Fitting several functions simultaneously
General considerations
The basic version of QNFIT can fit systems of n equations
in one variable, but some versions can also fit systems of n
equations in several variables. If the same parameters
do not occur in more than one of the equations, then the
system will be uncoupled and corresponding elements of the
covariance matrix will be zero. In such cases nothing is gained
over fitting the functions independently to their respective
data sets.
More usually, some parameters
will be present in more than one of the equations, and then
the system will be coupled and more difficult to fit.
Systems of differential
equations are of this type, but they should be simulated and
fitted using DEQSOL.
Simultaneous fitting of n independent functions of one variable
To do this you create a library file for the n separate data
sets and an ASCII text model file with the n model equations.
As with DEQSOL, you can denote missing data sets by a % in the
corresponding line of the library file. To see how this all
works you should practise with the library file provided called
line3.tfl, and the model file line3.mod to fit 3 lines.
A more interesting example is to use the data in consec3.tfl
for consecutive irreversible chemical reactions as in
A --> B --> C, A(0) > 0, B(0) = C(0) = 0
k(1) = p(1) > 0, k(2) = p(2) > 0, A(0) = p(3) > 0
and the model file consec3.mod, which illustrates how to code
a model with a branch point, as in this case when k(1) = k(2).
Special considerations
A number of points should be noted when using multi-function
mode. The data sets may not be checked for consistency or for the
x-values being in increasing order. You cannot edit the data
interactively since QNFIT makes a look up table for distinct
values which are then used to build up predicted values in an
economical way. For goodness of fit, a long table with all the
sequential values is constructed, and this should be kept in
mind when interpreting runs tests. You can read starting
parameters and limits from data files as in EXPERT mode but
the
begin{limits} ... end{limits}
section must be at the end of
the first data file referenced by the library file.
You can still supply a parameter limits file with three columns
(lower-limit, starting values and upper limits) just as with
any single models.
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