# 1dNLfit¶

```
Program to fit a model to a vector of data. The model is given by a
symbolic expression, with parameters to be estimated.
Usage: 1dNLfit OPTIONS
Options: [all but '-meth' are actually mandatory]
--------
-expr eee = The expression for the fit. It must contain one symbol from
'a' to 'z' which is marked as the independent variable by
option '-indvar', and at least one more symbol which is
a parameter to be estimated.
++ Expressions use the same syntax as 3dcalc, ccalc, and 1deval.
++ Note: expressions and symbols are not case sensitive.
-indvar c d = Indicates which variable in '-expr' is the independent
variable. All other symbols are parameters, which are
either fixed (constants) or variables to be estimated.
++ Then, read the values of the independent variable from
1D file 'd' (only the first column will be used).
++ If the independent variable has a constant step size,
you can input it via with 'd' replaced by a string like
'1D: 100%0:2.1'
which creates an array with 100 value, starting at 0,
then adding 2.1 for each step:
0 2.1 4.2 6.3 8.4 ...
-param ppp = Set fixed value or estimating range for a particular
symbol.
++ For a fixed value, 'ppp' takes the form 'a=3.14', where the
first letter is the symbol name, which must be followed by
an '=', then followed by a constant expression. This
expression can be symbolic, as in 'a=cbrt(3)'.
++ For a parameter to be estimated, 'ppp' takes the form of
two constant expressions separated by a ':', as in
'q=-sqrt(2):sqrt(2)'.
++ All symbols in '-expr' must have a corresponding '-param'
option, EXCEPT for the '-indvar' symbol (which will be set
by its data file).
-depdata v = Read the values of the dependent variable (to be fitted to
'-expr') from 1D file 'v'.
++ File 'v' must have the same number of rows as file 'd'
from the '-indvar' option!
++ File 'v' can have more than one column; each will be fitted
separately to the expression.
-meth m = Set the method for fitting: '1' for L1, '2' for L2.
(The default method is L2, which is usually better.)
Example:
--------
Create a sin wave corrupted by logistic noise, to file ss.1D.
Create a cos wave similarly, to file cc.1D.
Put these files together into a 2 column file sc.1D.
Fit both columns to a 3 parameter model and write the fits to file ff.1D.
Plot the data and the fit together, for fun and profit(?).
1deval -expr 'sin(2*x)+lran(0.3)' -del 0.1 -num 100 > ss.1D
1deval -expr 'cos(2*x)+lran(0.3)' -del 0.1 -num 100 > cc.1D
1dcat ss.1D cc.1D > sc.1D ; \rm ss.1D cc.1D
1dNLfit -depdata sc.1D -indvar x '1D: 100%0:0.1' -expr 'a*sin(b*x)+c*cos(b*x)' \
-param a=-2:2 -param b=1:3 -param c=-2:2 > ff.1D
1dplot -one -del 0.1 -ynames sin:data cos:data sin:fit cos:fit - sc.1D ff.1D
Notes:
------
* PLOT YOUR RESULTS! There is no guarantee that you'll get a good fit.
* This program is not particularly efficient, so using it on a large
scale (e.g., for lots of columns, or in a shell loop) will be slow.
* The results (fitted time series models) are written to stdout,
and should be saved by '>' redirection (as in the example).
The first few lines of the output from the example are:
# 1dNLfit output (meth=L2)
# expr = a*sin(b*x)+c*cos(b*x)
# Fitted parameters:
# A = 1.0828 0.12786
# B = 1.9681 2.0208
# C = 0.16905 1.0102
# ----------- -----------
0.16905 1.0102
0.37753 1.0153
0.57142 0.97907
* Coded by Zhark the Well-Fitted - during Snowzilla 2016.
```