def testRefinement2d_two(self):
from pysgpp import Grid, DataVector, SurplusRefinementFunctor
factory = Grid.createLinearBoundaryGrid(2)
storage = factory.getStorage()
gen = factory.createGridGenerator()
gen.regular(0)
alpha = DataVector(4)
for i in xrange(len(alpha)):
alpha[i] = 0.0
alpha[0] = 1.0
func = SurplusRefinementFunctor(alpha)
gen.refine(func)
alpha2 = DataVector(8)
for i in xrange(len(alpha2)):
alpha2[i] = 0.0
alpha2[4] = 1.0
func = SurplusRefinementFunctor(alpha2)
gen.refine(func)
self.failUnlessEqual(storage.size(), 13)
def refineGrid(grid, alpha, f, refnums):
"""
This function refines a sparse grid function refnum times.
Arguments:
grid -- Grid sparse grid from pysgpp
alpha -- DataVector coefficient vector
f -- function to be interpolated
refnums -- int number of refinement steps
Return nothing
"""
gs = grid.getStorage()
gridGen = grid.getGenerator()
x = DataVector(gs.getDimension())
for _ in range(refnums):
# refine a single grid point each time
gridGen.refine(SurplusRefinementFunctor(alpha, 1))
# extend alpha vector (new entries uninitialized)
alpha.resizeZero(gs.getSize())
# set function values in alpha
for i in range(gs.getSize()):
gs.getCoordinates(gs.getPoint(i), x)
alpha[i] = f(x)
# hierarchize
createOperationHierarchisation(grid).doHierarchisation(alpha)
def testFreeRefineTrapezoidBoundaries(self):
"""Tests surplus based refine for Hash-Storage"""
from pysgpp import GridStorage, HashGenerator
from pysgpp import SurplusRefinementFunctor, HashRefinementBoundaries, DataVector
s = GridStorage(2)
g = HashGenerator()
g.regularWithBoundaries(s, 1, True)
d = DataVector(9)
d[0] = 0.0
d[1] = 0.0
d[2] = 0.0
d[3] = 0.0
d[4] = 0.0
d[5] = 0.0
d[6] = 0.0
d[7] = 0.0
d[8] = 1.0
f = SurplusRefinementFunctor(d)
r = HashRefinementBoundaries()
r.free_refine(s, f)
self.failUnlessEqual(s.size(), 21)
def refineGrid(self):
self.notifyEventControllers(LearnerEvents.REFINING_GRID)
pointsNum = self.specification.getNumOfPointsToRefine(
self.grid.getGenerator().getNumberOfRefinablePoints())
self.grid.getGenerator().refine(
SurplusRefinementFunctor(self.alpha, pointsNum,
self.specification.getAdaptThreshold()))
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)
def testSurplusFunctor(self):
"""Tests if surplus functor correctly considers absolute values"""
from pysgpp import GridStorage
from pysgpp import SurplusRefinementFunctor, DataVector
s = GridStorage(2)
d = DataVector(1)
f = SurplusRefinementFunctor(d)
d[0] = -10.0
self.failUnless(f(s, 0) > f.start())
d[0] = 10.0
self.failUnless(f(s, 0) > f.start())
def testRefinement(self):
from pysgpp import Grid, DataVector, SurplusRefinementFunctor
factory = Grid.createLinearGrid(2)
storage = factory.getStorage()
gen = factory.createGridGenerator()
gen.regular(1)
self.failUnlessEqual(storage.size(), 1)
alpha = DataVector(1)
alpha[0] = 1.0
func = SurplusRefinementFunctor(alpha)
gen.refine(func)
self.failUnlessEqual(storage.size(), 5)
def test_InconsistentRefinement1Point(self):
"""Dimensionally adaptive refinement using surplus coefficients as local
error indicator and inconsistent hash refinement.
"""
# point ((3,7), (1,1)) (middle most right) gets larger surplus coefficient
alpha = DataVector(self.grid.getSize())
alpha.setAll(1.0)
alpha[12] = 2.0
functor = SurplusRefinementFunctor(alpha, 1, 0.0)
refinement = HashRefinementInconsistent()
refinement.free_refine(self.HashGridStorage, functor)
self.assertEqual(self.grid.getSize(), 17)
def test_ANOVA_Refinement_Surplus(self):
"""Dimensionally adaptive refinement using surplus coefficients as local
error indicator
"""
# point ((3,7), (1,1)) (middle most right) gets larger surplus coefficient
alpha = DataVector(self.grid.getSize())
point_to_refine = None
for i in range(17):
point = self.grid_storage.getPoint(i)
if point.getLevel(0) == 3 and point.getIndex(0) == 7 \
and point.getLevel(1) == 1 and point.getIndex(1) == 1:
point_to_refine = point
alpha[i] = 2.0
else:
alpha[i] = 1.0
# refine one point
functor = SurplusRefinementFunctor(alpha, 1, 0.0)
anova_refinement = ANOVAHashRefinement()
#refinement_strategy = ANOVARefinement(hash_refinement)
anova_refinement.free_refine(self.grid_storage, functor)
# check if only the children along x1 direction were inserted
self.assertEqual(
self.grid.getSize(), 19,
'Number of grid points doesn\'t match: %d != %d' %
(self.grid.getSize(), 19))
child = point_to_refine.__class__(point_to_refine)
child.getLeftChild(0)
self.assertTrue(self.grid_storage.isContaining(child),
'Left x1 left child was not found')
child = point_to_refine.__class__(point_to_refine)
child.getRightChild(0)
self.assertTrue(self.grid_storage.isContaining(child),
'Left x1 right child was not found')
child = point_to_refine.__class__(point_to_refine)
child.getLeftChild(1)
self.assertFalse(
self.grid_storage.isContaining(child),
'Left x2 left child is present, though should not be')
child = point_to_refine.__class__(point_to_refine)
child.getRightChild(1)
self.assertFalse(
self.grid_storage.isContaining(child),
'Left x2 right child is present, though should not be')
def testRefinement3d(self):
from pysgpp import Grid, DataVector, SurplusRefinementFunctor
factory = Grid.createLinearTrapezoidBoundaryGrid(3)
storage = factory.getStorage()
gen = factory.createGridGenerator()
gen.regular(1)
self.failUnlessEqual(storage.size(), 27)
alpha = DataVector(27)
for i in xrange(len(alpha)):
alpha[i] = 0.0
alpha[26] = 1.0
func = SurplusRefinementFunctor(alpha)
gen.refine(func)
self.failUnlessEqual(storage.size(), 81)
def testFreeRefine(self):
"""Tests surplus based refine for Hash-Storage"""
from pysgpp import GridStorage, HashGenerator
from pysgpp import SurplusRefinementFunctor, HashRefinement, DataVector
s = GridStorage(2)
g = HashGenerator()
g.regular(s, 1)
d = DataVector(1)
d[0] = 1.0
f = SurplusRefinementFunctor(d)
r = HashRefinement()
r.free_refine(s, f)
self.failUnlessEqual(s.size(), 5)
def test_freeRefineSubspaceIsotropic(self):
"""Refine the isotropic middle subspace"""
alpha = DataVector(self.grid.getSize())
alpha.setAll(1.0)
for i in [13, 14, 15, 16]:
alpha[i] = 2.
#refinement stuff
refinement = HashRefinement()
decorator = SubspaceRefinement(refinement)
# refine a single grid point each time
functor = SurplusRefinementFunctor(alpha, 1)
decorator.free_refine(self.HashGridStorage, functor)
for i in range(self.grid.getSize()):
HashGridPoint = self.HashGridStorage.getPoint(i)
self.assertEqual(self.grid.getSize(), 33)
for i in range(self.grid.getSize()):
HashGridPoint = self.HashGridStorage.getPoint(i)
levelIndex = eval(HashGridPoint.toString())
self.assertFalse(levelIndex[0] == 4 or levelIndex[2] == 4)
def test_freeRefineSubspaceIsotropic(self):
"""Refine the isotropic middle subspace"""
alpha = DataVector(self.grid.getSize())
alpha.setAll(1.0)
alpha[12] = 2.
#refinement stuff
refinement = HashRefinement()
decorator = GSGRefinement(refinement)
# refine a single grid point each time
functor = SurplusRefinementFunctor(alpha, 1)
decorator.freeRefineSubspace(self.HashGridStorage, functor)
for i in xrange(self.grid.getSize()):
HashGridIndex = self.HashGridStorage.get(i)
print i, HashGridIndex.toString()
self.assertEqual(self.grid.getSize(), 15)
for i in xrange(self.grid.getSize()):
HashGridIndex = self.HashGridStorage.get(i)
levelIndex = eval(HashGridIndex.toString())
self.assertFalse(levelIndex[0] == 4 or levelIndex[2] >= 3)
def testPrewaveletAdaptivedD_two(self):
from pysgpp import Grid, DataVector, SurplusRefinementFunctor
factory = Grid.createPrewaveletGrid(4)
training = buildTrainingVector(
readDataVector('data/data_dim_4_nops_4096_float.arff.gz'))
level = 2
gen = factory.createGridGenerator()
gen.regular(level)
alpha = DataVector(factory.getStorage().size())
for i in xrange(factory.getStorage().size()):
alpha[i] = i + 1
gen.refine(SurplusRefinementFunctor(alpha, 1))
m = generateBBTMatrix(factory, training)
m_ref = readReferenceMatrix(
self, factory.getStorage(),
'data/BBT_prewavelet_dim_4_nopsgrid_17_adapt_float.dat.gz')
# compare
compareBBTMatrices(self, m, m_ref)
def test_freeRefineSubspaceAnisotropic(self):
"""Refine Anisotropic subspace (x2)"""
alpha = DataVector(self.grid.getSize())
alpha.setAll(1.0)
for i in [9, 10, 11, 12]:
alpha[i] = 2.
#refinement stuff
refinement = HashRefinement()
decorator = SubspaceRefinement(refinement)
# refine a single grid point each time
functor = SurplusRefinementFunctor(alpha, 1)
decorator.free_refine(self.HashGridStorage, functor)
for i in xrange(self.grid.getSize()):
HashGridIndex = self.HashGridStorage.get(i)
print i, HashGridIndex.toString()
self.assertEqual(self.grid.getSize(), 33)
for i in xrange(self.grid.getSize()):
HashGridIndex = self.HashGridStorage.get(i)
levelIndex = eval(HashGridIndex.toString())
self.assertFalse(levelIndex[0] == 4)
def test_Spatial_Refinement_Surplus(self):
"""Spatial refinement using surplus coefficients as local error
indicator
"""
# point ((2,1), (2,3)) (top right) gets larger surplus coefficient
alpha = DataVector(self.grid.getSize())
point_to_refine = None
for i in xrange(17):
point = self.grid_storage.get(i)
if point.getLevel(0) == 2 and point.getIndex(0) == 1 \
and point.getLevel(1) == 2 and point.getIndex(1) == 3:
point_to_refine = point
alpha[i] = 2.0
else:
alpha[i] = 1.0
# refine one point
self.grid.createGridGenerator().refine(
SurplusRefinementFunctor(alpha, 1, 0))
# check that all children were inserted
self.assertEqual(self.grid.getSize(), 21,
'Number of grid points doesn\'t match')
child = point_to_refine.__class__(point_to_refine)
self.grid_storage.left_child(child, 0)
self.assertTrue(self.grid_storage.has_key(child),
'Left x1 left child was not found')
child = point_to_refine.__class__(point_to_refine)
self.grid_storage.right_child(child, 0)
self.assertTrue(self.grid_storage.has_key(child),
'Left x1 right child was not found')
child = point_to_refine.__class__(point_to_refine)
self.grid_storage.left_child(child, 1)
self.assertTrue(self.grid_storage.has_key(child),
'Left x2 left child was not found')
child = point_to_refine.__class__(point_to_refine)
self.grid_storage.right_child(child, 1)
self.assertTrue(self.grid_storage.has_key(child),
'Left x2 right child was not found')
def testFreeRefineTrapezoidBoundaries(self):
"""Tests surplus based refine for Hash-Storage"""
from pysgpp import GridStorage, HashGenerator
from pysgpp import SurplusRefinementFunctor, HashRefinementBoundaries, DataVector
s = GridStorage(2)
g = HashGenerator()
g.regularWithBoundaries(s, 2, False)
d = DataVector(17)
for i in xrange(len(d)):
d[i] = 0.0
d[12] = 1.0
f = SurplusRefinementFunctor(d)
r = HashRefinementBoundaries()
r.free_refine(s, f)
self.failUnlessEqual(s.size(), 21)
def testRefinement2d(self):
from pysgpp import Grid, DataVector, SurplusRefinementFunctor
factory = Grid.createLinearTrapezoidBoundaryGrid(2)
storage = factory.getStorage()
gen = factory.createGridGenerator()
gen.regular(1)
self.failUnlessEqual(storage.size(), 9)
alpha = DataVector(9)
alpha[0] = 0.0
alpha[1] = 0.0
alpha[2] = 0.0
alpha[3] = 0.0
alpha[4] = 0.0
alpha[5] = 0.0
alpha[6] = 0.0
alpha[7] = 0.0
alpha[8] = 1.0
func = SurplusRefinementFunctor(alpha)
gen.refine(func)
self.failUnlessEqual(storage.size(), 21)
print "dimensionality: {}".format(dim)
# create regular grid, level 3
level = 3
gridGen = grid.createGridGenerator()
gridGen.regular(level)
print "number of initial grid points: {}".format(gridStorage.size())
# definition of function to interpolate - nonsymmetric(!)
f = lambda x0, x1: 16.0 * (x0 - 1) * x0 * (x1 - 1) * x1 * x1
# create coefficient vector
alpha = DataVector(gridStorage.size())
print "length of alpha vector: {}".format(alpha.getSize())
# now refine adaptively 5 times
for refnum in range(5):
# set function values in alpha
for i in xrange(gridStorage.size()):
gp = gridStorage.get(i)
alpha[i] = f(gp.getCoord(0), gp.getCoord(1))
# hierarchize
createOperationHierarchisation(grid).doHierarchisation(alpha)
# refine a single grid point each time
gridGen.refine(SurplusRefinementFunctor(alpha, 1))
print "refinement step {}, new grid size: {}".format(
refnum + 1, gridStorage.size())
# extend alpha vector (new entries uninitialized)
alpha.resize(gridStorage.size())
def discretize(grid,
alpha,
f,
epsilon=0.,
refnums=0,
pointsNum=10,
level=0,
deg=1,
useDiscreteL2Error=True):
"""
discretize f with a sparse grid
@param grid: Grid
@param alpha: surplus vector
@param f: function
@param epsilon: float, error tolerance
@param refnums: int, number of refinment steps
@param pointsNum: int, number of points to be refined per step
@param level: int, initial grid level
@param deg: int, degree of lagrange basis
"""
# copy grid
jgrid = copyGrid(grid, level=level, deg=deg)
jgs = jgrid.getStorage()
jgn = jgrid.createGridGenerator()
basis_alpha = DataVector(alpha)
# compute joined sg function
jalpha = computeCoefficients(jgrid, grid, alpha, f)
# compute errors
maxdrift = None
accMiseL2 = None
l2error_grid = alpha.l2Norm()
if useDiscreteL2Error:
maxdrift, accMiseL2 = computeErrors(jgrid, jalpha, grid, alpha, f)
else:
accMiseL2 = l2error_grid
# print "iteration 0/%i (%i, %i, %g): %g, %g, %s" % \
# (refnums, jgs.size(), len(jalpha),
# epsilon, accMiseL2, l2error_grid, maxdrift)
ref = 0
errs = [jgs.size(), accMiseL2, l2error_grid, maxdrift]
bestGrid, bestAlpha, bestL2Error = copyGrid(jgrid), DataVector(
jalpha), accMiseL2
# repeat refinement as long as there are iterations and the
# minimum error epsilon is reached
while ref < refnums and bestL2Error > epsilon:
oldgrid = copyGrid(jgrid)
rp = jgn.getNumberOfRefinablePoints(
) # max(1, min(pointsNum, jgn.getNumberOfRefinablePoints()))
jgn.refine(SurplusRefinementFunctor(jalpha, rp, epsilon))
# if grid point has been added in the last iteration step
if len(basis_alpha) == jgs.size():
break
# extend alpha vector...
basis_alpha.resizeZero(jgs.size())
# ------------------------------
# compute joined sg function
jalpha = computeCoefficients(jgrid, grid, basis_alpha, f)
# compute useDiscreteL2Error
l2error_grid = estimateL2error(oldgrid, jgrid, jalpha)
# do Monte Carlo integration for obtaining the accMiseL2
if useDiscreteL2Error:
maxdrift, accMiseL2 = computeErrors(jgrid, jalpha, grid, alpha, f)
# ------------------------------
print "iteration %i/%i (%i, %i, %i, %i, %g): %g, %g, %s -> current best %g" % \
(ref + 1, refnums,
jgs.size(), len(jalpha),
bestGrid.getSize(), len(bestAlpha),
epsilon,
accMiseL2, l2error_grid, maxdrift, bestL2Error)
# check whether the new grid is better than the current best one
# using the discrete l2 error. If no MC integration is done,
# use the l2 error approximation via the sparse grid surpluses
if (not useDiscreteL2Error and l2error_grid < bestL2Error) or \
(useDiscreteL2Error and accMiseL2 < bestL2Error):
bestGrid = copyGrid(jgrid)
bestAlpha = DataVector(jalpha)
if useDiscreteL2Error:
bestL2Error = accMiseL2
else:
bestL2Error = l2error_grid
errs = [jgs.size(), accMiseL2, l2error_grid, maxdrift]
ref += 1
return bestGrid, bestAlpha, errs