def _checkOrth(self, T, TT, eps=0.0001, output=False):
"""check if the basis is orthogonal on a set of points x: TT == T*transpose(T) == c*Identity
INPUT: T: matrix of values of polynomials calculated at common reference points (x)
TT = T * transpose(T)
eps: max numeric error
"""
TTd0 = (-1.*Numeric.identity(Numeric.shape(TT)[0])+1) * TT # TTd0 = TT with 0s on the main diagonal
s = Numeric.sum(Numeric.sum(Numeric.absolute(TTd0)))
minT = MLab.min(MLab.min(T))
maxT = MLab.max(MLab.max(T))
minTTd0 = MLab.min(MLab.min(TTd0))
maxTTd0 = MLab.max(MLab.max(TTd0))
if not s < eps:
out = "NOT ORTHOG, min(T), max(T):\t%f\t%f\n" % (minT, maxT)
out += " min(TTd0), max(TTd0), sum-abs-el(TTd0):\t%f\t%f\t%f" % (minTTd0, maxTTd0, s)
if output:
print out
return False
else:
raise out
elif output:
out = "ORTHOGONAL, min(T), max(T):\t%f\t%f\n" % (minT, maxT)
out += " min(TTd0), max(TTd0), sum-abs-el(TTd0):\t%f\t%f\t%f" % (minTTd0, maxTTd0, s)
print out
return True
def _checkOrth(self, T, TT, eps=0.0001, output=False):
"""check if the basis is orthogonal on a set of points x: TT == T*transpose(T) == c*Identity
INPUT: T: matrix of values of polynomials calculated at common reference points (x)
TT = T * transpose(T)
eps: max numeric error
"""
TTd0 = (-1. * Numeric.identity(Numeric.shape(TT)[0]) +
1) * TT # TTd0 = TT with 0s on the main diagonal
s = Numeric.sum(Numeric.sum(Numeric.absolute(TTd0)))
minT = MLab.min(MLab.min(T))
maxT = MLab.max(MLab.max(T))
minTTd0 = MLab.min(MLab.min(TTd0))
maxTTd0 = MLab.max(MLab.max(TTd0))
if not s < eps:
out = "NOT ORTHOG, min(T), max(T):\t%f\t%f\n" % (minT, maxT)
out += " min(TTd0), max(TTd0), sum-abs-el(TTd0):\t%f\t%f\t%f" % (
minTTd0, maxTTd0, s)
if output:
print out
return False
else:
raise out
elif output:
out = "ORTHOGONAL, min(T), max(T):\t%f\t%f\n" % (minT, maxT)
out += " min(TTd0), max(TTd0), sum-abs-el(TTd0):\t%f\t%f\t%f" % (
minTTd0, maxTTd0, s)
print out
return True
def _create_matrix_plot(z_, r_x=0, r_y=0, colorcode=0,
min_area=100000, scale=1):
import numpy.oldnumeric.mlab as ml
# Scale z and find appropriate colormap.
z = z_.copy()
zmax = ml.max(ml.max(z))
zmin = ml.min(ml.min(z))
if (zmin < 0) and (0 < zmax) and (not colorcode):
colormap = create_bipolar_colormap()
zmax = ml.max(asarray([-zmin, zmax]))
z += zmax
z *= (len(colormap)-1)/(2*zmax)
else:
if colorcode == whiteblack:
colormap = create_white_black_colormap()
elif colorcode == blackwhite:
colormap = create_black_white_colormap()
else:
colormap = create_unipolar_colormap()
z -= zmin
if (zmax != zmin):
z *= (len(colormap)-1)/(zmax-zmin)
return _create_scaled_matrix_plot(colormap, z, r_x, r_y,
min_area = min_area, scale = scale)
def getAppxCoef2d_significant(self, arr2d, maxNumCoef, alpha):
"""Returns[:,j] approx. coeffcients with p-value < alpha; subsequent coef. are equal to 0.
Reference: Ott, pp.606.
The significance of the coef. estimated by comparing the variance drop of the model2 with the variance of the model1, where:
model 1: complete model with maxNumCoef coef. different from 0
model 2: reduced model with coef. in range (0,k) different from 0
null hypothesis (H0): coef. k,k+1,...,maxNumCoef are equal to 0
if H0 rejected (pval below some alpha (e.g. 0.05) -> there exist an important coef. among coef. k,k+1,...,maxNumCoef
repeat the test for k=0,1,...maxNumCoef-1
"""
assert len(arr2d.shape) == 2, "2d array expected"
assert 0 < maxNumCoef <= self.k
coefMax = self.getAppxCoef(arr2d, maxNumCoef)
curveMax = self.getAppxCurve(coefMax)
SSE1 = Numeric.add.reduce((arr2d - curveMax)**2, 1)
MSE1 = SSE1 / (arr2d.shape[1] - maxNumCoef)
#print "SSE1[0], MSE1[0]",SSE1[0], MSE1[0]
pvals = Numeric.zeros((arr2d.shape[0], maxNumCoef), Numeric.Float)
for k in range(
maxNumCoef): # test cofInd: [maxNum-1, maxNum-2, ..., minNum]
#print "Keeping %i coeff" % (k)
shpk = list(coefMax.shape)
shpk[1] -= k
coefk = Numeric.concatenate(
(coefMax[:, :k], Numeric.zeros((shpk), Numeric.Float)), 1)
curvek = self.getAppxCurve(coefk)
SSE2 = Numeric.add.reduce((arr2d - curvek)**2, 1)
MSdrop = (SSE2 - SSE1) / (maxNumCoef - k)
F = MSdrop / MSE1
#2007-10-11: F -> F.filled(???)
pvals[:, k] = scipy.stats.fprob(
(maxNumCoef - k), arr2d.shape[1] - maxNumCoef,
F.filled(ApproxOrthPolyBasis._F_fillValue))
pvals = Numeric.where(
pvals > alpha,
Numeric.resize(Numeric.arange(pvals.shape[1]), pvals.shape),
pvals.shape[1]) # MAX where significant, idx where nonsignificant
firstNonSignIdx = MLab.min(pvals,
1) # idx of the first non-significant coef.
coefSign = Numeric.zeros(coefMax.shape, Numeric.Float)
for idx in range(coefSign.shape[1]):
coefSign[:, idx] = Numeric.where(idx < firstNonSignIdx,
coefMax[:, idx], 0)
return coefSign
def getAppxCoef2d_significant(self, arr2d, maxNumCoef, alpha):
"""Returns[:,j] approx. coeffcients with p-value < alpha; subsequent coef. are equal to 0.
Reference: Ott, pp.606.
The significance of the coef. estimated by comparing the variance drop of the model2 with the variance of the model1, where:
model 1: complete model with maxNumCoef coef. different from 0
model 2: reduced model with coef. in range (0,k) different from 0
null hypothesis (H0): coef. k,k+1,...,maxNumCoef are equal to 0
if H0 rejected (pval below some alpha (e.g. 0.05) -> there exist an important coef. among coef. k,k+1,...,maxNumCoef
repeat the test for k=0,1,...maxNumCoef-1
"""
assert len(arr2d.shape) == 2, "2d array expected"
assert 0 < maxNumCoef <= self.k
coefMax = self.getAppxCoef(arr2d, maxNumCoef)
curveMax = self.getAppxCurve(coefMax)
SSE1 = Numeric.add.reduce((arr2d-curveMax)**2,1)
MSE1 = SSE1 / (arr2d.shape[1]-maxNumCoef)
#print "SSE1[0], MSE1[0]",SSE1[0], MSE1[0]
pvals = Numeric.zeros((arr2d.shape[0], maxNumCoef), Numeric.Float)
for k in range(maxNumCoef): # test cofInd: [maxNum-1, maxNum-2, ..., minNum]
#print "Keeping %i coeff" % (k)
shpk = list(coefMax.shape)
shpk[1] -= k
coefk = Numeric.concatenate((coefMax[:,:k], Numeric.zeros((shpk), Numeric.Float)),1)
curvek = self.getAppxCurve(coefk)
SSE2 = Numeric.add.reduce((arr2d-curvek)**2,1)
MSdrop =(SSE2-SSE1) / (maxNumCoef-k)
F = MSdrop / MSE1
#2007-10-11: F -> F.filled(???)
pvals[:,k] = scipy.stats.fprob((maxNumCoef-k), arr2d.shape[1]-maxNumCoef, F.filled(ApproxOrthPolyBasis._F_fillValue))
pvals = Numeric.where(pvals > alpha, Numeric.resize(Numeric.arange(pvals.shape[1]),pvals.shape), pvals.shape[1]) # MAX where significant, idx where nonsignificant
firstNonSignIdx = MLab.min(pvals, 1) # idx of the first non-significant coef.
coefSign = Numeric.zeros(coefMax.shape, Numeric.Float)
for idx in range(coefSign.shape[1]):
coefSign[:,idx] = Numeric.where(idx<firstNonSignIdx, coefMax[:,idx], 0)
return coefSign