Determining if data is monotone increasing, monotone decreasing or level.

[lefti]

Dear Members,

I am trying to determine when a set of data is monotone increasing, monotone decreasing or neither that is level. The data is not in a form of a function but rather data points. How do I determine the characteristics of the data. The independent variable in my case is time. How do I determine for the range [t1,t2] the data is monotone increasing, for the data [t3,t4] the data is level and then for the data [t5,t6] the data is monotone increasing. I need this information to determine rise time, fall time of the data.

Below I have a link that explains how to determine the rise and fall times in defenition. Also please find the data.txt file that has a sample of the data in question.

 

http://www.geocities.com/left_freedom/index.html?1100826250452

 

All help is much appreciated. Thanks

 

lefti ;)

[Tormod]

Welcome left!

 

This is very interesting. I must confess ignorance to what you are talking about. Bo is our expert on maths and physics (and also the moderator of this group) and I am sure he or someone else will try to help you out as soon as they can.

[Bo]

If you are able to let a computer take the gradient (derivative) of your data, then the 3 cases you try to distinguish are equivalent to

gradient constant, positive ( monotome increase)

gradient constant, negative (monotome decrease)

gradient constant, zero (data constant)

 

any nonconstant gradient will give anything else then monotomeous.

 

if you don't have a computer to do this work, you can do it by yourself, e.g. by taking the difference between 2 data points, and devide by the time in between the 2 points. do this for all 2 following points, and see if the numbers you get are constant.

 

Bo

[lefti]

Hi Bo,

Thanks for the reply. This does work but it is a local derivative. For example if you have 12 points

 

T Q

--- ---

T1 1.0

T2 2.0

T3 1.99

T4 3.0

T5 4.0

T6 5.0

T7 5.0

T8 5.0

T9 4.0

T10 3.0

T11 2.0

T12 1.0

 

Q2-Q1=1.0,Q3-Q2=-0.01,Q4-Q3=3.0-1.99=1.01,Q5-Q4=1.0,Q6-Q5=1.0

We can say that the data is increasing for all T between T1 and T6 except between [T2,T3] where it is decreasing. This point should not really be considered since it does not fit with the trend. This is to say that the derivative could be positive locally but for a certain range it is negative. Since all this data is non ideal the slope is not expected to be always the same sign. This leads to the question how do I determine for which range the data is increasing , decreasing or level. In the data provided on the link the data should increase, decrease and remain level at least 2 times.

 

 

 

 

Graphically it is quite easy to see for what range V(q) is increasing , decreasing or staying the same but with data there needs to be more inteligence built into it. Any ideas? Thanks for your help.

 

Regards,

Lefti

[sanctus]

So to me it seems you go looking to far.

I would just take th points on a computer program (Excel, Matlab), you plot them and then you fit a function of the type you want (linear, exponential ...) which suits you beast and then you can determine all the intervals needed.

[Bo]

i think another solution is to let a datafit program make a linear polynomial fit, and look at the given slope, with errors and standard deviation it produces.

There is always some arbitraryness if you want to exclude datapoints.

 

Bo