distKDE = analysis.estimateDensity(dtype="gaussianKDE")
config = {
"grid_level": 6,
"grid_type": "Linear",
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"regularization_type": "Laplace",
"crossValidation_lambda": 3.16228e-06,
"crossValidation_enable": True,
"crossValidation_kfold": 5,
"crossValidation_silent": False
}
distSGDE = analysis.estimateDensity(dtype="sgde", config=config)
print("mean(u) = %g ~ %g (KDE) ~ %g (SGDE)" %
(analysis.mean()[0], distKDE.mean(), distSGDE.mean()))
print("var(u) = %g ~ %g (KDE) ~ %g (SGDE)" %
(analysis.var()[0], distKDE.var(), distSGDE.var()))
# ---------------------------------------------------------------------------
y = analysis.eval(analysis.generateUnitSamples())
fig = plt.figure()
plotDensity1d(distSGDE, label="SGDE", linewidth=3)
plt.vlines(distSGDE.mean(),
0,
distSGDE.pdf(distSGDE.mean()),
linewidth=3,
color="red")
plt.vlines(distSGDE.mean() - distSGDE.std(),
0,
distSGDE.pdf(distSGDE.mean() - distSGDE.std()),
def testAnova(self):
# ----------------------------------------------------------
# define the learner
# ----------------------------------------------------------
# define UQ setting
builder = ASGCUQManagerBuilder()
builder.withParameters(self.params)\
.withTypesOfKnowledge([KnowledgeTypes.SIMPLE,
KnowledgeTypes.SQUARED,
KnowledgeTypes.EXPECTATIONVALUE])\
.useInterpolation()
builder.defineUQSetting().withSimulation(self.simulation)
samplerSpec = builder.defineSampler()
samplerSpec.withGrid().hasType(GridType_PolyBoundary)\
.withLevel(4)\
.withDegree(5)\
.withBoundaryLevel(1)
# ----------------------------------------------------------
# discretize the stochastic space with the ASGC method
# ----------------------------------------------------------
uqManager = builder.andGetResult()
# ----------------------------------------------
# first run
while uqManager.hasMoreSamples():
uqManager.runNextSamples()
# ----------------------------------------------------------
# specify ASGC estimator
# ----------------------------------------------------------
analysis = ASGCAnalysisBuilder().withUQManager(uqManager)\
.withAnalyticEstimationStrategy()\
.andGetResult()
# ----------------------------------------------------------
# expectation values and variances
_, _ = analysis.mean(), analysis.var()
# ----------------------------------------------------------
# estimated anova decomposition
anova = analysis.getAnovaDecomposition(nk=len(self.params))
# ----------------------------------------------------------
# check interpolation and decomposition
m = np.random.rand(100, self.params.getDim())
for i in range(m.shape[0]):
self.assertTrue(abs(analysis.eval(m[i, :]) - anova.eval(m[i, :])) < 1e-14)
# ----------------------------------------------------------
# main effects
me = anova.getSobolIndices()
print("-------------- Sobol Indices (t = %i) ------------------" % 1)
for (key, val) in sorted(me.items()):
print("%s: %s" % (key, val))
print(sum([val for val in list(me.values())]), "==", 1)
# ----------------------------------------------------------
# total effects
te = anova.getTotalEffects()
print("-------------- Total Effects (t = %i) -----------------" % 1)
for key, val in sorted(te.items()):
print("%s: %s" % (key, val))
print("---------------------------------------------")
print()
names = anova.getSortedPermutations(list(me.keys()))
values = [me[name] for name in names]
fig, _ = plotSobolIndices(values, legend=True, names=names)
fig.show()
plt.show()
def run_adaptive_sparse_grid(self, gridType, level, maxGridSize, refinement,
boundaryLevel=None, isFull=False, out=False,
plot=False):
test_samples, test_values = self.getTestSamples()
# ----------------------------------------------------------
# define the learner
# ----------------------------------------------------------
uqManager = TestEnvironmentSG().buildSetting(self.params,
self.simulation,
level,
gridType,
deg=20,
maxGridSize=maxGridSize,
isFull=isFull,
adaptive=refinement,
adaptPoints=10,
adaptRate=0.05,
epsilon=1e-10,
boundaryLevel=boundaryLevel)
# ----------------------------------------------
# first run
while uqManager.hasMoreSamples():
uqManager.runNextSamples()
# ----------------------------------------------------------
# specify ASGC estimator
# ----------------------------------------------------------
analysis = ASGCAnalysisBuilder().withUQManager(uqManager)\
.withAnalyticEstimationStrategy()\
.andGetResult()
analysis.setVerbose(False)
# ----------------------------------------------------------
# expectation values and variances
sg_mean, sg_var = analysis.mean(), analysis.var()
stats = {}
iterations = uqManager.getKnowledge().getAvailableIterations()
for k, iteration in enumerate(iterations):
# ----------------------------------------------------------
# estimated anova decomposition
anova = analysis.getAnovaDecomposition(iteration=iteration,
nk=len(self.params))
# estimate the l2 error
grid, alpha = uqManager.getKnowledge().getSparseGridFunction(iteration=iteration)
test_values_pred = evalSGFunction(grid, alpha, test_samples)
l2test, l1test, maxErrorTest, meanError, varError = \
self.getErrors(test_values, test_values_pred,
sg_mean[iteration][0], sg_var[iteration][0])
# ----------------------------------------------------------
# main effects
sobol_indices = anova.getSobolIndices()
total_effects = computeTotalEffects(sobol_indices)
print("-" * 60)
print("iteration=%i, N=%i" % (iteration, grid.getSize()))
print("E[x] = %g ~ %g (err=%g)" % (self.E_ana[0], sg_mean[iteration]["value"],
np.abs(self.E_ana[0] - sg_mean[iteration]["value"])))
print("V[x] = %g ~ %g (err=%g)" % (self.V_ana[0], sg_var[iteration]["value"],
np.abs(self.V_ana[0] - sg_var[iteration]["value"])))
stats[grid.getSize()] = {'num_model_evaluations': grid.getSize(),
'l2test': l2test,
'l1test': l1test,
'maxErrorTest': maxErrorTest,
'mean_error': meanError,
'var_error': varError,
'mean_estimated': sg_mean[iteration]["value"],
'var_estimated': sg_var[iteration]["value"],
'sobol_indices_estimated': sobol_indices,
'total_effects_estimated': total_effects}
if plot:
self.plotResultsSG(grid, alpha, level,
maxGridSize, refinement,
iteration, out)
if out:
# store results
filename = os.path.join(self.pathResults,
"%s_%s_d%i_%s_l%i_Nmax%i_r%s_N%i.pkl" % (self.radix,
"sg" if not isFull else "fg",
self.numDims,
grid.getTypeAsString(),
level,
maxGridSize,
refinement,
grid.getSize()))
fd = open(filename, "w")
pkl.dump({'surrogate': 'sg',
'model': "full" if self.numDims == 4 else "reduced",
'num_dims': self.numDims,
'grid_type': grid.getTypeAsString(),
'level': level,
'max_grid_size': maxGridSize,
'is_full': isFull,
'refinement': refinement,
'mean_analytic': self.E_ana[0],
'var_analytic': self.V_ana[0],
'results': stats},
fd)
fd.close()
def run_regular_sparse_grid(self, gridType, level, maxGridSize,
boundaryLevel=1,
isFull=False,
out=False,
plot=False):
np.random.seed(1234567)
test_samples, test_values = self.getTestSamples()
stats = {}
while True:
print("-" * 80)
print("level = %i" % level)
uqManager = TestEnvironmentSG().buildSetting(self.params,
self.simulation,
level,
gridType,
deg=20,
maxGridSize=maxGridSize,
isFull=isFull,
boundaryLevel=boundaryLevel)
if uqManager.sampler.getSize() > maxGridSize:
print("DONE: %i > %i" % (uqManager.sampler.getSize(), maxGridSize))
break
# ----------------------------------------------
# first run
while uqManager.hasMoreSamples():
uqManager.runNextSamples()
# ----------------------------------------------------------
# specify ASGC estimator
analysis = ASGCAnalysisBuilder().withUQManager(uqManager)\
.withAnalyticEstimationStrategy()\
.andGetResult()
analysis.setVerbose(False)
# ----------------------------------------------------------
# expectation values and variances
sg_mean, sg_var = analysis.mean(), analysis.var()
# ----------------------------------------------------------
# estimate the l2 error
grid, alpha = uqManager.getKnowledge().getSparseGridFunction()
test_values_pred = evalSGFunction(grid, alpha, test_samples)
l2test, l1test, maxErrorTest, meanError, varError = \
self.getErrors(test_values, test_values_pred,
sg_mean["value"], sg_var["value"])
print("-" * 60)
print("test: |.|_2 = %g" % l2test)
print("E[x] = %g ~ %g (err=%g)" % (self.E_ana[0], sg_mean["value"],
np.abs(self.E_ana[0] - sg_mean["value"])))
print("V[x] = %g ~ %g (err=%g)" % (self.V_ana[0], sg_var["value"],
np.abs(self.V_ana[0] - sg_var["value"])))
# ----------------------------------------------------------
# estimated anova decomposition
if self.inputSpace != "sgde":
anova = analysis.getAnovaDecomposition(nk=len(self.params))
sobol_indices = anova.getSobolIndices()
total_effects = computeTotalEffects(sobol_indices)
else:
sobol_indices = {}
total_effects = {}
# ----------------------------------------------------------
stats[level] = {'num_model_evaluations': grid.getSize(),
'l2test': l2test,
'l1test': l1test,
'maxErrorTest': maxErrorTest,
'mean_error': meanError,
'var_error': varError,
'mean_estimated': sg_mean["value"],
'var_estimated': sg_var["value"],
'sobol_indices_estimated': sobol_indices,
'total_effects_estimated': total_effects}
if plot:
self.plotResultsSG(grid, alpha, level, maxGridSize, False, 0, out)
level += 1
if out:
# store results
filename = os.path.join(self.pathResults,
"%s_%s_d%i_%s_Nmax%i_r%i_N%i.pkl" % (self.radix,
"sg" if not isFull else "fg",
self.numDims,
grid.getTypeAsString(),
maxGridSize,
False,
grid.getSize()))
fd = open(filename, "w")
pkl.dump({'surrogate': 'sg',
'num_dims': self.numDims,
'grid_type': grid.getTypeAsString(),
'max_grid_size': maxGridSize,
'level': level,
'boundaryLevel': boundaryLevel,
'is_full': isFull,
'refinement': False,
'mean_analytic': self.E_ana[0],
'var_analytic': self.V_ana[0],
'results': stats},
fd)
fd.close()
def run_sparse_grids(self,
gridType,
level,
maxGridSize,
isFull,
refinement=None,
out=False):
# ----------------------------------------------------------
# define the learner
# ----------------------------------------------------------
uqManager = TestEnvironmentSG().buildSetting(self.params,
self.simulation,
level,
gridType,
deg=10,
maxGridSize=maxGridSize,
isFull=isFull,
adaptive=refinement,
adaptPoints=3,
epsilon=1e-3)
# ----------------------------------------------
# first run
while uqManager.hasMoreSamples():
uqManager.runNextSamples()
# ----------------------------------------------------------
# specify ASGC estimator
# ----------------------------------------------------------
analysis = ASGCAnalysisBuilder().withUQManager(uqManager)\
.withAnalyticEstimationStrategy()\
.andGetResult()
# ----------------------------------------------------------
# expectation values and variances
sg_mean, sg_var = analysis.mean(), analysis.var()
print("-" * 60)
print("V[x] = %g ~ %s" % (self.var, sg_var))
iterations = uqManager.getKnowledge().getAvailableIterations()
stats = [None] * len(iterations)
for k, iteration in enumerate(iterations):
# ----------------------------------------------------------
# estimated anova decomposition
anova = analysis.getAnovaDecomposition(iteration=iteration,
nk=len(self.params))
# estimate the l2 error
test_samples = np.random.random((1000, self.effectiveDims))
test_values = np.ndarray(1000)
for i, sample in enumerate(test_samples):
test_values[i] = self.simulation(sample)
grid, alpha = uqManager.getKnowledge().getSparseGridFunction()
test_values_pred = evalSGFunction(grid, alpha, test_samples)
l2test = np.sqrt(np.mean(test_values - test_values_pred)**2)
# ----------------------------------------------------------
# main effects
sobol_indices = anova.getSobolIndices()
total_effects = computeTotalEffects(sobol_indices)
stats[k] = {
'num_model_evaluations': grid.getSize(),
'l2test': l2test,
'var_estimated': sg_var[0],
'var_analytic': self.var,
'sobol_indices_estimated': sobol_indices,
'total_effects_estimated': total_effects
}
if out:
# store results
filename = os.path.join(
"results", "%s_%s_d%i_%s_l%i_Nmax%i_%s_N%i.pkl" %
(self.radix, "sg" if not isFull else "fg", self.effectiveDims,
grid.getTypeAsString(), level, maxGridSize, refinement,
grid.getSize()))
fd = open(filename, "w")
pkl.dump(
{
'surrogate': 'sg',
'model': "full" if self.effectiveDims == 4 else "reduced",
'num_dims': self.effectiveDims,
'grid_type': grid.getTypeAsString(),
'level': level,
'max_grid_size': maxGridSize,
'is_full': isFull,
'refinement': refinement,
'sobol_indices_analytic': self.sobol_indices,
'total_effects_analytic': self.total_effects,
'results': stats
}, fd)
fd.close()
return sobol_indices, grid.getSize()
def run_regular_sparse_grid(self,
gridTypeStr,
level,
maxGridSize,
boundaryLevel=1,
out=False):
np.random.seed(1234567)
test_samples, test_values = self.getTestSamples()
gridType = Grid.stringToGridType(gridTypeStr)
stats = {}
while True:
print("-" * 80)
print("level = %i, boundary level = %i" % (level, boundaryLevel))
print("-" * 80)
uqManager = TestEnvironmentSG().buildSetting(
self.params,
self.simulation,
level,
gridType,
deg=20,
maxGridSize=maxGridSize,
boundaryLevel=min(level, boundaryLevel),
knowledgeTypes=[KnowledgeTypes.SIMPLE])
if uqManager.sampler.getSize() > maxGridSize:
print("DONE: %i > %i" %
(uqManager.sampler.getSize(), maxGridSize))
break
# ----------------------------------------------
# first run
while uqManager.hasMoreSamples():
uqManager.runNextSamples()
# ----------------------------------------------------------
if False:
grid, alpha = uqManager.knowledge.getSparseGridFunction()
samples = DataMatrix(grid.getSize(), self.numDims)
grid.getStorage().getCoordinateArrays(samples)
samples = self.dist.ppf(samples.array())
fig = plt.figure()
plotFunction2d(self.simulation,
color_bar_label=r"$u(\xi_1, \xi_2)$")
plt.scatter(
samples[:, 0],
samples[:, 1],
color=load_color(3),
label=r"SG (CC-bound., $\ell=%i, \ell^{\text{b}}=%i$)" %
(level, boundaryLevel))
plt.xlabel(r"$\xi_1$")
plt.xlabel(r"$\xi_2$")
lgd = insert_legend(fig, loc="bottom", ncol=1)
savefig(fig,
"plots/genz_with_grid_l%i_b%i" %
(level, boundaryLevel),
lgd,
tikz=False)
# ----------------------------------------------------------
# specify ASGC estimator
analysis = ASGCAnalysisBuilder().withUQManager(uqManager)\
.withMonteCarloEstimationStrategy(n=1000,
npaths=10)\
.andGetResult()
analysis.setVerbose(False)
# ----------------------------------------------------------
# expectation values and variances
sg_mean, sg_var = analysis.mean(), analysis.var()
# ----------------------------------------------------------
# estimate the l2 error
grid, alpha = uqManager.getKnowledge().getSparseGridFunction()
test_values_pred = evalSGFunction(grid, alpha, test_samples)
l2test, l1test, maxErrorTest = \
self.getErrors(test_values, test_values_pred)
print("-" * 60)
print("test: |.|_2 = %g" % l2test)
# ----------------------------------------------------------
stats[level] = {
'num_model_evaluations': grid.getSize(),
'l2test': l2test,
'l1test': l1test,
'maxErrorTest': maxErrorTest,
'mean_estimated': sg_mean["value"],
'var_estimated': sg_var["value"]
}
level += 1
if out:
# store results
radix = "%s_sg_d%i_%s_Nmax%i_N%i_b%i" % (
self.radix, self.numDims, grid.getTypeAsString(), maxGridSize,
grid.getSize(), boundaryLevel)
if self.rosenblatt:
radix += "_rosenblatt"
filename = os.path.join(self.pathResults, "%s.pkl" % radix)
fd = open(filename, "w")
pkl.dump(
{
'surrogate': 'sg',
'num_dims': self.numDims,
'grid_type': grid.getTypeAsString(),
'max_grid_size': maxGridSize,
'is_full': False,
'refinement': False,
'rosenblatt': self.rosenblatt,
'boundaryLevel': boundaryLevel,
'results': stats
}, fd)
fd.close()
def run_regular_sparse_grid_boundary(self,
gridTypeStr,
level,
maxGridSize,
boundaryLevel=1,
out=False):
np.random.seed(1234567)
test_samples, test_values = self.getTestSamples()
gridType = Grid.stringToGridType(gridTypeStr)
stats = {}
while boundaryLevel <= level:
print("-" * 80)
print("level = %i, boundary level = %i" % (level, boundaryLevel))
print("-" * 80)
uqManager = TestEnvironmentSG().buildSetting(
self.params,
self.simulation,
level,
gridType,
deg=20,
maxGridSize=maxGridSize,
boundaryLevel=boundaryLevel,
knowledgeTypes=[KnowledgeTypes.SIMPLE])
# ----------------------------------------------
# first run
while uqManager.hasMoreSamples():
uqManager.runNextSamples()
# ----------------------------------------------------------
# specify ASGC estimator
analysis = ASGCAnalysisBuilder().withUQManager(uqManager)\
.withMonteCarloEstimationStrategy(n=1000,
npaths=10)\
.andGetResult()
analysis.setVerbose(False)
# ----------------------------------------------------------
# expectation values and variances
sg_mean, sg_var = analysis.mean(), analysis.var()
# ----------------------------------------------------------
# estimate the l2 error
grid, alpha = uqManager.getKnowledge().getSparseGridFunction()
test_values_pred = evalSGFunction(grid, alpha, test_samples)
l2test, l1test, maxErrorTest = \
self.getErrors(test_values, test_values_pred)
print("-" * 60)
print("test: |.|_2 = %g" % l2test)
# ----------------------------------------------------------
# ----------------------------------------------------------
stats[boundaryLevel] = {
'num_model_evaluations': grid.getSize(),
'l2test': l2test,
'l1test': l1test,
'maxErrorTest': maxErrorTest,
'mean_estimated': sg_mean["value"],
'var_estimated': sg_var["value"]
}
boundaryLevel += 1
if out:
# store results
filename = os.path.join(
self.pathResults, "%s_sg_d%i_%s_Nmax%i_N%i_b%i.pkl" %
(self.radix, self.numDims, grid.getTypeAsString(), maxGridSize,
grid.getSize(), boundaryLevel))
fd = open(filename, "w")
pkl.dump(
{
'surrogate': 'sg',
'num_dims': self.numDims,
'grid_type': grid.getTypeAsString(),
'max_grid_size': maxGridSize,
'is_full': False,
'refinement': False,
'results': stats
}, fd)
fd.close()