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GNU Emacs Calc 2.02 Manual

3.7.26 List Tutorial Exercise 8

The first step is to build a list of values of x.

1: [1, 2, 3, ..., 21] 1: [0, 1, 2, ..., 20] 1: [0, 0.25, 0.5, ..., 5] . . . v x 21 RET 1 - 4 / s 1

Next, we compute the Bessel function values.

1: [0., 0.124, 0.242, ..., -0.328] . V M ' besJ(1,$) RET

(Another way to do this would be 1 TAB V M f j.)

A way to isolate the maximum value is to compute the maximum using V R X, then compare all the Bessel values with that maximum.

2: [0., 0.124, 0.242, ... ] 1: [0, 0, 0, ... ] 2: [0, 0, 0, ... ] 1: 0.5801562 . 1: 1 . . RET V R X V M a = RET V R + DEL

It's a good idea to verify, as in the last step above, that only one value is equal to the maximum. (After all, a plot of sin(x) might have many points all equal to the maximum value, 1.)

The vector we have now has a single 1 in the position that indicates the maximum value of x. Now it is a simple matter to convert this back into the corresponding value itself.

2: [0, 0, 0, ... ] 1: [0, 0., 0., ... ] 1: 1.75 1: [0, 0.25, 0.5, ... ] . . . r 1 V M * V R +

If a = had produced more than one 1 value, this method would have given the sum of all maximum x values; not very useful! In this case we could have used v m (calc-mask-vector) instead. This command deletes all elements of a "data" vector that correspond to zeros in a "mask" vector, leaving us with, in this example, a vector of maximum x values.

The built-in a X command maximizes a function using more efficient methods. Just for illustration, let's use a X to maximize `besJ(1,x)' over this same interval.

2: besJ(1, x) 1: [1.84115, 0.581865] 1: [0 .. 5] . . ' besJ(1,x), [0..5] RET a X x RET

The output from a X is a vector containing the value of x that maximizes the function, and the function's value at that maximum. As you can see, our simple search got quite close to the right answer.