Representation of multivariate functional data

Examples of representation of multivariate functional data.

# Author: Steven Golovkine <steven_golovkine@icloud.com>
# License: MIT

# Load packages
import numpy as np

from FDApy import (
    DenseFunctionalData,
    IrregularFunctionalData,
    MultivariateFunctionalData,
)
from FDApy.representation import DenseArgvals, IrregularArgvals
from FDApy.representation import DenseValues, IrregularValues
from FDApy.visualization import plot_multivariate

The representation of multivariate functional data

Multivariate functional data are defined as a list of univariate functional data. The univariate functional data can be of whatever dimension (curves, surfaces, …) and dense or irregular. There is no restriction on the number of elements in the list but each univariate element must have the same number of observations.

First example

First, we will define two univariate unidimensional dense functional data. By putting them as a list, we can define a MultivariateFunctionalData object.

argvals = np.linspace(0, np.pi, num=100)
X = np.array([np.sin(2 * np.pi * argvals), np.cos(2 * np.pi * argvals)])
fdata_first = DenseFunctionalData(
    argvals=DenseArgvals({"input_dim_0": argvals}), values=DenseValues(X)
)

argvals = np.linspace(0, 1, num=50)
X = np.array([np.exp(-argvals), np.log(1 + argvals)])
fdata_second = DenseFunctionalData(
    argvals=DenseArgvals({"input_dim_0": argvals}), values=DenseValues(X)
)

fdata = MultivariateFunctionalData([fdata_first, fdata_second])

_ = plot_multivariate(fdata)

Second exmaple

Second, we will define a univariate unidimensional irregular functional data and a univariate two-dimensional dense functional data. By putting them as a list, we can define a MultivariateFunctionalData object.

argvals = IrregularArgvals(
    {
        0: DenseArgvals(
            {
                "input_dim_0": np.linspace(0, 1, num=20),
                "input_dim_1": np.linspace(0, 1, num=20),
            }
        ),
        1: DenseArgvals(
            {
                "input_dim_0": np.linspace(0.2, 0.8, num=15),
                "input_dim_1": np.linspace(0.2, 0.8, num=15),
            }
        ),
    }
)
X = IrregularValues(
    {
        0: np.outer(
            np.sin(argvals[0]["input_dim_0"]), np.cos(argvals[0]["input_dim_1"])
        ),
        1: np.outer(
            np.sin(-argvals[1]["input_dim_0"]), np.cos(argvals[1]["input_dim_1"])
        ),
    }
)

fdata_first = IrregularFunctionalData(argvals=argvals, values=X)

argvals = np.linspace(0, np.pi, num=100)
X = np.array(
    [
        np.outer(np.sin(argvals), np.cos(argvals)),
        np.outer(np.sin(-argvals), np.cos(argvals)),
    ]
)
fdata_second = DenseFunctionalData(
    argvals=DenseArgvals({"input_dim_0": argvals, "input_dim_1": argvals}),
    values=DenseValues(X),
)

fdata = MultivariateFunctionalData([fdata_first, fdata_second])

_ = plot_multivariate(fdata)