def mean(self, grid, alpha, U, T):
r"""
Estimate the expectation value using Monte-Carlo.
\frac{1}{N}\sum\limits_{i = 1}^N f_N(x_i)
where x_i \in \Gamma
@return: (mean, error of bootstrapping)
"""
# init
_, W, D = self._extractPDFforMomentEstimation(U, T)
moments = np.zeros(self.__npaths)
for i in range(self.__npaths):
samples = self.__getSamples(W, D, bootstrapping=True)
res = evalSGFunctionMulti(grid, alpha, samples)
# compute the moment
moments[i] = np.mean(res)
# error statistics
if self.__npaths > 1:
lower_percentile = np.percentile(moments, q=self.__percentile)
upper_percentile = np.percentile(moments, q=100 - self.__percentile)
err = max(lower_percentile, upper_percentile)
else:
err = lower_percentile = upper_percentile = np.Inf
# calculate moment
samples = self.__getSamples(W, D, bootstrapping=False)
res = evalSGFunctionMulti(grid, alpha, samples)
return {"value": np.mean(res),
"err": err,
"confidence_interval": (lower_percentile, upper_percentile)}
def var(self, grid, alpha, U, T, mean):
r"""
Estimate the expectation value using Monte-Carlo.
\frac{1}{N}\sum\limits_{i = 1}^N (f_N(x_i) - E(f))^2
where x_i \in \Gamma
@return: (variance, error of bootstrapping)
"""
# init
_, W, D = self._extractPDFforMomentEstimation(U, T)
moments = np.zeros(self.__npaths)
for i in range(self.__npaths):
samples = self.__getSamples(W, D, bootstrapping=True)
res = evalSGFunctionMulti(grid, alpha, samples)
# compute the moment
moments[i] = np.sum((res - np.mean(res))**2) / (len(res) - 1.)
# error statistics
if self.__npaths > 1:
lower_percentile = np.percentile(moments, q=self.__percentile)
upper_percentile = np.percentile(moments,
q=100 - self.__percentile)
err = max(lower_percentile, upper_percentile)
else:
err = lower_percentile = upper_percentile = np.Inf
# calculate moment
samples = self.__getSamples(W, D, bootstrapping=False)
# plt.figure()
# plt.hist(samples[:, 0], normed=True, cumulative=False, label="histogram")
# plt.title("0: lognormal [%g, %g]" % (samples[:, 0].min(),
# samples[:, 0].max()))
# plt.figure()
# plt.hist(samples[:, 1], normed=True, cumulative=False, label="histogram")
# plt.title("0: beta [%g, %g]" % (samples[:, 1].min(),
# samples[:, 1].max()))
# plt.figure()
# plt.hist(samples[:, 2], normed=True, cumulative=False, label="histogram")
# plt.title("0: lognormal [%g, %g]" % (samples[:, 2].min(),
# samples[:, 2].max()))
# plt.show()
res = evalSGFunctionMulti(grid, alpha, samples)
return {
"value": np.sum((res - mean)**2) / (len(res) - 1.),
"err": err,
"confidence_interval": (lower_percentile, upper_percentile)
}
def evalError(self, data, alpha):
"""
computes the discrete L2-error of the sparse grid interpolant
with respect to some MC samples at given time steps
@param data: DataContainer samples
@param alpha: numpy array hierarchical coefficients
@return: mean squared error
"""
# check if points are in [0, 1]^d
allPoints = data.getPoints().array()
allModelValues = data.getValues().array()
points = np.ndarray((0, data.dim))
modelValues = np.array([])
for i, point in enumerate(allPoints):
if np.all(point >= 0) and np.all(point <= 1):
points = np.vstack((points, point))
modelValues = np.append(modelValues, allModelValues[i])
if allPoints.shape[1] == 0:
return np.array([])
surrogateValues = evalSGFunctionMulti(self.grid, alpha, points)
# compute error
return np.abs(surrogateValues - modelValues)
def testEval(self):
grid = Grid.createLinearGrid(1)
grid.getGenerator().regular(3)
gs = grid.getStorage()
# prepare surplus vector
nodalValues = DataVector(gs.getSize())
nodalValues.setAll(0.0)
# interpolation on nodal basis
p = DataVector(gs.getDimension())
for i in range(gs.getSize()):
gs.getCoordinates(gs.getPoint(i), p)
nodalValues[i] = f(p[0])
# nodalValues[i] = f(p[0], p[1])
# hierarchization
alpha = hierarchize(grid, nodalValues)
# eval the sparse grid function
x = np.linspace(0, 1, 1000)
y = [f(xi) for xi in x]
y1 = [evalSGFunction(grid, alpha, np.array([xi])) for xi in x]
y2 = evalSGFunctionMulti(grid, alpha, np.array([x]).T)
assert np.all(y1 - y2 <= 1e-13)
def var(self, grid, alpha, U, T, mean):
r"""
Estimate the expectation value using Monte-Carlo.
\frac{1}{N}\sum\limits_{i = 1}^N (f_N(x_i) - E(f))^2
where x_i \in \Gamma
"""
# init
_, W = self._extractPDFforMomentEstimation(U, T)
moments = np.zeros(self.__npaths)
vecMean = DataVector(self.__n)
vecMean.setAll(mean)
for i in xrange(self.__npaths):
samples = self.__getSamples(W, T, self.__n)
res = evalSGFunctionMulti(grid, alpha, samples)
res.sub(vecMean)
res.sqr()
# compute the moment
moments[i] = res.sum() / (len(res) - 1.)
# error statistics
err = np.Inf
# calculate moment
return np.sum(moments) / self.__npaths, err
def mean(self, grid, alpha, U, T):
r"""
Estimate the expectation value using Monte-Carlo.
\frac{1}{N}\sum\limits_{i = 1}^N f_N(x_i)
where x_i \in \Gamma
"""
# init
_, W = self._extractPDFforMomentEstimation(U, T)
moments = np.zeros(self.__npaths)
for i in xrange(self.__npaths):
samples = self.__getSamples(W, T, self.__n)
res = evalSGFunctionMulti(grid, alpha, samples)
# multiply the result with the corresponding pdf value
# sample = DataVector(samples.getNcols())
# for j in xrange(samples.getNrows()):
# samples.getRow(j, sample)
# res[j] *= W.pdf(sample)
# compute the moment
moments[i] = res.sum() / len(res)
# error statistics
if self.__npaths > 1:
err_clt = self.__c * np.sqrt(np.var(moments, ddof=1) / len(moments))
else:
err_clt = np.Inf
# calculate moment
return np.sum(moments) / self.__npaths, err_clt
def var(self, grid, alpha, U, T, mean):
r"""
Estimate the expectation value using Monte-Carlo.
\frac{1}{N}\sum\limits_{i = 1}^N (f_N(x_i) - E(f))^2
where x_i \in \Gamma
"""
# init
_, W = self._extractPDFforMomentEstimation(U, T)
moments = np.zeros(self.__npaths)
vecMean = DataVector(self.__n)
vecMean.setAll(mean)
for i in xrange(self.__npaths):
samples = self.__getSamples(W, T, self.__n)
res = evalSGFunctionMulti(grid, alpha, samples)
res.sub(vecMean)
res.sqr()
# compute the moment
moments[i] = res.sum() / (len(res) - 1.)
# error statistics
err = np.Inf
# calculate moment
return np.sum(moments) / self.__npaths, err
def mean(self, grid, alpha, U, T):
r"""
Estimate the expectation value using Monte-Carlo.
\frac{1}{N}\sum\limits_{i = 1}^N f_N(x_i)
where x_i \in \Gamma
"""
# init
_, W = self._extractPDFforMomentEstimation(U, T)
moments = np.zeros(self.__npaths)
for i in xrange(self.__npaths):
samples = self.__getSamples(W, T, self.__n)
res = evalSGFunctionMulti(grid, alpha, samples)
# multiply the result with the corresponding pdf value
# sample = DataVector(samples.getNcols())
# for j in xrange(samples.getNrows()):
# samples.getRow(j, sample)
# res[j] *= W.pdf(sample)
# compute the moment
moments[i] = res.sum() / len(res)
# error statistics
if self.__npaths > 1:
err_clt = self.__c * np.sqrt(
np.var(moments, ddof=1) / len(moments))
else:
err_clt = np.Inf
# calculate moment
return np.sum(moments) / self.__npaths, err_clt
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.__uqManager.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.getDimension()
# -----------------------------------------
# do full grid sampling of sparse grid function
# -----------------------------------------
data = eval_fullGrid(4, dim)
res = evalSGFunctionMulti(grid, surplus, data)
data = np.vstack((data.T, res)).T
# write results
data_vec = DataMatrix(data)
writeDataARFF({
'filename': "%s.t%f.samples.arff" % (filename, t),
'data': data_vec,
'names': names
})
del data_vec
# -----------------------------------------
# write sparse grid points to file
# -----------------------------------------
data = np.ndarray((gs.getSize(), dim))
x = DataVector(dim)
for i in range(gs.getSize()):
gp = gs.getPoint(i)
gs.getCoordinates(gp, x)
data[i, :] = x.array()
# write results
data_vec = DataMatrix(data)
writeDataARFF({
'filename': "%s.t%f.gridpoints.arff" % (filename, t),
'data': data_vec,
'names': names
})
del data_vec
# -----------------------------------------
# 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 evalError(self, data, alpha):
"""
computes the discrete L2-error of the sparse grid interpolant
with respect to some MC samples at given time steps
@param data: DataContainer samples
@param alpha: DataVector hierarchical coefficients
@return: mean squared error
"""
points = data.getPoints()
values = data.getValues()
size = points.getNrows()
if size == 0:
return 0
self.error = evalSGFunctionMulti(self.grid, alpha, points)
# compute L2 error
self.error.sub(values)
self.error.sqr()
return self.error.sum() / len(self.error)
def evalError(self, data, alpha):
"""
computes the discrete L2-error of the sparse grid interpolant
with respect to some MC samples at given time steps
@param data: DataContainer samples
@param alpha: DataVector hierarchical coefficients
@return: mean squared error
"""
points = data.getPoints()
values = data.getValues()
size = points.getNrows()
if size == 0:
return 0
self.error = evalSGFunctionMulti(self.grid, alpha, points)
# compute L2 error
self.error.sub(values)
self.error.sqr()
return self.error.sum() / len(self.error)
def __estimate(self, vol, grid, alpha, U, T, f, npaths):
n = npaths * self.__n
A = self.__getSamples(U, T, n)
# import matplotlib.pyplot as plt
# fig = plt.figure()
# plt.plot(A[:, 0], A[:, 1], ' ', marker='^')
# fig.show()
# override the old samples with the new ones
# A[:, :2] = self.__getSamples(l)
# A[:, :2] = self.__getDataSamples()
# fig = plt.figure()
# plt.plot(A[:, 0], A[:, 1], ' ', marker='^')
# fig.show()
# A[:, :2] = self.__getDataSamples()
# fig = plt.figure()
# plt.plot(A[:, 0], A[:, 1], ' ', marker='^')
# fig.show()
# import ipdb; ipdb.set_trace()
vals = evalSGFunctionMulti(grid, alpha, A).array()
fx = np.ndarray([len(vals)], dtype='float')
p = DataVector(A.getNcols())
for i, val in enumerate(vals):
A.getRow(i, p)
fx[i] = f(p.array(), val)
# q = T.unitToProbabilistic(p)
# A.setRow(i, DataVector(q))
# get the pdf of the values
# fx *= U.pdf(A.array())
if self.__isPositive:
fx = abs(fx)
# # define here grid for corners and run the samples here too
# grid_file = '/home/franzefn/Promotion/Projekte/CO2/UQ5analytical/results/co2_leakage_analytical/sgb1deg2/sg_l1/grids/sg.t%g.grid' % t
# alpha_file = '/home/franzefn/Promotion/Projekte/CO2/UQ5analytical/results/co2_leakage_analytical/sgb1deg2/sg_l1/grids/sg.t%g.alpha.arff' % t
# borderGrid = readGrid(grid_file)
# borderAlpha = readAlphaARFF(alpha_file)
# nodalValues = dehierarchize(grid, alpha)
# gs = grid.getStorage()
# bordergs = borderGrid.getStorage()
# p = DataVector(gs.dim())
# for i in xrange(gs.size()):
# gs.get(i).getCoords(p)
# nodalValues[i] -= evalSGFunction(borderGrid, borderAlpha, p)
# nalpha = hierarchize(grid, nodalValues)
# # # check if interpolation criterion is fulfilled for splitted grid
# # p = DataVector(gs.dim())
# # for i in xrange(gs.size()):
# # gp = gs.get(i)
# # if bordergs.has_key(gp):
# # gp.getCoords(p)
# # res1 = evalSGFunction(grid, alpha, p)
# # res2 = evalSGFunction(grid, nalpha, p) + evalSGFunction(borderGrid, borderAlpha, p)
# # print res1, res2, abs(res1 - res2)
# # fig = scatterplot_matrix(A.T, ['phi', 'e', 'kl'], linestyle=' ', marker='o')
# # fig.show()
# res1 = evalSGFunctionMulti(grid, nalpha, DataMatrix(A)).array()
# res2 = evalSGFunctionMulti(borderGrid, borderAlpha, DataMatrix(A)).array()
# res = res1 + res2
mean = np.ndarray(npaths, dtype='float')
for i in xrange(npaths):
mean[i] = np.mean(fx[(i * self.__n):((i + 1) * self.__n)]) # * vol
return mean
def __estimate(self, vol, grid, alpha, U, T, f, npaths):
n = npaths * self.__n
A = self.__getSamples(U, T, n)
# import matplotlib.pyplot as plt
# fig = plt.figure()
# plt.plot(A[:, 0], A[:, 1], ' ', marker='^')
# fig.show()
# override the old samples with the new ones
# A[:, :2] = self.__getSamples(l)
# A[:, :2] = self.__getDataSamples()
# fig = plt.figure()
# plt.plot(A[:, 0], A[:, 1], ' ', marker='^')
# fig.show()
# A[:, :2] = self.__getDataSamples()
# fig = plt.figure()
# plt.plot(A[:, 0], A[:, 1], ' ', marker='^')
# fig.show()
# import ipdb; ipdb.set_trace()
vals = evalSGFunctionMulti(grid, alpha, A).array()
fx = np.ndarray([len(vals)], dtype='float')
p = DataVector(A.getNcols())
for i, val in enumerate(vals):
A.getRow(i, p)
fx[i] = f(p.array(), val)
# q = T.unitToProbabilistic(p)
# A.setRow(i, DataVector(q))
# get the pdf of the values
# fx *= U.pdf(A.array())
if self.__isPositive:
fx = abs(fx)
# # define here grid for corners and run the samples here too
# grid_file = '/home/franzefn/Promotion/Projekte/CO2/UQ5analytical/results/co2_leakage_analytical/sgb1deg2/sg_l1/grids/sg.t%g.grid' % t
# alpha_file = '/home/franzefn/Promotion/Projekte/CO2/UQ5analytical/results/co2_leakage_analytical/sgb1deg2/sg_l1/grids/sg.t%g.alpha.arff' % t
# borderGrid = readGrid(grid_file)
# borderAlpha = readAlphaARFF(alpha_file)
# nodalValues = dehierarchize(grid, alpha)
# gs = grid.getStorage()
# bordergs = borderGrid.getStorage()
# p = DataVector(gs.dim())
# for i in xrange(gs.size()):
# gs.get(i).getCoords(p)
# nodalValues[i] -= evalSGFunction(borderGrid, borderAlpha, p)
# nalpha = hierarchize(grid, nodalValues)
# # # check if interpolation criterion is fulfilled for splitted grid
# # p = DataVector(gs.dim())
# # for i in xrange(gs.size()):
# # gp = gs.get(i)
# # if bordergs.has_key(gp):
# # gp.getCoords(p)
# # res1 = evalSGFunction(grid, alpha, p)
# # res2 = evalSGFunction(grid, nalpha, p) + evalSGFunction(borderGrid, borderAlpha, p)
# # print res1, res2, abs(res1 - res2)
# # fig = scatterplot_matrix(A.T, ['phi', 'e', 'kl'], linestyle=' ', marker='o')
# # fig.show()
# res1 = evalSGFunctionMulti(grid, nalpha, DataMatrix(A)).array()
# res2 = evalSGFunctionMulti(borderGrid, borderAlpha, DataMatrix(A)).array()
# res = res1 + res2
mean = np.ndarray(npaths, dtype='float')
for i in xrange(npaths):
mean[i] = np.mean(fx[(i * self.__n):((i + 1) * self.__n)]) # * vol
return mean