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.
x and y should be numpy float arrays of equal length. The return value is
also a numpy float array of that length.
e.g.
>>> import numpy
>>> x = numpy.array([4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12,
... 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16,
... 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20,
... 20, 22, 23, 24, 24, 24, 24, 25], numpy.float)
>>> y = numpy.array([2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24,
... 28, 26, 34, 34, 46, 26, 36, 60, 80, 20, 26, 54, 32, 40,
... 32, 40, 50, 42, 56, 76, 84, 36, 46, 68, 32, 48, 52, 56,
... 64, 66, 54, 70, 92, 93, 120, 85], numpy.float)
>>> result = lowess(x, y)
>>> len(result)
50
>>> print "[%0.2f, ..., %0.2f]" % (result[0], result[-1])
[4.85, ..., 84.98]
"""
n = len(x)
r = int(numpy.ceil(f * n))
h = [numpy.sort(abs(x - x[i]))[r] for i in range(n)]
w = numpy.clip(abs(([x] - numpy.transpose([x])) / h), 0.0, 1.0)
w = 1 - w * w * w
w = w * w * w
yest = numpy.zeros(n)
delta = numpy.ones(n)
for iteration in range(iter):
for i in xrange(n):
weights = delta * w[:, i]
weights_mul_x = weights * x
b1 = numpy.dot(weights, y)
b2 = numpy.dot(weights_mul_x, y)
A11 = sum(weights)
A12 = sum(weights_mul_x)
A21 = A12
A22 = numpy.dot(weights_mul_x, x)
determinant = A11 * A22 - A12 * A21
beta1 = (A22 * b1 - A12 * b2) / determinant
beta2 = (A11 * b2 - A21 * b1) / determinant
yest[i] = beta1 + beta2 * x[i]
residuals = y - yest
s = median(abs(residuals))
delta[:] = numpy.clip(residuals / (6 * s), -1, 1)
delta[:] = 1 - delta * delta
delta[:] = delta * delta
return yest
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
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.
x and y should be numpy float arrays of equal length. The return value is
also a numpy float array of that length.
e.g.
>>> import numpy
>>> x = numpy.array([4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12,
... 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16,
... 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20,
... 20, 22, 23, 24, 24, 24, 24, 25], numpy.float)
>>> y = numpy.array([2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24,
... 28, 26, 34, 34, 46, 26, 36, 60, 80, 20, 26, 54, 32, 40,
... 32, 40, 50, 42, 56, 76, 84, 36, 46, 68, 32, 48, 52, 56,
... 64, 66, 54, 70, 92, 93, 120, 85], numpy.float)
>>> result = lowess(x, y)
>>> len(result)
50
>>> print "[%0.2f, ..., %0.2f]" % (result[0], result[-1])
[4.85, ..., 84.98]
"""
n = len(x)
r = int(numpy.ceil(f * n))
h = [numpy.sort(abs(x - x[i]))[r] for i in range(n)]
w = numpy.clip(abs(([x] - numpy.transpose([x])) / h), 0.0, 1.0)
w = 1 - w * w * w
w = w * w * w
yest = numpy.zeros(n)
delta = numpy.ones(n)
for iteration in range(iter):
for i in xrange(n):
weights = delta * w[:, i]
weights_mul_x = weights * x
b1 = numpy.dot(weights, y)
b2 = numpy.dot(weights_mul_x, y)
A11 = sum(weights)
A12 = sum(weights_mul_x)
A21 = A12
A22 = numpy.dot(weights_mul_x, x)
determinant = A11 * A22 - A12 * A21
beta1 = (A22 * b1 - A12 * b2) / determinant
beta2 = (A11 * b2 - A21 * b1) / determinant
yest[i] = beta1 + beta2 * x[i]
residuals = y - yest
s = median(abs(residuals))
delta[:] = numpy.clip(residuals / (6 * s), -1, 1)
delta[:] = 1 - delta * delta
delta[:] = delta * delta
return yest
def test_median_mean(self):
if TestCluster.module == 'Bio.Cluster':
from Bio.Cluster import mean, median
elif TestCluster.module == 'Pycluster':
from Pycluster import mean, median
data = numpy.array([34.3, 3, 2])
self.assertAlmostEqual(mean(data), 13.1, places=3)
self.assertAlmostEqual(median(data), 3.0, places=3)
data = [5, 10, 15, 20]
self.assertAlmostEqual(mean(data), 12.5, places=3)
self.assertAlmostEqual(median(data), 12.5, places=3)
data = [1, 2, 3, 5, 7, 11, 13, 17]
self.assertAlmostEqual(mean(data), 7.375, places=3)
self.assertAlmostEqual(median(data), 6.0, places=3)
data = [100, 19, 3, 1.5, 1.4, 1, 1, 1]
self.assertAlmostEqual(mean(data), 15.988, places=3)
self.assertAlmostEqual(median(data), 1.45, places=3)
def test_mean_median(module):
if module == 'Bio.Cluster':
from Bio.Cluster import mean, median
elif module == 'Pycluster':
from Pycluster import mean, median
else:
raise 'Unknown module name', module
print "test_mean_median:"
data1 = array([34.3, 3, 2])
data2 = [5, 10, 15, 20]
data3 = [1, 2, 3, 5, 7, 11, 13, 17]
data4 = [100, 19, 3, 1.5, 1.4, 1, 1, 1]
for data in [data1, data2, data3, data4]:
print "data =",
print_row(data)
print "mean is %7.3f; median is %7.3f" % (mean(data), median(data))
print
def test_mean_median(module):
if module=='Bio.Cluster':
from Bio.Cluster import mean, median
elif module=='Pycluster':
from Pycluster import mean, median
else:
raise 'Unknown module name', module
print "test_mean_median:"
data1 = array([ 34.3, 3, 2 ])
data2 = [ 5, 10 ,15, 20]
data3 = [ 1, 2, 3, 5, 7, 11, 13, 17]
data4 = [ 100, 19, 3, 1.5, 1.4, 1, 1, 1]
for data in [data1, data2, data3, data4]:
print "data =",
print_row(data)
print "mean is %7.3f; median is %7.3f" % (mean(data), median(data))
print
