Copyright: Copyright © Momentum Engineering Software


Activation Codes
Activation Codes:

Before the MathModeler program can be installed an activation code must be entered.  This reduces software piracy and allows us to sell you software at a lower price.

To obtain a copy of MathModeler:

1.  Go the Momentum Engineering Software Internet site:  www.momentumware.com

2.  Download the MathModeler setup program, MMsetup.exe.

3.  Run the setup program and when it asks for an activation code from the US and Canada call  877-256-7745 or from outside the US and Canada call  409-239-1315.  You will need to supply your name, company, the installation code and a VISA or Master Card credit card number.

4.  Once the activation code is entered the setup program will install MathModeler on your computer.


Antoine Equation
The Antoine equation is commonly used to represent pure component vapor pressures:

log (P) = A - B / (C + T)

MathModeler regress a more general form of this equation:

log (Y) = (aX + c) / (1 - bX)

You can obtain the Antoine coefficients, (A, B, C), from the MathModeler coefficients, (a, b, c) by substituting:

A = -a / b

B = (c + a / b) / b

C = - 1 / b


Auto Update
If Auto Update is checked the minimum, maximum and constant graph values are calculated automatically.  This is the recommended method.  Do not select Auto Update If you want to set these values manually.


Backgound Color
Set the graph background color.


Base 10 Logarithms
All logarithms used in MathModeler are natural or base 'e' logarithms.  If a base 10 logarithm is required you can divide each of the coefficients by the natural log of 10, (2.30258509), to convert the equation to a base 10 log form, example:

ln (Y) = a X1 + b X2 + c X3 . . .

A = a / ln(10)

B = b / ln(10)

C = c / ln (10)

log10 (Y) = A X1 + B X2 + C X3 . .


Black and White Graph Colors
Set graph colors to black and white.


Border Color
Set the graph border color.


Case Titles
The optional titles are printed on all printed output.  Title 1 is printed on the top line and title 2 is printed on the second line.


Contents

Introduction

Getting Started

License Agreement

Registering MathModeler


Copy Equation
Copy the currently displayed equation item to the clipboard; coefficients, residuals, std errors or a function.  You can then paste the item into other applications.


Create Function
Output the function to a disk file.


Cube Edge Color
Set the cube edge color.


Data Cell
Input data cells are arranged in columns and rows.  The left most column is the dependent variable and the other columns contain from 1 through 16 independent variables.  Each row represents a data point.


Data Header
The data header displays the variable names.  You can right click on the header to perform operations on the data columns such as copy, paste, scale or format.  You can also drag the dividers to change the column widths.


Data Points Color
Set the graph data points color.


Data Side Bar
The data side bar displays the data row numbers 1 through 99.  You can right click on the side bar to perform operations on the data rows such as copy, paste, clear, delete.


Default Graph Colors
Set graph colors to the default values.


Draw Graph
Select the 'Draw' button to draw the graph.


Entering Data
Entering Data:

Data are entered into MathModeler on the 'Data' tab in worksheet fashion.


Equation Grid Color
Set the equation grid color.  This is also the color for the equation line on 2D graphs.


Equation Sets
Regress equations in equation set.  If this box is not checked these equations are skipped, reducing the regression time.


Equation Surface Color
Set the equation surface color.


Equation Text Color
Set the equation text color.


Equations List
The equations list displays the best, (largest R squared), 1000 equations regressed.  To display the equation statistics select the equation and then select the Stats button or double click the equation.


Font Size
Select the print font size in points.


Functions
Output the equation as a function in one of four languages, Basic, C, C++ or FORTRAN.


Getting Started
Getting Started:

MathModeler displays three main pages, Data, Equations and Graph.  You can switch pages by selecting the tabs or by entering Alt+D, Alt+Q and Alt+G.

The Data page allows you enter and edit the input data.  This is the first step in finding an equation to represent a data set.  The data are entered in a worksheet manner, arranged in rows and columns.  Each row represents a data point.  The left most column 'Y' is the dependent variable.  The other columns 'X1, X2, ...' are from 1 to 16 independent variables.  The column header displays the variable names.  You can change the names of the variables by selecting the Variables option on the View menu.

You can copy, paste, delete, scale, clear and format columns by right clicking on the column headers.  You can also change the width of a column by draging the header column divider lines.  You can copy, paste, delete and clear rows by right clicking on the row side bar just to the left of column 'Y'.

A sample data file is shipped with MathModeler, to load the sample file select the File menu - Open.  Select the file "Sample" and then select the Open button.

Data Page

After the data are entered select the Equations tab to display the equations page.  Select the 'Start' button to begin the regression.  Wait a few seconds and then select the 'Stop' Button'.  The Equations list displays the best 1000 equations regressed to this point.  The equations are ranked and sorted by the regression coefficient, (R squared).  The regression coefficient varies from 1 (best fit) to 0 (worst fit).

Equations Page

On the left of the page the equation sets are displayed as they are regressed.  Mathmodeler divides the equations into 9 types called sets.  You can specify which sets are regressed by selecting Options on the View menu.  This is also where you can specify the maximum number of terms in the equations.  The regression time can be greatly reduced by limiting the maximum number of terms.

To view the equation statistics select an equation from the list and press the 'Stats' button, or double click the equation.

Equation Statistics

At the bottom of the Statistics window are six buttons the top three display different equation statistics while the bottom buttons print and copy the currently displayed statistics or close the statistics window.  The Residuals button displays the input Y values, the calculated Y values and the difference.  At the top right of the residuals is a button to display a scattergram.

Equation Residuals

The Std Errs button displays the regression standard errors

The Function button allows you to copy, print or create a file of the equation in the form of a computer function in four languages, Basic, C++, C and FORTRAN.  To paste the equation in a worksheet select the Function button and then the Copy Function Button.  You can then paste the equation into a worksheet as a Basic macro.  The default function name is "Func".  Select the Close button to close the Equation Statistics window.

Select the Graph tab to display the Graph page.  On the left side of the Graph page are the variables that appear in the selected equation.  Select two variables to graph then select the Draw button.

Graph Page

You can enter Ctrl+C and Ctrl+P to copy and print the graph.  When you copy the graph MathModeler will ask if you want to copy a picture (Bitmap Format) or the graph data points (Text Format).  If text format is selected 2D graph data points are copied to the clipboard in two columns X and Y.  If text format is selected for a 3D graph the Z values are copied to the top row and the X values are copied to the left most column.  The Y values are then copied as an array at the intersection of the X and Zs.  This is the format worksheets use for 3D surface charts.


Graph
You can zoom into a portion of the graph by clicking on the graph with the left mouse button, hold the button down and drag the rectangle to the portion of the graph to be displayed.  Click the graph again to zoom out.


Input Data
You can enter data in the cells or in the input data window located above the cells.


Input Location
The input location display.  The column is the variable name and the rows are numbered from 1 through 99.


Introduction
Introduction:

Many times we want to represent data with a mathematical equation so it can be used in a worksheet or computer program.  This can be done in a worksheet program if the form of the equation is known, but sometimes the equation form is not known.  Also, there may be several independent variables some correlate to the dependent variable and some do not.

MathModeler searches for a mathematical model to represent a data set.  The data are entered on the 'Data' tab in worksheet fashion.  Each row is a data point or observation.  The left most column (Y) is the dependent variable.  The other columns are the independent variables.  There can be from one to sixteen independent variables, (X1-X16).

Example:  Y = function (X1, X2, X3, ...)

After the data are entered you can select the 'Equations' tab.  You select the Start button to begin the regression.  MathModeler regresses many equations and lists them in order of the regression coefficient, (R squared).  R squared is a measure of how well the equation fits the data.  R squared varies from 0 to 1 with 1 being a perfect fit.  The number of equations regressed depends on the equation sets selected and the number of independent variables, from as few as 1100 to millions.

To view an equation statistics, select the equation from the list and then select the Stats button.  You can then print and copy the equation, view the regression statistics and output the equation to a file or the Windows clipboard as a Basic, C, C++ or FORTRAN procedure.

To view a graph of the equation select the 'Graph' tab.  Select the independent variables to graph and select the Draw button.


License Agreement

IMPORTANT - PLEASE READ CAREFULLY:  This Momentum Engineering Software, Inc. End User License Agreement ("EULA") is a legal agreement between you (either an individual or a single entity) and Momentum Engineering Software, Inc. ("MOMENTUM") for the software product identified above, which includes computer software and may include associated media, printed materials, and "online" or electronic documentation ("SOFTWARE PRODUCT"). By installing, copying, or otherwise using the software, you are agreeing to be bound by the terms of this EULA.  If you do not agree to the terms of this EULA, promptly return the unused software to MOMENTUM and your money will be refunded.

Information contained in this software product has been obtained by Momentum Engineering Software, Inc. ("MOMENTUM") from sources believed to be reliable.  However, MOMENTUM does not guarantee the accuracy or completeness of any information contained in this product and MOMENTUM is not responsible for any errors, omissions or damage arising out of the use of this product.  This product is licensed with the understanding that MOMENTUM is supplying information but is not attempting to render engineering or other professional services.  If such services are required, the assistance of an appropriate professional should be sought.

The SOFTWARE PRODUCT is licensed, not sold.

1.	GRANT OF LICENSE.  This EULA grants you the following rights:

Applications Software Use and Storage - You may install and use one copy of the SOFTWARE PRODUCT.  The primary user of the computer on which the SOFTWARE PRODUCT is installed may also install a second copy on a portable computer for his or her exclusive use.   The SOFTWARE PRODUCT should not be in use on both computers at the same time by different users.  You may also make a copy of the software on a portable diskette for backup purposes.

2.	DESCRIPTION OF OTHER RIGHTS AND LIMITATIONS.

Limitations on Reverse Engineering, Decompilation, and Disassembly.  The SOFTWARE PRODUCT contains copyrighted material, trade secrets, and other proprietary material, and in order to protect them you may not decompile, reverse engineer, or disassemble  the SOFTWARE PRODUCT.

Software Transfer.  You may transfer all of your rights under this EULA and all of the components of the SOFTWARE PRODUCT  to another user, provided you retain no copies, and provided the other party reads and accepts terms and conditions of this EULA.

Resale.  You may not resell, or otherwise transfer for value, the SOFTWARE PRODUCT.

Rental.  You may not rent, lease, or lend the SOFTWARE PRODUCT.

Copyright.  The SOFTWARE PRODUCT is protected by copyright laws and international copyright treaties, as well as other intellectual property laws and treaties.   Therefore, you may not copy or reprint any portion of the SOFTWARE PRODUCT except as described in this EULA or without written consent of MOMENTUM.

Termination.  Without prejudice to any other rights, MOMENTUM may terminate this EULA if you fail to comply with the terms and conditions of this EULA.  In such event, you must destroy the SOFTWARE PRODUCT. You may terminate this EULA at any time by destroying the SOFTWARE PRODUCT.

Export Law Assurances.  You agree that the SOFTWARE PRODUCT nor any other data related to MOMENTUM will be exported outside the United States except as authorized and as permitted by the laws and regulations of the United States

Limited Warranty.  MOMENTUM warrants that the SOFTWARE PRODUCT will perform substantially in accordance with the accompanying written materials for a period of ninety (90) days from the date if receipt.

Waiver of Implied Warranties.  As a material part of the consideration for this Agreement, you agree that you are taking the software "as is" with any and all latent and patent defects and that there is no warranty by MOMENTUM that the software is fit for a particular purpose.  You acknowledge that you are not relying upon any representation, statement or other assertion outside of the Agreement with respect to the performance, characteristics, quality or condition of the software, but are relying upon your investigation and use of the software. You are taking the software under the express understanding there are no express or implied warranties (except for the limited warranties set forth in the above paragraph).

Limited Liability.  In no event will MOMENTUM, or it's directors, officers, or employees be liable to you for any special, consequential, incidental, or indirect damages whatsoever (including, without limitation, damages for loss of business profits, business interruption, loss of business information, or any other pecuniary loss) arising out of the use or inability to use this software, even if MOMENTUM has been advised of the possibility of such damages.  The parties agree that the actual damages and consequential damages that might be sustained by you as a result of use of this software in accordance with this Agreement are uncertain and would be difficult to ascertain, and that the sum of Fifty and 00/100 Dollars ($50.00) would be reasonable compensation for any such damages. MOMENTUM hereby promises to pay, and you hereby agree to accept, such sum as liquidated damages, and not as a penalty, in the event of any such damages.  The provisions of this section shall apply if loss or damage, irrespective of cause or origin, results directly or indirectly to persons or property, from performance or nonperformance of the obligations imposed by this contract, or from negligence, active or otherwise.


Max Equation Terms
The maximum number of terms in an equation can be set from 1 through 20.  Equations with more terms than the maximum are skipped reducing the regression time.


Maximum Equation Terms
The maximum number of terms in an equation can be set from 1 through 20.  Equations with more terms than the maximum are skipped reducing the regression time.


Maximum Terms
The maximum number of terms in an equation can be set from 1 through 20.  Equations with more terms than the maximum are skipped reducing the regression time.


Menu Items
Select menu items to perform task operations.


Move Selection
If this box is checked the worksheet data entry box is moved when the enter key is pressed.


Move Selection Direction
When the enter key is pressed the worksheet data entry box is moved in the selected direction.


Number of Copies
Select the number of copies to print.


Print Equation
Print the currently displayed equation item; coefficients, residuals, std errors or a function.


Print Equation Item
Print the currently displayed equation item; coefficients, residuals, std errors or a function.


Print Font
Select the print font.


Print Landscape
Print in landscape orientation.


Print Portrait
Print in portrait orientation.


Registering MathModeler
Registering MathModeler:

Before you can enter and regress your own data you must register this copy of MathModeler.  This reduces software piracy and allows us to sell you software at a lower cost.  When you register your copy of MathModeler Momentum Engineering Software will provide you with an activation code.

In the MathModeler program select the menu option Help/About MathModeler, then select the Register button to display the serial number and enter the activation code.

To register your copy of MathModeler in the US and Canada call 1-877-256-7645 or outside the US and Canada call 1-979-239-1315.

You will need the serial number and a VISA or MasterCard number.  The cost is $195 US.  Texas residents add 8.25% sales tax.

If you get a recording leave your phone number and an Email address and we will send you an activation code.


Regression Statistics
The 'Stats' button displays the equation regression statistics.


Residuals
Display the equation residuals.  The residuals are the difference between the observed and calculated values.


Rotate Graph
Select the 'Rotate' button to start and stop graph rotation.


Select Colors
Select the current color with the mouse or use the up and down arrow keys.  Then select the graph items to make them the current color.


Select Printer
Select the output printer.


Select Variables
Select the variables to graph.  Select one variable for a 2 dimensional graph and two variables for a 3 dimensional graph.  Variables in the equation not selected are set to the constant value specified in the 'Variables' dialog box.


Set Graph Values
Calculate the graph minimum, maximum and constant values.  Selecting this button is not necessary if the Auto Update box is checked.


Standard Errors
Display the standardized error for each equation term.


Start Regression
The 'Start' button starts the data regression process.  You can also press the F9 key.


Status Bar
The status bar display the current status of the program, (Working, Ready, . . .) and the progress of the data regression.


Stop Regression
The 'Stop' button stops the data regression process.  Equations regressed to this point are displayed.


Surface Shading
Apply shading effect to the equation surface.


Tabs
Select the tabs to display the pages, (Data, Equations, Graph).

The Data page is used to enter the data to be regressed.  The left most column is the dependent variable.  The other columns contain from 1 to 16 independent variables.  Each row represents a data point.

The Equations page regresses the data and displays the equations sorted by the regression coefficients, (R squared).

The Graph page displays a graph of the selected equation.


Titles
The optional titles are printed on all printed output.  Title 1 is printed on the top line and title 2 is printed on the second line.


Tool Tips
When the cursor is held over a control a text box appears describing the control, this is called a 'Tool Tip".  Tool tips are only displayed if this box is checked.


Variable Constant Value
The constant value of a variable on the graphs.  The maximum number of independent variables that can be graphed at one time is two.  If a variable appears in an equation but is not selected as a graph variable it is set to this value.  If 'Auto Update' at the bottom of the Variables box is checked this value is the average input value.


Variable Maximum Value
The maximum value of a variable on the graphs.  If 'Auto Update' at the bottom of the Variables box is checked this value is calculated from the input data.


Variable Minimum Value
The minimum value of a variable on the graphs.  If 'Auto Update' at the bottom of the Variables box is checked this value is calculated from the input data.


Variable Name
The independent variable name, default 'X1, X2, ...', can be changed for input and output purposes.  However 'Xn' is used in the equations and functions for readability.  The maximum length is 15 characters.


Worksheet functions
Worksheet Functions:

You can copy equations to worksheets as macro functions.  Select the equation from the equations list and press the 'Stats' button on the Equations page.  On the Regression Statistics dialog box select the 'Function' button.  Select Basic Function as the Language if it is not already.  Then select the 'Copy Function' button.

You can then open your worksheet program and paste the function as a macro.  The default function name is "Func".

In Microsoft Excel you access the macros by pressing Alt+F8.  Enter the macro name, "Func", and select Create.

Enter Ctrl+A and press Delete to clear the edit box and then press Ctrl+V to paste the macro code.  Enter Alt+Q to close the edit macro dialog and return to the worksheet.

You can then call the macro by entering =Func(X1, X2, . . . into a cell.


X Axis Label Color
Set the X axis label color.


X Segments
Set the number of segments, (grid lines), along the X axis.


XY Grid Line Color
Set the X-Y (back) plane grid color.


XY Surface Color
Set the XY plane, (back), surface color.


XZ Grid Line Color
Set the X-Z (bottom) plane grid color.


XZ Surface Color
Set the XZ plane, (bottom), surface color.


Y Axis Label Color
Set the Y axis label color.


Y Segments
Set the number of segments, (grid lines), along the Y axis.


Y Variable Name
The dependent variable name, default 'Y', can be changed for input and output purposes.  However 'Y' is used in the equations and functions for readability.  The maximum length is 15 characters.


YZ Grid Line Color
Set the Y-Z (right) plane grid color.


YZ Surface Color
Set the YZ plane, (bottom), surface color.


Z Axis Label Color
Set the Z axis label color.


Z Segments
Set the number of segments, (grid lines), along the Z axis.