Tag Archives: TI-84 Plus Pocket SE

Nelder-Mead algorithm on the TI-84 Plus SE

This mean nothing more than to prove that implementing the Nelder-Mead algorithm on the TI-84 is possible. In reality, the time it will take for a TI-84 Plus SE to arrive a solution for any practical non-linear problem renders this somewhat a last resort option. That is, in the absence of any modern computer or even a decent mobile phone 🙂

The program is implemented in the native TI-Basic, which is ported from the program for the same problem previously done on TI Nspire and Casio fx-9860GII. It took some efforts to port the program as the resources on the TI-84 is comparatively limited. For example,variable names are also restricted to single character, but thanks to list, things are easier.

With the availability of the new generation TI-Connect software, the Program Editor has returned and this tool greatly helped programming the Nelder-Mead on TI-84. Although unlike the more advanced Nspire Software which is able to run the program on PC instead of having to download the program to the TI-84 every time, editing TI-Basic in PC with a full keyboard and full screen is way more comfortable than to doing so on the calculator. The new TI-Connect CE PC software looks really nice.

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Screens of the actual program running on a TI-84 Plus Pocket SE. The equation to solve is the Rosenbrock function of f(x,y) = (a-x)^2 + b(y-x^2)^2, using a=1 and b=100.

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The TI-84 Plus Pocket SE took 12 minutes to complete, while its big brother TI Nspire took only 22 seconds.

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TI-84 Plus Pocket SE and the Simplex Algorithm

The TI-84+ Pocket SE is the little brother of the TI-84 Plus. They are almost identical in terms of screen resolution, processor architecture and speed, and also the OS. The Pocket version measured only 160 x 80 x 21mm in dimension and weighted at 142g, considerably more compact than the classic version.

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This little critter is full of features from the 2.55 MP OS. It will easily blow away the mainstream Casio series of the same size like the fx991 and even fx5800P with TI’s built-in advanced functions like ANOVA. Nevertheless, the TI-84 Plus series is still considered a stripped down version of the TI Nspire and TI-89 Titanium, and as such personally I do not expect or intent to run on it sophisticated calculations or programs like the Nelder-Mead algorithm that fits comfortably on the Nspire or Titanium.

Having said that, many complex calculation can easily be accomplished with the rich set of advanced features available out-of-the box in the TI-84, even without programming. One such example is the linear programming method implemented in the simplex algorithm for optimization. Consider the following example: In order to maximize profit, number of products to be produced given a set of constraints can be determined by linear programming. This set of constraints can be expressed in linear programming as system of equations as

8x + 7y ≤ 4400   :Raw Material P
2x + 7y ≤ 3200   :Raw Material Q
3x + y ≤ 1400    :Raw Material R
x,y ≥ 0

In the above, two products are considered by variable x and y, representing the constraints for product A and B respectively. Each of the first three equations denote the raw material requirements to manufacture each product, for material P, Q, and R. Specifically, product A requires 8 units of raw material P, 2 units of raw material Q, and 3 units of raw material R. The total available units for these three raw materials in a production run are 4400, 3200, and 1400 units respectively. When using the Simple Algorithm to maximize the function

P = 16x + 20y

which represents the profits for product A and B are $16 and $20 each, the tableau below is set up initially with slack variables set as

  8   7 1 0 0 0 4400
  2   7 0 1 0 0 3300
  3   1 0 0 1 0 1400
-16 -20 0 0 0 1    0

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Using the *row() and *row+() matrix function, the Simplex Algorithm can be implemented without even one line of code. The final answer is obtained as 11200 which is the maximum profit by producing 200 Product A and 400 Product B.

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