def distSpearman(x, y):
"""distance corresponding to 1 - spearman's correlation coefficient for arrays x,y
returns distance: 1 - spearman_r
"""
x = MA.asarray(x)
y = MA.asarray(y)
assert MA.rank(x) == MA.rank(y) == 1
cond = MA.logical_not(MA.logical_or(MA.getmaskarray(x),
MA.getmaskarray(y)))
return 1 - statc.spearmanr(
MA.compress(cond, x).tolist(),
MA.compress(cond, y).tolist())[0]
def _distSpearmanW_MA(x, y, w):
"""if any of x,y,w is a MA array containing masked values
"""
x = MA.asarray(x)
y = MA.asarray(y)
w = MA.asarray(w)
assert MA.rank(x) == MA.rank(y) == MA.rank(w) == 1
cond = MA.logical_not(
MA.logical_or(MA.logical_or(MA.getmaskarray(x), MA.getmaskarray(y)),
MA.getmaskarray(w)))
# with MA use compress before tolist() !
rankx = Numeric.array(statc.rankdata(MA.compress(cond, x).tolist()))
ranky = Numeric.array(statc.rankdata(MA.compress(cond, y).tolist()))
return distPearsonW(rankx, ranky, MA.compress(cond, w))
def loessMA(m,
windowSize,
axis=0,
approxMasked=True,
verbose=False,
callback=None):
"""Returns a new array with values at the given axis smoothed by loess;
if approxMasked==True: the masked values are approximated by loess;
assumes equidistant spacing of points on the given axis.
"""
assert 0 < windowSize <= m.shape[
axis] + 0.1, "0 < windowSize[%s] <= 1 OR windowSize in range(1.1,m.shape[axis]+1) expected, got %f" % (
"%", windowSize)
m = MA.asarray(m)
if m.dtype.char <> Numeric.Float:
m = m.astype(Numeric.Float)
shp_other = list(m.shape)
shp_other.pop(axis)
# get a transposed and reshaped mask and data from m; if m.mask() == None, construct a new array of zeros
mask = Numeric.reshape(
Numeric.transpose(MA.getmaskarray(m), [axis] + range(0, axis) +
range(axis + 1, len(m.shape))),
(m.shape[axis], Numeric.multiply.reduce(shp_other)))
data = MA.reshape(
MA.transpose(m,
[axis] + range(0, axis) + range(axis + 1, len(m.shape))),
(m.shape[axis], Numeric.multiply.reduce(shp_other)))
maskInv = -1 * (mask - 1)
xall = Numeric.arange(data.shape[0])
xallList = xall.tolist()
for ii in Numeric.compress(
Numeric.add.reduce(maskInv, 0) > 1, range(data.shape[1])
): # run loess if the profile contains more than 2 values
try:
data[:, ii] = MA.array(
statc.loess(
zip(
MA.compress(maskInv[:, ii], xall).tolist(),
MA.compress(maskInv[:, ii], data[:, ii]).tolist()),
xallList, windowSize))[:, 1]
except:
if verbose:
print "Warning: loessMA: could not loess axis %i index %i" % (
axis, ii)
if callback:
callback()
if not approxMasked:
data = MA.array(data, mask=mask)
return MA.transpose(MA.reshape(data, [m.shape[axis]] + shp_other), [axis] +
range(0, axis) + range(axis + 1, len(m.shape)))
def loessMA(m, windowSize, axis=0, approxMasked=True, verbose=False, callback=None):
"""Returns a new array with values at the given axis smoothed by loess;
if approxMasked==True: the masked values are approximated by loess;
assumes equidistant spacing of points on the given axis.
"""
assert 0 < windowSize <= m.shape[axis]+0.1, "0 < windowSize[%s] <= 1 OR windowSize in range(1.1,m.shape[axis]+1) expected, got %f" % ("%", windowSize)
m = MA.asarray(m)
if m.dtype.char <> Numeric.Float:
m = m.astype(Numeric.Float)
shp_other = list(m.shape)
shp_other.pop(axis)
# get a transposed and reshaped mask and data from m; if m.mask() == None, construct a new array of zeros
mask = Numeric.reshape(Numeric.transpose(MA.getmaskarray(m), [axis] + range(0,axis) + range(axis+1,len(m.shape))), (m.shape[axis], Numeric.multiply.reduce(shp_other)))
data = MA.reshape(MA.transpose(m, [axis] + range(0,axis) + range(axis+1,len(m.shape))), (m.shape[axis], Numeric.multiply.reduce(shp_other)))
maskInv = -1*(mask-1)
xall = Numeric.arange(data.shape[0])
xallList = xall.tolist()
for ii in Numeric.compress(Numeric.add.reduce(maskInv,0) > 1, range(data.shape[1])): # run loess if the profile contains more than 2 values
try:
data[:,ii] = MA.array(statc.loess(zip(MA.compress(maskInv[:,ii], xall).tolist(), MA.compress(maskInv[:,ii], data[:,ii]).tolist()), xallList, windowSize))[:,1]
except:
if verbose:
print "Warning: loessMA: could not loess axis %i index %i" % (axis, ii)
if callback:
callback()
if not approxMasked:
data = MA.array(data, mask=mask)
return MA.transpose(MA.reshape(data, [m.shape[axis]] + shp_other), [axis] + range(0,axis) + range(axis+1,len(m.shape)))
def ttest_rsmplA(self, ma3d, callback):
"""conducts related samples t-test on individual examples wrt factor A (variables, ma3d axis 1);
returns Numeric array of p-values in shape (1, numExamples).
"""
ps = -1*Numeric.ones((ma3d.shape[0],), Numeric.Float)
for eIdx in range(ma3d.shape[0]):
a = ma3d[eIdx][0]
b = ma3d[eIdx][1]
cond = Numeric.logical_not(Numeric.logical_or(MA.getmaskarray(a), MA.getmaskarray(b)))
a = Numeric.asarray(MA.compress(cond, a))
b = Numeric.asarray(MA.compress(cond, b))
if len(a) >= 2:
try:
ps[eIdx] = scipy.stats.ttest_rel(a,b)[1]
except Exception, inst:
print "Warning: %s" % str(inst)
print "Example %i:\n%s\n%s\n" % (eIdx, str(a), str(b))
ps[eIdx] = 1.0
else:
print "Warning: removing example %i:\n%s\n%s\n" % (eIdx, str(a), str(b))
ps[eIdx] = 1.0
callback()
def kNNimputeMA(arr2d, K=20, callback=None):
"""Returns a new 2D MA.array with missing values imputed from K nearest neighbours.
Find K rows (axis 0) with the most similar values where similarity measure corresponds to weighted Euclidean distance.
Imputed value = weighted average of the corresponding values of K nearest neighbours,
where weights equal to tricubic distribution of distances to all rows.
Impute missing rows by average over all rows.
Version: 30.8.2005
"""
arr2d = MA.asarray(arr2d)
assert len(arr2d.shape) == 2, "2D array expected"
# make a copy for imputation
aImp2 = MA.array(arr2d)
# leave out columns with 0 known values (columnInd: non-zero columns)
columnCond = Numeric.greater(MA.count(arr2d, axis=0), 0)
columnIndAll = Numeric.arange(arr2d.shape[1])
columnInd = Numeric.compress(columnCond, columnIndAll)
# impute the rows where 0 < #known_values < #non_zero_columns, i.e. exclude the rows with 0 and all (non-zero-column) values
countByRows = MA.count(arr2d, axis=1)
for rowIdx in Numeric.compress(Numeric.logical_and(Numeric.greater(countByRows, 0), Numeric.less(countByRows, columnInd.shape[0])), Numeric.arange(arr2d.shape[0])):
rowResized = MA.resize(arr2d[rowIdx], arr2d.shape)
diff = arr2d - rowResized
distances = MA.sqrt(MA.add.reduce((diff)**2, 1) / MA.count(diff, axis=1))
# nearest neighbours row indices (without the current row index)
indSorted = MA.argsort(distances)[1:]
distSorted = distances.take(indSorted)
# number of distances different from MA.masked
numNonMasked = distSorted.shape[0] - Numeric.add.reduce(Numeric.asarray(MA.getmaskarray(distSorted), Numeric.Int))
# number of distances to account for (K or less)
if numNonMasked > 1:
weightsSorted = MA.power(1-MA.power(distSorted/distSorted[numNonMasked-1],3),3) # tricubic distribution of all weights
else:
weightsSorted = Numeric.ones(distSorted.shape[0])
# compute average for each column separately in order to account for K non-masked values
colInd4CurrRow = Numeric.compress(Numeric.logical_and(MA.getmaskarray(arr2d[rowIdx]), columnCond), columnIndAll)
for colIdx in colInd4CurrRow:
# column values sorted by distances
columnVals = arr2d[:,colIdx].take(indSorted)
# take only those weights where columnVals does not equal MA.masked
weightsSortedCompressed = MA.compress(1-MA.getmaskarray(columnVals), weightsSorted)
# impute from K (or possibly less) values
aImp2[rowIdx,colIdx] = MA.average(columnVals.compressed()[:K], weights=weightsSortedCompressed[:K])
if callback:
callback()
# impute the unknown rows with average profile
avrgRow = MA.average(arr2d, 0)
for rowIdx in Numeric.compress(Numeric.equal(countByRows, 0), Numeric.arange(arr2d.shape[0])):
aImp2[rowIdx] = avrgRow
if callback:
callback()
return aImp2
def anova2(self, ma3d, groupLens, addInteraction, repMeasuresOnA, callback):
"""Conducts two-way ANOVA on individual examples;
returns a Numeric array of p-values in shape (2, numExamples) or (3, numExamples), depending whether we test for interaction;
Note: levels of factors A and B that cause empty cells are removed prior to conducting ANOVA.
"""
groupLens = Numeric.asarray(groupLens)
# arrays to store p-vals
if addInteraction:
ps = Numeric.ones((3, ma3d.shape[0]), Numeric.Float)
else:
ps = Numeric.ones((2, ma3d.shape[0]), Numeric.Float)
# decide between non-repeated / repeated measures ANOVA for factor time
if repMeasuresOnA:
fAnova = Anova.AnovaRM12LR
else:
fAnova = Anova.Anova2wayLR
# check for empty cells for all genes at once and remove them
tInd2rem = []
ax2Ind = Numeric.concatenate(([0], Numeric.add.accumulate(groupLens)))
for aIdx in range(ma3d.shape[1]):
for rIdx in range(groupLens.shape[0]):
if Numeric.add.reduce(MA.count(ma3d[:,aIdx,ax2Ind[rIdx]:ax2Ind[rIdx+1]],1)) == 0:
tInd2rem.append(aIdx)
break
if len(tInd2rem) > 0:
print "Warning: removing time indices %s for all genes" % (str(tInd2rem))
tInd2keep = range(ma3d.shape[1])
for aIdx in tInd2rem:
tInd2keep.remove(aIdx)
ma3d = ma3d.take(tInd2keep, 1)
# for each gene...
for eIdx in range(ma3d.shape[0]):
# faster check for empty cells for that gene -> remove time indices with empty cells
ma2d = ma3d[eIdx]
cellCount = MA.zeros((ma2d.shape[0], groupLens.shape[0]), Numeric.Int)
for g,(i0,i1) in enumerate(zip(ax2Ind[:-1], ax2Ind[1:])):
cellCount[:,g] = MA.count(ma2d[:,i0:i1], 1)
ma2dTakeInd = Numeric.logical_not(Numeric.add.reduce(Numeric.equal(cellCount,0),1)) # 1 where to take, 0 where not to take
if Numeric.add.reduce(ma2dTakeInd) != ma2dTakeInd.shape[0]:
print "Warning: removing time indices %s for gene %i" % (str(Numeric.compress(ma2dTakeInd == 0, Numeric.arange(ma2dTakeInd.shape[0]))), eIdx)
ma2d = MA.compress(ma2dTakeInd, ma2d, 0)
an = fAnova(ma2d, groupLens, addInteraction, allowReductA=True, allowReductB=True)
ps[:,eIdx] = an.ps
callback()
return ps
def kNNimputeMA(arr2d, K=20, callback=None):
"""Returns a new 2D MA.array with missing values imputed from K nearest neighbours.
Find K rows (axis 0) with the most similar values where similarity measure corresponds to weighted Euclidean distance.
Imputed value = weighted average of the corresponding values of K nearest neighbours,
where weights equal to tricubic distribution of distances to all rows.
Impute missing rows by average over all rows.
Version: 30.8.2005
"""
arr2d = MA.asarray(arr2d)
assert len(arr2d.shape) == 2, "2D array expected"
# make a copy for imputation
aImp2 = MA.array(arr2d)
# leave out columns with 0 known values (columnInd: non-zero columns)
columnCond = Numeric.greater(MA.count(arr2d, axis=0), 0)
columnIndAll = Numeric.arange(arr2d.shape[1])
columnInd = Numeric.compress(columnCond, columnIndAll)
# impute the rows where 0 < #known_values < #non_zero_columns, i.e. exclude the rows with 0 and all (non-zero-column) values
countByRows = MA.count(arr2d, axis=1)
for rowIdx in Numeric.compress(
Numeric.logical_and(Numeric.greater(countByRows, 0),
Numeric.less(countByRows, columnInd.shape[0])),
Numeric.arange(arr2d.shape[0])):
rowResized = MA.resize(arr2d[rowIdx], arr2d.shape)
diff = arr2d - rowResized
distances = MA.sqrt(
MA.add.reduce((diff)**2, 1) / MA.count(diff, axis=1))
# nearest neighbours row indices (without the current row index)
indSorted = MA.argsort(distances)[1:]
distSorted = distances.take(indSorted)
# number of distances different from MA.masked
numNonMasked = distSorted.shape[0] - Numeric.add.reduce(
Numeric.asarray(MA.getmaskarray(distSorted), Numeric.Int))
# number of distances to account for (K or less)
if numNonMasked > 1:
weightsSorted = MA.power(
1 - MA.power(distSorted / distSorted[numNonMasked - 1], 3),
3) # tricubic distribution of all weights
else:
weightsSorted = Numeric.ones(distSorted.shape[0])
# compute average for each column separately in order to account for K non-masked values
colInd4CurrRow = Numeric.compress(
Numeric.logical_and(MA.getmaskarray(arr2d[rowIdx]), columnCond),
columnIndAll)
for colIdx in colInd4CurrRow:
# column values sorted by distances
columnVals = arr2d[:, colIdx].take(indSorted)
# take only those weights where columnVals does not equal MA.masked
weightsSortedCompressed = MA.compress(
1 - MA.getmaskarray(columnVals), weightsSorted)
# impute from K (or possibly less) values
aImp2[rowIdx,
colIdx] = MA.average(columnVals.compressed()[:K],
weights=weightsSortedCompressed[:K])
if callback:
callback()
# impute the unknown rows with average profile
avrgRow = MA.average(arr2d, 0)
for rowIdx in Numeric.compress(Numeric.equal(countByRows, 0),
Numeric.arange(arr2d.shape[0])):
aImp2[rowIdx] = avrgRow
if callback:
callback()
return aImp2