# FreeBSD Manual Pages

```Linfit(3)	      User Contributed Perl Documentation	     Linfit(3)

NAME
PDL::Fit::Linfit	- routines for fitting data with linear	combinations
of functions.

DESCRIPTION
This module contains routines to	perform	general	curve-fits to a	set
(linear combination) of specified functions.

Given a set of Data:

(y0, y1, y2, y3, y4, y5, ...ynoPoints-1)

The fit routine tries to	model y	as:

y' = beta0*x0 + beta1*x1 + ...	beta_noCoefs*x_noCoefs

Where x0, x1, ... x_noCoefs, is a set of	functions (curves) that	the
are combined linearly using the beta coefs to yield an approximation of
the input data.

The Sum-Sq error	is reduced to a	minimum	in this	curve fit.

Inputs:

\$data
This is	your data you are trying to fit. Size=n

\$functions
2D array. size (n, noCoefs). Row 0 is the evaluation of	function x0 at
all the	points in y. Row 1 is the evaluation of	of function x1 at all
the points in y, ... etc.

Example	of \$functions array Structure:

\$data is a set of 10 points that we are	trying to model	using the
linear combination of 3	functions.

\$functions = (	[ 1, 1,	1, 1, 1, 1, 1, 1, 1, 1 ],  # Constant Term
[ 0, 1,	2, 3, 4, 5, 6, 7, 8, 9 ],  # Linear Slope Term
[ 0, 2,	4, 9, 16, 25, 36, 49, 64, 81] #	quadradic term
)

SYNOPSIS
\$yfit = linfit1d \$data, \$funcs

FUNCTIONS
linfit1d
1D Fit linear combination of supplied functions to data using min chi^2
(least squares).

Usage: (\$yfit, [\$coeffs]) = linfit1d [\$xdata], \$data, \$fitFuncs, [Options...]

Signature: (xdata(n); ydata(n); \$fitFuncs(n,order); [o]yfit(n); [o]coeffs(order))

Uses a standard matrix inversion	method to do a least squares/min chi^2
fit to data.

Returns the fitted data and optionally the coefficients.

One can thread over extra dimensions to do multiple fits	(except	the
order can not be	threaded over -	i.e. it	must be	one fixed set of fit
functions "fitFuncs".

The data	is normalised internally to avoid overflows (using the mean of
the abs value) which are	common in large	polynomial series but the
returned	fit, coeffs are	in unnormalised	units.

# Generate data from a	set of functions
\$xvalues = sequence(100);
\$data = 3*\$xvalues + 2*cos(\$xvalues) +	3*sin(\$xvalues*2);

# Make	the fit	Functions
\$fitFuncs = cat \$xvalues, cos(\$xvalues), sin(\$xvalues*2);

# Now fit the data, Coefs should be the coefs in the linear combination
#   above: 3,2,3
(\$yfit, \$coeffs) = linfit1d \$data,\$fitFuncs;

Options:
Weights    Weights to use in fit, e.g. 1/\$sigma**2 (default=1)

perl v5.32.1			  2018-05-05			     Linfit(3)
```

NAME | DESCRIPTION | SYNOPSIS | FUNCTIONS

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