Physics 241 Class #10 Outline (9/25/2013) Plotting Handle graphics Numerical derivatives and functions Next time numerical integrals

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1 Physics 241 Class #10 Outline (9/25/2013) Plotting Handle graphics Numerical derivatives and functions Next time numerical integrals

2 Announcements HW4 grades are up. HW5a HW5 revised Same problems, now due Monday 9/30 Also I added two more problem (#3 and #9) due Wednesday. Exam is still next Wednesday Sample Exam (last year's is posted now)

3 Saving figures as images There are two ways to share data-plots (other than printing them). 1) Make a.fig file. A.fig file contains both the plot and the data used to make the plot. The advantage of it is that it can be edited and customized further by you or the recipient. The disadvantage is that they cannot see the file without loading Matlab, and the fact that it CAN be changed makes it not good for archives and publications. 2) Make a.jpeg, bmp, png, eps (an image). Method 2 is what I am requesting in this course. (That is please don't submit.fig files) >> print(1,'dpng') >> print(3,'deps') >> print(1,'-djpeg','homework2_2.jpeg') >> print(1,'-dbmp','-r300','homework2_2.bmp')

4 Advanced Plotting %a _zvstfancy.m -- Loads and plots a balloon trajectory. %Demonstrates changing fonts. %("listfonts" command gives you font options) a=load('bflight1_ _mod.pos'); time=a(:,4); alt=a(:,3); %Get 3rd and 4th columns plot(time,alt,'r.',time,alt,'b-','markersize',22,'linewidth',2); %Plot alt with red dots and also with a blue line %Make the dots and line bigger than default xlabel('time (s)','fontname','times','fontsize',18); ylabel('altitude (m)','fontname','times','fontsize',18); %Label the axes with nice readable fonts. title('telemetry test flight','fontname','times','fontsize',22); text(400,1700,'july 25, 2003','FontSize',16) %Add explanatory text a=gca; set(a,'fontname','arial','fontsize',16) %Change the text size of the tick marks

5 Handle graphics >> f=gcf %Gets handle for current figure >> get(f) %Gets properties of current figure >> a=gca %Gets handle for current axes >> get(a) %Gets properties of current axes >> get(a,'xtick') >> set(a,'xtick',[ ]) %Sets tick marks to [ ] Can set any property that you have gotten. >> set(a,'xlim',[ ]); >> set(a,'xlim',[ inf inf]); set(a,'xaxislocation','top');

6 Handle graphics >> a=gca a= >> get(a) ColorOrder = [ (7 by 3) double array] FontAngle = normal FontName = Helvetica FontSize = [10] FontUnits = points FontWeight = normal GridLineStyle = : LineStyleOrder = LineWidth = [0.5] TickLength = [ ] TickDir = in Title = [ ] XGrid = off XLabel = [ ] XAxisLocation = bottom XLim = [ ] XTickLabel = Parent = [1] >> b=get(a,'xlabel') b= >> get(b) BackgroundColor = none Color = [0 0 0] Extent = [ (1 by 4) double array] FontAngle = normal FontName = Helvetica FontSize = [10] FontUnits = points FontWeight = normal HorizontalAlignment = center Position = [ ] Rotation = [0] Units = data Interpreter = tex VerticalAlignment = cap Parent = [ ] Visible = on

7 Handle graphics >> xlab=get(a,'xlabel') % Gets Xlabel properties on current figure Xlabel is child of current axes which are child of current figure. Figure is parent of axes. Can get a handle to things like legends to customize them h=legend('first legend','second legend') set(h,'fontsize',14)

8 Numerical derivative forward derivative Math Matlab element by element lim f t t f t f ' t = t 0 t len=length(f);d=zeros(1,len); for k=1:len-1 D(k)=(f(k+1)-f(k))/deltat; deltat=t(k+1)-t(k); end Assuming that f and t are the same length, the above code is bug-free Advantages: Can use for first point of data set. Disadvantage: Can't use for real-time data.

9 Numerical derivative backward derivative Math Matlab element by element Array oriented f t f t t f ' t = lim t t 0 deltay=y(k)-y(k-1) deltat=t(k)-t(k-1) yprime(k)=deltay/deltat deltay=diff(y) deltat=diff(t) Advantages: Can use for last point of data set, there is no next point. Also, for real-time data when you don't know the future.

10 Numerical derivatives central derivative Math Matlab f t t f t t f ' t = lim 2 t t 0 deltay=y(k+1)-y(k-1) deltat=t(k+1)-t(k-1) yprime(k)=deltay/deltat Advantages: Less noisy than other formulae. Symmetrical

12 Forward derivative Central derivative

13 Errors in Numerical derivatives Taylor Series 2 3 t t f t t =f t f ' t t f ' ' t f ' ' ' t... 2! 3! 2 f t t f t t t f ' t = f ' ' t f ' ' ' t... t 2! 3! Note: Error decreases at step-size decreases

14 Script Examples Derivative example. Calculate a derivative and print it in a pretty way. Then Break into function and calling script Then demonstrate subplot

15 Left Riemann Sum Left Riemann sum. Overestimates decreasing functions.

17 Numerical Integrals t1 Math I(t 1 )= f (t)dt 0 t=t 1 Matlab I t 1 = lim f t t t 0 t=0 I(1)=y(0); deltat=t(k)-t(k-1) I(k)=I(k-1)+y(k)*deltat Left Riemann sum. Overestimates decreasing functions.

18 Numerical Integrals t1 Math I(t 1 )= f (t)dt 0 t=t 1 Matlab I t 1 = lim f t t t 0 t=0 I(1)=y(0); deltat=t(k+1)-t(k) I(k)=I(k-1)+y(k+1)*deltat Right Riemann sum. Underestimates decreasing functions.

Introduction to MatLab

Introduction to MatLab 1 Introduction to MatLab Graduiertenkolleg Kognitive Neurobiologie Friday, 05 November 2004 Thuseday, 09 Novemer 2004 Kurt Bräuer Institut für Theoretische Physik, Universität Tübingen