A tutorial covering curve fitting is available. Select Open from the File menu, then look in the Experiments folder to access it.
Draft Graph
You can fit a function either to the whole graph or just to a
region
of interest. To select a portion of the graph, drag the mouse across
the
desired region. After selecting Try Fit, the curve fit will be
displayed
on the graph in the curve fit dialog. You can select a region within
that
graph, zoom in, etc., and the fit you perform will be applied to your
actual
graph.
Options
Fit Type
Select which type of curve fit you would like to perform: Automatic or Manual.
Note: if Automatic Fit Type is disabled, then "Allow Automatic Curve Fit" is not enabled in the Preferences dialog. To allow automatic fits, check the box in Preferences.
The Create Calculated Column option will
create a column in
the data table holding the y-values of the fitted function at each
value
for the X-Axis. Selecting this option will call up display options. You
can choose to have the new column plotted on the graph and/or have the
curve fit helper object
displayed on
the graph.
Once a calculated column has been plotted on the graph, you can adjust the variables by adding a Parameter Control from the Insert menu.
General Equation
Here you select an equation to be fit to the data. You can either choose a formula from the list in the scrolling box, or you can click the Define Function button and type a formula in the text box. Many common functions, such as linear, exponential, inverse, and polynomial are included in the list.
The Degree/Power box is activated and available for editing when the appropriate general equation is selected, e.g. A*x^n (Variable Power).
Offset (t0)
When Offset (t0) is checked, the "t" variable in the equation
will
change to "(t-t0)" as displayed under Coefficients. This allows you to
specify
a different t0 for the fit equation based on the left edge of the
currently selection region.
User Defined Functions
You can define and add customized mathematical functions to the general
equation list. Up to six parameters can be used in the equation; each
parameter can occur only once in the expression. Click the Define
Function button and type in the function in the box. Delete added
functions and equations from the list by highlighting and clicking the
Delete Function button. If you must use an expression that contains
repeated terms, use the model feature instead of the automatic curve
fit.
Gaussian Curve Fits
The Gaussian distribution function (also known as the Normal
distribution)
is available among the various curve fit equations. The Normalized
Gaussian
function (with an integrated area of one) is
Normal
in which µ
and σ >0 are
the mean
and standard deviation
The normalized function will only fit data well if the data are
normalized
to an area of one.
If non-normalized data are used, select the Gaussian function,
which
fits to any area, as well as including a constant offset. Frequently
nuclear
radiation counting statistics will require the non-normalized Gaussian
function.
Coefficients*
The coefficients can be adjusted individually to improve the
fit of
the function to the data. Either type in a new value, or use the up and
down arrow buttons to step the value of the parameter up and
down.
Depending on the coefficients initially chosen, a function may not fall within the graph window. In this case it may be difficult to adjust the coefficients to achieve a good fit. You may want to calculate the necessary values to force the function to pass through one data point (often the y-intercept) and begin with these values.
Clicking the open triangle
will call up the Set Delta dialog:
The delta dialog lets you enable/disable an automatic calculation for the delta to use when using the spin controls to the right of the coefficients. If you choose to disable the automatic calculation of the delta, you can type in whatever delta value you like.
After you Click Done, a floating box (helper object) containing the equation and fit coefficients of the function will be added to the graph. Black brackets mark the beginning and end of the range. These can be clicked and dragged to adjust the fit. To remove the fitted line, click the box in the upper left corner of the helper object.
You can adjust the parameters of a manual fit after it has been drawn on the main graph. Click a parameter name in the helper object to select it. An arrow symbol next to the parameter name will appear. Use the up and down cursor keys to raise or lower the value. Use the left and right cursor keys to decrease and increase the step size for changing the value. You can also click the numeric value and type in a new value. The graph will be updated. Click another parameter to change it. Double-clicking the helper object will open its options dialog where you can change all the values at once.
The helper object can be hidden to show just the fitted line. Double click the helper and deselect the "Show On Graph" option. Restore the helper object by choosing Additional Object Options->Reveal Hidden Objects from the Options menu.
Note: For complete details about
Curve
Fitting,
we recommend that you consult Numerical Recipes in C ©.
The book in its entirety can be viewed at the following address: http://lib-www.lanl.gov/numerical/bookcpdf.html
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NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING. Copyright © 1988-92 Cambridge University Press.