wsolve uses the singular value decomposition for increased accuracy. Estimates the uncertainty for the solution from the scatter in the data.

Example

Weighted system:

import numpy,wsolve
A = numpy.matrix("1,2,3;2,1,3;1,1,1",'d').A
xin = numpy.array([1,2,3],'d')
dy = numpy.array([0.2,0.01,0.1])
y = numpy.random.normal(numpy.dot(A,xin),dy)
print A,y,dy
s = wsolve.wsolve(A,y,dy)
print "xin,x,dx", xin, s.x, s.std

Note there is a counter-intuitive result that scaling the estimated uncertainty in the data does not affect the computed uncertainty in the fit. This is the correct result --- if the data were indeed selected from a process with ten times the uncertainty, you would expect the scatter in the data to increase by a factor of ten as well. When this new data set is fitted, it will show a computed uncertainty increased by the same factor. Monte carlo simulations bear this out. The conclusion is that the dataset carries its own information about the variance in the data, and the weight vector serves only to provide relative weighting between the points.

wsolve(A, y, dy=1, rcond=1e-12)

source code

Given a linear system y = A*x + e(dy), estimates x,dx

A is an n x m array y is an n x k array or vector of length n dy is a scalar or an n x 1 array x is a m x k array

wpolyfit(x, y, dy=1, degree=None, origin=False)

source code

Return the polynomial of degree n that minimizes sum( (p(x_i) - y_i)**2/dy_i**2).

if origin is True, the fit should go through the origin.

Classes
	LinearModel Model evaluator for linear solution to Ax = y.
	PolynomialModel Model evaluator for best fit polynomial p(x) = y.

Module wsolve

Example

wsolve(A, y, dy=1, rcond=1e-12)

wpolyfit(x, y, dy=1, degree=None, origin=False)