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| -rw-r--r-- | least_square_fit/script.rst | 36 |
1 files changed, 21 insertions, 15 deletions
diff --git a/least_square_fit/script.rst b/least_square_fit/script.rst index 850223a..429b640 100644 --- a/least_square_fit/script.rst +++ b/least_square_fit/script.rst @@ -58,8 +58,8 @@ Let us start this tutorial with the help of an example. .. R4 -Generate a least square fit line for l v/s t^2 using the data in the file -'pendulum.txt'. +Generate a least square fit line for l v/s t^2 using the data in the +file 'pendulum.txt'. .. L5 @@ -69,11 +69,12 @@ Generate a least square fit line for l v/s t^2 using the data in the file We have an input file generated from a simple pendulum experiment. -It contains two columns of data. The first column is the length of the -pendulum and the second is the corresponding time period of the pendulum. +It contains two columns of data. The first column is the length +of the pendulum and the second is the corresponding time period +of the pendulum. -As we know, the square of time period of a pendulum is directly proportional to -its length, we shall plot l vs t^2 and verify this. +As we know, the square of time period of a pendulum is directly +proportional to its length, we shall plot l vs t^2 and verify this. To read the input file and parse the data, we are going to use the loadtxt function.Switch to the terminal. @@ -88,8 +89,8 @@ loadtxt function.Switch to the terminal. .. R6 -We can see that l and t are two sequences containing length and time values -correspondingly. +We can see that l and t are two sequences containing length and time +values correspondingly. Let us first plot l vs t^2. @@ -118,8 +119,8 @@ values of m and c. .. R8 let us now generate the A matrix with l values. -We shall first generate a 2 x 90 matrix with the first row as l values and the -second row as ones. Then take the transpose of it. Type +We shall first generate a 2 x 90 matrix with the first row as l values +and the second row as ones. Then take the transpose of it. Type .. L9 :: @@ -129,7 +130,8 @@ second row as ones. Then take the transpose of it. Type .. R9 -We see that we have intermediate matrix. Now we need the transpose. Type +We see that we have intermediate matrix. Now we need the transpose. +Type .. L10 :: @@ -139,7 +141,8 @@ We see that we have intermediate matrix. Now we need the transpose. Type .. R10 -Now we have both the matrices A and tsq. We only need to use the ``lstsq`` +Now we have both the matrices A and tsq. We only need to use +the ``lstsq`` Type .. L11 @@ -161,7 +164,8 @@ is the matrix p i.e., the values of m and c. .. R12 -Now that we have m and c, we need to generate the fitted values of t^2. Type +Now that we have m and c, we need to generate the fitted values of t^2. +Type .. L13 :: @@ -202,7 +206,8 @@ Here are some self assessment questions for you to solve - Error 2. The plot of ``u`` vs ``v`` is a bunch of scattered points that show a - linear trend. How do you find the least square fit line of ``u`` vs ``v``. + linear trend. How do you find the least square fit line + of ``u`` vs ``v``. .. L16 @@ -214,7 +219,8 @@ And the answers, 1. The function ``ones_like([1, 2, 3])`` will generate 'array([1, 1, 1])'. -2. The following set of commands will produce the least square fit line of ``u`` vs ``v`` +2. The following set of commands will produce the least square fit + line of ``u`` vs ``v`` :: A = array(u, ones_like(u)).T |