A number of application tasks use the interactive curve fitting tools based on the curfit package for fitting curves to data. Interactive graphical curve fitting begins by graphing the data points and the current fit in one of five formats. When the cursor appears the user may modify the graphs and the fit in a number of ways with cursor mode keystrokes and colon commands. These are described below.
?
The terminal is cleared and a menu of cursor keys and colon commands is printed.
a
Add points to contrain the fit. When adding points a query is made to set
the weights. A large weight will force the fit to go near the added point.
The added points are internal to the fitting routine and are not returned
or otherwise available to the particular task using the ICFIT capability.
c
The coordinates of the data point nearest the cursor and the fitted value
are printed on the status line.
d
The data point nearest the cursor and not previously deleted is marked with an
X. It will not be used in futher fits unless it is undeleted.
f
A curve is fit to the data and the fit is graphed in the current format.
g
Redefine the graph keys "h-l" from their defaults. A prompt is given for the
graph key which is to be redefined and then for the graph desired.
A '?' to either prompt prints help information. A graph
is given by a pair of comma separated data types. The first data type defines
the horizontal axis and the second defines the vertical axis. Any of the
data types may be graphed along either axis. The data types are
x Independent variable y Dependent variable
f Fitted value r Residual (y - f)
d Ratio (y / f) n Nonlinear part of y
.le
o
Overplot the next fit provided the graph format is not changed.
q
Exit from the interactive curve fitting. Two consecutive carriage returns
(cursor end-of-file) may also be used.
r
Redraw the current graph.
s
Select a sample range. Set the cursor at one end point of the sample before
typing 's' and then set the cursor to the other endpoint and type any key
in response to the prompt "again:". Sample ranges are intersected unless
the sample ranges have been initialized to all the points with the key 't'.
t
Initialize the sample to include all data points.
u
Undelete the data point nearest the cursor which was previously deleted.
w
Set the graph window (range along each axis to be graphed). This is a
gtools option which prints the prompt "window:". The set of cursor
keys is printed with '?' and help is available under the keyword gtools.
x
Change the x value of the point nearest the cursor.
y
Change the y value of the point nearest the cursor.
z
Delete the nearest sample region to the cursor.
Colon commands are show or set the values of parameters. The parameter names may be abbreviated as may the function type.
:show [file]
Show the current values of all the fitting parameters. The default output
is the terminal (STDOUT) and the screen is cleared before the information
is output. If a file is specified then the information is appended to the
named file.
:vshow [file]
A verbose version of "show" which includes the fitted coefficients and their
errors.
:xyshow [file]
A version of "show" which lists the input independent (X), fitted (Y fit), and
input dependent (Y) data values.
:errors [file]
Show the fitted function and square root of the chi square of the fit.
The default output
is the terminal (STDOUT) and the screen is cleared before the information
is output. If a file is specified then the information is appended to the
named file.
:function [value]
Show the current value or set the function type. The functions types are
"chebyshev", "legendre", "spline1", or "spline3" for chebyshev or legendre
polynomial or linear or cubic spline.
:grow [value]
Show the current value or set the rejection growing radius. Any points within
this distance of rejected points are also rejected.
:markrej [value]
Mark rejected points? If there are many rejected points then it might be
desired not to mark the points.
:naverage [value]
Show the current value or set the number of points to average or median to form
fitting points. A positive value select an mean and negative values select
a median. The averaged points are also shown in the graphs.
:order [value]
Show the current value or set the order of the function. For legendre or
chebyshev polynomials the order is the number of terms (i.e. an order of 2
has two terms and is a linear function). For the splines the order is the
number of spline pieces.
:low_reject [value], :high_reject [value]
Show the current values or set the rejection limits. When a fit is made
if the rejection threshold is greater than zero then the sigma of the
residuals about the fit is computed. Points with residuals more than
this number of times the sigma are removed from the final fit. These
points are marked on the graphs with diamonds.
:niterate [value]
Show the current value or set a new value for the number of rejection
interations.
:sample [value]
Show the current value or set the sample points to use in the fits. This
parameter is a string consisting of single points, colon separated ranges,
or "*" to indicate all points. A file containing sample strings may also
be specified by prefixing the file name with the character '@'.
Note that sample ranges may also be set with the cursor mode key 's'.
A one dimensional function is fit to a set of x and y data points. The function may be a legendre polynomial, chebyshev polynomial, linear spline, or cubic spline of a given order or number of spline pieces.
The points fit are determined by selecting a sample of data specified by the parameter sample and taking either the average or median of the number of points specified by the parameter naverage. The type of averaging is selected by the sign of the parameter and the number of points is selected by the absolute value of the parameter.
If niterate is greater than zero the sigma of the residuals between the fitted points and the fitted function is computed and those points whose residuals are less than -low_reject * sigma or high_reject * sigma value are excluded from the fit. Points within a distance of grow pixels of a rejected pixel are also excluded from the fit. The function is then refit without the rejected points. The rejection can be iterated the number of times specified by the parameter niterate. Note a rejection value of zero is the same as no rejection. The rejected points may be marked with diamonds. The marking of rejected points is controlled by the :markrej command.
There are five types or formats of graphs selected by the keys 'h', 'i', 'j', 'k', and 'l'. The graphs are defined by what is plotted on each axis of the graph. There are six data types, any of which may be plotted on either axis. These data types are the independent data points (x), the dependent data points (y), the fitted values (f), the residuals (r=y-f), the ratio of the data to the fit (d=y/f), and the data with the linear term of the fit (determined by the endpoints of the fit) subtracted. The default graph keys are shown in the cursor key section though the definitions may be modified by the application. The user may also redefine the graph keys using the 'g' key. This gives a choice of 36 different graph types.
It is important to remember that changing the value of a fitting parameter does not change the fit until 'f' is typed.
The sample region is stored internally as a string of length 1024 characters. This is greatly increased over versions prior to V2.10. However, due to the fixed default size of string parameters in parameter files (160 characters), initial sample regions input with a CL parameter are limited to this smaller length string. The limitation may be escaped by using the new capability of specifying a file containing ranges. Also sample regions initialize by a task parameter may be extended interactively.