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"""
This module implements the Lowess function for nonparametric regression.
Functions:
lowess Fit a smooth nonparametric regression curve to a scatterplot.
For more information, see
William S. Cleveland: "Robust locally weighted regression and smoothing
scatterplots", Journal of the American Statistical Association, December 1979,
volume 74, number 368, pp. 829-836.
"""
try:
from Numeric import *
from LinearAlgebra import solve_linear_equations
except ImportError, x:
raise ImportError, "This module requires NumPy with the LinearAlgebra and MLab libraries"
try:
from Bio.Cluster import median
# The function median in Bio.Cluster is faster than the function median
# in NumPy's MLab, as it does not require a full sort.
except ImportError, x:
# Use the median function in NumPy's MLab if Bio.Cluster is not available
try:
from MLab import median
except ImportError, x:
raise ImportError, "This module requires NumPy with the LinearAlgebra and MLab libraries"
def lowess(x, y, f=2./3., iter=3):
"""lowess(x, y, f=2./3., iter=3) -> yest
Lowess smoother: Robust locally weighted regression.
The lowess function fits a nonparametric regression curve to a scatterplot.
The arrays x and y contain an equal number of elements; each pair
(x[i], y[i]) defines a data point in the scatterplot. The function returns
the estimated (smooth) values of y.
The smoothing span is given by f. A larger value for f will result in a
smoother curve. The number of robustifying iterations is given by iter. The
function will run faster with a smaller number of iterations."""
n = len(x)
r = int(ceil(f*n))
h = [sort(abs(x-x[i]))[r] for i in range(n)]
w = clip(abs(([x]-transpose([x]))/h),0.0,1.0)
w = 1-w*w*w
w = w*w*w
yest = zeros(n,'d')
delta = ones(n,'d')
for iteration in range(iter):
for i in range(n):
weights = delta * w[:,i]
b = array([sum(weights*y), sum(weights*y*x)])
A = array([[sum(weights), sum(weights*x)],
[sum(weights*x), sum(weights*x*x)]])
beta = solve_linear_equations(A,b)
yest[i] = beta[0] + beta[1]*x[i]
residuals = y-yest
s = median(abs(residuals))
delta = clip(residuals/(6*s),-1,1)
delta = 1-delta*delta
delta = delta*delta
return yest
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