Varying the pressure during optimization

[rahulgaur104]

It would be a useful tool to vary the pressure profile during optimization to see the effect of the pressure profile on various objectives, quality of equilibrium etc.

The pressure profile must always satisfy the following conditions

1. monotonic and strictly non-increasing from core to edge
2. pressure must always be a positive value

If we optimize for pressure using the current framework, it will violate one or both of these conditions.
Therefore, it would be useful to create an objective that uses a parametrization that always satisfies the two necessary conditions.

Something like p = a^2 * (1-rho) * ((1-rho)/(1 + (b^2)*rho^2))^(m^2) where a, b, m can vary during optimization. There must be a general way to do this.

[dpanici]

A way to account for simple effects like same shape profile but changing beta is to use eq.pressure=ScaledProfile(1.0, eq.pressure) as the pressure profile. The parameters of the new profile now is [scale, old_params] and so if you when you optimize do FixPressure(eq, indices=np.arange(eq.pressure.params.size)[1:]), it fixes all the params except for the scale factor on the pressure profile.

[dpanici]

TwoPowerProfile, MTanhProfile

desc.random has a monotonic profile generation method.

Parametrize derivative, enforce to be positive