calcBasisIntegrals

If the element $X^{(j)}$ is expanded in basis functions $b_i^{(j)}(t),~ i = 1, \ldots, K_j$,
this function calculates the $K_j \times K_j$ matrix $B^{(jj)}$ with entries
$$B^{(jj)}_{mn} = \int_{\mathcal{T_j}} b_m^{(j)}(t) b_n^{(j)}(t) \mathrm{d} t$$.

internal

Calculate a multivariate functional principal component analysis
for data observed on different dimensional domains. The estimation algorithm
relies on univariate basis expansions for each element of the multivariate
functional data (Happ & Greven, 2018) <doi:10.1080/01621459.2016.1273115>.
Multivariate and univariate functional data objects are
represented by S4 classes for this type of data implemented in the package
'funData'. For more details on the general concepts of both packages and a case
study, see Happ-Kurz (2020) <doi:10.18637/jss.v093.i05>.

Clara Happ-Kurz

MFPCA

Multivariate Functional Principal Component Analysis for Data
Observed on Different Dimensional Domains

calcBasisIntegrals function

<dl><dt>basisFunctions</dt>
<dd>Array of <code>npc</code> basis functions of dimensions <code>npc x M1</code> or <code>npc x M1 x M2</code>.</dd>
<dt>dimSupp</dt>
<dd>dimension of the support of the basis functions (1 or 2)</dd>
<dt>argvals</dt>
<dd>List of corresponding x-values.</dd></dl>

Arguments

This function is implemented only for functions on one- or two-dimensional domains.

Warning

Utility function that calculates matrix of basis-scalar products (one dimension) — calcBasisIntegrals

<dl>

<dt>basisFunctions</dt>
<dd>Array of <code>npc</code> basis functions of dimensions <code>npc x M1</code> or <code>npc x M1 x M2</code>.</dd>


<dt>dimSupp</dt>
<dd>dimension of the support of the basis functions (1 or 2)</dd>


<dt>argvals</dt>
<dd>List of corresponding x-values.</dd>

</dl>

calcBasisIntegrals: Utility function that calculates matrix of basis-scalar products (one dimension)

Description

Usage

Value

Arguments

Warning

See Also