from matplotlib import pyplot as plt from openturns.viewer import View # Create the time grid # In the context of the spectral estimate or Fourier transform use, # we use data blocs with size of form 2^p tMin = 0. timeStep = 0.1 size = pow(2, 12) myTimeGrid = ot.RegularGrid(tMin, timeStep, size) # We fix the parameter of the Cauchy model amplitude = [5] scale = [3] model = ot.CauchyModel(scale, amplitude) gp = ot.SpectralGaussianProcess(model, myTimeGrid) # Get a time series or a sample of time series # myTimeSeries = gp.getRealization() mySample = gp.getSample(1000) mySegmentNumber = 10 myOverlapSize = 0.3 # Build a spectral model factory myFactory = ot.WelchFactory(ot.Hanning(), mySegmentNumber, myOverlapSize) # Estimation on a TimeSeries or on a ProcessSample # myEstimatedModel_TS = myFactory.build(myTimeSeries) myEstimatedModel_PS = myFactory.buildAsUserDefinedSpectralModel(mySample)
# %% # generate some data # Create the time grid # In the context of the spectral estimate or Fourier transform use, # we use data blocs with size of form 2^p tMin = 0. tstep = 0.1 size = 2**12 tgrid = ot.RegularGrid(tMin, tstep, size) # We fix the parameter of the Cauchy model amplitude = [5.0] scale = [3.0] model = ot.CauchyModel(amplitude, scale) process = ot.SpectralGaussianProcess(model, tgrid) # Get a time series or a sample of time series tseries = process.getRealization() sample = process.getSample(1000) # %% # Build a spectral model factory segmentNumber = 10 overlapSize = 0.3 factory = ot.WelchFactory(ot.Hann(), segmentNumber, overlapSize) # %% # Estimation on a TimeSeries or on a ProcessSample estimatedModel_TS = factory.build(tseries) estimatedModel_PS = factory.build(sample)
from matplotlib import pyplot as plt from openturns.viewer import View # Create the time grid # In the context of the spectral estimate or Fourier transform use, # we use data blocs with size of form 2^p tMin = 0. timeStep = 0.1 size = pow(2, 12) myTimeGrid = ot.RegularGrid(tMin, timeStep, size) # We fix the parameter of the Cauchy model amplitude = [5] scale = [3] model = ot.ExponentialCauchy(scale, amplitude) myNormalProcess = ot.SpectralGaussianProcess(model, myTimeGrid) # Get a time series or a sample of time series # myTimeSeries = myNormalProcess.getRealization() mySample = myNormalProcess.getSample(1000) mySegmentNumber = 10 myOverlapSize = 0.3 # Build a spectral model factory myFactory = ot.WelchFactory(ot.Hanning(), mySegmentNumber, myOverlapSize) # Estimation on a TimeSeries or on a ProcessSample # myEstimatedModel_TS = myFactory.build(myTimeSeries) myEstimatedModel_PS = myFactory.buildAsUserDefinedSpectralModel(mySample)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.SpectralGaussianProcess().__class__.__name__ == 'Process':
# default to Gaussian for the interface class
process = ot.GaussianProcess()
elif ot.SpectralGaussianProcess().__class__.__name__ == 'DiscreteMarkovChain':
process = ot.SpectralGaussianProcess()
process.setTransitionMatrix(
ot.SquareMatrix([[0.0, 0.5, 0.5], [0.7, 0.0, 0.3], [0.8, 0.0, 0.2]]))
origin = 0
process.setOrigin(origin)
else:
process = ot.SpectralGaussianProcess()
process.setTimeGrid(ot.RegularGrid(0.0, 0.02, 50))
process.setDescription(['$x$'])
sample = process.getSample(6)
sample_graph = sample.drawMarginal(0)
sample_graph.setTitle(str(process))
fig = plt.figure(figsize=(10, 4))
sample_axis = fig.add_subplot(111)
View(sample_graph, figure=fig, axes=[sample_axis], add_legend=False)
# In this paragraph we build a gaussian process from its spectral density.
#
# %%
# We first define a spectral model :
amplitude = [1.0, 2.0]
scale = [4.0, 5.0]
spatialCorrelation = ot.CorrelationMatrix(2)
spatialCorrelation[0, 1] = 0.8
mySpectralModel = ot.CauchyModel(scale, amplitude, spatialCorrelation)
# %%
# As usual we define a mesh,
myTimeGrid = ot.RegularGrid(0.0, 0.1, 20)
# %%
# and create the process thereafter
process = ot.SpectralGaussianProcess(mySpectralModel, myTimeGrid)
print(process)
# %%
# Eventually we draw the first marginal of a sample of size 6 :
sample = process.getSample(6)
graph = sample.drawMarginal(0)
graph.setTitle("First marginal of six realizations of the process")
view = viewer.View(graph)
# %%
# Display figures
plt.show()
import openturns as ot from matplotlib import pyplot as plt from openturns.viewer import View process = ot.SpectralGaussianProcess() process.setTimeGrid(ot.RegularGrid(0.0, 0.02, 50)) process.setDescription(['$x$']) sample = process.getSample(6) sample_graph = sample.drawMarginal(0) fig = plt.figure(figsize=(10, 4)) plt.suptitle(str(process)) sample_axis = fig.add_subplot(111) View(sample_graph, figure=fig, axes=[sample_axis], add_legend=False)