Normally the first window on the display is the 2-D Window, which is opened automatically at the beginning of the program.  It shows you immediately a coordinate system (this is a chart) with some data in it. The content is depending from your last preferences saving.

• Clicks with Mouse
  
• Subscript and Superscript
  
• Error Handling
  
• Program Concept
  
• AutoScale
  
• What is a Graph?
  

Here now a short description of some interactive control elements of SimplexNumerica in connection with the 2-D Window. You can test the physical x/y coordinate system to bring up the following diagram on the display. 

The numbers in the above picture are the place in the window, to which you must click with the left mouse button. You can either double clicking or simply with the right mouse button, in order to cause the following functions.

1        Double-click with the left mouse button or single-click with the right mouse button in the inside of the coordinate system activates the dialogbox for <System Configuration>.

2        Double-click with the left mouse button on the tick Marks activates the dialogbox for <Interval dimension>.

 Single-click with the right mouse button on the Tiick Marks activates the dialogbox <Coordinate System>.

3         Double-click with the left mouse button or single-click with the right mouse button on the text scaling activates the dialogbox format of numbers. 

4         Double-click with the left mouse button or single-click with the right mouse button on the axis labelling activates the dialogbox for labelling (depend on which one was clicked).

With control plus single-click with the left mouse button text can be freely positioned in the window.  The control key should be pressed only briefly.

5         Double-click with the left mouse button or single-click with the right mouse button on the markers activates a popup menu for the current graph and hence for the current memory record. 

6        With control plus single-click with the left mouse button the additional axes can be positioned.  The control key must be pressed also here only briefly. 

The above-mentioned interactive calls can you apply at present only in the 2-D Window. In the 3-D Window the particular functions can be called only with help of the right mouse button. Then a popup menu appears, similarly to the Pulldown-menu at the mouse position.

The texts of the coordinate system inscription can be placed also in Subscript and Superscript.  The input of the texts occurs as follows in the dialogbox:

Highly (Superscript):                  with ` or `[...]

                     e.g. s`2                results in                 s²

                     min`[-1 ]              results in                 min^-1  

Deeply (Subscript):                    with ' or '[...]

                     e.g.  H'2SO'4         results in                 H₂ SO₄

                     P'[Engine]             results in                 P_Engine

The text will be correctly represented in the coordinate system. 

A disregard of the definition of individual Interpolation and Approximation functions must lead inevitably errors.  In advance the foreseeable possible errors by the program are intercepted as far as possible.

These problems do not occur e.g. with none math programs, since one can estimate exactly, which user or function error could occur.  A user error would e.g. be present if an x-value with two y-values is occupied and afterwards e.g. the Cubic Spline function is called instead of the Cyclic Spline function.  So it will be fine when the user knows what he wants and what really feasible is.

SimplexNumerica differentiates between two program modes, TestMode and EvaluationMode.  All calculations are executed basically in the TestMode, even if you are in the EvaluationMode. E.g., a pocket calculator executes always the calculation with the number in the display.  SimplexNumerica proceeds similarly.  If e.g. several series of measurements in form of graphs are overlaid, then you are inevitably in the EvaluationMode.  If an interpolation for all series of measurements is starting, afterwards, SimplexNumerica copies the results from TestMode to EvaluationMode.

Normally this would not care the user, if he is not intervening in this automation.  But exactly, you can intervene when you want.  The TestMode is particularly suitable for fast, direct calculations and tests, e.g. if you would select the suitable interpolation function for a certain measuring data series, by liking to execute several calculations for the same data record.

In the TestMode the coordinate system is restructured after each modification. The TestMode is only for algorithm relevant executed calculations; therefore it held no inscriptions and diagram features.

In addition, you can operate in the EvaluationMode and influence directly the internal memory record.  This takes place over a special dialogbox, which appears automatic with each relevant calculation or you can call it manually from the Pulldown-menu <Edit>, menu option <Memory Dialog>.  You will find a better description of this dialogbox under next chapters. 

If you are in the TestMode and want to turn into to the EvaluationMode, then you can select the menu option <Set EvaluationMode> in the Pulldown-menu <Edit>. If you would like to return later briefly to the TestMode, then you can do this over the key SPACE or in the Statusbar icon.  Renewed pressing of the key lets you return again to the EvaluationMode.  If you would like to leave however the EvaluationMode completely, then you can do this over the selection of the Pulldown-menus <Edit>, menu option <Set TestMode>.  You will be asked whether the overlapping memory is to be preserved or deleted. If the memory is cleared, then the memory record must again be re-structured. 

AutoScale is used to automatically scale the axes of any chart based on the extremes (maximum/minimum) of all Memory Record Graphs.

Autoscaling may be set individually on the x, y or z axis or globally on all extra axes. The default is to AutoScale all axes.

When Autoscaling, the axis range is automatically computed and the dependent axis is scaled to include the range of the graph or data being plotted.

In the TestMode an AutoScale dialogbox for the interval calculation appears after each calculation, which leads to an output in the coordinate system.  This dialogbox and the dialogbox for the interval input and partitioning of the interval are explained in the following chapter.

The program flow will be improved by this AutoScale dialogbox crucially, because the user does not have to look in a Pulldown-menu for the continuation of the program, because it is explicitly referred what to do next. 

The AutoScale dialogbox inquires to you whether SimplexNumerica is to make the interval scaling automatically or whether it will be done manually, whereby you can combine both methods. Further is it important to know to which coordinate system axis (e.g. right axis) the interval scale refers.

By which data array the interval boundaries are calculated is depend from selection SampleData or CurveData. 

Meaning of the individual branches:

AutoScale (automatic interval calculation and scaling)

Call that AutoScale routine for the calculation of optimal interval delimitation and rounded numbers at the axes. How the interval delimitation has to take place can be decided under Pulldown-menu <Edit>, menu option <Properties>. 

Manual with Auto (manually with automatic interval calculation)

Here the AutoScale menu option will become executed and the values are automatically entered in an interval dialogbox, of where they can be edited. The automatically calculated physical dimensions are thus always only once to be entered. 

Manual without Auto (manually without automatic interval calculation)

Here the menu option AutoScale is not executed.  Use it, if you like to determine the interval boundaries manually.

Remain (Interval like before)

Here the originally available interval will be preserved.  If you want to use the same interval delimitation several times consecutively, please click on remain button, and the coordinate system is represented immediately.  An exception represents the logarithmic coordinate system; whereby a dialogbox will be appearing for the input of the logarithmic interval border. 

Cancel (Does nothing)

Clicking cancel causes that the following program run will be interrupted, i.e. the coordinate system is not re-structured.

Next, the editing boxes of the interval delimitation and partitioning follows. 

The following dialogbox appears after pressing the Manual buttons:

The interval delimitation (Xmin, Xmax, Ymin, Ymax) can be determined separately for the coordinate system and the graph border.

To avoid the input off the Graph Interval you can select <Copy to Graph Interval>. Simplex Numerica adapts automatically the interval boundaries of the graph to those of the coordinate system. 

The next dialogbox will be showing the axes Subdivisions. Before it appears, it is possible to recalculate this depend on your interval setting. To avoid this, please unhook the entry <Calc Axis Subdivision>.

Furthermore additional characters can be attached for Scaling Text. This can take place separately for each axis, or even for further axes, e.g. the right hand axis. Use also here subscript and superscript for text input.

You can break a coordinate system on two sides. Hook <Break between> to do this and put in the coordinates for the break point. You can do it only in x direction.

Axis from right to the left

Normally we scale from left to right side. To do it vice versa, e.g. from 20 to 5 instead from 5 to 20, we have to define xmin > xmax (e.g. xmin = 20 and xmax = 5) and using for the Axis Subdivision dx and dy negative values (e.g. dx = -2).  We can do that with each axis.

Business Diagram

A Business Diagram is in SimplexNumerica a coordinate system, which used no genuine x-values. This means that only y-data occur to be entered.  SimplexNumerica utilize the legend in the ArrayEditor for the x-Axis (first grey column in the ArrayEditor).

Business diagrams are usually Business Diagrams. To show a Business Diagram, you must select y-Columns in the ArrayEditor. Only when y-Columns are selected with a red border, then it concerns a Business Diagram.  Only even if one x or z-column is selected with a red border, then it is no longer more a Business Diagram.

Hint:

You can select a y-Column for Business Diagram purposes when you click with the left mouse button below the column header. 

In SimplexNumerica, a Graph is only one Record among other Memory Records. A graph consists of measurement data (SampleData) and [not necessary] a curve (CurveData).

Sample and GraphData

• SampleData are shown in form of Markers.
• Each measurement point is represented by one marker.
• A curve consists on sample data (called CurveData).
• CurveData are normally calculated by the program.

Graph = SampleData + CurveData

• A Graph is not a chart!
• A chart can have more than one Graph.
• Is there more than one graph in a chart than the program stays in the EvaluationMode.
• Is there only one graph in a chart than the program can stay in the Evaluation or TestMode.

Now, we will explain these topics in the next figure.