute! function. This mutates the workspace in-place.

compute!(y,problem,workspace)

plot!(plt, x, workspace.deriv,
      linestyle=:dash,
      color=:red,
      label="f'(x)",
      framestyle = :box)
xlabel!("x")
ylabel!("y")
plt

Second case

You can update the derivative order (e.g., to a fractional derivative) directly on the existing structures without reallocating memory or creating new objects.

update_order!(problem,workspace,0.5)
compute!(y,problem,workspace)
plt1 = plot(size = (500, 500))
plot!(plt1, x, y,
      linestyle=:dash,
      color=:blue,
      label="f(x)",
      framestyle = :box)
plot!(plt1, x, workspace.deriv,
      linestyle=:dash,
      color=:green,
      label="f^0.5(x)",
      framestyle = :box)
compute!(workspace.deriv,problem,workspace)
plot!(plt1, x, workspace.deriv,
      linestyle=:dash,
      color=:red,
      label="f'(x)",
      framestyle = :box)
xlabel!("x")
ylabel!("y")
plt1

Third case

The library can be used to integrate as well, using a negative order.

y= x .* 2
update_order!(problem,workspace,-0.5)
compute!(y,problem,workspace)
plt2 = plot(size = (500, 500))
plot!(plt2, x, y,
      linestyle=:dash,
      color=:blue,
      label="f(x)",
      framestyle = :box)
plot!(plt2, x, workspace.deriv,
      linestyle=:dash,
      color=:green,
      label="f^(-0.5)(x)",
      framestyle = :box)
compute!(workspace.deriv,problem,workspace)
plot!(plt2, x, workspace.deriv,
      linestyle=:dash,
      color=:red,
      label="f^(-1.0)(x)",
      framestyle = :box)
xlabel!("x")
ylabel!("y")

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