Help Manual

Contents






Sigma Magic Help Version 17

Contour Plot

Overview

The Contour Plot tool can create a contour and 3D surface plot for the data points. These plots can help visualize the data in 2/3 dimensions. Contour Plot is typically used to plot data for the continuous data type where the output is a function of two input variables.

To add the Contour Plot tool to your active workbook, simply follow these steps: Click on the 'Graph' tab, then select 'Contour Plot' from the dropdown menu.

Inputs

Click on Analysis Setup to open the menu options for this tool.

Setup

A sample screenshot of the setup menu is shown below.
inputs
1
Chart Type: Specify the type of chart to create. The following options are available:
OptionDescription
ContourCreate a 2D contour plot of the data. Note that the contour plot is created as a projected top view of a surface plot.
SurfaceCreate a 3D surface plof of the data.
2
Num Levels: Specify the number of contours or levels that should be shown on the plot. If you set the value to Auto, the system will pick an appropriate number of levels. You can pick up to 20 levels for this plot.
3
Colors: Specify the colors to use for the contours. The system will pick the default colors if you set the value as Auto. Otherwise, it will use the color index you specify.
4
Legend: Specify if you want to display the legend on the chart. The available options are:
OptionDescription
NoneDo not display any legend on the chart.
BottomDisplay the legend at the bottom of the chart.
LeftDisplay the legend on the left side of the chart.
RightDisplay the legend on the right side of the chart.
TopDisplay the legend on top of the chart.
5
Help Button: Click on this button to open the help file for this topic.
6
Cancel Button: Click on this button to discard any changes and close the dialog box.
7
OK Button: If possible, click this button to save any changes and compute the analysis outputs.

Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis. Data
1
Variable Names: Specify the names of the X, Y, and Z variables. Make sure you have no special characters or spaces in the name. The default names for these variables are X, Y, and Z.
2
X Values: Specify the minimum, increment, and maximum values for the X-axis. Use a reasonable number to get a good resolution for the contour plot while keeping the total number of iterations low. The default value is ten intervals between the minimum and maximum values.
3
Y Values: Specify the minimum, increment, and maximum values for the Y axis. Use a reasonable number to get a good resolution for the contour plot while keeping the total number of iterations low. The default value is ten intervals between the minimum and maximum values.
4
Z Equation: Specify the equation that relates the Z variable to the X and Y variables. This equation will generate the data points for the contour plot. Use valid mathematical equations such as sin(X) + Y^2.

Charts

You will see the following dialog box if you click the Charts button. Charts
1
Title: The system will automatically pick a title for your chart. However, if you want to override that with your title, you can specify a title for your chart here. Note that this input is optional.
2
Sub Title: The system will automatically pick a subtitle for your chart. However, if you want to override that with your subtitle, specify a subtitle for your chart here. Note that this input is optional.
3
X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your label for the x-axis, you can specify a different label here. Note that this input is optional.
4
Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your label for the y-axis, you can specify a different label here. Note that this input is optional.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. Verify The software checks if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, they are shown as green-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. The verification checks are shown in the orange exclamation mark if the verification checks result in a warning. Finally, any checks required to be performed by the user are shown as blue info icons.
1
Item: The left-hand side shows the major tabs and the items checked within each section
2
Status: The right-hand side shows the status of the checks.
3
Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below.
outputs
>
Notes: The text output of the analysis is sent to the notes section. This section contains the minimum, number of increments, and maximum X and Y values. It also specifies the formula to calculate the Z values (if specified). The Analysis Results section contains the name of the Z variable and the minimum, maximum, and average values of the Z values.
>
Graphs: The graphs section contains the contour and surface plot of the given data set. You can use the Excel functionality to rotate the graph as required.
1
Item: The left-hand side shows the major tabs and the items checked within each section
2
Status: The right-hand side shows the status of the checks.
3
Overall Status: Shows the overall status of all the checks performed. If all the checked items are okay, the status image in the header will show a green checkmark. If any checks fail, the header status image will show a red cross mark.
If the verification is unsuccessful, you cannot compute the analysis outputs.

Notes

Here are a few pointers regarding this analysis:
  • The background color of the graph can be changed by clicking the Options button in the Sigma Magic software. However, most formatting can be accomplished using standard Excel functions to format the graph. For example, you can change the orientation view of the graph using Excel. If you click on Compute Outputs again, any formatting you do with the Excel functions will be lost.
  • You can change the chart's orientation using Excel to view it from the top. In Excel 2010, you can change the view by clicking on the graph, selecting Layout, 3-D Rotation, and setting the X angle to 0 degrees and the Y angle to 90 degrees. This results in a traditional 2D contour plot.
  • The names of the X and Y variables have to be unique and cannot contain special characters like spaces, commas, plus signs, percentage signs, minus signs, division signs, etc. This ensures no calculation errors for the Z if a formula is defined.
  • Note that variable names are not case-sensitive. A variable named X is the same as x. You can either use X or x in the formula for Z.
  • The worksheet is updated once you define the variables in the dialog box and click OK. Any values you have already defined in the worksheet are cleared and over-written. This ensures that your analysis is not corrupted with older values.

Examples

The following examples are in the Examples folder.
  • Create a contour plot for the function Z = sin^2(x) + cos^2(y) for x and y values between 0 and 360 degrees (Optimization Equation 1.xlsx).
  • Create a contour plot for the function Z = 2x^2 + 2y^2 - 4 to determine its minimum value (Optimization Equation 2.xlsx).
  • Create a contour plot for the function Z = x^2+2xy+y^2-2x-3 to visualize the shape of the function (Optimization Equation 3.xlsx).