def __computeRanking(self, v, A, b):
"""
Compute ranking for variance estimation
\argmax_{i \in \A} | v (2 Av - vb) |
@param v: DataVector, coefficients of known grid points
@param A: DataMatrix, stiffness matrix
@param b: DataVector, squared expectation value contribution
@return: numpy array, contains the ranking for the given samples
"""
# update the ranking
av = DataVector(A.getNrows())
av.setAll(0.0)
# = Av
for i in xrange(A.getNrows()):
for j in xrange(A.getNcols()):
av[i] += A.get(i, j) * v[j]
av.mult(2.) # = 2 * Av
b.componentwise_mult(v) # = v * b
av.sub(b) # = 2 * Av - v * b
w = DataVector(v)
w.componentwise_mult(av) # = v * (2 * Av - v * b)
w.abs() # = | v * (2 * Av - v * b) |
return w.array()
def estimate(self, vol, grid, alpha, f, U, T):
r"""
Extraction of the expectation the given sparse grid function
interpolating the product of function value and pdf.
\int\limits_{[0, 1]^d} f(x) * pdf(x) dx
"""
# first: discretize f
fgrid, falpha, discError = discretize(grid, alpha, f, self.__epsilon,
self.__refnums, self.__pointsNum,
self.level, self.__deg, True)
# extract correct pdf for moment estimation
vol, W, pdfError = self.__extractDiscretePDFforMomentEstimation(U, T)
D = T.getTransformations()
# compute the integral of the product
gs = fgrid.getStorage()
acc = DataVector(gs.size())
acc.setAll(1.)
tmp = DataVector(gs.size())
for i, dims in enumerate(W.getTupleIndices()):
sgdeDist = W[i]
# accumulate objects needed for computing the bilinear form
gpsi, basisi = project(fgrid, dims)
gpsj, basisj = project(sgdeDist.grid, range(len(dims)))
A = self.__computeMassMatrix(gpsi, basisi, gpsj, basisj, W, D)
# A = ScipyQuadratureStrategy(W, D).computeBilinearForm(fgrid)
self.mult(A, sgdeDist.alpha, tmp)
acc.componentwise_mult(tmp)
moment = falpha.dotProduct(acc)
return vol * moment, discError[1] + pdfError
def __computeRanking(self, v, A, b):
"""
Compute ranking for variance estimation
\argmax_{i \in \A} | v (2 Av - vb) |
@param v: DataVector, coefficients of known grid points
@param A: DataMatrix, stiffness matrix
@param b: DataVector, squared expectation value contribution
@return: numpy array, contains the ranking for the given samples
"""
# update the ranking
av = DataVector(A.getNrows())
av.setAll(0.0)
# = Av
for i in xrange(A.getNrows()):
for j in xrange(A.getNcols()):
av[i] += A.get(i, j) * v[j]
av.mult(2.) # = 2 * Av
b.componentwise_mult(v) # = v * b
av.sub(b) # = 2 * Av - v * b
w = DataVector(v)
w.componentwise_mult(av) # = v * (2 * Av - v * b)
w.abs() # = | v * (2 * Av - v * b) |
return w.array()
def mean(self, grid, alpha, U, T):
r"""
Extraction of the expectation the given sparse grid function
interpolating the product of function value and pdf.
\int\limits_{[0, 1]^d} f_N(x) * pdf(x) dx
"""
# extract correct pdf for moment estimation
vol, W = self._extractPDFforMomentEstimation(U, T)
D = T.getTransformations()
# compute the integral of the product
gs = grid.getStorage()
acc = DataVector(gs.size())
acc.setAll(1.)
tmp = DataVector(gs.size())
err = 0
# run over all dimensions
for i, dims in enumerate(W.getTupleIndices()):
dist = W[i]
trans = D[i]
# get the objects needed for integration the current dimensions
gpsi, basisi = project(grid, dims)
if isinstance(dist, SGDEdist):
# if the distribution is given as a sparse grid function we
# need to compute the bilinear form of the grids
# accumulate objects needed for computing the bilinear form
gpsj, basisj = project(dist.grid, range(len(dims)))
# compute the bilinear form
bf = BilinearGaussQuadratureStrategy()
A, erri = bf.computeBilinearFormByList(gpsi, basisi,
gpsj, basisj)
# weight it with the coefficient of the density function
self.mult(A, dist.alpha, tmp)
else:
# the distribution is given analytically, handle them
# analytically in the integration of the basis functions
if isinstance(dist, Dist) and len(dims) > 1:
raise AttributeError('analytic quadrature not supported for multivariate distributions')
if isinstance(dist, Dist):
dist = [dist]
trans = [trans]
lf = LinearGaussQuadratureStrategy(dist, trans)
tmp, erri = lf.computeLinearFormByList(gpsi, basisi)
# print error stats
# print "%s: %g -> %g" % (str(dims), err, err + D[i].vol() * erri)
# import ipdb; ipdb.set_trace()
# accumulate the error
err += D[i].vol() * erri
# accumulate the result
acc.componentwise_mult(tmp)
moment = alpha.dotProduct(acc)
return vol * moment, err
def testOps(self):
from pysgpp import DataVector
# sum
self.assertAlmostEqual(self.d_rand.sum(), sum(self.l_rand_total))
# sqr
d = DataVector(self.d_rand)
d.sqr()
for i in xrange(self.N):
self.assertEqual(self.d_rand[i]**2, d[i])
# abs
d = DataVector(self.d_rand)
d.abs()
for i in xrange(self.N):
self.assertEqual(abs(self.d_rand[i]), d[i])
# componentwise_mult
d = DataVector(self.d_rand)
# d2 = DataVector(self.nrows, self.ncols)
d2 = DataVector(self.N)
for i in xrange(self.N):
d2[i] = i
d.componentwise_mult(d2)
for i in xrange(self.N):
self.assertEqual(self.d_rand[i]*i, d[i])
# componentwise_div
d = DataVector(self.d_rand)
for i in xrange(self.N):
d2[i] = i+1
d.componentwise_div(d2)
for i in xrange(self.N):
self.assertEqual(self.d_rand[i]/(i+1), d[i])
def testOps(self):
from pysgpp import DataVector
# sum
self.assertAlmostEqual(self.d_rand.sum(), sum(self.l_rand_total))
# sqr
d = DataVector(self.d_rand)
d.sqr()
for i in xrange(self.N):
self.assertEqual(self.d_rand[i]**2, d[i])
# abs
d = DataVector(self.d_rand)
d.abs()
for i in xrange(self.N):
self.assertEqual(abs(self.d_rand[i]), d[i])
# componentwise_mult
d = DataVector(self.d_rand)
# d2 = DataVector(self.nrows, self.ncols)
d2 = DataVector(self.N)
for i in xrange(self.N):
d2[i] = i
d.componentwise_mult(d2)
for i in xrange(self.N):
self.assertEqual(self.d_rand[i] * i, d[i])
# componentwise_div
d = DataVector(self.d_rand)
for i in xrange(self.N):
d2[i] = i + 1
d.componentwise_div(d2)
for i in xrange(self.N):
self.assertEqual(self.d_rand[i] / (i + 1), d[i])
class Regressor(Learner):
"""
Subclass of Learner, responsible for regression.
The methods specific for regression are implemented here.
"""
def __init__(self):
"""
Constructor
"""
super(self.__class__, self).__init__()
# Errors per basis function
self.errors = None
# Error vector
self.error = None
def __getattr__(self, attr):
"""
Overrides built-in method if method called is not a object
method of this Descriptor, most probably it's a method of
the learner so it tries to call the method
from our specification
@param attr: string method name
@return: method call in specification
"""
return getattr(self.specification, attr)
def getL2NormError(self):
"""
calculate L2-norm of error
@return: last L2-norm of error
"""
return np.sqrt(self.error.sum())
def getMaxError(self):
"""
calculate max error
@return: max error
"""
return np.sqrt(self.error.max())
def getMinError(self):
"""
calculate min error
@return: min error
"""
return np.sqrt(self.error.min())
def evalError(self, data, alpha):
"""
Evaluate regression MSE
@param data: DataContainer data set
@param alpha: DataVector alpha-vector
@return: mean square error
"""
size = data.getPoints().getNrows()
if size == 0:
return 0
self.error = DataVector(size)
self.getBOperator().mult(alpha, self.error)
# error vector
self.error.sub(data.getValues())
# entries squared
self.error.sqr()
errorsum = self.error.sum()
# MSE
mse = errorsum / size
# calculate error per basis function
self.errors = DataVector(len(alpha))
self.getBOperator().multTranspose(self.error, self.errors)
self.errors.componentwise_mult(alpha)
# calculate error per basis function
# self.errors = DataVector(alpha.getSize())
# self.specification.getBOperator().mult(self.error, data.getPoints(), self.errors)
return mse
def updateResults(self, alpha, trainSubset, testSubset=None):
"""
Update different statistics about training progress
@param alpha: DataVector alpha-vector
@param trainSubset: DataContainer with training data
@param testSubset: DataContainer with validation data
"""
# self.knowledge.update(alpha)
# eval Error for training data and append it to other in this iteration
self.trainAccuracy.append(self.evalError(trainSubset, alpha))
i = float(len(self.trainAccuracy))
# eval error for test data and append it to other in this iteration
if testSubset is not None:
self.testAccuracy.append(self.evalError(testSubset, alpha))
self.testingOverall.append(sum(self.testAccuracy) / i)
self.trainingOverall.append(sum(self.trainAccuracy) / i)
self.numberPoints.append(self.grid.getSize())
def refineGrid(self):
"""
Refines grid with the number of points as specified in corresponding
TrainingSpecification object
"""
self.notifyEventControllers(LearnerEvents.REFINING_GRID)
refinableNum = self.grid.createGridGenerator(
).getNumberOfRefinablePoints()
pointsNum = self.getNumOfPointsToRefine(refinableNum)
functor = SurplusRefinementFunctor(self.errors, pointsNum,
self.getAdaptThreshold())
self.grid.createGridGenerator().refine(functor)
class Regressor(Learner):
## Errors per basis function
errors = None
## Error vector
error = None
##constructor
def __init__(self):
super(Regressor, self).__init__()
##calculate L2-norm of error
# @return: last L2-norm of error
def getL2NormError(self):
return sqrt(self.error.sum())
## calculate max error
# @return: max error
def getMaxError(self):
return sqrt(self.error.max())
## calculate min error
# @return: min error
def getMinError(self):
return sqrt(self.error.min())
## Evaluate regression MSE
#
# @param data: DataContainer dataset
# @param alpha: DataVector alpha-vector
# @return: mean square error
def evalError(self, data, alpha):
size = data.getPoints().getNrows()
if size == 0: return 0
self.error = DataVector(size)
self.specification.getBOperator(data.getName()).mult(alpha, self.error)
self.error.sub(data.getValues()) # error vector
self.error.sqr() # entries squared
errorsum = self.error.sum()
mse = errorsum / size # MSE
# calculate error per basis function
self.errors = DataVector(len(alpha))
self.specification.getBOperator(data.getName()).multTranspose(
self.error, self.errors)
self.errors.componentwise_mult(alpha)
return mse
##Update different statistics about training progress
# @param alpha: DataVector alpha-vector
# @param trainSubset: DataContainer with training data
# @param testSubset: DataContainer with validation data, default value: None
def updateResults(self, alpha, trainSubset, testSubset=None):
self.knowledge.update(alpha)
#eval Error for training data and append it to other in this iteration
self.trainAccuracy.append(self.evalError(trainSubset, alpha))
i = float(len(self.trainAccuracy))
#eval error for test data and append it to other in this iteration
if testSubset != None:
self.testAccuracy.append(self.evalError(testSubset, alpha))
self.testingOverall.append(sum(self.testAccuracy) / i)
self.trainingOverall.append(sum(self.trainAccuracy) / i)
self.numberPoints.append(self.grid.getSize())
##Refines grid with the number of points as specified in corresponding TrainingSpecification object
def refineGrid(self):
self.notifyEventControllers(LearnerEvents.REFINING_GRID)
pointsNum = self.specification.getNumOfPointsToRefine(
self.grid.getGenerator().getNumberOfRefinablePoints())
self.grid.getGenerator().refine(
SurplusRefinementFunctor(self.errors, pointsNum,
self.specification.getAdaptThreshold()))
class Regressor(Learner):
"""
Subclass of Learner, responsible for regression.
The methods specific for regression are implemented here.
"""
def __init__(self):
"""
Constructor
"""
super(self.__class__, self).__init__()
# Errors per basis function
self.errors = None
# Error vector
self.error = None
def __getattr__(self, attr):
"""
Overrides built-in method if method called is not a object
method of this Descriptor, most probably it's a method of
the learner so it tries to call the method
from our specification
@param attr: string method name
@return: method call in specification
"""
return getattr(self.specification, attr)
# # Learn data from training data set and use validation data set to prevent overfitting
#
# @param dataset: DataContainer object with data sets, default value None (initialized data set used)
# @return: DataVector of alpha
def learnDataWithTest(self, dataset=None):
self.notifyEventControllers(
LearnerEvents.LEARNING_WITH_TESTING_STARTED)
B = createOperationMultipleEval(
self.grid,
self.dataContainer.getPoints(DataContainer.TRAIN_CATEGORY))
self.specification.setBOperator(B)
if dataset is None:
dataset = self.dataContainer
# learning step
trainSubset = dataset.getTrainDataset()
# testpoint = data.allPoint\points
# testvalues = data.allValues\values
testSubset = dataset.getTestDataset()
while True: # repeat until policy says "stop"
self.notifyEventControllers(
LearnerEvents.LEARNING_WITH_TESTING_STEP_STARTED)
self.alpha = self.doLearningIteration(trainSubset)
# calculate avg. error for training and test data and avg. for refine alpha
self.updateResults(self.alpha, trainSubset, testSubset)
self.notifyEventControllers(
LearnerEvents.LEARNING_WITH_TESTING_STEP_COMPLETE)
self.iteration += 1
if self.stopPolicy.isTrainingComplete(self):
break
# refine grid
self.refineGrid()
self.notifyEventControllers(
LearnerEvents.LEARNING_WITH_TESTING_COMPLETE)
return self.alpha
# # Simple data learning
#
# @return: DataVector of alpha
def learnData(self):
self.notifyEventControllers(LearnerEvents.LEARNING_STARTED)
self.specification.setBOperator(
createOperationMultipleEval(
self.grid,
self.dataContainer.getPoints(DataContainer.TRAIN_CATEGORY)))
print(self.getL())
while True: # repeat until policy says "stop"
print(
"Learning %i/%i" %
(self.iteration, self.stopPolicy.getAdaptiveIterationLimit()))
self.notifyEventControllers(LearnerEvents.LEARNING_STEP_STARTED)
# learning step
self.alpha = self.doLearningIteration(self.dataContainer)
# calculate avg. error for training and test data and avg. for refine alpha
self.updateResults(self.alpha, self.dataContainer)
self.notifyEventControllers(LearnerEvents.LEARNING_STEP_COMPLETE)
self.iteration += 1
if (self.stopPolicy.isTrainingComplete(self)):
break
# refine grid
self.refineGrid()
# from pysgpp.extensions.datadriven.uq.plot import plotNodal3d
# plotNodal3d(self.grid, self.alpha)
# data = self.dataContainer.getPoints('train').array()
# fig = plt.figure()
# plt.plot(data[:, 0], data[:, 1], ' ', marker='v')
# fig.show()
# plt.show()
self.notifyEventControllers(LearnerEvents.LEARNING_COMPLETE)
return self.alpha
# # Learn data with cross-fold validation
#
# @return: list of DataVector alpha in different folds
def learnDataWithFolding(self, ):
self.notifyEventControllers(
LearnerEvents.LEARNING_WITH_FOLDING_STARTED)
self.specification.setBOperator(
createOperationMultipleEval(
self.grid,
self.dataContainer.getPoints(DataContainer.TRAIN_CATEGORY)))
# update folding
self.updateFoldingPolicy()
alphas = []
for dataset in self.foldingPolicy:
alphas.append(self.learnDataWithTest(dataset))
self.notifyEventControllers(
LearnerEvents.LEARNING_WITH_FOLDING_COMPLETE)
return alphas
# # Perform one learning step
#
# @param set: DataContainer training data set
# @return: DataVector alpha vector
def doLearningIteration(self, set):
# initialize values
self.linearSystem = DMSystemMatrix(self.grid, set.getPoints(),
self.specification.getCOperator(),
self.specification.getL())
size = self.grid.getSize()
# Reuse data from old alpha vector increasing its dimension
if self.solver.getReuse() and self.alpha is not None:
alpha = DataVector(self.alpha)
alpha.resize(size)
# Use new alpha vector
else:
alpha = DataVector(size)
alpha.setAll(0.0)
b = DataVector(size)
self.linearSystem.generateb(set.getValues(), b)
# calculates alphas
self.solver.solve(self.linearSystem, alpha, b, self.solver.getReuse(),
False, self.solver.getThreshold())
return alpha
def getL2NormError(self):
"""
calculate L2-norm of error
@return: last L2-norm of error
"""
return np.sqrt(self.error.sum())
def getMaxError(self):
"""
calculate max error
@return: max error
"""
return np.sqrt(self.error.max())
def getMinError(self):
"""
calculate min error
@return: min error
"""
return np.sqrt(self.error.min())
def evalError(self, data, alpha):
"""
Evaluate regression MSE
@param data: DataContainer data set
@param alpha: DataVector alpha-vector
@return: mean square error
"""
size = data.getPoints().getNrows()
if size == 0:
return 0
self.error = DataVector(size)
self.getBOperator().mult(alpha, self.error)
# error vector
self.error.sub(data.getValues())
# entries squared
self.error.sqr()
errorsum = self.error.sum()
# MSE
mse = errorsum / size
# calculate error per basis function
self.errors = DataVector(len(alpha))
self.getBOperator().multTranspose(self.error, self.errors)
self.errors.componentwise_mult(alpha)
# calculate error per basis function
# self.errors = DataVector(alpha.getSize())
# self.specification.getBOperator().mult(self.error, data.getPoints(), self.errors)
return mse
def updateResults(self, alpha, trainSubset, testSubset=None):
"""
Update different statistics about training progress
@param alpha: DataVector alpha-vector
@param trainSubset: DataContainer with training data
@param testSubset: DataContainer with validation data
"""
# self.knowledge.update(alpha)
# eval Error for training data and append it to other in this iteration
self.trainAccuracy.append(self.evalError(trainSubset, alpha))
i = float(len(self.trainAccuracy))
# eval error for test data and append it to other in this iteration
if testSubset is not None:
self.testAccuracy.append(self.evalError(testSubset, alpha))
self.testingOverall.append(sum(self.testAccuracy) / i)
self.trainingOverall.append(sum(self.trainAccuracy) / i)
self.numberPoints.append(self.grid.getSize())
def refineGrid(self):
"""
Refines grid with the number of points as specified in corresponding
TrainingSpecification object
"""
self.notifyEventControllers(LearnerEvents.REFINING_GRID)
refinableNum = self.grid.getGenerator().getNumberOfRefinablePoints()
pointsNum = self.getNumOfPointsToRefine(refinableNum)
functor = SurplusRefinementFunctor(self.errors, pointsNum,
self.getAdaptThreshold())
self.grid.getGenerator().refine(functor)
class Regressor(Learner):
## Errors per basis function
errors = None
## Error vector
error = None
##constructor
def __init__(self):
super(Regressor,self).__init__()
##calculate L2-norm of error
# @return: last L2-norm of error
def getL2NormError(self):
return sqrt(self.error.sum())
## calculate max error
# @return: max error
def getMaxError(self):
return sqrt(self.error.max())
## calculate min error
# @return: min error
def getMinError(self):
return sqrt(self.error.min())
## Evaluate regression MSE
#
# @param data: DataContainer dataset
# @param alpha: DataVector alpha-vector
# @return: mean square error
def evalError(self, data, alpha):
size = data.getPoints().getNrows()
if size == 0: return 0
self.error = DataVector(size)
self.specification.getBOperator(data.getName()).mult(alpha, self.error)
self.error.sub(data.getValues()) # error vector
self.error.sqr() # entries squared
errorsum = self.error.sum()
mse = errorsum / size # MSE
# calculate error per basis function
self.errors = DataVector(len(alpha))
self.specification.getBOperator(data.getName()).multTranspose(self.error, self.errors)
self.errors.componentwise_mult(alpha)
return mse
##Update different statistics about training progress
# @param alpha: DataVector alpha-vector
# @param trainSubset: DataContainer with training data
# @param testSubset: DataContainer with validation data, default value: None
def updateResults(self, alpha, trainSubset, testSubset = None):
self.knowledge.update(alpha)
#eval Error for training data and append it to other in this iteration
self.trainAccuracy.append(self.evalError(trainSubset, alpha))
i = float(len(self.trainAccuracy))
#eval error for test data and append it to other in this iteration
if testSubset != None:
self.testAccuracy.append(self.evalError(testSubset, alpha))
self.testingOverall.append(sum(self.testAccuracy)/i)
self.trainingOverall.append(sum(self.trainAccuracy)/i)
self.numberPoints.append(self.grid.getSize())
##Refines grid with the number of points as specified in corresponding TrainingSpecification object
def refineGrid(self):
self.notifyEventControllers(LearnerEvents.REFINING_GRID)
pointsNum = self.specification.getNumOfPointsToRefine( self.grid.createGridGenerator().getNumberOfRefinablePoints() )
self.grid.createGridGenerator().refine( SurplusRefinementFunctor(self.errors, pointsNum, self.specification.getAdaptThreshold()) )
def mean(self, grid, alpha, U, T):
r"""
Extraction of the expectation the given sparse grid function
interpolating the product of function value and pdf.
\int\limits_{[0, 1]^d} f_N(x) * pdf(x) dx
"""
# extract correct pdf for moment estimation
vol, W = self._extractPDFforMomentEstimation(U, T)
D = T.getTransformations()
# compute the integral of the product
gs = grid.getStorage()
acc = DataVector(gs.size())
acc.setAll(1.)
tmp = DataVector(gs.size())
err = 0
# run over all dimensions
for i, dims in enumerate(W.getTupleIndices()):
dist = W[i]
trans = D[i]
# get the objects needed for integration the current dimensions
gpsi, basisi = project(grid, dims)
if isinstance(dist, SGDEdist):
# if the distribution is given as a sparse grid function we
# need to compute the bilinear form of the grids
# accumulate objects needed for computing the bilinear form
gpsj, basisj = project(dist.grid, range(len(dims)))
# compute the bilinear form
bf = BilinearGaussQuadratureStrategy()
A, erri = bf.computeBilinearFormByList(gpsi, basisi, gpsj,
basisj)
# weight it with the coefficient of the density function
self.mult(A, dist.alpha, tmp)
else:
# the distribution is given analytically, handle them
# analytically in the integration of the basis functions
if isinstance(dist, Dist) and len(dims) > 1:
raise AttributeError(
'analytic quadrature not supported for multivariate distributions'
)
if isinstance(dist, Dist):
dist = [dist]
trans = [trans]
lf = LinearGaussQuadratureStrategy(dist, trans)
tmp, erri = lf.computeLinearFormByList(gpsi, basisi)
# print error stats
# print "%s: %g -> %g" % (str(dims), err, err + D[i].vol() * erri)
# import ipdb; ipdb.set_trace()
# accumulate the error
err += D[i].vol() * erri
# accumulate the result
acc.componentwise_mult(tmp)
moment = alpha.dotProduct(acc)
return vol * moment, err
