MATLAB

Find the area under the curve for the original data set. Compare it to the area under the curve for your fitted polynomial from under script. Plot the sorted data to show it is sorted. Extra credit: Compare to the fitted polynomial at increasing degree (2,3,4). Are you converging (getting closer) to the answer from the original data set as you increase the degree?

Deliverables:

Script for calculating area under the curve

Must use trapz and integral

Command window output of answers

Plot of data, sorted, with line rendering style

[Extra credit:] Answer to question, degree 3 & 4 polynomials

Step by Step Instructions:

Start with your answer to problem 1.

Calculate the area under the polynomial by using integral and the anonymous function you made for the fplot. The bounds for integral (xmin, xmax) should be the same as for fplot

If you plot the data points with a line, youll notice that they double back on themselves. If you just call trapz on the raw data (go ahead and do it) youll get a number thats wrong. To fix this, you need to sort the data by the x values first

The tricky part of this is you need to sort the y values by the x values if you call sort(data) youll get every column of data sorted (try it and see). If you do sort(data, 1) to sort by rows, youll sort x and y independently. What you really want is what happens in Excel when you select a bunch of data and sort ALL of it by a specific column

Sort by x valuesSort the first row of data. Just like min, sort will return both the sorted numbers AND the order they ended up in

[sortedValues, sortedIndices] = sort( data(1,:) )

You can use the sortedIndices variable to sort the y values

sortedYs = data(2, sortedIndices)

Once the data is sorted, you can call trapz. Plot the data with a line to verify that you have it sorted correctly

Extra credit: Same as before just add a for loop

Problem 1 script:

a = [2 3 4]; adtad = dlmread('Lab6Data.txt'); str = {'-r','-g-','-b'}; x = data(1,:); y = data(2,:); plot(x,y,'.') hold on for D = 1:3 p = polyfit(x,y,a(D)); y = @(I) polyval(p,I); fplot(y,[0,12],str{D}) hold on end

Lab6Data:

0.054351,0.17427,0.32544,0.38166,0.51262,0.61905,0.64539,0.84047,0.87187,0.9825,1.0579,1.2079,1.2491,1.3722,1.4461,1.581,1.707,1.7663,1.888,2.0435,2.0689,2.3991,2.7059,2.9831,3.2929,3.5675,3.9572,4.1492,4.4663,4.8072,5.1001,5.441,5.6924,5.9913,6.2658,6.6198,6.9079,7.1738,7.5331,7.7671,8.0886,8.4397,8.7064,8.9809,9.2565,9.5737,9.8301,0.10023,0.35641,0.52273,0.59058,0.89248,1.0296,1.2644,1.4489,1.743,1.7998,2.0865,2.6327,3.2776,4.0285,4.4078,5.1601,5.6326,6.2969,6.8884,7.5776,8.1572,8.7709,9.3004,9.7822 11.063,7.3294,5.1865,4.7502,3.8699,3.6388,3.3969,2.7292,2.4653,2.2054,1.9528,1.4672,1.3368,1.0796,0.97911,0.69672,0.47526,0.39946,0.17504,-0.06427,-0.10579,-0.55552,-0.91853,-1.2676,-1.4107,-1.8233,-2.0986,-2.2012,-2.3148,-2.7529,-2.8396,-2.8852,-3.0497,-3.5468,-3.4766,-3.6104,-3.7682,-3.8951,-4.0557,-4.1869,-3.9526,-4.2936,-4.3077,-4.3005,-4.4625,-4.72,-4.7369,8.7267,5.01,3.8411,3.5156,2.4489,2.0794,1.3557,0.95831,0.43264,0.33053,-0.12925,-0.86481,-1.5214,-2.0664,-2.4092,-2.7707,-3.0428,-3.5027,-3.7204,-3.9608,-4.2605,-4.546,-4.6492,-4.7869