Plotting graphs where the data table contains function coeffcients

stephen_pearson

I am trying to plot an equation in Graph Builder e.g. 1/(1+exp(-1*alpha + (beta * T))) for which I have 36,000 plausible estimates of alpha and beta. T is in the range 50 to 350 °C. By applying some transparency to each line it is possible to see where the weight of the data is. The example below used matlibplot in python (which is where my coefficients are generated).

I have over 1500 different groups of estimated equation coeffcients to plot and I would like to do it in a way that:

• Doesn't create huge files
• Can work for different equations with varying number of coefficients
• Works with a local data filter (or table filter)
• Looks good

One simple way would be to concatenate all my files with the same equation including a source table column. I could then cartesian join a table of temperatures, and add the formula column. This is scriptable but it turns a file of less than 1MB into one over 300MB.

 

I was wondering if the new expression column containing a vector might be able to do something better? Or there is some more elegant way using virtual joins?

 

I have attached some sample data and look forward to any suggestions.

EquationEstimates.jmp

TemperatureList.jmp

gzmorgan0

Stephen,

I understand your question, but hesitant to recommend a solution at least for this data. I am not sure how you generated your 36,000 coefficients; based upon the data, this seems to be 36,000 iterations of an unstable non-linear fit.  Of course I could be wrong, but let me explain.  First of all your model y = 1/(1 +exp(-1*alpha + beta *T) ), doesn't seem to fit your graph.  All of your alpha coefficients are negative and beta are all positive and T ranges from 50 to 350 so -1*alpha + beta * T is always positive , in other words, Y can never be 1. Shouldn't your  alpha values be positive, so when -1*alpha + beta*T=0, or T = alpha/beta then y = 1/2 and when -1*alpha+beta*T < 0 (a large negative value), then Y approximates 1.  I think you intended

y =1 /(1 + exp(-1*(alpha +beta*T)), then a negative alpha makes sense and the plotted matches your graph. 

 

The reason for my (possibly incorrect) assessment is that the correlation of your coefficients alpha and beta as specified in the table is -0.99994.  Create a column alpha/beta. The distribution is a random uniform distribution of -101.8 to -99 (the graph vbelow is shwing abs(alpha/beta).  Since alpha is a function of beta, look at the distribution of beta.  I'd only plot the functions for beta at say the minimum, the maximum and the 10, 25, 50, 75, 90 percentiles.

 

So maybe this was a poor example for what you want. I think you might be wanting a custom display, similar to the nonlinear library.