def testOperationTest_test(self):
from pysgpp import Grid, DataVector, DataMatrix
factory = Grid.createLinearBoundaryGrid(1)
gen = factory.createGridGenerator()
gen.regular(1)
alpha = DataVector(factory.getStorage().size())
data = DataMatrix(1, 1)
data.setAll(0.25)
classes = DataVector(1)
classes.setAll(1.0)
testOP = factory.createOperationTest()
alpha[0] = 0.0
alpha[1] = 0.0
alpha[2] = 1.0
c = testOP.test(alpha, data, classes)
self.failUnless(c > 0.0)
alpha[0] = 0.0
alpha[1] = 0.0
alpha[2] = -1.0
c = testOP.test(alpha, data, classes)
self.failUnless(c == 0.0)
def cdf(self, x):
# convert the parameter to the right format
if isList(x):
x = DataVector(x)
elif isNumerical(x):
x = DataVector([x])
elif isMatrix(x):
x = DataMatrix(x)
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
self.dist.cdf(A, B)
# transform the outcome
if isNumerical(x) or isinstance(x, DataVector):
return B.get(0, 0)
elif isinstance(x, DataMatrix):
return B.array()
def computeBilinearForm(self, grid):
"""
Compute bilinear form for the current grid
@param grid: Grid
@return DataMatrix
"""
# create bilinear form of the grid
gs = grid.getStorage()
A = DataMatrix(gs.size(), gs.size())
A.setAll(0.)
createOperationLTwoDotExplicit(A, grid)
gs = grid.getStorage()
A = DataMatrix(gs.size(), gs.size())
createOperationLTwoDotExplicit(A, grid)
# multiply the entries with the pdf at the center of the support
p = DataVector(gs.dim())
q = DataVector(gs.dim())
for i in xrange(gs.size()):
gpi = gs.get(i)
gpi.getCoords(p)
for j in xrange(gs.size()):
gpj = gs.get(j)
gpj.getCoords(q)
y = float(A.get(i, j) * self._U.pdf(p))
A.set(i, j, y)
A.set(j, i, y)
self._map[self.getKey(gpi, gpj)] = A.get(i, j)
return A
def testOperationTest_test(self):
from pysgpp import Grid, DataVector, DataMatrix
factory = Grid.createLinearBoundaryGrid(1)
gen = factory.createGridGenerator()
gen.regular(1)
alpha = DataVector(factory.getStorage().size())
data = DataMatrix(1,1)
data.setAll(0.25)
classes = DataVector(1)
classes.setAll(1.0)
testOP = factory.createOperationTest()
alpha[0] = 0.0
alpha[1] = 0.0
alpha[2] = 1.0
c = testOP.test(alpha, data, classes)
self.failUnless(c > 0.0)
alpha[0] = 0.0
alpha[1] = 0.0
alpha[2] = -1.0
c = testOP.test(alpha, data, classes)
self.failUnless(c == 0.0)
def ppf(self, x):
# convert the parameter to the right format
if isList(x):
x = DataVector(x)
elif isNumerical(x):
x = DataVector([x])
elif isMatrix(x):
x = DataMatrix(x)
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
opInvRosen = createOperationInverseRosenblattTransformationKDE(self.dist)
opInvRosen.doTransformation(A, B)
# transform the outcome
if isNumerical(x) or isinstance(x, DataVector):
return B.get(0, 0)
elif isinstance(x, DataMatrix):
return B.array()
def ppf(self, x):
# convert the parameter to the right format
if isList(x):
x = DataVector(x)
elif isNumerical(x):
x = DataVector([x])
elif isMatrix(x):
x = DataMatrix(x)
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
self.dist.ppf(A, B)
# transform the outcome
if isNumerical(x) or isinstance(x, DataVector):
return B.get(0, 0)
elif isinstance(x, DataMatrix):
return B.array()
def computeBilinearForm(self, grid):
"""
Compute bilinear form for the current grid
@param grid: Grid
@return DataMatrix
"""
# create bilinear form of the grid
gs = grid.getStorage()
A = DataMatrix(gs.getSize(), gs.getSize())
A.setAll(0.)
createOperationLTwoDotExplicit(A, grid)
# multiply the entries with the pdf at the center of the support
p = DataVector(gs.getDimension())
q = DataVector(gs.getDimension())
for i in range(gs.getSize()):
gpi = gs.getPoint(i)
gs.getCoordinates(gpi, p)
for j in range(gs.getSize()):
gpj = gs.getPoint(j)
gs.getCoordinates(gpj, q)
y = float(A.get(i, j) * self._U.pdf(p))
A.set(i, j, y)
A.set(j, i, y)
self._map[self.getKey([gpi, gpj])] = A.get(i, j)
return A
def ppf(self, x):
# convert the parameter to the right format
if isList(x):
x = DataVector(x)
elif isNumerical(x):
x = DataVector([x])
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
assert A.getNcols() == B.getNcols() == self.trainData.getNcols()
op = createOperationInverseRosenblattTransformationKDE(self.trainData)
op.doTransformation(A, B)
# transform the outcome
if isNumerical(x) or isinstance(x, DataVector):
return B.get(0, 0)
elif isinstance(x, DataMatrix):
return B.array()
def sampleGrids(self, filename):
ts = self.__learner.getTimeStepsOfInterest()
names = self.__params.getNames()
names.append('f_\\mathcal{I}(x)')
for t in ts:
grid, surplus = self.__knowledge.getSparseGridFunction(
self._qoi, t)
# init
gs = grid.getStorage()
dim = gs.dim()
# -----------------------------------------
# do full grid sampling of sparse grid function
# -----------------------------------------
data = eval_fullGrid(4, dim)
res = evalSGFunctionMulti(grid, surplus, data)
data.transpose()
data.appendRow()
data.setRow(data.getNrows() - 1, res)
data.transpose()
# write results
writeDataARFF({
'filename': "%s.t%f.samples.arff" % (filename, t),
'data': data,
'names': names
})
# -----------------------------------------
# write sparse grid points to file
# -----------------------------------------
data = DataMatrix(gs.size(), dim)
data.setAll(0.0)
for i in xrange(gs.size()):
gp = gs.get(i)
v = np.array([gp.getCoord(j) for j in xrange(dim)])
data.setRow(i, DataVector(v))
# write results
writeDataARFF({
'filename': "%s.t%f.gridpoints.arff" % (filename, t),
'data': data,
'names': names
})
# -----------------------------------------
# write alpha
# -----------------------------------------
writeAlphaARFF("%s.t%f.alpha.arff" % (filename, t), surplus)
def sampleGrids(self, filename):
ts = self.__learner.getTimeStepsOfInterest()
names = self.__params.getNames()
names.append('f_\\mathcal{I}(x)')
for t in ts:
grid, surplus = self.__knowledge.getSparseGridFunction(self._qoi, t)
# init
gs = grid.getStorage()
dim = gs.dim()
# -----------------------------------------
# do full grid sampling of sparse grid function
# -----------------------------------------
data = eval_fullGrid(4, dim)
res = evalSGFunctionMulti(grid, surplus, data)
data.transpose()
data.appendRow()
data.setRow(data.getNrows() - 1, res)
data.transpose()
# write results
writeDataARFF({'filename': "%s.t%f.samples.arff" % (filename, t),
'data': data,
'names': names})
# -----------------------------------------
# write sparse grid points to file
# -----------------------------------------
data = DataMatrix(gs.size(), dim)
data.setAll(0.0)
for i in xrange(gs.size()):
gp = gs.get(i)
v = np.array([gp.getCoord(j) for j in xrange(dim)])
data.setRow(i, DataVector(v))
# write results
writeDataARFF({'filename': "%s.t%f.gridpoints.arff" % (filename, t),
'data': data,
'names': names})
# -----------------------------------------
# write alpha
# -----------------------------------------
writeAlphaARFF("%s.t%f.alpha.arff" % (filename, t),
surplus)
def ppf(self, x, shuffle=True):
# convert the parameter to the right format
x = self._convertEvalPoint(x)
# do the transformation
if self.dim == 1:
op = createOperationInverseRosenblattTransformation1D(self.grid)
x_unit = np.ndarray((x.shape[0], x.shape[1]))
for i, xi in enumerate(x[:, 0]):
x_unit[i,
0] = op.doTransformation1D(self.unnormalized_alpha_vec,
xi)
# transform the samples to the unit hypercube
if self.trans is not None:
x_prob = self.trans.unitToProbabilisticMatrix(x_unit)
else:
x_prob = x
# extract the outcome
if x_prob.shape[0] == 1 and x_prob.shape[1] == 1:
return x_prob[:, 0]
else:
return x_prob.flatten()
else:
A_vec = DataMatrix(x)
B_vec = DataMatrix(x.shape[0], x.shape[1])
B_vec.setAll(0.0)
# do the transformation
op = createOperationInverseRosenblattTransformation(self.grid)
if shuffle:
op.doTransformation(self.unnormalized_alpha_vec, A_vec, B_vec)
else:
op.doTransformation(self.unnormalized_alpha_vec, A_vec, B_vec,
0)
# transform the samples to the unit hypercube
B = B_vec.array()
if self.trans is not None:
B_prob = self.trans.unitToProbabilisticMatrix(B)
else:
B_prob = B
# extract the outcome
if x.shape == (1, 1):
return B_prob.get(0, 0)
else:
return B_prob
def ppf(self, x, shuffle=False):
x = self._convertEvalPoint(x)
x_matrix = DataMatrix(x)
res_matrix = DataMatrix(x_matrix.getNrows(), x_matrix.getNcols())
res_matrix.setAll(0.0)
# do the transformation
opRosen = createOperationInverseRosenblattTransformationKDE(self.dist)
if shuffle:
opRosen.doShuffledTransformation(x_matrix, res_matrix)
else:
opRosen.doTransformation(x_matrix, res_matrix)
# transform the outcome
res = res_matrix.array()
if res.shape[0] == 1 and res.shape[1] == 1:
return res[0, 0]
else:
return res
def computeBilinearForm(self, grid):
"""
Compute bilinear form for the current grid
@param grid: Grid
@return: DataMatrix
"""
gs = grid.getStorage()
A = DataMatrix(gs.size(), gs.size())
A.setAll(0.)
createOperationLTwoDotExplicit(A, grid)
# store the result in the hash map
for i in xrange(gs.size()):
gpi = gs.get(i)
for j in xrange(gs.size()):
gpj = gs.get(j)
key = self.getKey(gpi, gpj)
self._map[key] = A.get(i, j)
return A
def ppf(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 = createOperationInverseRosenblattTransformation1D(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 = createOperationInverseRosenblattTransformation(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 ppf(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 = createOperationInverseRosenblattTransformation1D(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 = createOperationInverseRosenblattTransformation(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 createNullVector(self, size, dim):
vector = DataMatrix(size, dim)
vector.setAll(0)
return vector
def createNullVector(self, size, dim):
vector = DataMatrix(size, dim)
vector.setAll(0)
return vector
def var(self, grid, alpha, U, T, mean):
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) - E(f))^2 * pdf(x) dx
"""
# extract correct pdf for moment estimation
vol, W = self._extractPDFforMomentEstimation(U, T)
D = T.getTransformations()
# copy the grid, and add a trapezoidal boundary
# ngrid = GridDescriptor().fromGrid(grid)\
# .withBorder(BorderTypes.TRAPEZOIDBOUNDARY)\
# .createGrid()
# compute nodalValues
# ngs = ngrid.getStorage()
# nodalValues = DataVector(ngs.size())
# p = DataVector(ngs.dim())
# for i in xrange(ngs.size()):
# ngs.get(i).getCoords(p)
# nodalValues[i] = evalSGFunction(grid, alpha, p) - mean
#
# # hierarchize the new function
# nalpha = hierarchize(ngrid, nodalValues)
ngs = grid.getStorage()
ngrid, nalpha = grid, alpha
# compute the integral of the product times the pdf
acc = DataMatrix(ngs.size(), ngs.size())
acc.setAll(1.)
err = 0
for i, dims in enumerate(W.getTupleIndices()):
dist = W[i]
trans = D[i]
# get the objects needed for integrating
# the current dimensions
gpsi, basisi = project(ngrid, dims)
if isinstance(dist, SGDEdist):
# project distribution on desired dimensions
# get the objects needed for integrating
# the current dimensions
gpsk, basisk = project(dist.grid, range(len(dims)))
# compute the bilinear form
tf = TrilinearGaussQuadratureStrategy([dist], trans)
A, erri = tf.computeTrilinearFormByList(
gpsk, basisk, dist.alpha, gpsi, basisi, gpsi, basisi)
else:
# we compute the bilinear form of the grids
# compute the bilinear form
if len(dims) == 1:
dist = [dist]
trans = [trans]
bf = BilinearGaussQuadratureStrategy(dist, trans)
A, erri = bf.computeBilinearFormByList(gpsi, basisi, gpsi,
basisi)
# accumulate the results
acc.componentwise_mult(A)
# accumulate the error
err += acc.sum() / (acc.getNrows() * acc.getNcols()) * erri
# compute the variance
tmp = DataVector(acc.getNrows())
self.mult(acc, nalpha, tmp)
moment = vol * nalpha.dotProduct(tmp)
moment = moment - mean**2
return moment, err
def var(self, grid, alpha, U, T, mean):
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) - E(f))^2 * pdf(x) dx
"""
# extract correct pdf for moment estimation
vol, W = self._extractPDFforMomentEstimation(U, T)
D = T.getTransformations()
# copy the grid, and add a trapezoidal boundary
# ngrid = GridDescriptor().fromGrid(grid)\
# .withBorder(BorderTypes.TRAPEZOIDBOUNDARY)\
# .createGrid()
# compute nodalValues
# ngs = ngrid.getStorage()
# nodalValues = DataVector(ngs.size())
# p = DataVector(ngs.dim())
# for i in xrange(ngs.size()):
# ngs.get(i).getCoords(p)
# nodalValues[i] = evalSGFunction(grid, alpha, p) - mean
#
# # hierarchize the new function
# nalpha = hierarchize(ngrid, nodalValues)
ngs = grid.getStorage()
ngrid, nalpha = grid, alpha
# compute the integral of the product times the pdf
acc = DataMatrix(ngs.size(), ngs.size())
acc.setAll(1.)
err = 0
for i, dims in enumerate(W.getTupleIndices()):
dist = W[i]
trans = D[i]
# get the objects needed for integrating
# the current dimensions
gpsi, basisi = project(ngrid, dims)
if isinstance(dist, SGDEdist):
# project distribution on desired dimensions
# get the objects needed for integrating
# the current dimensions
gpsk, basisk = project(dist.grid, range(len(dims)))
# compute the bilinear form
tf = TrilinearGaussQuadratureStrategy([dist], trans)
A, erri = tf.computeTrilinearFormByList(gpsk, basisk, dist.alpha,
gpsi, basisi,
gpsi, basisi)
else:
# we compute the bilinear form of the grids
# compute the bilinear form
if len(dims) == 1:
dist = [dist]
trans = [trans]
bf = BilinearGaussQuadratureStrategy(dist, trans)
A, erri = bf.computeBilinearFormByList(gpsi, basisi,
gpsi, basisi)
# accumulate the results
acc.componentwise_mult(A)
# accumulate the error
err += acc.sum() / (acc.getNrows() * acc.getNcols()) * erri
# compute the variance
tmp = DataVector(acc.getNrows())
self.mult(acc, nalpha, tmp)
moment = vol * nalpha.dotProduct(tmp)
moment = moment - mean ** 2
return moment, err
