@Swanson-Hysell If this looks okay, would you like this implemented in rockmagpy or are you pretty happy with that implementation?

Can you help me understand the warning saying that delta T should be integer, be careful! given that the delta T is irregular throughout the data set?

There is another method to implement which is the linearity of inverse susceptibility when dealing with high-temperature susceptibility data:

https://doi.org/10.1029/2006JB004507

Can you help me understand the warning saying that delta T should be integer, be careful! given that the delta T is irregular throughout the data set?

Yeah. Well, sort of. I believe the input arrays are being regularized (delta = 1) up until the last pair of values.

I don't think that this has much affect on the behavior of the function result, so we could remove the warning, I suppose. Better yet would be to figure out how to continue the regularization through the whole array...which I'm working on.

There is a broader discussion here about implementing varied approaches in the context of this function:

• peak of first derivative
• two tangent method
• second derivative zero crossing
  Can you think about adding these different approaches and having there be parameters that can do one method or another?

Yes. I think that's a good idea. Including your most recent comment as far as approaches goes. I can work on this over the weekend.

The goal is to avoid duplicative functions between rockmagpy and other pmagpy libraries is the ipmag implementation is what we can be using in rockmagpy.

Right. I think eventually the function should have some comprehensive approaches and only needs to live in one module.

There appears to be a fundamental issue in this ipmag.curie() function given that it is searching for the peak of the 2nd derivative. One could search for the peak of the first derivative, but this isn't appropriate for the second derivative which instead should be the zero crossing (as in this Verwey temperature example: https://pmagpy.github.io/RockmagPy-notebooks/MPMS_verwey_fit.html). In this example (and the other example file) the data are too noisy for this approach (two tangent is likely better).

Right. That's been the implementation in the software for a while. Can see it in the 1998 textbook version. I think, looking at Fabian et al., 2013 Figure 8 that it probably does okay. But I think adjusting it is in our best interest going forward.

So, a summary on the methods to implement:

1. I think we'd want the minimum of the first derivative (Fabian et al., 2013)

2. I was pretty convinced by (Petrovsky and A. Kapicka, 2006) that the two tangent method is not the correct way to go.

3. Zero crossing is fine, but problematic when the data is noisy. Honestly, it seems as if the smoothing function ipmag.smooth() isn't doing too much until a pretty impressive large window size is reached.

It would be pretty easy to modify the function to address 1 and 3 together, really just a matter of reporting the minimum of the first derivative instead of the maximum of the second derivative. I have to see what exactly is up with the smoothing function.

There is another method to implement which is the linearity of inverse susceptibility when dealing with high-temperature susceptibility data:

https://doi.org/10.1029/2006JB004507

Yes, this can be added as well, I think. I'll play around with these additions.

@Swanson-Hysell

Okay, whew. I've rewritten the function so that it gives the Curie point estimate based on first derivative min and second derivative zero crossing.

Also, the interpolation for irregular input is better, that error is gone.

The plotting is now done by matplotlib, since the plot_xy() function in pmagplotlib is, according to the docstring, deprecated.

I don't think the two tangent method is necessary, since it isn't particularly good for susceptibility data. The current iteration is probably a viable point to provide an update to the ipmag.curie() function. I haven't implemented the inverse susceptibility operability yet. Trying to figure out if it makes sense to let a user pick a linear section or to linefind through the 1/kT curve for them. Options, options.

@Swanson-Hysell I have now added the option to use inverse susceptibility. It is called by setting inverse_sus = True in the function (default is False).

There is an additional import added to ipmag.py:

from scipy.stats import linregress

And a small additional utility function called ez_line which uses matplotlib to plot a line from slope and intercept on the graph.

The basic flow of the addition is:

1. Plot inverse susceptibility.
2. Ask user to provide the high temperature window they want to examine (since its hard to view the whole curve).
3. Plot that window.
4. Ask user to provide the high and low temperature values that define the linear segment.
5. Regress a line through that segment, calculate its parameters. Return the x-intercept and R-squared value, and plot the window, values used in the regression, and line (image of final output shown below).

I will dig into this tomorrow. What are your thoughts on having this as an option within a single function (which I know is what I originally suggested) vs having it be its own function. Given how many specific parameters for the inverse susceptibility analysis the user needs to provide, it seems like it might work better was its own function.

The overall function does end up pretty busy. However, there isn't much the user needs to do, necessarily. The inverse_sus flag is probably the most involved piece by a fair degree.

So...yeah. I think its reasonable break it out into its own function. Let me know if you want that to happen and it should be easy enough to implement.

Okay, the inverse method is now broken out into its own function as suggested.

Any improvements wished, @Swanson-Hysell?

This PR request is out of date due to the incorporation of the rockmag module. As discussed in #802, curie should probably move out of ipmag. #776 incorporates the useful part of this PR.