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)