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18 *** Script |
18 *** Script |
19 Welcome. |
19 Welcome. |
20 |
20 |
21 In this tutorial we shall look at obtaining the least squares fit |
21 In this tutorial we shall look at obtaining the least squares fit |
22 of a given data-set. For this purpose, we shall use the same |
22 of a given data-set. For this purpose, we shall use the same |
23 pendulum data used in the tutorial on plotting from files. |
23 pendulum data that we used in the tutorial on plotting from files. |
24 |
24 |
25 To be able to follow this tutorial comfortably, you should have a |
25 To be able to follow this tutorial comfortably, you should have a |
26 working knowledge of arrays, plotting and file reading. |
26 working knowledge of arrays, plotting and file reading. |
27 |
27 |
28 A least squares fit curve is the curve for which the sum of the |
28 A least squares fit curve is the curve for which the sum of the |
40 |
40 |
41 In matrix form... |
41 In matrix form... |
42 {Show a slide here?} |
42 {Show a slide here?} |
43 |
43 |
44 We have already seen (in a previous tutorial), how to read a file |
44 We have already seen (in a previous tutorial), how to read a file |
45 and obtain the data set. We shall quickly get the required data |
45 and obtain the data set. Let's quickly get the required data |
46 from our file. |
46 from our file. |
47 |
47 |
48 In []: l = [] |
48 In []: l = [] |
49 In []: t = [] |
49 In []: t = [] |
50 In []: for line in open('pendulum.txt'): |
50 In []: for line in open('pendulum.txt'): |
77 and c. lstsq returns a lot of things along with these |
77 and c. lstsq returns a lot of things along with these |
78 coefficients. Look at the documentation of lstsq, for more |
78 coefficients. Look at the documentation of lstsq, for more |
79 information. |
79 information. |
80 In []: result = lstsq(A,tsq) |
80 In []: result = lstsq(A,tsq) |
81 |
81 |
82 We take put the required coefficients, which are the first thing |
82 We extract the required coefficients, which is the first element |
83 in the list of things that lstsq returns, into the variable coef. |
83 in the list of things that lstsq returns, and store them into the variable coef. |
84 In []: coef = result[0] |
84 In []: coef = result[0] |
85 |
85 |
86 To obtain the plot of the line, we simply use the equation of the |
86 To obtain the plot of the line, we simply use the equation of the |
87 line, we have noted before. T^2 = mL + c. |
87 line, we have noted before. T^2 = mL + c. |
88 |
88 |