def writeCheckpoints(self, filename):
ts = self.__uqManager.getTimeStepsOfInterest()
names = self.__params.getNames()
names.append('f_\\mathcal{I}(x)')
for iteration in range(self.__knowledge.getIteration() + 1):
# myjson = {"Grid": {"dimNames": ["E", "K_1c", "rho", "n"],
# "matrixEntries": ["E", "K_1c", "rho", "n"]},
# "Set": {"path": "",
# "grids": [],
# "alphas": [],
# "paramValues": list(ts),
# "paramName": "Time"}}
myjson = {
"Grid": {
"dimNames": ["phi", "e", "K_L"],
"matrixEntries": ["phi", "e", "K_L"]
},
"Set": {
"path": "",
"grids": [],
"alphas": [],
"paramValues": list(ts),
"paramName": "Time"
}
}
for t in ts:
grid, surplus = self.__knowledge.getSparseGridFunction(
self._qoi, t, iteration=iteration)
out = "%s.t%f.i%i" % (filename, t, iteration)
out_grid = "%s.grid" % out
out_alpha = "%s.alpha.arff" % out
writeGrid(out_grid, grid)
writeAlphaARFF(out_alpha, surplus)
# collect information for json
myjson["Set"]["grids"].append(os.path.abspath(out_grid))
myjson["Set"]["alphas"].append(os.path.abspath(out_alpha))
# write json to file
fd = open("%s.%i.json" % (filename, iteration), "w")
json.dump(myjson, fd, indent=2)
fd.close()
def writeCheckpoints(self, filename):
ts = self.__learner.getTimeStepsOfInterest()
names = self.__params.getNames()
names.append('f_\\mathcal{I}(x)')
for iteration in xrange(self.__knowledge.getIteration() + 1):
# myjson = {"Grid": {"dimNames": ["E", "K_1c", "rho", "n"],
# "matrixEntries": ["E", "K_1c", "rho", "n"]},
# "Set": {"path": "",
# "grids": [],
# "alphas": [],
# "paramValues": list(ts),
# "paramName": "Time"}}
myjson = {"Grid": {"dimNames": ["phi", "e", "K_L"],
"matrixEntries": ["phi", "e", "K_L"]},
"Set": {"path": "",
"grids": [],
"alphas": [],
"paramValues": list(ts),
"paramName": "Time"}}
for t in ts:
grid, surplus = self.__knowledge.getSparseGridFunction(self._qoi, t,
iteration=iteration)
out = "%s.t%f.i%i" % (filename, t, iteration)
out_grid = "%s.grid" % out
out_alpha = "%s.alpha.arff" % out
writeGrid(out_grid, grid)
writeAlphaARFF(out_alpha, surplus)
# collect information for json
myjson["Set"]["grids"].append(os.path.abspath(out_grid))
myjson["Set"]["alphas"].append(os.path.abspath(out_alpha))
# write json to file
fd = open("%s.%i.json" % (filename, iteration), "w")
json.dump(myjson, fd, indent=2)
fd.close()
def computeHierarchicalCoefficients(self,
grid,
alpha,
addedGridPoints=None):
nodalValues = dehierarchize(grid, alpha)
ixs = np.array([], dtype="int")
for i, yi in enumerate(nodalValues):
if yi < 0:
ixs = np.append(ixs, i)
nodalValues[i] = 0.0
if len(ixs) > 0:
# compute the coefficients for each grid point by estimating
# the local density
config = {
'grid_filename': "positive.grid",
"regularization_type": "Laplace",
"crossValidation_enable": True,
"crossValidation_enable": True,
"crossValidation_kfold": 5,
"crossValidation_silent": True
}
writeGrid(config['grid_filename'], grid)
alpha = SGDEdist.byLearnerSGDEConfig(self.trainSamples.array(),
bounds=None,
config=config).alpha.array()
# check if the coefficients of the new grid points are positive
if addedGridPoints is not None:
gs = grid.getStorage()
assert all([
alpha[gs.getSequenceNumber(gp)] > -1e-13
for gp in addedGridPoints
])
return alpha
def estimateSGDEDensity(functionName,
trainSamples,
testSamples=None,
bounds=None,
iteration=0,
plot=False,
out=True,
label="sgde_zero",
candidates="intersections",
interpolation="setToZero"):
print("train: %i x %i (mean=%g, var=%g)" %
(trainSamples.shape[0], trainSamples.shape[1], np.mean(trainSamples),
np.var(trainSamples)))
if testSamples is not None:
print("test : %i x %i (mean=%g, var=%g)" %
(testSamples.shape[0], testSamples.shape[1],
np.mean(testSamples), np.var(testSamples)))
candidateSearchAlgorithm = strToCandidateSearchAlgorithm(candidates)
interpolationAlgorithm = strToInterpolationAlgorithm(interpolation)
results = {}
crossEntropies = {}
config = {
"grid_level": 1,
"grid_type": "linear",
"grid_maxDegree": 1,
"refinement_numSteps": 0,
"refinement_numPoints": 3,
"solver_threshold": 1e-10,
"solver_verbose": False,
"regularization_type": "Laplace",
"crossValidation_enable": True,
"crossValidation_kfold": 5,
"crossValidation_silent": True,
"sgde_makePositive": False
}
pathResults = os.path.join("data", label)
key = 1
bestCV = float("Inf")
bestDist = None
# stats
stats = {
'config': {
'functionName': functionName,
'numDims': 2,
'adaptive': True,
'refnums': 0,
'consistentGrid': True,
'candidateSearchAlgorithm': candidates,
'interpolationAlgorithm': interpolation,
'maxNumGridPoints': 0,
'iteration': iteration
},
'trainSamples': trainSamples,
'testSamples': testSamples
}
for level in range(2, 7):
print("-" * 60)
print("l=%i" % level)
for refinementSteps in range(0, 5):
config["grid_level"] = level
config["refinement_numSteps"] = refinementSteps
sgdeDist = SGDEdist.byLearnerSGDEConfig(trainSamples,
config=config,
bounds=bounds)
# -----------------------------------------------------------
grid, alpha = sgdeDist.grid, sgdeDist.alpha
cvSgde = sgdeDist.crossEntropy(testSamples)
maxLevel = grid.getStorage().getMaxLevel()
numDims = grid.getStorage().getDimension()
print(" " + "-" * 30)
print(" #ref = %i: gs=%i -> CV test = %g" %
(refinementSteps, sgdeDist.grid.getSize(), cvSgde))
# -----------------------------------------------------------
# make it positive
positiveGrid = grid.clone()
positiveAlpha_vec = DataVector(alpha)
opPositive = createOperationMakePositive(candidateSearchAlgorithm,
interpolationAlgorithm,
True, False)
opPositive.makePositive(positiveGrid, positiveAlpha_vec, True)
# scale to unit integrand
positiveAlpha = positiveAlpha_vec.array()
positiveSgdeDist = SGDEdist(positiveGrid,
positiveAlpha,
trainSamples,
bounds=bounds)
# -----------------------------------------------------------
cvPositiveSgde = positiveSgdeDist.crossEntropy(testSamples)
if plot and numDims == 2:
fig = plt.figure()
plotSG2d(grid,
alpha,
show_negative=True,
show_grid_points=True)
plt.title("pos: N=%i: vol=%g, log=%g" %
(positiveGrid.getSize(),
doQuadrature(positiveGrid,
positiveAlpha), cvPositiveSgde))
plt.tight_layout()
if out:
plt.savefig(
os.path.join(
pathResults, "%s_density_pos_i%i_l%i_r%i.jpg" %
(label, iteration, level, refinementSteps)))
plt.savefig(
os.path.join(
pathResults, "%s_density_pos_i%i_l%i_r%i.pdf" %
(label, iteration, level, refinementSteps)))
else:
plt.close(fig)
# -----------------------------------------------------------
print(" positive: gs=%i -> CV test = %g" %
(positiveGrid.getSize(), cvPositiveSgde))
# -----------------------------------------------------------
# select the best density available based on the given criterion
results[key] = {'config': config, 'dist': positiveSgdeDist}
crossEntropies[key] = cvPositiveSgde
key += 1
candidateSearch = opPositive.getCandidateSetAlgorithm()
if cvPositiveSgde < bestCV:
bestCV = cvPositiveSgde
bestDist = positiveSgdeDist
numComparisons = candidateSearch.costsComputingCandidates()
# update the stats -> just for the current best one
# write the stats of the current best results to the stats dict
C = np.ndarray(numDims - 1, dtype="int")
M = np.sum([1 for i in range(len(alpha)) if alpha[i] < 0])
for d in range(2, numDims + 1):
C[d - 2] = binom(M, d)
stats['config']['refnums'] = refinementSteps
stats['config']['adaptive'] = refinementSteps > 0
stats['negSGDE_json'] = sgdeDist.toJson()
stats['posSGDE_json'] = positiveSgdeDist.toJson()
stats['level'] = level
stats['maxLevel'] = maxLevel
stats['fullGridSize'] = (2**maxLevel - 1)**numDims
stats['sparseGridSize'] = grid.getSize()
stats['discretizedGridSize'] = positiveGrid.getSize()
stats['crossEntropyTrainZeroSGDE'] = sgdeDist.crossEntropy(
trainSamples)
stats[
'crossEntropyTrainDiscretizedSGDE'] = positiveSgdeDist.crossEntropy(
trainSamples)
stats['crossEntropyTestZeroSGDE'] = cvSgde
stats['crossEntropyTestDiscretizedSGDE'] = cvPositiveSgde
stats['numCandidates'] = int(candidateSearch.numCandidates())
stats['numCandidatesPerLevel'] = np.array(
candidateSearch.numCandidatesPerLevel().array(),
dtype="int")
stats['numCandidatesPerIteration'] = np.array(
candidateSearch.numCandidatesPerIteration().array(),
dtype="int")
stats[
'costsCandidateSearch'] = candidateSearch.costsComputingCandidates(
)
stats['costsCandidateSearchBinomial'] = int(C.sum())
stats['costsCandidateSearchPerIteration'] = np.array(
candidateSearch.costsComputingCandidatesPerIteration(
).array(),
dtype="int")
stats['costsCandidateSearchPerIterationBinomial'] = C
if plot and numDims == 2:
fig = plt.figure()
plotSG2d(
positiveGrid,
positiveAlpha,
show_negative=True,
show_grid_points=False,
colorbarLabel=
r"$f_{\mathcal{I}^\text{SG} \cup \mathcal{I}^\text{ext}}$"
)
plt.title(r"positive: $N=%i/%i$; \# comparisons$=%i$" %
(positiveGrid.getSize(),
(2**maxLevel - 1)**numDims, numComparisons))
plt.xlabel(r"$\xi_1$")
plt.ylabel(r"$\xi_2$")
# plt.title(r"N=%i $\rightarrow$ %i: log=%g $\rightarrow$ %g" % (sgdeDist.grid.getSize(),
# positiveSgdeDist.grid.getSize(),
# cvSgde,
# cvPositiveSgde))
plt.tight_layout()
plt.savefig(
os.path.join(
pathResults, "%s_pos_i%i_l%i_r%i.jpg" %
(label, iteration, level, refinementSteps)))
plt.savefig(
os.path.join(
pathResults, "%s_pos_i%i_l%i_r%i.pdf" %
(label, iteration, level, refinementSteps)))
if out:
plt.close(fig)
fig, ax, _ = plotSG3d(positiveGrid, positiveAlpha)
ax.set_zlabel(
r"$f_{\mathcal{I}^{\text{SG}} \cup \mathcal{I}^\text{ext}}(\xi_1, \xi_2)$",
fontsize=20)
ax.set_xlabel(r"$\xi_1$", fontsize=20)
ax.set_ylabel(r"$\xi_2$", fontsize=20)
plt.tight_layout()
plt.savefig(
os.path.join(
pathResults, "%s_pos_i%i_l%i_r%i_3d.jpg" %
(label, iteration, level, refinementSteps)))
plt.savefig(
os.path.join(
pathResults, "%s_pos_i%i_l%i_r%i_3d.pdf" %
(label, iteration, level, refinementSteps)))
if out:
plt.close(fig)
if plot and numDims == 2 and not out:
plt.show()
if out:
# save stats
filename = os.path.join(
"data", label, "stats_d%i_a%i_r%i_i%i_%s_%s.pkl" %
(numDims, 1, refinementSteps, iteration, candidates,
interpolation))
fd = open(filename, "w")
pkl.dump(stats, fd)
fd.close()
print("stats saved to -> '%s'" % filename)
# dictionary that stores the information on the estimated densities
myjson = {
"Grid": {
"dimNames": ["phi", "log(K_A)"],
"matrixEntries": ["phi", "log(K_A)"]
},
"Set": {
"path": "",
"grids": [],
"alphas": [],
"paramValues": [],
"paramName": "grid_size"
}
}
for key, result in list(results.items()):
config = result['config']
dist = result['dist']
# serialize grid and coefficients
out = "sgde.i%i.k%i.N%i" % (iteration, key, dist.grid.getSize())
out_grid = os.path.join(pathResults, "%s.grid" % out)
out_alpha = os.path.join(pathResults, "%s.alpha.arff" % out)
writeGrid(out_grid, dist.grid)
writeAlphaARFF(out_alpha, dist.alpha)
# collect information for json
myjson["Set"]["grids"].append(os.path.abspath(out_grid))
myjson["Set"]["alphas"].append(os.path.abspath(out_alpha))
myjson["Set"]["paramValues"].append(crossEntropies[key])
# -----------------------------------------------------------
# serialize the config
out_config = os.path.join(pathResults,
"sgde.i%i.k%i.config" % (iteration, key))
fd = open(out_config, "w")
json.dump(config, fd, ensure_ascii=True, indent=True)
fd.close()
crossEntropies[key] = (crossEntropies[key], out_grid, out_alpha,
out_config)
# sort the results in myjson according to the cross entropy
ixs = np.argsort(myjson["Set"]["paramValues"])
myjson["Set"]["grids"] = [myjson["Set"]["grids"][ix] for ix in ixs]
myjson["Set"]["alphas"] = [myjson["Set"]["alphas"][ix] for ix in ixs]
myjson["Set"]["paramValues"] = [
myjson["Set"]["paramValues"][ix] for ix in ixs
]
# serialize myjson
out_config = os.path.join(pathResults,
"sgde_visualization.i%i.config" % iteration)
fd = open(out_config, "w")
json.dump(myjson, fd, ensure_ascii=True, indent=True)
fd.close()
# serialize cross entropies
out_crossEntropies = os.path.join(
pathResults, "sgde_cross_entropies.i%i.csv" % iteration)
fd = open(out_crossEntropies, 'wb')
file_writer = csv.writer(fd)
file_writer.writerow(["crossEntropy", "grid", "alpha", "sgdeConfig"])
for out in list(crossEntropies.values()):
file_writer.writerow(out)
fd.close()
# serialize samples
np.savetxt(
os.path.join(pathResults,
"sgde_train_samples.i%i.csv" % iteration),
trainSamples)
np.savetxt(
os.path.join(pathResults, "sgde_test_samples.i%i.csv" % iteration),
testSamples)
# serialize best configuration to json
out_bestDist = os.path.join(pathResults,
"sgde_best_config.i%i.json" % iteration)
text = bestDist.toJson()
fd = open(out_bestDist, "w")
fd.write(text)
fd.close()
return bestDist, stats