def MA_zscore(G, R, window=1./5., padded=False, progressCallback=None):
""" Return the Z-score of log2 fold ratio estimated from local
distribution of log2 fold ratio values on the MA-plot
"""
ratio, intensity = ratio_intensity(G, R)
z_scores = numpy.ma.zeros(G.shape)
sorted = list(numpy.ma.argsort(intensity))
import math, random
r = int(math.ceil(len(sorted)*window)) # number of window elements
def local_indices(i, sorted):
""" local indices in sorted (mirror padded if out of bounds)
"""
start, end = i - r/2, i + r/2 + r%2
pad_start , pad_end = [], []
if start < 0:
pad_start = sorted[:abs(start)]
random.shuffle(pad_start)
start = 0
if end > len(sorted):
pad_end = sorted[end - len(sorted):]
random.shuffle(pad_end)
end = len(sorted)
if padded:
return pad_start + sorted[start: end] + pad_end
else:
return sorted[start:end]
milestones = orngMisc.progressBarMilestones(len(sorted))
for i in range(len(sorted)):
indices = local_indices(i, sorted)
localRatio = numpy.take(ratio, indices)
local_std = numpy.ma.std(localRatio)
ind = sorted[i]
z_scores[ind] = ratio[ind] / local_std
if progressCallback and i in milestones:
progressCallback(100. * i / len(sorted))
z_scores._mask = - numpy.isfinite(z_scores)
return z_scores
def lowess2(x, y, xest, f=2./3., iter=3, progressCallback=None):
"""Returns estimated values of y in data points xest (or None if estimation fails).
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.
Taken from Peter Juvan's numpyExtn.py, modified for numpy, computes pairwise
distances inplace
"""
x = numpy.asarray(x, 'f')
y = numpy.asarray(y, 'f')
xest = numpy.asarray(xest, 'f')
n = len(x)
nest = len(xest)
r = min(int(numpy.ceil(f*n)),n-1) # radius: num. of points to take into LR
# h = [numpy.sort(numpy.abs(x-x[i]))[r] for i in range(n)] # distance of the r-th point from x[i]
dist = [x] - numpy.transpose([x])
dist = numpy.abs(dist, dist)
dist.sort(axis=1)
h = dist[:, r]
del dist # to free memory
w = [x] - numpy.transpose([x])
w /= h
w = numpy.abs(w, w)
w = numpy.clip(w, 0.0, 1.0, w)
# w = numpy.clip(numpy.abs(([x]-numpy.transpose([x]))/h),0.0,1.0)
w **= 3
w *= -1
w += 1
# w = 1 - w**3 #1-w*w*w
w **= 3
# w = w**3 #w*w*w
# hest = [numpy.sort(numpy.abs(x-xest[i]))[r] for i in range(nest)] # r-th min. distance from xest[i] to x
dist = [x] - numpy.transpose([xest])
dist = numpy.abs(dist, dist)
dist.sort(axis=1)
hest = dist[:, r]
del dist # to free memory
# west = numpy.clip(numpy.abs(([xest]-numpy.transpose([x]))/hest),0.0,1.0) # shape: (len(x), len(xest)
west = [xest]-numpy.transpose([x])
west /= hest
west = numpy.abs(west, west)
west = numpy.clip(west, 0.0, 1.0, west)
# west = 1 - west**3 #1-west*west*west
west **= 3
west *= -1
west += 1
# west = west**3 #west*west*west
west **= 3
yest = numpy.zeros(n,'f')
yest2 = numpy.zeros(nest,'f')
delta = numpy.ones(n,'f')
iter_count = iter*(nest + n) if iter > 1 else nest
milestones = orngMisc.progressBarMilestones(iter_count)
curr_iter = 0
for iteration in range(iter):
# fit xest
for i in range(nest):
weights = delta * west[:,i]
b = numpy.array([numpy.sum(weights*y), numpy.sum(weights*y*x)])
A = numpy.array([[numpy.sum(weights), numpy.sum(weights*x)], [numpy.sum(weights*x), numpy.sum(weights*x*x)]])
beta = numpy.linalg.solve(A, b)
yest2[i] = beta[0] + beta[1]*xest[i]
if progressCallback and curr_iter in milestones:
progressCallback(100. * curr_iter / iter_count)
curr_iter += 1
# fit x (to calculate residuals and delta)
if iter > 1:
for i in range(n):
weights = delta * w[:,i]
b = numpy.array([numpy.sum(weights*y), numpy.sum(weights*y*x)])
A = numpy.array([[numpy.sum(weights), numpy.sum(weights*x)], [numpy.sum(weights*x), numpy.sum(weights*x*x)]])
beta = numpy.linalg.solve(A,b)
yest[i] = beta[0] + beta[1]*x[i]
if progressCallback and curr_iter in milestones:
progressCallback(100. * curr_iter / iter_count)
curr_iter += 1
residuals = y-yest
s = numpy.median(numpy.abs(residuals))
delta = numpy.clip(residuals/(6*s), -1, 1)
delta = 1-delta*delta
delta = delta*delta
return yest2
def lowess(x, y, f=2./3., iter=3, progressCallback=None):
""" Lowess taken from Bio.Statistics.lowess, modified to compute pairwise
distances inplace.
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,
... 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 = min(int(numpy.ceil(f*n)), n - 1)
# h = [numpy.sort(numpy.abs(x-x[i]))[r] for i in range(n)]
# h, xtmp = numpy.zeros_like(x), numpy.zeros_like(x)
# for i in range(n):
# xtmp = numpy.abs(x - x[i], xtmp)
# h[i] = numpy.sort(xtmp)[r]
# w = numpy.clip(numpy.abs(([x]-numpy.transpose([x]))/h),0.0,1.0)
dist = [x] - numpy.transpose([x])
dist = numpy.abs(dist, dist)
dist.sort(axis=1)
h = dist[:, r]
del dist
w = [x]-numpy.transpose([x])
w /= h
w = numpy.abs(w, w)
w = numpy.clip(w, 0.0, 1.0, w)
# w = 1-w*w*w
w **= 3
w *= -1
w += 1
# w = w*w*w
w **= 3
yest = numpy.zeros(n)
delta = numpy.ones(n)
milestones = orngMisc.progressBarMilestones(iter*n)
for iteration in range(iter):
for i in xrange(n):
weights = delta * w[:,i]
weights_mul_x = weights * x
b1 = numpy.ma.dot(weights,y)
b2 = numpy.ma.dot(weights_mul_x,y)
A11 = sum(weights)
A12 = sum(weights_mul_x)
A21 = A12
A22 = numpy.ma.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]
if progressCallback and (iteration*n + i) in milestones:
progressCallback((100. * iteration*n + i) / (iter * n))
residuals = y-yest
s = median(abs(residuals))
delta[:] = numpy.clip(residuals/(6*s),-1,1)
delta[:] = 1-delta*delta
delta[:] = delta*delta
return yest
