Smooth steps

ODE solvers have a hard time with step changes, where the derivative changes discontinuously. The following function help to avoid associated problems by approximating the step by a smoother function. Argument dx controls the smoothness.

MTKHelpers.smoothstep — Function

smoothstep(x, x_step, dx, a=zero(x), b=one(x))

smooth step function:

= a for x <= x_step - dx
= b for x >= x_step + dx
= (a-b)/2 for x == x_step

and smooth in between.

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