Trendline with Slope of zero

Hello,

I have a vector of raw lamp radiance data, and a vector of the moving standard deviation of that data. I want to add a trendline for the range of the standard deviation in which the slope is zero, in order to show when the lamp is stable. I have used polyfit to place the trendline to the graph, but it is not perfectly straight over the entire range of data. Is there a function in MATLAB that does this for me, or do I just have to keep adjusting which range of data I would like to look at manually?

Answer 1

[Image Analyst]

A line with slope zero will have a fixed constant y value. If you know that y value, you can draw a line there with line():

line(xlim, [y, y], 'LineWidth', 2, 'Color', 'r');
grid on;

Attach your data if you want more help so we can offer a solution with your exact data.

[Heather]

Here you go. The idea is for MATLAB to plot time vs. Deviation, and look through all of the data within that graph, in order to put a trendline onto the graph that is closest to having a slope of zero. Currently, I have to keep changing the window manually until I see the trendline that I'm looking for. If you plot column A vs column C from data points 46:151, you will see the (mostly) horizontal trendline I'm speaking of. But, I had to keep changing my data points manually in order to get here. (46:165, 46:160, etc.). Does MATLAB have a function that will look through all of the data and do this automatically?

[Image Analyst]

Heather:

Your whole premise is wrong. The lamp will not have the most stable intensity when the standard deviation is more or less constant with a zero slope fitted through that region. Who/what gave you that idea? That is wrong. The lamp will be most stable when the standard deviation plot is at a min.

Let's take an example to clear that up. Let's say you had a time period where the standard deviation bounced along in a tight range of 0.1 from 6.9 to 7.0. Now let's say you had another time period where the standard deviation varied in a wider range of 0.5 but went from 2.0 to 2.5. Which time period would you say had the most stable light intensity? Answer: NOT the one where the standard deviation bounced around in a tight 0.1 range. It would be the period where the stdev bounced along in the 0.5 range. Why? Because a standard deviation of 2.5 is much less variable than 7.

So to find the time period where your lamp is most stable find out where the std dev curve is lowest, not where it is flattest/least variable.

I say this because in your workbook the column header is "deviation" rather than "radiance" or "intensity". Presumably that's also what's plotted. Of course if the column is really intensity and not "deviation" like it's labeled, then you would want the flattest section.

-Image Analyst (Ph.D. Optics)

[Heather]

I apologize, I have the 2nd column incorrectly labeled because I was copying stuff over from my master spreadsheet. Column B is the radiance and column C is the standard deviation of that radiance. By plotting the radiance over time, you can see that the lamp begins to stabilize between 11-1130 so I want to show that with the standard deviation plot

[Star Strider]

None of the ‘11-1130’ makes sense. None of the data you posted have those values or index values.

This is a complete waste of our time.

[Heather]

The first column is in excel time. You can change it to HH:MM:SS and see what I'm talking about without getting so harsh. I'm sorry that I forgot to include that in my earlier response.

[Star Strider]

Such details are important.

Regardless, I’m gone.

Have fun!

[Image Analyst]

What I would do it fit this to "the rate equation" and decide how far below the theoretical assymptote defines "stable" for you. I attach a rate equation fitting. See if you can adapt it to your data and determine when the assymptote is. It should be around 0.14835.

[Heather]

This was excellent! Thank you so much! I adjusted it a few times and got just below and above the 0.14835 gridline. I really appreciate all of your help and explanations. I think I misunderstood which graph to plot the trendline on, so I appreciate you explaining the standard deviation graph to me.