def test_derivatives(self):
print "Testing derivatives w.r.t. data ... "
sys.stdout.flush()
P = []
for k in range(10):
myp = 2.0 * np.random.rand(1)[0] + .5
mys = 3.0 * np.random.rand(1)[0] + 1.0
p = Distributions.ExponentialPower({'p': myp, 's': mys})
P.append(p)
p = Distributions.ProductOfExponentialPowerDistributions({'P': P})
dat = p.sample(100)
h = 1e-7
tol = 1e-4
Y0 = dat.X.copy()
df = p.dldx(dat)
df2 = 0.0 * df
for i in xrange(dat.size(0)):
y = Y0.copy()
y[i, :] = y[i, :] + h
df2[i, :] = (p.loglik(Data(y)) - p.loglik(dat)) / h
prot = {}
prot[
'message'] = 'Difference in derivative of log-likelihood for PowerExponential greater than ' + str(
tol)
prot['max difference'] = np.max(np.abs((df - df2).flatten()))
prot['mean difference'] = np.mean(np.abs((df - df2).flatten()))
self.assertTrue(
np.max(np.abs(df - df2)) < tol, Auxiliary.prettyPrintDict(prot))
def test_derivatives(self):
print "Testing derivative for p-spherically symmetric distribution with radial gamma"
sys.stdout.flush()
myu = 3.0 * np.random.rand(1)[0] + 1.0
mys = 3.0 * np.random.rand(1)[0] + 1.0
myp = 2 * np.random.rand(1)[0] + .5
n = 4
p = Distributions.LpSphericallySymmetric({
'p':
myp,
'n':
n,
'rp':
Distributions.Gamma({
's': mys,
'u': myu
})
})
dat = p.sample(50)
df = p.dldx(dat)
h = 1e-8
df2 = np.array(dat.X * np.Inf)
for k in range(n):
y = np.array(dat.X)
y[k, :] += h
df2[k, :] = (p.loglik(Data(y)) - p.loglik(dat)) / h
self.assertFalse(np.max(np.abs(df-df2).flatten()) > self.llTol,\
'Difference ' + str(np.max(np.abs(df-df2).flatten())) + ' in derivative of log-likelihood for p-spherically symmetric greater than ' + str(self.llTol))
print "[Ok]"
def test_RadialFactorizationVsLpNestedNonlinearICA(self):
print "Testing Radial Factorization vs. Lp-nested ICA..."
sys.stdout.flush()
p = np.random.rand() + 1.0
psource = Distributions.LpSphericallySymmetric({
'p':
p,
'rp':
Distributions.Gamma({
'u': 2.0 * np.random.rand() + 1.0,
's': 5.0 * np.random.rand() + 1.0
})
})
F = NonlinearTransformFactory.RadialFactorization(psource)
dat = psource.sample(10)
L = Auxiliary.LpNestedFunction('(0,0:2)', np.array([p]))
psource2 = Distributions.LpNestedSymmetric({
'f':
L,
'n':
2.0,
'rp':
psource.param['rp'].copy()
})
F2 = NonlinearTransformFactory.LpNestedNonLinearICA(psource2)
tol = 1e-6
self.assertTrue(np.max(np.abs(F.logDetJacobian(dat) - F2.logDetJacobian(dat))) < tol,\
'log-determinants of Lp-nestedICA and Radial Factorization are not equal!')
def test_estimate(self):
print "Testing parameter estimation of Gamma distribution ..."
sys.stdout.flush()
myp = 2.0 * np.random.rand(1)[0] + .5
mys = 10.0 * np.random.rand(1)[0]
p1 = Distributions.ExponentialPower({'p': myp, 's': mys})
dat = p1.sample(50000)
myp = 2.0 * np.random.rand(1)[0] + .5
mys = 10.0 * np.random.rand(1)[0]
p2 = Distributions.ExponentialPower({'p': myp, 's': mys})
p2.estimate(dat)
prot = {}
prot[
'message'] = 'Difference in parameters for Exponential Power distribution greater than threshold'
prot['s-threshold'] = self.TolParamS
prot['p-threshold'] = self.TolParamP
prot['true model'] = p1
prot['estimated model'] = p2
self.assertTrue(np.abs(p2.param['p'] - p1.param['p']) < self.TolParamP or np.abs(p2.param['s'] - p1.param['s']) < self.TolParamS,\
Auxiliary.prettyPrintDict(prot))
def test_MarginalHistogramEqualization(self):
print "Testing MarginalHistogramEqualization ..."
sys.stdout.flush()
psource = Distributions.ISA(
n=10,
P=[Distributions.MixtureOfGaussians(K=5) for k in range(10)],
S=[(k, ) for k in range(10)])
ptarget = Distributions.ISA(
n=10,
P=[Distributions.Gaussian(n=1) for k in range(10)],
S=[(k, ) for k in range(10)])
F = NonlinearTransformFactory.MarginalHistogramEqualization(
psource, ptarget)
dat = psource.sample(20000)
ld = F.logDetJacobian(dat)
ld = np.mean(np.abs(ld)) / dat.size(0) / np.log(2)
all_source = psource.all(dat)
all_target = ptarget.all(F * dat)
tol = 1e-2
prot = {}
prot['message'] = 'Difference in logdet correted ALL > ' + str(tol)
prot["1/n/log(2) * <|det J|> "] = ld
prot["ALL(TARGET)"] = all_target
prot["ALL(SOURCE)"] = all_source
prot[
"ALL(TARGET) + 1/n/log(2) * <|det J|> - ALL(SOURCE)"] = all_target + ld - all_source
def test_derivatives(self):
print "Testing derivative for p-nested symmetric distribution with radial gamma"
sys.stdout.flush()
myu = 10 * np.random.rand(1)[0]
mys = 10 * np.random.rand(1)[0]
n = 10
L = Auxiliary.LpNestedFunction('(0,0,(1,1:4),4,(1,5:8),8:10)')
p = Distributions.LpNestedSymmetric({
'f':
L,
'n':
n,
'rp':
Distributions.Gamma({
's': mys,
'u': myu
})
})
dat = p.sample(50)
df = p.dldx(dat)
h = 1e-8
df2 = np.array(dat.X * np.Inf)
for k in range(n):
y = np.array(dat.X)
y[k, :] += h
df2[k, :] = (p.loglik(Data(y)) - p.loglik(dat)) / h
self.assertFalse(np.max(np.abs(df-df2).flatten()) > self.llTol,\
'Difference in derivative of log-likelihood for p-nested symmetric greater than ' + str(self.llTol))
def test_loglik(self):
print 'Testing log-likelihood of p-spherically symmetric distribution with radial gamma'
sys.stdout.flush()
for k in range(5):
print '\t--> test case ' + str(k)
dat = io.loadmat(self.matpath + '/TestPSphericallySymmetric' +
str(k) + '.mat',
struct_as_record=True)
truell = np.squeeze(dat['ll'])
p = Distributions.LpSphericallySymmetric({
'p':
dat['p'],
'n':
dat['n'],
'rp':
Distributions.Gamma({
's': dat['s'],
'u': dat['u']
})
})
dat = Data(dat['X'])
ll = p.loglik(dat)
for i in range(len(ll)):
self.assertFalse(np.abs(ll[i]-truell[i]) > self.Tol,\
'Log-likelihood for p-spherically symmetric with radial gamma deviates from test case')
def test_DeterminantOfRadialFactorization(self):
print "Testing Determimant of Radial Factorization ..."
sys.stdout.flush()
p = np.random.rand() + 1.0
psource = Distributions.LpSphericallySymmetric({
'p':
p,
'rp':
Distributions.Gamma({
'u': 2.0 * np.random.rand() + 1.0,
's': 5.0 * np.random.rand() + 1.0
})
})
# L = Auxiliary.LpNestedFunction('(0,0:2)',np.array([p]))
# psource2 = Distributions.LpNestedSymmetric({'f':L,'n':2.0,'rp':psource.param['rp'].copy()})
# F2 = NonlinearTransformFactory.LpNestedNonLinearICA(psource2)
dat = psource.sample(100)
F = NonlinearTransformFactory.RadialFactorization(psource)
n, m = dat.size()
h = 1e-7
logdetJ = F.logDetJacobian(dat)
for i in range(m):
J = np.zeros((n, n))
for j in range(n):
tmp = dat[:, i]
tmp2 = tmp.copy()
tmp2.X[j, :] = tmp2.X[j, :] + h
J[:, j] = ((F * tmp2).X - (F * tmp).X)[:, 0] / h
self.assertFalse( np.abs(np.log(linalg.det(J)) - logdetJ[i]) > self.DetTol,\
'Determinant of Jacobian deviates by more than ' + str(self.DetTol) + '!')
def test_loglik(self):
p1 = Distributions.Kumaraswamy({'a': 2.0, 'b': 3.0})
p2 = Distributions.Kumaraswamy({'a': 1.0, 'b': 1.0})
nsamples = 1000000
data = p2.sample(nsamples)
logZ = logsumexp(p1.loglik(data) - p2.loglik(data) - np.log(nsamples))
print "Estimated partition function: ", np.exp(logZ)
self.assertTrue(
np.abs(np.exp(logZ) - 1.0) < 0.1 * self.TolParam,
'Difference in estimated partition function (1.0) greater than' +
str(0.1 * self.TolParam))
def test_estimate(self):
print "Testing parameter estimation of LogNormal distribution ..."
sys.stdout.flush()
myu = 10 * np.random.rand(1)[0]
mys = 10 * np.random.rand(1)[0]
p = Distributions.LogNormal({'mu': myu, 's': mys})
dat = p.sample(1000000)
p = Distributions.LogNormal()
p.estimate(dat)
self.assertFalse( np.abs(p.param['mu'] - myu) > self.TolParam,\
'Difference in location parameter for LogNormal distribution greater than ' + str(self.TolParam))
self.assertFalse( np.abs(p.param['s'] - mys) > self.TolParam,\
'Difference in scale parameter for LogNormal distribution greater than ' + str(self.TolParam))
def test_estimate(self):
print "Testing parameter estimation of Dirichlet distribution ..."
sys.stdout.flush()
myalpha = 10.0 * np.random.rand(10)
p = Distributions.Dirichlet({'alpha': myalpha})
dat = p.sample(50000)
p = Distributions.Dirichlet({'alpha': np.random.rand(10)})
p.estimate(dat)
alpha = p.param['alpha']
self.assertTrue(
np.max(np.abs(alpha - myalpha)) < self.TolParam,
'Difference in alpha parameter for Dirichlet distribution greater than '
+ str(self.TolParam))
def test_loglik(self):
p1 = Distributions.Gamma({'u': 2.0, 's': 3.0})
p2 = Distributions.Gamma({'u': 1.0, 's': 1.0})
nsamples = 1000000
data = p2.sample(nsamples)
logZ = logsumexp(p1.loglik(data) - p2.loglik(data) - np.log(nsamples))
print "Estimated partition function: ", np.exp(logZ)
print "Testing log-likelihood of Gamma distribution ... "
sys.stdout.flush()
p = Distributions.Gamma({'u': 2.0, 's': 3.0})
l = p.loglik(self.X)
for k in range(len(self.LL)):
self.assertFalse(np.abs(l[k] - self.LL[k]) > self.Tol,\
'Difference in log-likelihood for Gamma greater than ' + str(self.Tol))
def test_dldtheta(self):
OK = np.zeros(5)
for i in range(5):
self.a = 1.0 * rand()
self.b = self.a + 10.0 * rand()
self.mu = (self.a + 10 * rand()) / 2.
self.s = 2.0 * rand() + 1.0
self.p = Distributions.TruncatedGaussian({
'a': self.a,
'b': self.b,
'mu': self.mu,
'sigma': self.s
})
p = self.p.copy()
p.primary = ['mu', 'sigma']
dat = p.sample(100)
def f(arr):
p.array2primary(arr)
return np.sum(p.loglik(dat))
def df(arr):
p.array2primary(arr)
return np.sum(p.dldtheta(dat), axis=1)
arr0 = p.primary2array()
arr0 = abs(np.random.randn(len(arr0)))
err = optimize.check_grad(f, df, arr0)
if err < 1e-02:
OK[i] = 1
M = np.max(OK)
self.assertTrue(
M > 0.5, 'Gradient error %.4g is greater than %.4g' % (err, 1e-02))
def test_dldtheta(self):
a = 1.0 * rand()
b = a
while b <= a:
b = 10.0 * rand()
mu = rand() + 1.0
s = 10.0 * rand() + 1.0
p = Distributions.TruncatedExponentialPower({
'a': a,
'b': b,
'p': mu,
's': s
})
p.primary = ['p', 's']
dat = p.sample(100)
def f(arr):
p.array2primary(arr)
return np.sum(p.loglik(dat))
def df(arr):
p.array2primary(arr)
return np.sum(p.dldtheta(dat), axis=1)
arr0 = p.primary2array()
arr0 = abs(np.random.randn(len(arr0)))
err = optimize.check_grad(f, df, arr0)
print "Error in gradient: ", err
self.assertTrue(
err < 1e-02,
'Gradient error %.4g is greater than %.4g' % (err, 1e-02))
def test_estimate(self):
print "Testing parameter estimation of Gamma distribution ..."
sys.stdout.flush()
myu = 10 * np.random.rand(1)[0]
mys = 10 * np.random.rand(1)[0]
p = Distributions.Gamma({'u': myu, 's': mys})
dat = p.sample(1000000)
p = Distributions.Gamma()
p.estimate(dat)
self.assertFalse(
np.abs(p.param['u'] - myu) > self.TolParam,
'Difference in Shape parameter for Gamma distribution greater than '
+ str(self.TolParam))
self.assertFalse(
np.abs(p.param['s'] - mys) > self.TolParam,
'Difference in Scale parameter for Gamma distribution greater than '
+ str(self.TolParam))
def test_estimate(self):
print "Testing parameter estimation of Kumaraswamy distribution ..."
sys.stdout.flush()
myu = 10 * rand()
mys = 10 * rand()
myB = 10 * rand()
p = Distributions.Kumaraswamy({'a': myu, 'b': mys, 'B': myB})
dat = p.sample(50000)
p = Distributions.Kumaraswamy(B=myB)
p.estimate(dat)
self.assertFalse(
np.abs(p.param['a'] - myu) > self.TolParam,
'Difference in Shape parameter for Kumaraswamy distribution greater than '
+ str(self.TolParam))
self.assertFalse(
np.abs(p.param['b'] - mys) > self.TolParam,
'Difference in Scale parameter for Kumaraswamy distribution greater than '
+ str(self.TolParam))
def test_loglik(self):
print "Testing log-likelihood of Dirichlet distribution ... "
sys.stdout.flush()
p = Distributions.Dirichlet({'alpha': self.alpha})
l = p.loglik(self.X)
for k in range(len(self.LL)):
self.assertTrue(
np.abs(l[k] - self.LL[k]) < self.Tol,
'Difference in log-likelihood for Dirichlet greater than ' +
str(self.Tol))
def test_LogDetRadialTransform(self):
print "Testing logdet of radial transformation ... "
sys.stdout.flush()
p = np.random.rand() * 3. + .5
# source distribution
psource = Distributions.LpSphericallySymmetric({'p': p})
# target distribution
ptarget = Distributions.LpSphericallySymmetric({
'p':
p,
'rp':
Distributions.Gamma({
'u': np.random.rand() * 3.0,
's': np.random.rand() * 2.0
})
})
# create Filter
F = NonlinearTransformFactory.RadialTransformation(psource, ptarget)
# sample data from source distribution
dat = psource.sample(100)
# apply filter to data
dat2 = F * dat
logDetJ = F.logDetJacobian(dat)
logDetJ2 = 0 * logDetJ
h = 1e-8
tmp = Data(dat.X.copy())
tmp.X[0, :] += h
W1 = ((F * tmp).X - dat2.X) / h
tmp = Data(dat.X.copy())
tmp.X[1, :] += h
W2 = ((F * tmp).X - dat2.X) / h
for i in range(dat.numex()):
logDetJ2[i] = np.log(
np.abs(W1[0, i] * W2[1, i] - W1[1, i] * W2[0, i]))
self.assertFalse(np.max(np.abs(logDetJ - logDetJ2)) > self.detTol,\
'Log determinant of radial transformation deviates by more than ' + str(self.detTol) + '!')
def setUp(self):
self.a = 1.0 * rand()
self.b = self.a + 10.0 * rand()
self.mu = (self.a + 10 * rand()) / 2.
self.s = 2.0 * rand() + 1.0
self.p = Distributions.TruncatedGaussian({
'a': self.a,
'b': self.b,
'mu': self.mu,
'sigma': self.s
})
def test_RadialFactorization(self):
print "Testing Radial Factorization ..."
sys.stdout.flush()
p = np.random.rand() + 1.0
n = 5
psource = Distributions.LpSphericallySymmetric({
'n':
n,
'p':
p,
'rp':
Distributions.Gamma({
'u': 2.0 * np.random.rand() + 1.0,
's': 5.0 * np.random.rand() + 1.0
})
})
ptarget = Distributions.LpGeneralizedNormal({
'n':
n,
'p':
p,
's': (special.gamma(1.0 / p) / special.gamma(3.0 / p))**(p / 2.0)
})
F = NonlinearTransformFactory.RadialFactorization(psource)
dat = psource.sample(10000)
ld = F.logDetJacobian(dat)
ld = np.mean(np.abs(ld)) / dat.size(0) / np.log(2)
all_source = psource.all(dat)
all_target = ptarget.all(F * dat)
tol = 1e-2
prot = {}
prot['message'] = 'Difference in logdet correted ALL > ' + str(tol)
prot["1/n/log(2) * <|det J|> "] = ld
prot["ALL(TARGET)"] = all_target
prot["ALL(SOURCE)"] = all_source
prot[
"ALL(TARGET) + 1/n/log(2) * <|det J|> - ALL(SOURCE)"] = all_target + ld - all_source
def test_derivatives(self):
print "Testing derivatives w.r.t. data ... "
sys.stdout.flush()
p = Distributions.MixtureOfGaussians({'K': 5})
dat = p.sample(100)
h = 1e-7
tol = 1e-6
y = np.array(dat.X) + h
df = p.dldx(dat)
df2 = (p.loglik(Data(y)) - p.loglik(dat)) / h
self.assertFalse(np.max(np.abs(df-df2)) > tol,\
'Difference ' +str(np.max(np.abs(df-df2))) +' in derivative of log-likelihood for MixtureOfGaussians greater than ' + str(tol))
def test_cdf(self):
print "Testing consistency of cdf and ppf"
sys.stdout.flush()
myu = 10 * rand()
mys = 10 * rand()
myB = 10 * rand()
p = Distributions.Kumaraswamy({'a': myu, 'b': mys, 'B': myB})
u = rand(10)
u2 = p.cdf(p.ppf(u))
self.assertFalse(
sum(np.abs(u - u2)) > self.TolParam,
'Difference u - cdf(ppf(u)) greater than %.4g' % (self.Tol, ))
def test_logdeterminantInCombinationWithLinearFilters(self):
print "Testing Log-Determinant of Nonlinear Lp-nested ICA in combination with linear filters..."
sys.stdout.flush()
L = Auxiliary.LpNestedFunction()
p = Distributions.LpNestedSymmetric({'f': L})
dat = p.sample(10)
Flin1 = LinearTransformFactory.oRND(dat)
Flin2 = LinearTransform(
np.random.randn(dat.size(0), dat.size(0)) +
0.1 * np.eye(dat.size(0)))
Fnl = NonlinearTransformFactory.LpNestedNonLinearICA(p)
Fd = {}
Fd['NL'] = Fnl
Fd['L1*L2'] = Flin1 * Flin2
Fd['L1*NL'] = Flin1 * Fnl
Fd['NL*L1'] = Fnl * Flin1
Fd['Nl*L1*L2'] = Fnl * Flin1 * Flin2
Fd['Nl*(L1*L2)'] = Fnl * (Flin1 * Flin2)
Fd['(Nl*L1)*L2'] = (Fnl * Flin1) * Flin2
Fd['L1*Nl*L2'] = Flin1 * Fnl * Flin2
Fd['L1*(Nl*L2)'] = Flin1 * (Fnl * Flin2)
Fd['(L1*Nl)*L2'] = (Flin1 * Fnl) * Flin2
Fd['L2*L1*Nl'] = Flin2 * Flin1 * Fnl
Fd['L2*(L1*Nl)'] = Flin2 * (Flin1 * Fnl)
Fd['(L2*L1)*Nl'] = (Flin2 * Flin1) * Fnl
for (tk, F) in Fd.items():
print "\t ... testing " + tk
sys.stdout.flush()
n, m = dat.size()
h = 5 * 1e-7
logdetJ = F.logDetJacobian(dat)
for i in range(m):
J = np.zeros((n, n))
for j in range(n):
tmp = dat[:, i]
tmp2 = tmp.copy()
tmp2.X[j, :] = tmp2.X[j, :] + h
J[:, j] = ((F * tmp2).X - (F * tmp).X)[:, 0] / h
Q, R = linalg.qr(J)
logdet2 = np.sum(np.log(np.diag(R)))
#print np.abs(logdet2 - logdetJ[i])
self.assertFalse(np.abs(logdet2 - logdetJ[i]) > self.DetTol,\
'Determinant of Jacobian deviates by %.4g which is more than more than %.4g' % (np.abs(logdet2 - logdetJ[i]), self.DetTol))
def test_derivatives(self):
print "Testing derivatives w.r.t. data ... "
sys.stdout.flush()
myu = 3.0 * np.random.rand(1)[0] + 1.0
mys = 3.0 * np.random.rand(1)[0] + 1.0
p = Distributions.Gamma({'u': myu, 's': mys})
dat = p.sample(100)
h = 1e-7
tol = 1e-4
y = np.array(dat.X) + h
df = p.dldx(dat)
df2 = (p.loglik(Data(y)) - p.loglik(dat)) / h
self.assertFalse(np.max(np.abs(df-df2)) > tol,\
'Difference ' + str(np.max(np.abs(df-df2)))+ 'in derivative of log-likelihood for Gamma greater than ' + str(tol))
def test_estimate(self):
print 'Testing parameter estimation for p-generalized normal distribution'
sys.stdout.flush()
for k in range(5):
print '\t--> test case ' + str(k)
dat = io.loadmat(self.matpath + '/TestPGeneralizedNormal' +
str(k) + '.mat',
struct_as_record=True)
trueparam = {'s': 2 * dat['s'], 'p': dat['p'], 'n': dat['n']}
p = Distributions.LpGeneralizedNormal({'n': dat['n']})
dat = Data(dat['X'])
p.estimate(dat)
for ke in trueparam.keys():
self.assertFalse( np.abs(trueparam[ke] - p.param[ke]) > self.TolParam[ke],\
'Estimated parameter ' + ke + ' deviates by more than ' + str(self.TolParam[ke]) + '!')
def test_dldtheta(self):
p = Distributions.Gamma({'u': 2.0, 's': 3.0})
p.primary = ['u', 's']
dat = p.sample(1000)
def f(arr):
p.array2primary(arr)
return np.sum(p.loglik(dat))
def df(arr):
p.array2primary(arr)
return np.sum(p.dldtheta(dat), axis=1)
arr0 = p.primary2array()
arr0 = abs(np.random.randn(len(arr0)))
err = optimize.check_grad(f, df, arr0)
print "Error in graident: ", err
self.assertTrue(err < 1e-02)
def test_loglik(self):
print 'Testing log-likelihood of p-generalized normal distribution'
print __file__
sys.stdout.flush()
for k in range(5):
print '\t--> test case ' + str(k)
dat = io.loadmat(self.matpath + '/TestPGeneralizedNormal' +
str(k) + '.mat',
struct_as_record=True)
truell = dat['ll']
p = Distributions.LpGeneralizedNormal({
's': 2 * dat['s'],
'p': dat['p'],
'n': dat['n']
})
dat = Data(dat['X'])
ll = p.loglik(dat)
for i in range(ll.shape[0]):
self.assertFalse( np.any(np.abs(ll[i]-np.squeeze(truell[0,i])) > self.Tol),\
'Log-likelihood for p-generalized normal deviates from test case')
def test_pdfloglikconsistency(self):
print "Testing consistency of pdf and loglik ... "
sys.stdout.flush()
p = Distributions.MixtureOfLogNormals({'K': 5})
dat = p.sample(100)
tol = 1e-6
ll = p.loglik(dat)
pdf = np.log(p.pdf(dat))
prot = {}
prot[
'message'] = 'Difference in log(p(x)) and loglik(x) MixtureOfLogNormals greater than ' + str(
tol)
prot['max diff'] = np.max(np.abs(pdf - ll))
prot['mean diff'] = np.mean(np.abs(pdf - ll))
self.assertFalse(
np.max(np.abs(ll - pdf)) > tol, Auxiliary.prettyPrintDict(prot))
def test_derivatives(self):
print "Testing derivatives w.r.t. data ... "
sys.stdout.flush()
p = Distributions.MixtureOfLogNormals({'K': 5})
dat = p.sample(100)
h = 1e-8
tol = 1e-4
y = np.array(dat.X) + h
df = p.dldx(dat)
df2 = (p.loglik(Data(y)) - p.loglik(dat)) / h
prot = {}
prot[
'message'] = 'Difference in derivative of log-likelihood for MixtureOfLogNormals greater than ' + str(
tol)
prot['max diff'] = np.max(np.abs(df - df2))
prot['mean diff'] = np.mean(np.abs(df - df2))
self.assertFalse(
np.mean(np.abs(df - df2)) > tol, Auxiliary.prettyPrintDict(prot))
def test_estimate(self):
print 'Testing parameter estimation for p-spherically symmetric distribution with radial gamma'
sys.stdout.flush()
for k in range(5):
print '\t--> test case ' + str(k)
sys.stdout.flush()
dat = io.loadmat(self.matpath + '/TestPSphericallySymmetric' +
str(k) + '.mat',
struct_as_record=True)
trueparam = {'s': dat['s'], 'p': dat['p'], 'u': dat['u']}
p = Distributions.LpSphericallySymmetric({'n': dat['n']})
dat = Data(dat['X'])
p.estimate(dat, prange=(.1, 4.0))
self.assertFalse(np.abs(trueparam['p'] - p.param['p']) > self.TolParam['p'],\
'Estimated parameter p deviates by more than ' + str(self.TolParam['p']) + '!')
self.assertFalse(np.abs(trueparam['u'] - p.param['rp'].param['u']) > self.TolParam['u'],\
'Estimated parameter u deviates by more than ' + str(self.TolParam['u']) + '!')
self.assertFalse(np.abs(trueparam['s'] - p.param['rp'].param['s']) > self.TolParam['s'],\
'Estimated parameter s deviates by more than ' + str(self.TolParam['s']) + '!')