How to draw this fractal using MATLAB?

Staged Linear Regression using MatLab?

• I have a set of test data (from material stress rupture tests) which when plotted gives a scatter graph with a strong positive correlation. It is quite obvious that there is a line of best fit, which is easily found using linear regression, for examply using the R2 value in Excel. However, in actual fact, 2 lines of best fit would be more accurate, as this would incorporate a yield point. My question is this: How do I write a MatLab program that examines all the data points, and tests all of them, then instead of simply plotting one line of best fit, it plots 2. Essentialy 1 line with a sudden change in gradient. This means the 2 lines of best fit must connect at some value, and combined the values of divergance must be at an overall minimum. I have some reasonable skill with MatLab, but I'm not even sure if I got my point accross, never mind starting it myself. I will try and sketch something up in paint or such which represents my point more accurately. Thanks Chris

• Answer:

  Does it seem wierd that electrons flow out of the minus terminal and go in the plus terminal of a battery? It is a gift (if memory from "The Mechanical Universe" serves) from Benjamin Franklin. Early conventions sometimes govern how we think today. Same thing goes for stress-strain curves. We think "input is stress" so stress is the x-axis and "output is strain" so strain is the y-axis. There is a reasonably good reason not to do that - the underlying relationships are piecewise polynomial and easier to fit if you reverse your x and y axis. I would use fminsearch, personally. Yes its a simplex search, but if you make the output a squared error then acts as a highly flexible, easy to program, poor mans least square. The way I would do it is: - have the data stored in csv, or a mat file - load the data in your main program - associate the x,y or even y,x data with global variables. - pick an initial close guess, it doesnt have to be good - make a called @myfunction function that takes as inputs the parameters, and outputs the sumsquare error of the generated equation vs the data - the myfunction also uses global variables.. this way data passing is transparent I like to get down and dirty with my data. Wrestle with it. Chew it for a while. You might do well to look at the curve fitting toolbox "cftool(x,y)" including gaussian mixtures. It will fit your data with nearly linear piecewise functions if you choose the right options. It is very structured, very gui. There are robust fitting options, but you are .. not as down and dirty with the data. It is not bad initially but is not good for building great .. understanding of what is really going on inside the data, or giving results that are entirely and immediately useful. function myMain function % housekeeping % load data % globalize variables % initial guess for parameters = x_zero or whatever % check that your myfunction is working using myfunction(x_zero) % after its working then use help on fminsearch to inform how to structure things to get it working % function [out] = myfunction(p1,p2,x1,x2,x3, switch) % p1 is the linear polynomial % p2 is the linear (or nonlinear) polynomial % x1 to x2 is the range where p1 lives % x2 to x3 is the range where p2 lives % use find to determine x that is withing x1 to x2 % use polyval to determine y for that region % repeat for range x2 to x3 % catenate the y-matrix to get the total fit equation evaluated at all the data points % error is (model-real) that way an over-estimate is positive, under is negative % output is the norm of the error % switch allows you to switch from a single output (norm) to total output for plotting purposes % fminsearch should not be allowed to control what "switch" does.