from math import exp 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)
view = viewer.View(graph)
# %%
# Create a gaussian process from spectral density
# -----------------------------------------------
#
# 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")
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
spectralModel = ot.CauchyModel()
if spectralModel.getInputDimension() == 1:
spec_graph = spectralModel.draw(0, 0, True)
spec_graph.setXTitle('f')
spec_graph.setYTitle('Spectral Density')
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(spectralModel))
spec_axis = fig.add_subplot(111)
View(spec_graph, figure=fig, axes=[spec_axis], add_legend=False)
# %% import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) # %% # 1. Define a spectral density function from correlation matrix amplitude = [1.0, 2.0, 3.0] scale = [4.0, 5.0, 6.0] spatialCorrelation = ot.CorrelationMatrix(3) spatialCorrelation[0, 1] = 0.8 spatialCorrelation[0, 2] = 0.6 spatialCorrelation[1, 2] = 0.1 spectralModel_Corr = ot.CauchyModel(amplitude, scale, spatialCorrelation) spectralModel_Corr # %% # 2. Define a spectral density function from a covariance matrix spatialCovariance = ot.CovarianceMatrix(3) spatialCovariance[0, 0] = 4.0 spatialCovariance[1, 1] = 5.0 spatialCovariance[2, 2] = 6.0 spatialCovariance[0, 1] = 1.2 spatialCovariance[0, 2] = 0.9 spatialCovariance[1, 2] = -0.2 spectralModel_Cov = ot.CauchyModel(scale, spatialCovariance) spectralModel_Cov