Curve Fit & Function Plot
Often, we are faced with the task of finding the relationship between
two sets of numbers, so that interpolation and extrapolation can be
done. Many laboratory experiments are sources for huge amounts
of numbers in which, if possible, should be replaced and
represented by an "easier to read" function. Measurements of physical
properties such as viscosity, density, vapor pressure or thermal
conductivity are examples of such data sources. If there is enough data
information to find the relationship between
X and Y, interpolation and extrapolation is possible.
The relationship was, in fact in earlier times, often found by plotting
on various graphs i.e. linear or log-log to see which one gave the best
To help determine how good the fit is for the curve selected, the SSE
(Sum of Squares Error) and the coefficient of fit performance (r2)
are reported. The best fit usually have the smallest SSE and a
coefficient of performance near 1.000. The curve is automatically
refitted anytime Calculate push button is used or a change in a
curve type occurs.
Fitting functions to empirical data are not always a straight forward
procedure. Two functions may have an approximately equal coefficient of
performance. If so, as a rule, the simplest function of these should be
School - Curve fit function plot
Starting a New Data Set
To fit a curve to a new data set, just remove the content (if any)
in Data (X Y) edit field and insert your data.
Numeric data must be separated by one or more spaces.
Examples of legal numbers are: -1.234, -1.234E-4,
The Curve Fit tool in CHEMIX allows you to define a data set
title, assign axis titles and select a curve type. The Edit list box
push buttons allows you to save, replace
and delete your X Y data sets.
Loading an Existing Data Set
To load a previously saved data set, double click one of the
elements in the Name (X Y data) list box. The application reads
the data from a file and displays it in the Data (X Y) text
Once you have entered a data set, enter a data title in the Name (X
Y data) edit field and
save your data using one of the push buttons in the Insert
(Before or After) in Edit list box
Function, r2 and SSE
Function: Function in which represent the output curve.
r2 The goodness of the fit - 1.0 is perfect.
SSE Sum of Squares Error. The sum of (Yi-Yfunc)2.
Function Plot f(x)
The CHEMIX function plotter allows you to insert and plot math
functions. Available functions are described in Calculator.
Enter a function e.g. sin(x) in the Plot function f(x) text
and Calculate. A plot can now be seen in the plot area.
You may plot derivatives of both the inserted function and XY-data
by selecting one of the radio buttons (Y' or Y'') in the Derivatives
NOTE: Taking derivatives of XY-data will not alter any of the
data presented in the XY Data field.
Zoom by moving the mouse cursor in plot area while left
mouse button is pressed. The zoom actually occurs when releasing the
mouse button. If you want
to go back to initial XY-max/min values (un-zoom), simply press left
mouse button in the plot area and release without moving the mouse
Note: If any zoom exceeds factor 1/2000, initial xy-max/min values
(before zoom) will automatically be selected.
Max/Min Limits in a Plot
A built-in feature in CHEMIX uses a set of rules finding the y-limits
in a function plot.
If both XY-data and a function are present,-
it will be the extreme max/min limits of the xy-data in which will
decide these limits. In the case of the presence of function plot only,
y-limits will be calculated automatically and x-limits manually.
Radians & Degrees
A function plot may involve trig.func. as sin(x),cos... You may select
Radians or Degrees (Degrees unselected).
Data Manipulation g(x,y)
It is possible to manipulate inserted or generated XY-data . This can
be done by inserting a function in the Data Manipulation f(x,y)
an Calculate. None of the raw data seen in the Data XY-field
will be altered during this operation,.. the result can only be seen
graphically as a plot. It is possible to insert both X and Y.
E.g. Y=Y meaning
Yi (new)=Yi (old)
does not change anything while Y=Y/X meaning Yi
does change all the Y-values in the plot.
All available functions are described in Calculator.
Interpolate (Data X Y)
By selecting Interpolate, lines may be drawn between points. Polyline
draw straight lines between the points. Natural cubic spline
assigns third order polynomials to the points.
You may send the plotted curve to a printer
by selecting the Print Button (printer graphic). The hard copy will
have the same format as seen on the screen.
Plot the selected curve by the use of the Calculate push
button. This button also automatically calculate max/min limits for the
plot, unless the content in one of the X-min X-max Y-min...
(manual limits) fields prior to the use of this button has been altered.
NOTE:In some cases when a data set contain "illegal values",
as when the denominator in a hyperbolic function equals zero, no
fit/plot will occur.
Curve fitting software
Graph plot software
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