# The number of observations within the data are obtained using the function # :func:`~FDApy.irregular_functional.IrregularFunctional.n_obs`. # Get the number of observations for the object print(cd4.n_obs) ############################################################################### # The number of sampling points per observation is given by the function # :func:`~FDApy.irregular_functional.IrregularFunctional.n_points`. # Retrieve the mean number of sampling points for the object print(cd4.n_points) ############################################################################### # The dimension of the data is given by the function # :func:`~FDApy.irregular_functional.IrregularFunctional.n_dim`. # Get the dimension of the domain of the observations print(cd4.n_dim) ############################################################################### # The extraction of observations is also easily done. # Extract observations from the object print(cd4[5:8]) ############################################################################### # Finally, we can plot the data. _ = plot(cd4)
# Print out an univariate functional data object. # Print univariate functional data print(temperature) ############################################################################### # Print out a multivariate functional data object. # Print multivariate functional data print(canadWeather) ############################################################################### # We can plot the data. # Plot the univariate functional data _ = plot(temperature) ############################################################################### # The attributs of the univariate functional data classes can easily be # accessed. ############################################################################### # The sampling points of the data can easily be accessed. # Accessing the argvals of the object print(precipitation.argvals) ############################################################################### # The number of observations within the data are obtained using the function # :func:`~FDApy.univariate_functional.UnivariateFunctional.n_obs`.
from FDApy.visualization.plot import plot
from FDApy.misc.loader import read_csv
###############################################################################
# Load the data into Pandas dataframe
temperature = read_csv('./data/canadian_temperature_daily.csv', index_col=0)
###############################################################################
# Perform a univariate functional PCA and explore the results.
# Perform a univariate FPCA on dailyTemp.
fpca = UFPCA(n_components=0.99)
fpca.fit(temperature)
# Plot the results of the FPCA (eigenfunctions)
_ = plot(fpca.eigenfunctions)
###############################################################################
# Compute the scores of the dailyTemp data into the eigenfunctions basis using
# numerical integration.
# Compute scores
temperature_proj = fpca.transform(temperature, method='NumInt')
# Plot the projection of the data onto the eigenfunctions
_ = pd.plotting.scatter_matrix(pd.DataFrame(temperature_proj), diagonal='kde')
###############################################################################
# Then, we can test if the reconstruction of the data is good.
# Test if the reconstruction is good.
from FDApy.representation.simulation import Brownian from FDApy.visualization.plot import plot ############################################################################### # Generate some data as Fractional Brownian motion. # # Simulate some fractional brownian motions. brownian = Brownian(name='standard') brownian.new(n_obs=1000, argvals=np.linspace(0, 1, 301)) brownian.add_noise(0.05) # Plot some simulations _ = plot(brownian.noisy_data) ############################################################################### # Now, we will smooth the data according the methodology from (add ref). # # Smooth the data data_smooth = brownian.noisy_data.smooth(points=0.5, neighborhood=14) # Plot of the smoothing data _ = plot(data_smooth) ############################################################################### # In order to look more precisely at the smoothing results, let's plot one # individual curve, along its noisy and smoothed version. #
# License: MIT
# shinx_gallery_thumbnail_number = 2
import numpy as np
from FDApy.representation.simulation import Brownian, KarhunenLoeve
from FDApy.visualization.plot import plot
###############################################################################
# Now, we will simulate some curves data using the Karhunen-Loève expansion.
#
kl = KarhunenLoeve(name='bsplines', n_functions=5)
kl.new(n_obs=100, argvals=np.linspace(0, 1, 301))
_ = plot(kl.data)
###############################################################################
# We can also add some noise to the data.
#
# First, we consider homoscedastic noise. Thus, we add realizations of the
# random variable :math:`\varepsilon \sim \mathcal{N}(0, \sigma^2)` to the
# data.
#
# Add some noise to the simulation.
kl.add_noise(0.05)
# Plot the noisy simulations
_ = plot(kl.noisy_data)
index_col=0)
temperature = read_csv('./data/canadian_temperature_daily.csv', index_col=0)
# Create multivariate functional data for the Canadian weather data.
canadWeather = MultivariateFunctionalData([precipitation, temperature])
###############################################################################
# Perform a multivariate functional PCA and explore the results.
# Perform multivariate FPCA
mfpca = MFPCA(n_components=[0.99, 0.95])
mfpca.fit(canadWeather, method='NumInt')
# Plot the results of the FPCA (eigenfunctions)
fig, (ax1, ax2) = plt.subplots(1, 2)
_ = plot(mfpca.basis[0], ax=ax1)
_ = plot(mfpca.basis[1], ax=ax2)
###############################################################################
# Compute the scores of the dailyTemp data into the eigenfunctions basis using
# numerical integration.
# Compute the scores
canadWeather_proj = mfpca.transform(canadWeather)
# Plot the projection of the data onto the eigenfunctions
_ = pd.plotting.scatter_matrix(pd.DataFrame(canadWeather_proj), diagonal='kde')
###############################################################################
# Then, we can test if the reconstruction of the data is good.