Scientist 3.0 Getting Started Guide - Version 1

Getting Started Guide
March 2006
Version 1
Liability Disclaimer
Micromath® and Scientist® are registered trademarks of Micromath.
© 2006 Micromath
Micromath reserves the right to change the specifications, functions, or
features, at any time, without notice.
Micromath has prepared this document for the exclusive use of its
employees and customers. The information contained herein is the
property of Micromath and shall not be reproduced without prior
written approval from Micromath.
Printed in the USA.
MS-DOS, Microsoft, Windows, Windows 2000, and Windows XP are
registered trademarks of Microsoft Corporation.
All other brand or product names mentioned may be trademarks,
service marks, or registered trademarks of their respective owners.
i
Contents
Introduction
1-1
About Scientist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
What's New In Scientist 3.0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Using This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Document Conventions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Terms and Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Fit or Least Squares Fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Dependent Variable Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Using Scientist Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Contents Tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Index Tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Search Tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Scientist Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Technical Support by Phone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
E-mail Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
First Model Assistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Feedback. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Requirements and Installation
2-1
System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1
Installing Scientist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
Create your Micromath Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Download and Install the Scientist Trial Software. . . . . . . . . . . . . . . . . . . . . . .
Register the Software and Create License Key . . . . . . . . . . . . . . . . . . . . . . . .
Unlock the Scientist Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientist® 3.0 Getting Started Guide - Version 1
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Contents
ii
Uninstalling Scientist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Understanding Scientist
3-1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
What Does Scientist Do? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
Types of Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model Entry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameter Entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Minimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Differential Equation Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laplace Transform Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistics Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Graphic Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-2
3-2
3-2
3-3
3-3
3-3
3-4
3-4
3-4
Components and File Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spreadsheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Variable and Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistics Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using Scientist
3-5
3-5
3-5
3-5
3-6
4-1
Starting Scientist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
About the Scientist Main Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Scientist Menus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3
Working with Data
5-1
About Spreadsheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1
Manual Entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2
Importing Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2
Charting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4
Quick Chart Command from the Spreadsheet Interface . . . . . . . . . . . . . . . . . . 5-4
Scientist® 3.0 Getting Started Guide - Version 1
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Quick Chart Command from the Variable and Parameter Interface . . . . . . . . . 5-5
Chart Properties Dialog. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-6
Creating a Model
6-1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1
Create a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1
Model Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2
Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Independent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laplace Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dependent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Initial Conditions and Parameter Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performing a Least Square Fit (Regression)
6-3
6-3
6-3
6-4
6-4
6-5
6-6
6-6
7-1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1
Performing a Least Square Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2
Simplex Fitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5
Performing a Simulation
8-1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1
Performing a Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1
Calculating Statistics
9-1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1
Calculating Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1
Scientist® 3.0 Getting Started Guide - Version 1
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Contents
Statistical Output Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-4
Data Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameter Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Goodness-of-Fit Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis of Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-4
9-4
9-4
9-4
Scientist® 3.0 Getting Started Guide - Version 1
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Figures
Figure
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5-1
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Title
Page
Welcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
License Agreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Choose Installation Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Choose Start Menu Folder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Installation Complete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientist 3.0 Main Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spreadsheet Window. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Import Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Import Data - Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spreadsheet with Imported Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quick Chart Command from the Spreadsheet Interface . . . . . . . . . . . . .
Quick Chart from the Variable and Parameter Interface . . . . . . . . . . . . .
Chart Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientist Default Model File Template . . . . . . . . . . . . . . . . . . . . . . . . . . .
Least Square Fit 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Least Square Fit 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Least Square Fit 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Least Square Fit 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simplex Fit 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simplex Fit 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simplex Fit 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calculating Statistics 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calculating Statistics 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calculating Statistics 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientist® 3.0 Getting Started Guide - Version 1
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5-1
5-3
5-3
5-4
5-5
5-6
5-7
6-2
7-2
7-3
7-4
7-5
7-6
7-7
7-7
8-2
8-2
8-3
8-4
9-2
9-2
9-3
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Figures
Scientist® 3.0 Getting Started Guide - Version 1
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Tables
Table
1-1
2-1
4-1
4-2
Title
Page
Document Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
System Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientist Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientist Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientist® 3.0 Getting Started Guide - Version 1
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2-1
4-2
4-3
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Tables
Scientist® 3.0 Getting Started Guide - Version 1
1-1
1
Introduction
The Scientist® 3.0 Getting Started Guide provides a brief overview of
Scientist and provides step-by-step instructions for the most commonly
used procedures.
The following topics are included in this chapter:
Chapter Topics
•
•
•
•
•
•
•
About Scientist
What's New In Scientist 3.0
Using This Guide
Terms and Nomenclature
Using Scientist Help
Scientist Technical Support
Feedback
About Scientist
Scientist is a comprehensive modeling, data analysis, curve fitting
(regression), and graphing application for scientists and engineers.
Scientist can fit data to almost any model, including many that are
difficult or impossible with other scientific analysis software. Scientist
models can consist of:
• Non-linear algebraic equations
• Differential equations
• Laplace transforms
• Implicit equations
• Multivariate equations
• Combinations or systems of the above
Scientist was developed on the belief that researchers should not have
to learn complex programming languages or syntax to model systems
and analyze data. Scientist was designed to perform regression analysis
without programming. With Scientist you create models by simply
entering equations much like you would with a pencil and paper. Just
provide Scientist with your data and reasonable initial estimates for your
parameter (coefficient) values and let Scientist's powerful regression
algorithms calculate the best fit values for your model. Scientist lets you
focus on science, not software.
Scientist® 3.0 Getting Started Guide - Version 1
1-2
Introduction
After fitting your data, Scientist gives a complete statistical analysis of
your results. Scientist provides descriptive statistics and parameter
statistics, including parameter estimates, confidence limits, various
measures of goodness-to-fit, variance-covariance and correlation
information, and analysis of residuals.
What's New In Scientist 3.0
Scientist 3.0 is the first revised version of Scientist in almost ten years.
Our goal in version 3.0 was to make Scientist easier to use and more
reliable while preserving Scientist's unique computational functionality.
The following are some of the improvements.
• Improved graphics Functionality
Scientist now supports over 50 different 2D and 3D chart types,
including statistical series, vector3D series, contour series, waterfall
series, and many more. In addition, every element of each chart can
be completely customized using context-sensitive, intuitive interfaces.
Hundreds of standard themes can be used to create a look and feel
that best presents your data, or you can create custom themes of
your own. Features such as lighting, transparency, and shading are
also adjustable. All formatting items can be saved as a customized
chart template, making formatting multiple charts a breeze.
• Project Interface
Scientist's new, easy-to-use project interface makes it easy to keep
track of your data, models, and results.
• Improved Import/Export Functionality
Scientist 3.0 makes it easier to get your data into and out of Scientist.
Now you can import your data directly from Microsoft Excel
spreadsheets, Access databases, SQL and DNS databases, or any
delimited file format. You can export your graphics in nine different
formats, including .jpeg, .pdf, postscript, and VML.
• Cutting and Pasting
Cutting and pasting is easier in Scientist 3.0. You can cut data from
any Windows application and paste it into a Scientist spreadsheet and
vice versa. Charts can be quickly and easily cut and pasted into any
Windows document, spreadsheet application, or presentation
application.
• Speed
Scientist 3.0 has been optimized for 32-bit operating environments
and takes full advantage of today's faster CPUs and abundant
memory. With proper hardware, Scientist 3.0 can fit data to the most
complex models in a fraction of the time required by earlier versions
or other data analysis applications.
• Stability
Scientist 3.0 has the powerful fitting algorithms that have made
Scientist the data analysis tool of choice for thousands of scientists
and engineers worldwide since 1995. Scientist 3.0 has improved error
handling and stability. On those rare occasions when Scientist 3.0
encounters an exception, the user is given an error message and the
opportunity to save data or work in progress.
Scientist® 3.0 Getting Started Guide - Version 1
Introduction
1-3
• Support
With the release of Scientist version 3.0, Micromath has expanded its
technical support. In addition to telephone and e-mail support, users
of Scientist 3.0 can report and track bugs or make suggestions on
Micromath's web site. Licensed users can also download service
releases from the web site as they become available.
Using This Guide
This guide is designed to make Scientist easy to use. This guide contains
screenshots and instructions for the procedures you need to perform.
Document Conventions
This guide uses the following document conventions, listed in Table 1-1:
Table 1-1 Document Conventions
When you see
Boldfaced
Capitalized
Menu > Submenu
(boldfaced font)
CTRL+S
It means
Example
• Field names
Enter an amount in the Minimum
Step Size field.
• Button names
Click OK.
• Drop-down list names
Select the font from the Font drop
down list.
• Menu names
From the File menu, choose Close
All.
• Window names
From the Spreadsheet window, select
File > Import.
• Dialog box names
Click OK to save and close the
Configuration dialog box.
• Menu paths
Select Edit > Modify.
• Shortcut keys
Press CTRL+S to save your changes.
• Click the left mouse button
Click OK to save your changes.
CTRL+Shift+S
Click
Right-click
Scientist® 3.0 Getting Started Guide - Version 1
• Click the right mouse button Right-click and select Merge Cells
from the shortcut menu.
1-4
Introduction
Terms and Nomenclature
For historical reasons, Scientist uses terms and nomenclature that differ
somewhat from those used today in discussing non-linear regression
analysis. New users of Scientist may find the following terms helpful.
Fit or Least Squares Fit
Linear or non-linear regression minimizes the sum of the squares of the
differences between the observed values and the calculated values of
the model using the "best fit" parameters.
Dependent Variable Values
Observed values or those measured during the experiment. The values
of the data to be fit to the model.
Parameters
Coefficients. Values that are allowed to vary during the regression
analysis to produce the best fit.
Scientist® 3.0 Getting Started Guide - Version 1
Introduction
1-5
Using Scientist Help
The Scientist Help is automatically installed during the installation of the
Scientist program. To access the Scientist Online Help, do the following:
Step
Select Contents from the Help menu in any of the Scientist windows.
Scientist Help topics are grouped according to function and content in
three tabs: Contents, Index, and Search.
Contents Tab
• The Contents tab is intended to be used as an online Table of
Contents.
• Click a Closed Book icon to display all the help topics contained
within the book.
• Click an Open Book icon to close the book and all of its help topics.
• Click a Help Topic icon to display the specific help topic window
related to the icon.
Index Tab
The Index tab enables you to search for a help topic by using a keyword.
Search Tab
The Search tab enables you to perform a full-text search for Help topics.
Scientist Technical Support
Below are the various methods for getting technical support.
Technical Support by Phone
Licensed users of Micromath products can call 1.800.942.6284 for live
technical support between the hours of 8:00 a.m. and 5:00 p.m. central
time, Monday through Friday. Telephone support is limited to licensed
users only.
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Introduction
E-mail Support
Users may e-mail questions to our technical support team at
support@Micromath.com. If you have a question about a particular
calculation, please attach the relevant file(s) to your e-mail so our
technical support team can attempt to reproduce your result. All e-mail
inquiries will receive a response within two business days.
First Model Assistance
First model assistance is for new users of Scientist who have
downloaded the trial version and are trying to determine if Scientist can
help them solve a particular problem or fit a particular data set. To get
assistance with your first model, E-mail our first model team at
firstmodelteam@Micromath.com. Provide a brief description of the
system you are trying to model. Please attach a sample data set and
include reasonable initial values for any parameters involved.
Feedback
We hope you will like Scientist 3.0. We welcome and appreciate your
comments, suggestions, and complaints. We value your feedback and
believe that feedback from our users is the best way to improve our
products.
You can provide feedback by E-mail to feedback@micromath.com or by
telephone at 1.800.942.6284. You may also report and track bugs on
our web site. If you are reporting a bug, please include the model file,
data file, and relevant parameter data with your report so we can
attempt to reproduce and correct the error.
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Requirements and Installation
This chapter describes the requirements and the steps necessary to
install, uninstall, and upgrade Scientist. The following topics are
included in this chapter:
Chapter Topics
• System Requirements
• Installing Scientist
• Uninstalling Scientist
System Requirements
The following are the system requirements for Scientist.
Table 2-1 System Requirements
Component
Requirement
Micromath recommends running Scientist on Microsoft Windows XP
Operating System
Microsoft Windows 98 or higher (includes Windows ME)
Microsoft Windows NT 4.0 or higher (includes Windows 2000)
Scientist is not available for the Macintosh (Linux) at this time.
CPU
Memory
Disk Space
Display
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133 MHz or higher speed Pentium-compatible processor
64 MB (Megabytes) or more of RAM
100 MB or more of available disk space
SVGA or better
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Requirements and Installation
Installing Scientist
There are four steps to installing Scientist 3.0:
1. Create your Micromath Account
2. Download and Install the Scientist Trial Software
3. Register the Software and Create License Key
4. Unlock the Scientist Software
If you have already downloaded a trial version of Scientist 3.0, you can skip directly
to Register the Software and Create License Key.
NOTE
Create your Micromath Account
To create a Micromath account, do the following:
Step 1
Go to www.micromath.com.
Step 2
Click Create an Account.
Step 3
Complete the account registration form and click Create Account.
You should receive a message asking you to follow the link in the
registration E-mail sent to you.
Step 4
Follow the link in your registration E-mail and log in to validate your
E-mail address and activate your account. You will be directed to the My
Micromath page.
Download and Install the Scientist Trial Software
To download and install the Scientist trial software, do the following:
IMPORTANT
Step 1
Log in (if you are not already logged in to the Micromath web site).
Step 2
Click My Downloads.
Step 3
Click the appropriate link to download the Scientist trial version.
Step 4
(Optional) Move the setup file (SetupScientist30.exe) to the computer
on which you wish to install Scientist.
Be sure to close all Windows programs and disable any virus protection applications
before beginning the Scientist Setup program. Depending on your PC’s
configuration, the computer may need to restart after the installation completes. The
Windows Installer performs this action automatically at the end of the installation
process.
Step 5
Click Run in the Download Complete dialog or double-click the
SetupScientist30.exe file.
The Welcome dialog displays (Figure 2-1).
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Requirements and Installation
Figure 2-1 Welcome
Step 6
Click Next. The License Agreement dialog displays (Figure 2-2).
Figure 2-2 License Agreement
Step 7
After reviewing the License Agreement, click I Agree. The Choose
Installation Location dialog displays (Figure 2-3).
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Requirements and Installation
Figure 2-3 Choose Installation Location
Step 8
Specify the location where you want to install Scientist and click Next.
The Choose Start Menu Folder dialog displays (Figure 2-4).
Figure 2-4 Choose Start Menu Folder
Step 9
Specify the Start Menu folder in which you would like to create the related
Scientist shortcuts and click Install.
Step 10 As the Setup program finishes installing Scientist on your computer, the
Scientist 3.0 Read Me file displays.
The Read Me file contains the latest information about Scientist from Micromath.
Please take time to review this document.
NOTE
Step 11
When installation is complete, the Installation Complete dialog displays
(Figure 2-5).
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Figure 2-5 Installation Complete
Step 12 Click Close to exit the Setup program.
Register the Software and Create License Key
Your Scientist order must be authorized by a Micromath sales
representative to register products and obtain license keys. If your
order was placed with a purchase order, requires validation, or if you
just created your account, it is possible that your order is not yet
authorized. If you do not see your product and type of license after
completing Step 4 below, please E-mail our sales department. After
receipt of your request, your account should be authorized in two
business days or less.
To register the software and create license key, do the following:
Step 1
Start the Scientist program. A dialog with three separate boxes displays.
Choose OK.
Step 2
When the program is starting up, a splash screen displays with
information about the program, including your hardware fingerprint. You
will need your hardware fingerprint to obtain your license key. You can
also obtain the hardware fingerprint by selecting Help > About from the
Scientist main interface.
Step 3
Log in (if you are not already logged in to the Micromath web site). Go to
the My Micromath page on the site.
Step 4
Select My Product Licenses. You should see the product and type of
license you purchased on this page.
Step 5
Select Generate a New Key next to the appropriate product.
Step 6
Enter the name of the user to whom the software will be registered.
Step 7
Enter the hardware fingerprint exactly as it appears in your product.
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Requirements and Installation
Step 8
Select the appropriate description of the computer on which the product
is installed.
Step 9
Select Generate Key. You will receive an E-mail containing your license
key.
Unlock the Scientist Software
Step 1
Start the Scientist program. A dialog with three separate boxes displays.
Choose Enter Key.
Step 2
Enter the registration name and license key exactly as they appear in the
E-mail you received from Micromath.
Step 3
The license key should validate, and you can now use the product in
accordance with the terms of your license.
Uninstalling Scientist
You can remove the Scientist program from your computer using the
Add/Remove Programs control panel. There are differences in the
control panel’s location between Microsoft Windows versions, so consult
your computer’s online help for specific instructions.
To remove the Scientist application, do the following:
Step 1
Locate the Add/Remove Programs control panel.
Step 2
Double-click the Add/Remove Programs icon. The Add/Remove
Programs Properties window displays.
Step 3
Select Scientist from the list of programs and click the Add/Remove
button.
Step 4
When asked to verify that you want to uninstall Scientist, click Yes to
begin the uninstall.
Step 5
Click the OK button. The uninstall is now complete.
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Understanding Scientist
The following topics are included in this chapter:
Chapter Topics
• Overview
• What Does Scientist Do?
• Components and File Types
Overview
Scientist is designed to provide a comprehensive solution to the
problem of fitting experimental data to mathematical models. It is
capable of solving systems of model equations that can include
nonlinear equations, ordinary differential equations, and Laplace
transforms. Scientist is an application for researchers who "know what's
going on" with their data and need to establish solid parameter values
to model real-world phenomena. The easy-to-use interface in Scientist
greatly facilitates model entry and manipulation, data management, and
control of initial estimates and constraints on parameter values, as well
as statistics and graphics output. The interactive nature of Scientist
leads to a higher likelihood of finding optimal parameter values than if
fitting were done in batch mode without the ability to examine and react
to computational results. It also enables users to develop a much
greater awareness of the sensitivity of models to parameter values. This
program allows users to develop and fit complicated models using
nonlinear, differential, and Laplace transform equations.
What Does Scientist Do?
Scientist's main use and most powerful feature is its ability to perform
nonlinear regression analysis (least squares fit calculations). Scientist
has extremely powerful regression algorithms that can frequently find
minima where other programs fail. One benefit of Scientist's powerful
regression capabilities is that initial parameter (coefficient) estimates
need not be particularly accurate. This is especially helpful when fitting
models that are sensitive to one or more parameters.
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Understanding Scientist
Scientist solves systems of equations, differential equations, and
equations expressed in terms of Laplace transforms. Scientist can
perform nonlinear regression on models expressed in terms of systems
of equations, differential equations, or even models expressed as
Laplace transforms. Of course, in order to perform this type of analysis,
Scientist must first find solution(s) to the equations. Scientist has
powerful algorithms and finds analytic solutions where they exist and
numeric solutions when analytical solutions are not possible.
There are many applications that will perform either of these functions,
but few, if any, will perform both simultaneously and achieve results
comparable to those achieved with Scientist.
Types of Problems
Scientist accommodates models from all disciplines and is being used in
many teaching and research areas including Physical, Organic,
Analytical and Pharmaceutical Chemistry, Health Physics, Heat Transfer
and Diffusion, Social Sciences, Econometrics, Biotechnology, Physics,
Mechanical Engineering, Applied Mathematics, and many others. Models
can consist of single functions defined by several lines of code, multiple
functions that may be fit simultaneously, implicit equations or systems
of equations, parametric equations (i.e., X and Y both defined in terms
of a third variable, say S), equations involving integration or
differentiation operators, equations that include Laplace transforms, and
equations involving ordinary differential equations.
Model Entry
Models may be entered in Scientist either from the keyboard at runtime,
simply by typing in the relevant equations, or they may be read from
files. Users may develop their own libraries of models by saving them in
text files at the time they are originally developed; a given model needs
to be entered only once. Since models are compiled inside the program,
there is no need for separate compilation or linking. Furthermore, errors
are flagged during compilation and can be corrected immediately in the
Scientist editor, without having to restart the entire job. A model
template is provided for typing in equations so that the user needs only
to fill in those portions of the model file that differ from his or her set of
equations.
Data Entry
Data may be entered into Scientist or read from a file. Acceptable data
formats include ASCII, Excel, XML, and Scientist's own spreadsheet
files. Data can be exported from Scientist in a number of formats
including ASCII, Excel, HTML, and XML. Scientist can simultaneously
handle numerous data sets for comparison or fitting.
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Parameter Entry
Initial estimates of parameter values are required by the program for
use in function evaluation during simulation or as starting values for
least squares minimization. Parameter entry is accomplished from the
Variable and Parameter Interface. Parameter values may be entered or
read from a file. Depending on the difficulty or complexity of the least
squares problem being attempted, good initial estimates may be very
important in finding an optimal solution.
Minimization Algorithms
By default, Scientist employs a least squares minimization procedure
based on a modification of Powell's algorithm. This algorithm is many
times faster than the more common microcomputer algorithms based
on sequential searches involving one parameter at a time. The algorithm
is a hybrid that combines the reliability of a steep descent method with
the speed (near convergence) of the Gauss-Newton method. At the
user's option, the steepest descent or Levenberg-Marquardt
minimization algorithms can be used. A nonlinear simplex algorithm
may also be selected for searching through the parameter space for the
general location of a minimum, i.e., improving parameter estimates
prior to least squares minimization.
Differential Equation Solving
Scientist provides comprehensive numerical integration of differential
equations. This feature makes Scientist a powerful, easy-to- use model
development tool for scientists, engineers, and students, both graduate
and undergraduate, in the physical sciences and engineering. Students
and researchers who use the software will be able to focus their
attention on the conceptual issues of the problem under investigation,
without spending time on the mathematical details of generating
numerical solutions. The algorithms used in Scientist are adapted from
various sources. We have implemented four standard methods and a
stiff equation package (EPISODE). They are:
• Euler's method
• Runge-Kutta fourth-order method
• Error-controlled Runge-Kutta method
• Bulirsch-Stoer method
• EPISODE
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Understanding Scientist
Laplace Transform Inversion
The use of Laplace transforms can greatly simplify the solution of
models representing very complicated physical systems. The Laplace
transform reduces differential equations to algebraic equations in order
to solve the models; Scientist can then calculate the numerical inverse
of the transformed model. This technique can be applied to a broad
range of scientific, engineering, and technical problems, and it allows
the solution of problems that would otherwise be impractical. The
inverse of the transform may be calculated for a single point, for a curve
representing a range of time values, or for a family of curves in
situations dependent on both space and time coordinates. This means
that equations involving Laplace transforms can be directly fitted to
data, freeing the user from the time-consuming iterative parameter
refinement process that would otherwise be required. Most of the
discussion and examples involving Laplace transforms will refer to
physical-chemical systems, but the technique itself can apply equally
well to situations in electronics and other areas of engineering. The
algorithms used for the inversion of Laplace transforms are adapted
from various sources. We have implemented Piessens' method and
Weeks' method.
Statistics Output
Scientist provides a broad range of statistics output, including
parameter estimates, confidence limits, various measures of goodnessof-fit, variance-covariance and correlation information, and analysis of
residuals. Confidence limits for parameter estimates are calculated
using the customary approach involving a local linearization of the
model, or optionally they may be calculated using a more rigorous
approach that locates various points on constant sum of squares
contours.
Graphic Output
Scientist is capable of producing publication-quality graphic output when
interfaced with appropriate output devices. Graphic information in
Scientist is represented as vectors, rather than pixels, so resolution on
the screen and on hardcopy output is limited only by the output device.
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Components and File Types
The following is a brief description of each component and how Scientist
uses each to perform calculations.
Models
Models are the components used by the Scientist compiler to define a
mathematical model. Models consist of independent variables,
dependent variables, parameters, equations, and constraints.
Spreadsheets
Spreadsheets are used by Scientist to store and manipulate data. The
spreadsheet can be used to sort, filter, sieve, auto type (create), and
transform data.
Variable and Parameter
Variable and Parameter sets are the components Scientist uses to tie
together Models and Spreadsheets when fitting data or performing a
simulation.
Variable and Parameter sets are used to do the following:
• Identify the Model and Spreadsheet to be used in the calculation.
• Set parameter values and determine whether they will be allowed to
vary.
• Select the dependent variables to be used and set weights if weighting
is desired.
• Determine the range and number of intervals of the independent
variable when performing a simulation.
Charts
Charts are used to present data and analysis in graphical format.
Scientist supports over 50 different types of charts.
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Understanding Scientist
Statistics Reports
Scientist provides a broad range of statistical output, including
parameter estimates, confidence limits, various measures of goodnessto-fit, variance-covariance and correlation information, and analysis of
residuals. Confidence limits for parameter estimates are calculated
using the customary approach involving a local linearization of the
model or a more rigorous approach that locates various points on
constant sum of squares contours.
From the Scientist interface, you can select or deselect the display of
descriptive statistics, confidence intervals, the variance/covariance
matrix, the correlation matrix, goodness-of-fit statistics, and rigorous
calculation of confidence intervals. The confidence interval level can also
be adjusted between 0% and 100% non-inclusive.
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4
Using Scientist
The following topics are included in this chapter:
Chapter Topics
• Starting Scientist
• About the Scientist Main Screen
Starting Scientist
To start Scientist, do the following:
Step
From the Windows desktop, select Start > Programs > Micromath >
Scientist 3.0. The Scientist main screen displays (Figure 4-1).
Figure 4-1 Scientist 3.0 Main Screen
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Using Scientist
About the Scientist Main Screen
The Scientist main screen provides access to the configuration options
contained in Scientist.
Scientist Menus
The Menu Bar in the Scientist screen (Figure 4-1) contains the available
menus. The Menu Bar is dockable, allowing you to specify where it
appears in the Scientist screen. Table 4-1 describes the menus in
Scientist.
Table 4-1 Scientist Menus
Menu
Action
• Create a new project, model, spreadsheet, or chart.
• Open files or reopen recently used files.
• Access examples and predefined models.
File
• Close an open screen.
• Import data.
• Configure the printer setup.
• Exit Scientist.
View
Tools
Window
• Configure the layout of the screen.
• Change the theme used by the Scientist application.
• Access tool options.
• Specify the window display options.
• Access the Help system.
Help
• View the software version and copyright information.
• Visit the Micromath home page.
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Toolbar
The Toolbar in the Scientist screen provides quick access to some of the
more common functions. Table 4-2 below describes the toolbar.
Table 4-2 Scientist Toolbar
Toolbar Icon
Action
Create a new project.
Create a new equation model.
Open an existing project.
Create a new spreadsheet.
Save a project.
Create new chart.
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5
Working with Data
The following topics are included in this chapter:
Chapter Topics
•
•
•
•
About Spreadsheets
Manual Entry
Importing Data
Charting Data
About Spreadsheets
Spreadsheet windows are where data are entered and manipulated, and
where calculated results are displayed (Figure 5-1).
Figure 5-1 Spreadsheet Window
There is always one active cell in the Spreadsheet window (indicated by
highlighting). You can move this selection by clicking on the desired cell
with the mouse or by using the arrow keys. Clicking on the column or
row headers or moving the selection to these cells with the arrow keys
causes the entire column or row to become selected. The column name
can be changed when the column header is selected.
To change the name of a column, double-click the column header, make any
necessary changes, and then press Tab.
NOTE
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Working with Data
A block of cells in the spreadsheet can be selected by clicking on a cell
with the mouse and holding the mouse button down while dragging the
mouse cursor to expand the block. Blocks of cells can also be selected
with the keyboard by holding down the Shift key while using the arrow
keys to expand the block.
To move down a page in the Spreadsheet window, press Page Down.
To move up a page, press Page Up. To move to the bottom or top of the
spreadsheet, press Ctrl+Page Down or Ctrl+Page Up, respectively.
To reach the left side of the spreadsheet, press Home. To reach the
right side, press the End. To move a page to the right or left, press
Ctrl+End or Ctrl+Home, respectively.
To overwrite the value in the currently selected cell, simply type in the
number that you wish to use to replace it and press Enter.
Manual Entry
You can enter data in a spreadsheet manually using the commands
described above.
To change the name of a column, double-click the column header, make any
necessary changes, and then press Tab.
NOTE
Importing Data
You can import data into a Scientist spreadsheet from a number of data
sources. Data can be imported from Microsoft Excel spreadsheets,
Access databases, delimited (CSV) files , XML files, SQL databases, and
more. In this example we will import data from an Excel spreadsheet
located in the Examples folder in the Scientist installation directory.
To import data into a Scientist spreadsheet, do the following:
Step 1
Select File > Import. The Import Data dialog displays (Figure 5-2).
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Figure 5-2 Import Data
Step 2
Select the appropriate format of the file you want to import. Figure 5-3
shows the Excel format selected.
Figure 5-3 Import Data - Excel
Step 3
In the File to Import field, enter the path for the file you want to import or
click the button to the right of the field to navigate and select the file you
want.
Step 4
Use the Sheet Name drop down to select the appropriate sheet within
the file you selected.
Step 5
Use the Options check boxes to specify the options you want.
Step 6
Click Import. The data is imported into a Scientist spreadsheet with the
appropriate column names. (Figure 5-4).
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Working with Data
Figure 5-4 Spreadsheet with Imported Data
Charting Data
Scientist makes it easy to chart your data. You can use the Quick Chart
command from either the Spreadsheet or Variable and Parameter
interfaces and then use the Chart Properties dialog to manipulate the
chart.
Quick Chart Command from the Spreadsheet Interface
The easiest way to create a chart in Scientist is to use the quick chart
command. The quick chart command is available under the Data menu
in the Spreadsheet window.
To create a chart using the quick chart functionality, do the following:
Step 1
Open a spreadsheet with data in it.
Step 2
Select Data > Chart. You can also use the Chart button on the toolbar.
Scientist quickly charts the values in columns A, B ,and C against the
values in the column labeled TIME (Figure 5-5).
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Figure 5-5 Quick Chart Command from the Spreadsheet Interface
The quick chart function assumes that the independent variable data is in the leftmost column and that the columns to the right are dependent variables.
NOTE
Quick Chart Command from the Variable and Parameter Interface
The quick chart command is available on the function toolbar in the
Variable and Parameter Interface.
To create a chart using the quick chart command from the Variable and
Parameter Interface, do the following:
Step 1
While on the Variable and Parameter window, select the Quick Chart
function button. Figure 5-6 shows results of a Least Squares Fit
calculation from the Variable and Parameter interface.
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Working with Data
Figure 5-6 Quick Chart from the Variable and Parameter Interface
The quick chart function assumes that the independent variable data is in the leftmost column and that the columns to the right are dependent variables.
NOTE
Chart Properties Dialog
Almost every aspect of a chart can be changed using the Chart
Properties dialog.
To access the Chart Properties, do the following:
Step 1
Open a chart.
Step 2
Select Edit > Properties from the Chart menu. The Chart Properties
dialog displays (Figure 5-7).
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Figure 5-7 Chart Properties
Step 3
Use the various settings to adjust the chart.
Step 4
Click Close.
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5-8
Working with Data
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Creating a Model
The following topics are included in this chapter:
Chapter Topics
• Overview
• Create a Model
• Model Format
Overview
Models are the primary means for entering equations into Scientist. Text
entered into a Scientist Model is compiled by the Scientist compiler then
used to perform calculations. It is not necessary to learn complex
programming syntax or constructs to create a Scientist model. The
Scientist model format is straightforward. If you can write the equations
that describe your system with a pencil and paper, you can create a
model that will perform the desired calculations.
Create a Model
To create a new Scientist model, do the following:
Step
Select File > New > Model from the main menu. The Scientist Default
Model File Template displays (Figure 6-1).
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Creating a Model
Figure 6-1 Scientist Default Model File Template
The default model file begins with a comment line identifying the file as
a Scientist Model file. The model defines T as the independent variable
and X, Y and Z as the independent variables. The file also defines KA, KB
and KC as parameters. You can now edit the file to create a Scientist
Model that describes the system you wish to model.
The default model file does not contain Laplace Variables, Constraints, or Implicit
Equations.
NOTE
Model Format
Model files must be in a format that can be parsed by the Scientist
compiler. In general, the format is (in order) Independent Variables,
Laplace Variables, Dependent Variables, Parameters, Equations, Initial
Conditions and Parameter Values, and Constraints.
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Comments
Comments can be added to an equation file by preceding the comment
line with two slashes, “//”.
For example:
//This is a comment line; the text
//here is not read by the equation
//compiler.
Comments must be placed on a separate line from equations and other
required elements.
Independent Variables
Independent variables are those variables in a set of equations that are
not constant and do not depend on any of the other variables. They are
used to determine the range of calculations. The declaration of
independent variables is preceded by the key word 'IndVars:'. The :
(colon) symbol is important here.
For example:
IndVars: T, X
This example declares T and X to be independent variables, probably for
a calculation that has both time and space dependence (as is often the
case in diffusion problems). Independent variable names may be
separated by commas, spaces, or both. The independent variable
declaration in an equation file must be the first line that is not a
comment line.
Laplace Variables
Laplace variables are the variables in the Laplace domain that are
equivalent to the time variable in the normal equation domain. They are
declared separately from the independent variables so that the model
parser can recognize Laplace domain equations and work with them
appropriately. The declaration of Laplace variables is preceded by the
key word 'LaplaceVars:'. As in the case of the independent variable
declaration, the colon is required.
Example:
LaplaceVars: S
In this example, S is the typical name for the Laplace variable. More
than one Laplace variable can be defined to allow several Laplace
transform equations to be separately inverted. The Laplace variable
declaration must be entered immediately below the independent
variables declaration and immediately prior to the dependent variables
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Creating a Model
declaration. The Laplace variables declaration can be omitted for
equation sets that do not include the inversion of Laplace transforms.
Dependent Variables
Dependent variables are the unknowns that can be calculated from
independent variables, parameters, constants, intermediate variables,
or other dependent variables. Only those variables for which you want
to see calculated values should be entered in the dependent variables
declaration. All other derived variables can be entered in the equations
section and handled as intermediate variables. The names of the
dependent variables to be declared are preceded by the key word
'DepVars:'. The variable names may be separated by commas or
spaces.
Example:
DepVars: Y, Z
Consider the following equations, with Q as the independent variable:
W=1/Q-EXP(-Q)
Y=Q/W
Y is the dependent variable and W is an intermediate variable.
Intermediate variables do not need to be declared; Scientist will detect
them while parsing the equations with the built-in parser-compiler. The
dependent variable declaration line should immediately follow the
Laplace variables declaration, or the independent variables declaration if
Laplace transforms are not being used.
Parameters
Parameters are those variables whose values are to be changed during
least squares fitting, or those that are to be held constant for fitting of a
single data set, but varied between sets of data. Parameter names are
preceded by the key word 'Params:'.
Example:
Params: B, R, G
Any values that are to be held constant at all times can be entered in
intermediate variable equations. The parameter declaration line should
immediately follow the dependent variable declaration line.
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Equations
Equations can be entered on the lines following the parameter definition
line. Each equation starts on a new line. For differential equations, the '
symbol (single apostrophe) is used to indicate the derivative of a
variable. The derivative of y would therefore be entered as y'. The
operators that can be used to make up an equation are described in
other entries.
Equations that depend on constants, dependent variables, or intermediate variables
should be entered below the equations defining those variables.
NOTE
Here are some sample entries:
B=0.5
W=S*(-X+B)
Y=1/W+A/(1-S)
Z=2*SIN(W)+Y
V'=-B*V+A*Y
The model parser processes the equations from the top of the model to
the bottom and therefore can only properly define equations when all of
their defining variables have previously been assigned. The only
exception to this rule is systems of mutually dependent differential
equations, which can be listed in any order.
Complex quantities can be entered in the equations section by enclosing
two variables or expressions in square brackets separated by a comma.
For example,
Y = [0, 1]
Z = [A, B*C]
Q = [1.5, PHASE]
all define complex quantities. These complex quantities can be used
with any of the built-in functions and in combination with real numbers.
The only limitation is that independent variables, dependent variables,
and parameters must be real numbers. You can use the above
procedure to convert two real numbers to a complex number. The RE
and IM functions described below can be used to convert a complex
quantity into its real and imaginary parts, respectively, for output.
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Creating a Model
Initial Conditions and Parameter Values
Initial conditions for differential equations and initial estimates for
parameter values may be entered in the model file. Each value occupies
one line.
Example,
T=0
X=5.0
Y=0
Z=0
B=2.6666667
These values will be used as the initial conditions for the solution of
differential equations if the variables for which the values are given are
defined by a differential equation or as the initial values for parameters
when performing simulation or fitting.
Variables that are not parameters or are not defined by differential
equations should not be assigned initial values since the model parser
may hold that variable fixed at the specified value. Initial conditions
must be defined below the differential equations to which they apply.
Constraints
Constraints on values may also be entered in a Scientist model.
Constraints are entered using the '<' symbol.
Example:
0.0<A<10.0
X<5.0
3.0<Y
1 < Z < 2
The manner in which constraints are used depends upon which type of
variable is being constrained. If the variable is independent variable, the
limits represent the lower and upper bounds over which the parameter
can vary during fitting. If the variable is an independent variable, the
limits represent the range over which simulation will be performed by
default if observed data is not used to determine the calculation points.
If the variable is defined by an implicit equation, the limits represent the
range over which Scientist can search for a solution to the implicit
equation. Unassigned limits are presumed to be -infinity for lower limits
and +infinity for upper limits.
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Creating a Model
6-7
The following is a sample of a complete Scientist model file that includes
differential equations, parameter values and constraints, and initial
conditions for the differential equations:
// Scientist Model Equation File
Independent Variable: T
Dependent Variables: A, B, C
Parameters: A0, KAB, KBC
A'=-KAB*A
B'=KAB*A-KBC*B
C'=KBC*B
// Parameter values and constraints
A0=0.30
KAB=0.03
KBC=0.04
0.0 < A0 < 100.0
0.0 < KAB < 10.0
0.0 < KBC < 10.0
// Initial conditions
t=0.0
A=A0
B=0
C=0
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Creating a Model
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7
Performing a Least Square Fit
(Regression)
The following topics are included in this chapter:
Chapter Topics
• Overview
• Performing a Least Square Fit
• Simplex Fitting
Overview
By default, least squares fitting is performed using a modified Powell
algorithm to find a local minimum, or possibly the global minimum, of
the sum of squared deviations between observed data and model
calculations. It is generally obvious from watching the performance of
this algorithm whether convergence has been achieved. Failure is
usually a consequence of the initial parameter estimates being so far
removed from the solution that Scientist cannot determine which
direction to search. The usual behavior is that the algorithm takes
anywhere from a few to several dozen iterations in converging to the
solution.
At the present time, the minimization algorithm is tuned to indicate
convergence after it detects an unchanging sum of squares value and a
subsequent attempt at restarting iteration also indicates convergence.
For this reason, Scientist will frequently take 5 to 10 iterations near the
solution in the process of ascertaining convergence.
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Performing a Least Square Fit (Regression)
Performing a Least Square Fit
To perform a Least Square Fit, do the following:
Step 1
In order to fit data to a model you will need to open both the data and the
model in Scientist. Open the model file containing the appropriate model
or create a new model. Create a new spreadsheet and enter your
experimental data, import existing data from another file, or open an
existing Scientist spreadsheet.
In the example below, we will use the model and data files from the
Simple Linear Equation example found in the Models > Examples folder
of the Scientist installation directory. We begin with the spreadsheet and
the model open as shown in Figure 7-1.
Figure 7-1 Least Square Fit 1
Step 2
To begin the fitting process, open a Variable and Parameter Set. If you
created a parameter set with a previous version of Scientist you could
simply open it from the File menu in the model interface, but it is just as
easy to create a new Variable and Parameter set. Select the model
interface and choose File > New Parameter Set from the menu. A new
Variable and Parameter set opens in a new tab in the model interface
(Figure 7-2).
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Performing a Least Square Fit (Regression)
7-3
Figure 7-2 Least Square Fit 2
NOTE
Notice in the Input Information section, the Simple Linear Model spreadsheet is
selected because it was the only spreadsheet open when the Variable and
Parameter set was created. In addition, the Parameters and Independent Variable
sections of the new Variable and Parameter set have been populated with the
parameters and dependent variables defined in the Simple Linear Equation model.
Step 3
To perform a least squares fit, you need to input initial values for the
parameters and determine which parameters will be allowed to vary
during the fit. In this example we allow all of the parameters to vary
during the fit and enter initial estimates of 1 for each of the parameters
(Figure 7-3).
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Performing a Least Square Fit (Regression)
Figure 7-3 Least Square Fit 3
Step 4
You now need to determine which dependent variables will be used
during the fit. Scientist uses all the dependent variables by default and
we will do the same in this example.
Step 5
Select Calculate > Least Squares Fit or press F7. Scientist displays the
estimated values for the parameters in a new Variable and Parameters
set tab in the model interface (Figure 7-4).
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Performing a Least Square Fit (Regression)
7-5
Figure 7-4 Least Square Fit 4
In addition, Scientist places the calculated values for the dependent variables in the
spreadsheet.
NOTE
Simplex Fitting
The simplex method offers a different algorithm for fitting nonlinear
equations to data. Since the convergence of this algorithm is slow when
it nears the solution, only a fixed number of iterations (depending on
the number of parameters being fit) is performed. It is expected that
this procedure will be used only when intuition and analysis fail to find
satisfactory initial estimates for the least squares minimization. Since a
fixed number of iterations is used, this procedure can be repeated if it
appears to be useful for a given problem.
To perform a Simplex Fit, do the following:
Step 1
Open the model and the spreadsheet containing the data to be fit in
Scientist. In this example we will used the Simple Linear Equation
example found in the Models > Examples folder in the Scientist
installation directory (Figure 7-5).
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Performing a Least Square Fit (Regression)
Figure 7-5 Simplex Fit 1
Step 2
Open a new Variable and Parameter set and enter initial estimates for
the parameters (Figure 7-6).
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Performing a Least Square Fit (Regression)
7-7
Figure 7-6 Simplex Fit 2
Step 3
Confirm all the dependent variables are selected for fitting.
Step 4
Select Calculate > Simplex Fit in the Variable and Parameter Interface.
Scientist outputs the calculated parameter values in a new Variable and
Parameter set in a new tab in the model interface (Figure 7-7).
Figure 7-7 Simplex Fit 3
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Performing a Least Square Fit (Regression)
NOTE
Notice these values are different from those obtained when the same model and
data were fit using a Least Squares Fit calculation. This is because the Simplex Fit
calculation runs for a specified number of iterations regardless of the result of the
calculation.
The simplex method can never diverge, but converges slowly near a minimum; thus,
when a Simplex Fit is run, Scientist computes a fixed number of iterations, with no
attempt to assess convergence. Successive Simplex Fit calculations can be used to
obtain better estimates for parameter values in most cases. The Simplex method has
been shown to be quite effective in approximately locating minima that are reached
from initial parameter estimates where other methods fail.
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8
Performing a Simulation
The following topics are included in this chapter:
Chapter Topics
• Overview
• Performing a Simulation
Overview
Simulation allows you to generate data using the selected model,
parameters, and data (if available). If the model was not compiled
before the Simulation command was selected, it is automatically
compiled; simulation will be performed only if compilation of the model
was completed successfully. Differential equations that are specified in
the model will be integrated using the algorithm chosen with the
Integrator command. If there is an active data set, the simulation will be
done for values of the independent variables that are available in the
active spreadsheet; otherwise, Scientist uses the default range and
number of iterations for the independent variables specified in the
Simulation and Independent Variables section of the Variable and
Parameter Interface.
Performing a Simulation
To run a simulation, do the following:
Step 1
Open the model you wish to simulate in Scientist. In this example, we will
use the Simple Linear Equation model from the Models > Examples
folder in the Scientist installation directory (Figure 8-1).
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Performing a Simulation
Figure 8-1 Simulation 1
Step 2
Select File > New Parameter Set.
Step 3
In the Parameters section of the Variables and Parameters Interface,
enter the values of the parameters you wish to use in the simulation
(Figure 8-2).
Figure 8-2 Simulation 2
Step 4
In the Simulation section, select the spreadsheet where you want the
simulated data output. If you leave this field blank, Scientist will place the
calculated values in a new spreadsheet. In the Independent Variables
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Performing a Simulation
8-3
section enter the Number of Intervals, Lower Limit, and Upper Limit of
the independent variable to be used in the simulation. If you want to
simulate data over a logarithmic interval check the box marked "Log
Interval?" next to the appropriate independent variable. In this case we
will simulate 10 intervals of X from 10 to 15 as shown in Figure 8-3.
Figure 8-3 Simulation 3
Step 5
Select Calculate > Run from the Variable and Parameter Interface.
Scientist puts the independent variable values and the calculated values
for each of the dependent parameters in a new spreadsheet as shown in
Figure 8-4.
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Performing a Simulation
Figure 8-4 Simulation 4
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9
Calculating Statistics
The following topics are included in this chapter:
Chapter Topics
• Overview
• Calculating Statistics
• Statistical Output Explanations
Overview
Statistics calculations are usually performed after a Least Square Fit or
Simplex Optimization to determine the accuracy of the calculation.
Calculating Statistics
To perform a Statistics calculation on a given Least Square Fit
calculation, do the following:
Step 1
Start with the Variable and Parameter set containing the parameter
values for the fit you wish to evaluate. In this example we will use a Least
Square Fit of the ABC Kinetic data to the ABC Kinetic model. We
calculated best fit values of the parameters as shown in
Figure 9-1.
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Calculating Statistics
Figure 9-1 Calculating Statistics 1
Step 2
Select Calculate > Statistics. Scientist opens a new Statistics Report in
a tab in the model interface (Figure 9-2).
Figure 9-2 Calculating Statistics 2
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Calculating Statistics
9-3
Step 3
There are no calculations in the Statistics Report at this time. The Input
Information section of the Statistics Report shows the Model, Data Set,
and Parameter Set to be used in the calculation. In addition, the Report
Options section is set to the options that have been set in the Scientist
Options Menu. You can change any of these options for this calculation
only by making the changes in the Report Options section of the
Statistics Report. These changes will not effect the Statistics Options
selected in the Scientist Options Menu.
Step 4
After you select the options you like, you calculate the Statistics Report
by choosing Calculate > Run. Scientist calculates a Statistics Report in
the same tab. The report contains all the information requested by the
user in the Report Options. In this case we have chosen Goodness-of-Fit
Statistics, Confidence Intervals, Variance-Covariance Matrix, Correlation
Matrix, and Residual Analysis as shown in Figure 9-3.
Figure 9-3 Calculating Statistics 3
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Calculating Statistics
Statistical Output Explanations
The statistical output that can be obtained with Scientist includes
statistics related solely to the data, statistics related to determination of
parameters, goodness-of-fit statistics, and analysis of residuals.
Data Statistics
The statistical information based solely on the observed data that is
provided by Scientist includes the minimum value, maximum value,
several means, the median value, sums of squares, deviation, variance,
skewness, and kurtosis.
Parameter Statistics
The statistical information on parameters provided by Scientist includes
the following:
• The best fit estimate for each parameter.
• The standard deviation of each estimate.
• The univariate and support plane 95% confidence ranges for each
parameter, based on the assumption of model linearity near the
least squares minimum.
• The variance-covariance matrix and the correlation matrix.
In addition, Scientist has the optional capability of performing a rigorous
iterative refinement of the confidence intervals assuming a nonlinear
response in the region of the parameter estimates.
Goodness-of-Fit Statistics
Several statistical parameters that may be used as indicators of
goodness-of-fit are reported by Scientist. These are the standard
deviation of data, the correlation, the coefficient of determination, Rsquared, and the Model Selection Criterion.
Analysis of Residuals
The analysis of residuals provides information as to how well the
distribution of residuals follows a normal distribution. It is most
meaningful for large samples (as obtained, for example, in quasi-elastic
light scattering experiments, or half-life determinations for mixtures of
radionuclides) and should therefore be viewed skeptically for samples
containing relatively small numbers of points (as is usually the case for
pharmacokinetic studies or other experiments where data is manually
acquired, on point at a time).
Scientist® 3.0 Getting Started Guide - Version 1
For additional information or support on this Micromath® product,
visit www.micromath.com
Scientist® 3.0 Getting Started Guide
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