def eval_rosenblattdd(sg_pdf, xs):
op = pysgpp.createOperationRosenblattTransformation(sg_pdf.grid)
X, Y = np.meshgrid(xs, xs)
input_points = pysgpp.DataMatrix(len(xs), sg_pdf.d)
output_points = pysgpp.DataMatrix(len(xs), sg_pdf.d)
for i in range(len(xs)):
for j in range(sg_pdf.d):
input_points.set(i, j , 0.5)
op.doTransformation(sg_pdf.alpha, input_points, output_points)
print(output_points)
def cdf(self, x):
# convert the parameter to the right format
if isList(x):
x = DataVector(x)
elif isNumerical(x):
x = DataVector([x])
# do the transformation
if self.grid.getStorage().dim() == 1:
op = createOperationRosenblattTransformation1D(self.grid)
ans = np.ndarray(len(x))
for i, xi in enumerate(x.array()):
ans[i] = op.doTransformation1D(self.alpha, xi)
if len(ans) == 1:
return ans[0]
else:
return ans
else:
if isinstance(x, DataMatrix):
A = x
B = DataMatrix(A.getNrows(), A.getNcols())
B.setAll(0.0)
elif isinstance(x, DataVector):
A = DataMatrix(1, len(x))
A.setRow(0, x)
B = DataMatrix(1, len(x))
B.setAll(0)
# do the transformation
op = createOperationRosenblattTransformation(self.grid)
op.doTransformation(self.alpha, A, B)
# extract the outcome
if isNumerical(x) or isinstance(x, DataVector):
return B.get(0, 0)
elif isinstance(x, DataMatrix):
return B.array()
def cdf(self, x, shuffle=True):
# convert the parameter to the right format
x = self._convertEvalPoint(x)
# transform the samples to the unit hypercube
if self.trans is not None:
x_unit = self.trans.probabilisticToUnitMatrix(x)
else:
x_unit = x
# do the transformation
if self.dim == 1:
op = createOperationRosenblattTransformation1D(self.grid)
ans = np.ndarray(x.shape[0])
for i, xi in enumerate(x_unit[:, 0]):
ans[i] = op.doTransformation1D(self.unnormalized_alpha_vec, xi)
if len(ans) == 1:
return ans[0]
else:
return ans
else:
A = DataMatrix(x_unit)
B = DataMatrix(x_unit.shape[0], x_unit.shape[1])
B.setAll(0.0)
# do the transformation
op = createOperationRosenblattTransformation(self.grid)
if shuffle:
op.doTransformation(self.alpha_vec, A, B)
else:
op.doTransformation(self.alpha_vec, A, B, 0)
# extract the outcome
if x_unit.shape == (1, 1):
return B.get(0, 0)
else:
return B.array()
def cdf(self, x):
# convert the parameter to the right format
if isList(x):
x = DataVector(x)
elif isNumerical(x):
x = DataVector([x])
# do the transformation
if self.grid.getStorage().dim() == 1:
op = createOperationRosenblattTransformation1D(self.grid)
ans = np.ndarray(len(x))
for i, xi in enumerate(x.array()):
ans[i] = op.doTransformation1D(self.alpha, xi)
if len(ans) == 1:
return ans[0]
else:
return ans
else:
if isinstance(x, DataMatrix):
A = x
B = DataMatrix(A.getNrows(), A.getNcols())
B.setAll(0.0)
elif isinstance(x, DataVector):
A = DataMatrix(1, len(x))
A.setRow(0, x)
B = DataMatrix(1, len(x))
B.setAll(0)
# do the transformation
op = createOperationRosenblattTransformation(self.grid)
op.doTransformation(self.alpha, A, B)
# extract the outcome
if isNumerical(x) or isinstance(x, DataVector):
return B.get(0, 0)
elif isinstance(x, DataMatrix):
return B.array()
def main():
# Generate data
print("generate dataset... ", end=' ')
data_tr,_ = generate_friedman1(123456)
print("Done")
print("generated a friedman1 dataset (10D) with 2000 samples")
# Config grid
print("create grid config... ", end=' ')
grid = sg.RegularGridConfiguration()
grid.dim_ = 10
grid.level_ = 3
grid.type_ = sg.GridType_Linear
print("Done")
# Config adaptivity
print("create adaptive refinement config... ", end=' ')
adapt = sg.AdaptivityConfiguration()
adapt.numRefinements_ = 0
adapt.noPoints_ = 10
print("Done")
# Config solver
print("create solver config... ", end=' ')
solv = sg.SLESolverConfiguration()
solv.maxIterations_ = 1000
solv.eps_ = 1e-14
solv.threshold_ = 1e-14
solv.type_ = sg.SLESolverType_CG
print("Done")
# Config regularization
print("create regularization config... ", end=' ')
regular = sg.RegularizationConfiguration()
regular.regType_ = sg.RegularizationType_Laplace
print("Done")
# Config cross validation for learner
print("create learner config... ", end=' ')
#crossValid = sg.CrossvalidationConfiguration()
crossValid = sg.CrossvalidationConfiguration()
crossValid.enable_ = False
crossValid.kfold_ = 3
crossValid.lambda_ = 3.16228e-06
crossValid.lambdaStart_ = 1e-1
crossValid.lambdaEnd_ = 1e-10
crossValid.lambdaSteps_ = 3
crossValid.logScale_ = True
crossValid.shuffle_ = True
crossValid.seed_ = 1234567
crossValid.silent_ = False
print("Done")
#
# Create the learner with the given configuration
#
print("create the learner... ")
learner = sg.LearnerSGDE(grid, adapt, solv, regular, crossValid)
learner.initialize(data_tr)
# Train the learner
print("start training... ")
learner.train()
print("done training")
#
# Estimate the probability density function (pdf) via a Gaussian kernel
# density estimation (KDE) and print the corresponding values
#
kde = sg.KernelDensityEstimator(data_tr)
x = sg.DataVector(learner.getDim())
x.setAll(0.5)
print("-----------------------------------------------")
print(learner.getSurpluses().getSize(), " -> ", learner.getSurpluses().sum())
print("pdf_SGDE(x) = ", learner.pdf(x), " ~ ", kde.pdf(x), " = pdf_KDE(x)")
print("mean_SGDE = ", learner.mean(), " ~ ", kde.mean(), " = mean_KDE")
print("var_SGDE = ", learner.variance(), " ~ ", kde.variance(), " = var_KDE")
# Print the covariances
C = sg.DataMatrix(grid.dim_, grid.dim_)
print("----------------------- Cov_SGDE -----------------------")
learner.cov(C)
print(C)
print("----------------------- Cov_KDE -----------------------")
kde.cov(C)
print(C)
#
# Apply the inverse Rosenblatt transformatio to a matrix of random points. To
# do this, first generate the random points uniformly, then initialize an
# inverse Rosenblatt transformation operation and apply it to the points.
# Finally print the calculated values
#
print("-----------------------------------------------")
opInvRos = sg.createOperationInverseRosenblattTransformation(learner.getGrid())
points = sg.DataMatrix(randu_mat(12, grid.dim_))
print(points)
pointsCdf = sg.DataMatrix(points.getNrows(), points.getNcols())
opInvRos.doTransformation(learner.getSurpluses(), points, pointsCdf)
#
# To check whether the results are correct perform a Rosenform transformation on
# the data that has been created by the inverse Rosenblatt transformation above
# and print the calculated values
#
points.setAll(0.0)
opRos = sg.createOperationRosenblattTransformation(learner.getGrid())
opRos.doTransformation(learner.getSurpluses(), pointsCdf, points)
print("-----------------------------------------------")
print(pointsCdf)
print("-----------------------------------------------")
print(points)
