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The Ultimate Windows Math Toolbox

 

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23 June 2008
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Optimise / Minimise

This window provides a tool to find the values of variables that produce the optimum (i.e. minimum) value of an expression. To gain access to this window, select the menu item File => Optimise/Minimise.

Navigation Special Tool

Purpose

Given an arbitrary expression containing n variables a1, a2 ... an, the aim here is to find a set of values for these variables so as to 'optimise' the value of the expression. By 'optimise' is meant finding the smallest value of the expression. (We can easily enough find the maximum of an expression by negating it and then finding the minimum value.) When n = 2, the problem can be conceived as to how to find the lowest point when hiking around in hilly countryside. Clearly, our finishing point can depend on where we started from.

Select the Order

First select the order, i.e. the number of variables, n, from 1 upwards by clicking on the spin buttons to the right of where the order is shown. The window will increase its height appropriately. You can change the width of the window by dragging either side.

Enter the Data

Having selected the number of variables, enter their names and initial values. Use the 'Tab' key to step forwards from box to box. Using Shift+Tab will take your approximately backwards in a convenient sequence. You can of course click into any box. Also enter the expression to be minimised.

Calculate

When all the data has been entered, click on the button marked 'Calc', or press the 'Enter' key. The solutions, i.e. the values of the variables a1, a2 ... an, will appear in the boxes in the column(s) labelled 'Calculated'. The value of the expression will be shown in the box at bottom right, labelled 'Value'. The solutions can also be viewed in the multiple results window, by clicking on the button marked 'Show'.

Erase the Data

All of the data can be conveniently cleared away by clicking on the 'Erase' button button and providing confirmation that you do want to do this.

Open and Save

The 'Open...' and 'Save...' buttons allow you to store the calculation data to a plain text file, and reload them later. The 'Notes' button 'Notes' button. Closed book indicates that there are no contents. allows you to write some notes to be saved along with the data, and to view any notes you wrote previously.

Logging

When calculation logging is enabled in UltimaCalc's main window, the equations and solutions are automatically recorded to the log file when they are calculated. If logging is not enabled, a log file button 'Logging' button in its inactive state. is shown. Clicking on this when it is highlighted will calculate the current solution and log the data and solution.