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GNU Emacs Calc 2.02 Manual

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3.7.20 List Tutorial Exercise 2

Given x and y vectors in quick variables 1 and 2 as before, the first job is to form the matrix that describes the problem.

 
   m*x + b*1 = y

Thus we want a 19x2 matrix with our x vector as one column and ones as the other column. So, first we build the column of ones, then we combine the two columns to form our A matrix.

 
2:  [1.34, 1.41, 1.49, ... ]    1:  [ [ 1.34, 1 ]
1:  [1, 1, 1, ...]                    [ 1.41, 1 ]
    .                                 [ 1.49, 1 ]
                                      ...

    r 1 1 v b 19 RET                M-2 v p v t   s 3

Now we compute trn(A) * y and trn(A) * A and divide.

 
1:  [33.36554, 13.613]    2:  [33.36554, 13.613]
    .                     1:  [ [ 98.0003, 41.63 ]
                                [  41.63,   19   ] ]
                              .

 v t r 2 *                    r 3 v t r 3 *

(Hey, those numbers look familiar!)

 
1:  [0.52141679, -0.425978]
    .

    /

Since we were solving equations of the form m*x + b*1 = y, these numbers should be m and b, respectively. Sure enough, they agree exactly with the result computed using V M and V R!

The moral of this story: V M and V R will probably solve your problem, but there is often an easier way using the higher-level arithmetic functions!

In fact, there is a built-in a F command that does least-squares fits. See section 11.8 Curve Fitting.


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