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and after [NXT] you will see
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Click on the items to browse the documentation.
is the basic input command. [NEW] opens an InputForm screen
and you are
asked to enter the data and a model function f. The field DATA takes
a matrix
with at least 2 columns and any number of rows.
This is also the place to choose between chi-square- and least-squarefitting:
entering a matrix with only two columns tells moda that you want to
use
least-square fitting (which is the only possibility, since you didn't
enter any
measurement errors) ... entering a matrix with 3 columns tells moda
thatyouwant
to use chi-square fitting.
Enter the model function f in the field named MODEL. f should depend
on X and
on at least one parameter which may have any name. Via the menu item
[CAT]
you can access the catalog of fit functions.
[OK] will lead you to a new screen where you are asked to enter the
initial values
of the parameters a_i.
moda does some checks on the data and on the model function f ... it
gives the
error message 'invalid input' if the data or the model function are
'invalid' for some
reason. (see error messages for more details)
The fitting is done in separate steps which are called iterations.The
subroutine
LEMA performs a specified number of these iterations and LEMA takes
therefore
one positive integer from the stack which counts the number of iterations.
The result of these iterations is a new (better) set of parametersa_i.
LEMA puts
the value of chi^2 that corresponds to these new parameters on thestack.
gives the current value of chi^2 together with a probability. Both
quantities
measure the 'goodness of the fit'. [INFO] also gives the covariance
matrix.
chi^2 is a number between 0 and infinity; it measures the difference
between
the data and the model function f(x,a_i) in a specific way. The smaller
the value
of chi^2 the better is the fit.
It takes some more lines to explain the meaning of the probability:
Suppose your model function f is the correct
model functionin the sense
that the deviations of the data from the values of f are only
dueto random
measurement errors. One could ask: What is the probabilitythat
random
measurement errors do produce a value of chi^2 as poor (i.e. as large)
as the
current value of chi^2? This probability is given by [INFO] together
with the
corresponding value of chi^2. The closer the value of this probability
is to 1 the
better is the fit.
takes a number from the stack and calculates the value ofthe
modelfunction
f for this argument and for the current values of the parameters a_i.
plots the data-points together with the model function f for
the current values
of the parameters a_i.
takes a number x from the stack and calculates the variance sigma(x)
of the model
function (with the current parameter estimates) at x. I.e. the value
of the model
function f at x will be between
f(x) PlusMinus 2*sigma(x)
with a probability of 0.95, etc. [CNFI] thus gives the size of the one-sigma
confidence interval (for the value of the model function).
takes a number p from the stack and plots the three functions
1. f(x)
2. f(x)+
p*sigma(x)
3. f(x)-
p*sigma(x)
where f(x) is the model function and sigma(x) is the variance of f.I.e.
setting p=2
will plot f(x) (for the current parameters) together with the functions(2.)
and (3.)
which are the upper and the lower bound for the 95% confidence interval.
Puts the data matrix and the model function on the stack; the currentvalues
of the
parameters are substituted in the model function.