Package 'ReMFPCA' reference manual

Package 'ReMFPCA'

Title:	Regularized Multivariate Functional Principal Component Analysis
Description:	Methods and tools for implementing regularized multivariate functional principal component analysis ('ReMFPCA') for multivariate functional data whose variables might be observed over different dimensional domains. 'ReMFPCA' is an object-oriented interface leveraging the extensibility and scalability of R6. It employs a parameter vector to control the smoothness of each functional variable. By incorporating smoothness constraints as penalty terms within a regularized optimization framework, 'ReMFPCA' generates smooth multivariate functional principal components, offering a concise and interpretable representation of the data. For detailed information on the methods and techniques used in 'ReMFPCA', please refer to Haghbin et al. (2023) <doi:10.48550/arXiv.2306.13980>.
Authors:	Hossein Haghbin [aut, cre] , Yue Zhao [aut] , Mehdi Maadooliat [aut]
Maintainer:	Hossein Haghbin <[email protected]>
License:	GPL (>= 2)
Version:	1.0.0
Built:	2024-11-15 03:06:12 UTC
Source:	https://github.com/haghbinh/remfpca

Title:

Regularized Multivariate Functional Principal Component Analysis

Description:

Methods and tools for implementing regularized multivariate functional principal component analysis ('ReMFPCA') for multivariate functional data whose variables might be observed over different dimensional domains. 'ReMFPCA' is an object-oriented interface leveraging the extensibility and scalability of R6. It employs a parameter vector to control the smoothness of each functional variable. By incorporating smoothness constraints as penalty terms within a regularized optimization framework, 'ReMFPCA' generates smooth multivariate functional principal components, offering a concise and interpretable representation of the data. For detailed information on the methods and techniques used in 'ReMFPCA', please refer to Haghbin et al. (2023) <doi:10.48550/arXiv.2306.13980>.

Authors:

Hossein Haghbin [aut, cre]

, Yue Zhao [aut]

, Mehdi Maadooliat [aut]

Maintainer:

Hossein Haghbin <[email protected]>

License:

GPL (>= 2)

Version:

1.0.0

Built:

2024-11-15 03:06:12 UTC

Source:

https://github.com/haghbinh/remfpca

Help Index

Subtract two 'mfd' objects

Description

Subtract two 'mfd' objects

Usage

## S3 method for class 'mfd'
obj1 - obj2 = NULL
## S3 method for class 'mfd'
obj1 - obj2 = NULL

Arguments

`obj1`	An 'mfd' object
`obj2`	An 'mfd' object or a scalar

Value

The difference between the two 'mfd' objects

Subtraction of two 'mvmfd' objects

Description

Subtraction of two 'mvmfd' objects

Usage

## S3 method for class 'mvmfd'
obj1 - obj2 = NULL
## S3 method for class 'mvmfd'
obj1 - obj2 = NULL

Arguments

`obj1`	An 'mvmfd' object
`obj2`	An optional 'mvmfd' object

Value

An 'mvmfd' object

Extract subsets of an 'mfd' object

Description

Extract subsets of an 'mfd' object

Usage

## S3 method for class 'mfd'
mfd_obj[i = "index"]
## S3 method for class 'mfd'
mfd_obj[i = "index"]

Arguments

`mfd_obj`	An 'mfd' object
`i`	An index or indices specifying the subsets to extract

Value

An 'mfd' object containing the specified subsets

Extract subsets of an 'mvmfd' object

Description

Extract subsets of an 'mvmfd' object

Usage

## S3 method for class 'mvmfd'
mvmfd_obj[i = "index", j = "index"]
## S3 method for class 'mvmfd'
mvmfd_obj[i = "index", j = "index"]

Arguments

`mvmfd_obj`	An 'mvmfd' object
`i`	An index or indices specifying the subsets to extract for the first dimension
`j`	An index or indices specifying the subsets to extract for the second dimension

Value

An 'mvmfd' object containing the specified subsets

Scalar multiplication of an 'mfd' object

Description

Scalar multiplication of an 'mfd' object. One object must be an 'mfd', and the other one a scalar

Usage

## S3 method for class 'mfd'
obj1 * obj2
## S3 method for class 'mfd'
obj1 * obj2

Arguments

`obj1`	An 'mfd' object or an scalar
`obj2`	An 'mfd' object or an scalar

Value

An 'mfd' object

Multiplication of an 'mvmfd' object with a scalar

Description

Multiplication of an 'mvmfd' object with a scalar

Usage

## S3 method for class 'mvmfd'
obj1 * obj2
## S3 method for class 'mvmfd'
obj1 * obj2

Arguments

`obj1`	An 'mvmfd' object or a scalar
`obj2`	An 'mvmfd' object or a scalar

Value

An 'mvmfd' object

Add two 'mfd' objects

Description

Add two 'mfd' objects

Usage

## S3 method for class 'mfd'
obj1 + obj2 = NULL
## S3 method for class 'mfd'
obj1 + obj2 = NULL

Arguments

`obj1`	An 'mfd' object
`obj2`	An 'mfd' object or a scalar

Value

The sum of the two 'mfd' objects

Addition of two 'mvmfd' objects

Description

Addition of two 'mvmfd' objects

Usage

## S3 method for class 'mvmfd'
obj1 + obj2 = NULL
## S3 method for class 'mvmfd'
obj1 + obj2 = NULL

Arguments

`obj1`	An 'mvmfd' object
`obj2`	An optional 'mvmfd' object

Value

An 'mvmfd' object

Define a Set of Multidimensional Functional Basis

Description

The 'basismfd' class represents a set of multidimensional basis functions. This class utilizes basis objects from the 'fda' package, such as B-splines and Fourier bases.

Constructor for 'basismfd' objects (same as Basismfd(...) )

Usage

Basismfd(...)

Basismfd(...)
Basismfd(...)

Basismfd(...)

Arguments

...

A list of 'basisfd' objects

Active bindings

basis: A list of basis objects from the 'fda' package.
dimSupp: The dimension of the support domain of the 'basismfd' object.
supp: The matrix representing the ranges of the dimensions.
gram: The Gram matrix.
nbasis: A numeric vector containing the number of bases.

Methods

Method `new()`

The constructor function for objects of the class 'basismfd' (same as Basismfd(...) )

Usage

basismfd$new(...)

Arguments

...: A list of 'basisfd' objects

Method `eval()`

Evaluate the 'basismfd' object at given argument values

Usage

basismfd$eval(evalarg)

Arguments

evalarg: A list of numeric vectors of argument values at which the 'basismfd' is to be evaluated

Returns

A list of evaluated values

Method `print()`

Print method for 'basismfd' objects

Usage

basismfd$print(...)

Arguments

...: Additional arguments to be passed to 'print' Getter and setter for 'basis' field Getter and setter for 'dimSupp' field Getter and setter for 'nbasis' field Getter and setter for 'supp' field Getter and setter for 'gram' field

Method `clone()`

The objects of this class are cloneable with this method.

Usage

basismfd$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

require(fda)
bs1 <- create.fourier.basis(c(0, 2 * pi), 5)
bs2 <- create.bspline.basis(c(0, 1), 7)
bs3 <- create.exponential.basis(c(0, 2), 3)
# 1-D Basis ######## (similar to the fd features)
mdbs1 <- Basismfd(bs1)
mdbs1$basis
mdbs1$dimSupp
mdbs1$nbasis
mdbs1$supp
mdbs1$gram
mdbs1$eval(1:7 / 10)
image(as.matrix(mdbs1$gram))

####### 2-D Basis ######## (fd cannot handle this)
mdbs2 <- Basismfd(bs1, bs2)
mdbs2$basis
mdbs2$dimSupp
mdbs2$nbasis
mdbs2$supp
dim(mdbs2$gram)
arg_mdbs <- list(1:10, 1:9 / 10)
mdbs2$eval(arg_mdbs)
image(as.matrix(mdbs2$gram))
require(fda)
bs1 <- create.fourier.basis(c(0, 2 * pi), 5)
bs2 <- create.bspline.basis(c(0, 1), 7)
bs3 <- create.exponential.basis(c(0, 2), 3)
# 1-D Basis ######## (similar to the fd features)
mdbs1 <- Basismfd(bs1)
mdbs1$basis
mdbs1$dimSupp
mdbs1$nbasis
mdbs1$supp
mdbs1$gram
mdbs1$eval(1:7 / 10)
image(as.matrix(mdbs1$gram))

####### 2-D Basis ######## (fd cannot handle this)
mdbs2 <- Basismfd(bs1, bs2)
mdbs2$basis
mdbs2$dimSupp
mdbs2$nbasis
mdbs2$supp
dim(mdbs2$gram)
arg_mdbs <- list(1:10, 1:9 / 10)
mdbs2$eval(arg_mdbs)
image(as.matrix(mdbs2$gram))

Bivariate plot for 'mvmfd' objects

Description

Bivariate plot for 'mvmfd' objects

Usage

bimfdplot(mvmfd_obj, type = "l", lty = 1, xlab = "", ylab = "", main = "", ...)
bimfdplot(mvmfd_obj, type = "l", lty = 1, xlab = "", ylab = "", main = "", ...)

Arguments

`mvmfd_obj`	An 'mvmfd' object
`type`	Type of plot ('l' for lines, 'p' for points, etc.)
`lty`	Line type
`xlab`	Label for the x-axis
`ylab`	Label for the y-axis
`main`	Main title
`...`	Additional arguments for the matplot function

Compute the inner product between two objects of class 'mfd'

Description

Compute the inner product between two objects of class 'mfd'

Usage

inprod_mfd(mfd_obj1, mfd_obj2)
inprod_mfd(mfd_obj1, mfd_obj2)

Arguments

`mfd_obj1`	An 'mfd' object
`mfd_obj2`	An 'mfd' object

Value

The inner products matrix between the two 'mfd' objects

Compute the inner product between two objects of class 'mvmfd'

Description

Compute the inner product between two objects of class 'mvmfd'

Usage

inprod_mvmfd(mvmfd_obj1, mvmfd_obj2)
inprod_mvmfd(mvmfd_obj1, mvmfd_obj2)

Arguments

`mvmfd_obj1`	An 'mvmfd' object
`mvmfd_obj2`	An 'mvmfd' object

Value

The inner products matrix between the two 'mvmfd' objects

Check if an object is of class 'basismfd'

Description

Check if an object is of class 'basismfd'

Usage

is.basismfd(fdobj)
is.basismfd(fdobj)

Arguments

fdobj

The object to check.

Value

TRUE if the object is of class 'basismfd', FALSE otherwise.

Check if an object is of class 'mfd'

Description

Check if an object is of class 'mfd'

Usage

is.mfd(fdobj)
is.mfd(fdobj)

Arguments

fdobj

The object to check.

Value

TRUE if the object is of class 'mfd', FALSE otherwise.

Check if an object is of class 'mvbasismfd'

Description

Check if an object is of class 'mvbasismfd'

Usage

is.mvbasismfd(fdobj)
is.mvbasismfd(fdobj)

Arguments

fdobj

The object to check.

Value

TRUE if the object is of class 'mvbasismfd', FALSE otherwise.

Check if an object is of class 'mvmfd'

Description

Check if an object is of class 'mvmfd'

Usage

is.mvmfd(fdobj)
is.mvmfd(fdobj)

Arguments

fdobj

The object to check.

Value

TRUE if the object is of class 'mvmfd', FALSE otherwise.

Length of an object of classes 'mfd'or 'mvmfd'.

Description

Length of an object of an object of classes 'mfd' or 'mvmfd'.

Usage

length(x, ...)
length(x, ...)

Arguments

`x`	An object of classes 'mfd' or 'mvmfd'.
`...`	all 'length' function arguments.

mean of an object of classes 'mfd'or 'mvmfd'.

Description

mean of an object of classes 'mfd'or 'mvmfd'.

Usage

mean(x, ...)
mean(x, ...)

Arguments

`x`	An object of classes 'mfd' or 'mvmfd'.
`...`	all 'mean' function arguments.

Value

An object of class 'mfd'

Define a Set of Multidimensional Functional Data objects

Description

The 'mfd' class represents a set of multidimensional functional data with 'basismfd' object. Functional data objects are constructed by specifying a set of basis functions and a set of coefficients defining a linear combination of these basis functions.

Constructor for 'mfd' objects (same as Mfd(...) )

Usage

Mfd(argval = NULL, X, mdbs, method = "data")
Mfd(argval = NULL, X, mdbs, method = "data")

Arguments

`argval`	A list of numeric vectors of argument values at which the 'mfd' object is to be evaluated
`X`	A numeric matrix corresponds to basis expansion coefficients if 'method="coefs"' and discrete observations if 'method="data"'.
`mdbs`	a basismfd object
`method`	determine the 'X' matrix type as "coefs" and "data".

Active bindings

basis: an object of the class 'basismfd'.
coefs: a matrix of the coefficients.
nobs: number of the observation

Methods

Public methods

mfd$new()
mfd$eval()
mfd$print()
mfd$clone()

Method `new()`

Constructor for 'mfd' objects (same as Mfd(...) )

Usage

mfd$new(argval = NULL, X, mdbs, method = "data")

Arguments

argval: A list of numeric vectors of argument values at which the 'mfd' object is to be evaluated
X: A numeric matrix corresponds to basis expansion coefficients if 'method="coefs"' and discrete observations if 'method="data"'.
mdbs: a basismfd object
method: determine the 'X' matrix type as "coefs" and "data".

Method `eval()`

Evaluation an 'mfd' object in some arguments.

Usage

mfd$eval(evalarg)

Arguments

evalarg: a list of numeric vector of argument values at which the mfd is to be evaluated.

Returns

A matrix of evaluated values

Method `print()`

Print method for 'mfd' objects

Usage

mfd$print(...)

Arguments

...: Additional arguments to be passed to 'print'

Method `clone()`

The objects of this class are cloneable with this method.

Usage

mfd$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

require(fda)
bs1 <- create.fourier.basis(c(0,2*pi),5)
bs2 <- create.bspline.basis(c(0,1),7)
bs3 <- create.exponential.basis(c(0,2),3)

#1-D mfd :_____________________________
argval <- seq(0,2*pi,length.out=100)
nobs <- 10;
X <- outer(sin(argval),seq(0.5,1.5,length.out=nobs))
mdbs1 <- Basismfd(bs1)
mfd1 <- Mfd(X=X, mdbs = mdbs1)
inprod_mfd(mfd1,mfd1)
norm_mfd(mfd1)
mfd0 <- 2.5*mfd1
mfd1-mfd0
mfd1[1:3]

mfd1$eval(argval)
mfd1c <- Mfd(X=mfd1$coefs, mdbs = mdbs1, method = "coefs")
all.equal(c(mfd1$basis,mfd1$coefs,mfd1$nobs),c(mfd1c$basis,mfd1c$coefs,mfd1c$nobs))
length(mfd1)
mean(mfd1)
plot(mfd1)

require(fda)
bs1 <- create.fourier.basis(c(0,2*pi),5)
bs2 <- create.bspline.basis(c(0,1),7)
bs3 <- create.exponential.basis(c(0,2),3)

#1-D mfd :_____________________________
argval <- seq(0,2*pi,length.out=100)
nobs <- 10;
X <- outer(sin(argval),seq(0.5,1.5,length.out=nobs))
mdbs1 <- Basismfd(bs1)
mfd1 <- Mfd(X=X, mdbs = mdbs1)
inprod_mfd(mfd1,mfd1)
norm_mfd(mfd1)
mfd0 <- 2.5*mfd1
mfd1-mfd0
mfd1[1:3]

mfd1$eval(argval)
mfd1c <- Mfd(X=mfd1$coefs, mdbs = mdbs1, method = "coefs")
all.equal(c(mfd1$basis,mfd1$coefs,mfd1$nobs),c(mfd1c$basis,mfd1c$coefs,mfd1c$nobs))
length(mfd1)
mean(mfd1)
plot(mfd1)

Define a Set of Multivariate Multidimensional Functional Basis

Description

The 'mvbasismfd' a set of multivariate multidimensional basis functions. This class utilizes basis objects 'basismfd'.

Constructor for 'mvbasismfd' objects (same as 'Mvbasismfd')

Usage

Mvbasismfd(basis)

Mvbasismfd(basis)

## S3 method for class 'mvbasismfd'
mvbasismfd_obj[i = "index"]
Mvbasismfd(basis)

Mvbasismfd(basis)

## S3 method for class 'mvbasismfd'
mvbasismfd_obj[i = "index"]

Arguments

`basis`	A list of basisfd objects
`mvbasismfd_obj`	An 'mvmfd' object
`i`	An index or indices specifying the subsets to extract for the first dimension

Value

An 'mvbasismfd' object containing the specified subsets

Active bindings

nvar: number of variables
basis: A list of 'mvbasisfd' objects
dimSupp: A sequence of positive integers specifying support domain of the 'mvbasismfd' object.
nbasis: A list of integers specifying the number of basis functions
supp: A list of matrices specifying the support of basis functions
gram: The Gram matrix.

Methods

Public methods

mvbasismfd$new()
mvbasismfd$eval()
mvbasismfd$clone()

Method `new()`

Constructor for 'mvbasismfd' objects (same as Mvbasismfd(...) )

Usage

mvbasismfd$new(basis)

Arguments

basis: A list of 'basismfd' objects

Method `eval()`

Evaluate the 'mvbasismfd' object at given argument values

Usage

mvbasismfd$eval(evalarg)

Arguments

evalarg: A list of numeric vectors of argument values at which the 'mvbasismfd' is to be evaluated

Returns

A list of evaluated values

Method `clone()`

The objects of this class are cloneable with this method.

Usage

mvbasismfd$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Define a Set of Multivariate Multidimensional Functional Data objects

Description

The 'mvmfd' class represents functional data ...

Constructor for 'mvmfd' objects (same as 'Mvmfd')

Usage

Mvmfd(...)
Mvmfd(...)

Arguments

...

A 'mfd' objects which have separated by comma

Active bindings

basis: A 'mvbasismfd' object
coefs: a matrix of the coefficients.
nobs: number of observation
nvar: number of variables

Methods

Public methods

mvmfd$new()
mvmfd$eval()
mvmfd$print()
mvmfd$clone()

Method `new()`

Constructor for ‘mvmfd' objects (same as ’Mvmfd')

Usage

mvmfd$new(...)

Arguments

...: A 'mfd' objects which have separated by comma

Method `eval()`

Eval method for 'mvmfd' objects

Usage

mvmfd$eval(evalarg)

Arguments

evalarg: A list of numeric vectors of argument values at which the 'mvmfd' is to be evaluated.

Returns

A list of evaluated values

Method `print()`

Print method for 'mvmfd' objects

Usage

mvmfd$print(...)

Arguments

...: Additional arguments to be passed to 'print'

Method `clone()`

The objects of this class are cloneable with this method.

Usage

mvmfd$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

require(fda)
bs1 <- create.fourier.basis(c(0, 2 * pi), 5)
bs2 <- create.bspline.basis(c(0, 1), 7)
bs3 <- create.exponential.basis(c(0, 2), 3)
nobs <- 10
argval1 <- seq(0, 2 * pi, length.out = 12)
X1 <- outer(sin(argval1), seq(0.5, 1.5, length.out = nobs))
mdbs1 <- Basismfd(bs1)
mfd1 <- Mfd(argval1, X1, mdbs1)
mdbs2 <- Basismfd(bs1)
argval2 <- argval1
X2 <- outer(cos(argval2), seq(0.2, 1.5, length.out = nobs))
mfd2 <- Mfd(argval2, X2, mdbs1)
mvmfd1 <- Mvmfd(mfd1, mfd2)
mvmfd1[1]
mvmfd1[1, 1]
mvmfd1[1:5, 2]
mvmfd1[, 1]
mvmfd1[1:5, ]
evalarg <- list(argval1, argval2)
mvmfd1$eval(evalarg)
mvmfd1 + mvmfd1
mean(mvmfd1)
inprod_mvmfd(mvmfd1, mvmfd1)
norm_mvmfd(mvmfd1)
plot(mvmfd1)
bimfdplot(mvmfd1)

require(fda)
bs1 <- create.fourier.basis(c(0, 2 * pi), 5)
bs2 <- create.bspline.basis(c(0, 1), 7)
bs3 <- create.exponential.basis(c(0, 2), 3)
nobs <- 10
argval1 <- seq(0, 2 * pi, length.out = 12)
X1 <- outer(sin(argval1), seq(0.5, 1.5, length.out = nobs))
mdbs1 <- Basismfd(bs1)
mfd1 <- Mfd(argval1, X1, mdbs1)
mdbs2 <- Basismfd(bs1)
argval2 <- argval1
X2 <- outer(cos(argval2), seq(0.2, 1.5, length.out = nobs))
mfd2 <- Mfd(argval2, X2, mdbs1)
mvmfd1 <- Mvmfd(mfd1, mfd2)
mvmfd1[1]
mvmfd1[1, 1]
mvmfd1[1:5, 2]
mvmfd1[, 1]
mvmfd1[1:5, ]
evalarg <- list(argval1, argval2)
mvmfd1$eval(evalarg)
mvmfd1 + mvmfd1
mean(mvmfd1)
inprod_mvmfd(mvmfd1, mvmfd1)
norm_mvmfd(mvmfd1)
plot(mvmfd1)
bimfdplot(mvmfd1)

Compute the norm of an object of class 'mfd'

Description

Compute the norm of an object of class 'mfd'

Usage

norm_mfd(mfd_obj)
norm_mfd(mfd_obj)

Arguments

mfd_obj

An object of class 'mfd'

Value

The norm vector of the an object of class 'mfd'

Compute the norm of an object of class 'mvmfd'

Description

Compute the norm of an object of class 'mvmfd'

Usage

norm_mvmfd(mvmfd_obj)
norm_mvmfd(mvmfd_obj)

Arguments

mvmfd_obj

An 'mvmfd' object

Value

The norm vector of the an object of class 'mvmfd'

Penalty Function

Description

Calculate the penalty matrix for 'mvmfd' objects.

Usage

pen_fun(data, devorder = 2, type)
pen_fun(data, devorder = 2, type)

Arguments

`data`	an object of class 'mvmfd'.
`devorder`	The order of the derivative.
`type`	The type of penalty. The types "coefpen" and "basispen" is supported.

Value

The penalty matrix.

plots an object of classes 'mfd', 'mvmfd' or 'remfpca'

Description

plot an object of classes 'mfd', 'mvmfd' or 'remfpca'

Usage

plot(x, ...)
plot(x, ...)

Arguments

`x`	An object of classes 'mfd', 'mvmfd' or 'remfpca'
`...`	all 'plot' function arguments.

A Class for 'ReMFPCA' objects

Description

The 'remfpca' class represents regularized functional principal components components.

The ‘remfpca' class represents regularized functional principal components (’ReMFPCs') components.

Usage

Remfpca(
  mvmfd_obj,
  ncomp,
  alpha = NULL,
  centerfns = TRUE,
  alpha_orth = TRUE,
  penalty_type = "coefpen"
)
Remfpca(
  mvmfd_obj,
  ncomp,
  alpha = NULL,
  centerfns = TRUE,
  alpha_orth = TRUE,
  penalty_type = "coefpen"
)

Arguments

`mvmfd_obj`	An 'mvmfd' object representing the multivariate functional data.
`ncomp`	The number of functional principal components to retain.
`alpha`	A list or vector specifying the regularization parameter(s) for each variable. If NULL, the regularization parameter is estimated internally.
`centerfns`	Logical indicating whether to center the functional data before analysis.
`alpha_orth`	Logical indicating whether to perform orthogonalization of the regularization parameters.
`penalty_type`	The type of penalty to be applied on the coefficients. The types "coefpen" and "basispen" is supported. Default is "coefpen".

Active bindings

pc_mfd: an object of class 'mvmfd' where the first indices (fields) represents harmonics and second indices represents variables
lsv: = Left singular values vectors
values: = the set of eigenvalues
alpha: = The vector of penalties parameters
GCVs: = generalized cross validations
mean_mfd: a multivariate functional data object giving the mean function

Methods

Public methods

remfpca$new()
remfpca$clone()

Method `new()`

Usage

remfpca$new(
  mvmfd_obj,
  ncomp,
  alpha = NULL,
  centerfns = TRUE,
  alpha_orth = TRUE,
  penalty_type = "coefpen"
)

Arguments

mvmfd_obj: An 'mvmfd' object representing the multivariate functional data.
ncomp: The number of functional principal components to retain.
alpha: A list or vector specifying the regularization parameter(s) for each variable. If NULL, the regularization parameter is estimated internally.
centerfns: Logical indicating whether to center the functional data before analysis.
alpha_orth: Logical indicating whether to perform orthogonalization of the regularization parameters.
penalty_type: The type of penalty to be applied on the coefficients. The types "coefpen" and "basispen" is supported. Default is "coefpen".

Method `clone()`

The objects of this class are cloneable with this method.

Usage

remfpca$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

require(fda)
# Brownian Bridge simulation on [0,1]
M <- 110 # number of components
N <- 20 # number of instances
n <- 100 # number of grides
t0 <- seq(0, 1, len = n)
j <- 1:M
alpha1 <- list(a1 = 2^seq(0, 1, length.out = 3), a2 = 2^seq(0, 1, length.out = 3))
psi_1 <- function(t, m) sin(m * pi * t) # eigenfunction of BB
psi_2 <- function(t, m) sin((2 * m - 1) * pi / 2 * t) # eigenfunction of BM
PC_1 <- outer(t0, j, FUN = psi_1) # n by M matrix
PC_2 <- outer(t0, j, FUN = psi_2) # n by M matrix
Z <- matrix(rnorm(N * M), nr = M)
lambda <- matrix(2 / (pi * (2 * j - 1)), nr = M, nc = N)
X_1t <- PC_1 %*% (lambda * Z)
X_2t <- PC_2 %*% (lambda * Z)
noise <- rnorm(n * N, 0, 0.1)
X_1 <- X_1t + noise
X_2 <- X_2t + noise
bs <- create.bspline.basis(c(0, 1), 51)
mdbs <- Basismfd(bs)
mfd1 <- Mfd(X = X_1, mdbs = mdbs)
mfd2 <- Mfd(X = X_2, mdbs = mdbs)
mvmfd_obj <- Mvmfd(mfd1, mfd2)
k <- 2
Re0 <- Remfpca(mvmfd_obj, ncomp = k, alpha = c(0, 0))
fpc0 <- Re0$pc_mfd
scores0 <- inprod_mvmfd(mvmfd_obj, fpc0)
dim(scores0)
Re0$alpha
Re1 <- Remfpca(mvmfd_obj, ncomp = k, alpha = alpha1)
Re1$alpha
Re3 <- Remfpca(mfd1, ncomp = k, alpha = alpha1$a1)
Re3$alpha
require(fda)
# Brownian Bridge simulation on [0,1]
M <- 110 # number of components
N <- 20 # number of instances
n <- 100 # number of grides
t0 <- seq(0, 1, len = n)
j <- 1:M
alpha1 <- list(a1 = 2^seq(0, 1, length.out = 3), a2 = 2^seq(0, 1, length.out = 3))
psi_1 <- function(t, m) sin(m * pi * t) # eigenfunction of BB
psi_2 <- function(t, m) sin((2 * m - 1) * pi / 2 * t) # eigenfunction of BM
PC_1 <- outer(t0, j, FUN = psi_1) # n by M matrix
PC_2 <- outer(t0, j, FUN = psi_2) # n by M matrix
Z <- matrix(rnorm(N * M), nr = M)
lambda <- matrix(2 / (pi * (2 * j - 1)), nr = M, nc = N)
X_1t <- PC_1 %*% (lambda * Z)
X_2t <- PC_2 %*% (lambda * Z)
noise <- rnorm(n * N, 0, 0.1)
X_1 <- X_1t + noise
X_2 <- X_2t + noise
bs <- create.bspline.basis(c(0, 1), 51)
mdbs <- Basismfd(bs)
mfd1 <- Mfd(X = X_1, mdbs = mdbs)
mfd2 <- Mfd(X = X_2, mdbs = mdbs)
mvmfd_obj <- Mvmfd(mfd1, mfd2)
k <- 2
Re0 <- Remfpca(mvmfd_obj, ncomp = k, alpha = c(0, 0))
fpc0 <- Re0$pc_mfd
scores0 <- inprod_mvmfd(mvmfd_obj, fpc0)
dim(scores0)
Re0$alpha
Re1 <- Remfpca(mvmfd_obj, ncomp = k, alpha = alpha1)
Re1$alpha
Re3 <- Remfpca(mfd1, ncomp = k, alpha = alpha1$a1)
Re3$alpha

Standard deviation of an object of class 'mfd'.

Description

Standard deviation an object of class 'mfd'.

Usage

sd(x, ...)
sd(x, ...)

Arguments

`x`	An object of class 'mfd'
`...`	all 'sd' function arguments.

Value

An object of class 'mfd'

Package 'ReMFPCA'

Help Index

Subtract two 'mfd' objects

Description

Usage

Arguments

Value

See Also

Subtraction of two 'mvmfd' objects

Description

Usage

Arguments

Value

See Also

Extract subsets of an 'mfd' object

Description

Usage

Arguments

Value

See Also

Extract subsets of an 'mvmfd' object

Description

Usage

Arguments

Value

See Also

Scalar multiplication of an 'mfd' object

Description

Usage

Arguments

Value

See Also

Multiplication of an 'mvmfd' object with a scalar

Description

Usage

Arguments

Value

See Also

Add two 'mfd' objects

Description

Usage

Arguments

Value

See Also

Addition of two 'mvmfd' objects

Description

Usage

Arguments

Value

See Also

Define a Set of Multidimensional Functional Basis

Description

Usage

Arguments

Active bindings

Methods

Public methods

Method new()

Usage

Arguments

Method eval()

Usage

Arguments

Returns

Method print()

Usage

Arguments

Method clone()

Usage

Arguments

Examples

Bivariate plot for 'mvmfd' objects

Description

Usage

Arguments

See Also

Compute the inner product between two objects of class 'mfd'

Description

Usage

Arguments

Method `new()`

Method `eval()`

Method `print()`

Method `clone()`

Method `new()`

Method `eval()`

Method `print()`

Method `clone()`