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Define a Set of Multidimensional Functional Basis

Source: R/basismfdClass.R
basismfd.Rd

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(...)

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

Public 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)
#> Loading required package: fda
#> Loading required package: splines
#> Loading required package: fds
#> Loading required package: rainbow
#> Loading required package: MASS
#> Loading required package: pcaPP
#> Loading required package: RCurl
#> Loading required package: deSolve
#> 
#> Attaching package: ‘fda’
#> The following object is masked from ‘package:graphics’:
#> 
#>     matplot
#> The following object is masked from ‘package:datasets’:
#> 
#>     gait
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
#> [[1]]
#> $call
#> basisfd(type = type, rangeval = rangeval, nbasis = nbasis, params = params, 
#>     dropind = dropind, quadvals = quadvals, values = values, 
#>     basisvalues = basisvalues)
#> 
#> $type
#> [1] "fourier"
#> 
#> $rangeval
#> [1] 0.000000 6.283185
#> 
#> $nbasis
#> [1] 5
#> 
#> $params
#> [1] 6.283185
#> 
#> $dropind
#> numeric(0)
#> 
#> $quadvals
#> NULL
#> 
#> $values
#> list()
#> 
#> $basisvalues
#> list()
#> 
#> $names
#> [1] "const" "sin1"  "cos1"  "sin2"  "cos2" 
#> 
#> attr(,"class")
#> [1] "basisfd"
#> 
mdbs1$dimSupp
#> [1] 1
mdbs1$nbasis
#> [1] 5
mdbs1$supp
#>          [,1]
#> [1,] 0.000000
#> [2,] 6.283185
mdbs1$gram
#> 5 x 5 Matrix of class "dsyMatrix"
#>               [,1]          [,2]          [,3]          [,4]          [,5]
#> [1,]  1.000000e+00 -1.040211e-16 -1.382536e-16  8.367298e-17 -6.370014e-17
#> [2,] -1.040211e-16  1.000000e+00  3.690370e-17 -5.743803e-17 -1.355597e-16
#> [3,] -1.382536e-16  3.690370e-17  1.000000e+00 -1.432435e-16 -1.754345e-16
#> [4,]  8.367298e-17 -5.743803e-17 -1.432435e-16  9.999986e-01 -8.323824e-17
#> [5,] -6.370014e-17 -1.355597e-16 -1.754345e-16 -8.323824e-17  1.000001e+00
mdbs1$eval(1:7 / 10)
#> [[1]]
#>          const       sin1      cos1      sin2       cos2
#> [1,] 0.3989423 0.05632497 0.5613710 0.1120872 0.55294335
#> [2,] 0.3989423 0.11208717 0.5529434 0.2197058 0.51965302
#> [3,] 0.3989423 0.16672942 0.5389909 0.3185654 0.46564576
#> [4,] 0.3989423 0.21970577 0.5196530 0.4047248 0.39307467
#> [5,] 0.3989423 0.27048689 0.4951229 0.4747492 0.30483293
#> [6,] 0.3989423 0.31856540 0.4656458 0.5258467 0.20443847
#> [7,] 0.3989423 0.36346091 0.4315160 0.5559805 0.09589369
#> 
image(as.matrix(mdbs1$gram))


####### 2-D Basis ######## (fd cannot handle this)
mdbs2 <- Basismfd(bs1, bs2)
mdbs2$basis
#> [[1]]
#> $call
#> basisfd(type = type, rangeval = rangeval, nbasis = nbasis, params = params, 
#>     dropind = dropind, quadvals = quadvals, values = values, 
#>     basisvalues = basisvalues)
#> 
#> $type
#> [1] "fourier"
#> 
#> $rangeval
#> [1] 0.000000 6.283185
#> 
#> $nbasis
#> [1] 5
#> 
#> $params
#> [1] 6.283185
#> 
#> $dropind
#> numeric(0)
#> 
#> $quadvals
#> NULL
#> 
#> $values
#> list()
#> 
#> $basisvalues
#> list()
#> 
#> $names
#> [1] "const" "sin1"  "cos1"  "sin2"  "cos2" 
#> 
#> attr(,"class")
#> [1] "basisfd"
#> 
#> [[2]]
#> $call
#> basisfd(type = type, rangeval = rangeval, nbasis = nbasis, params = params, 
#>     dropind = dropind, quadvals = quadvals, values = values, 
#>     basisvalues = basisvalues)
#> 
#> $type
#> [1] "bspline"
#> 
#> $rangeval
#> [1] 0 1
#> 
#> $nbasis
#> [1] 7
#> 
#> $params
#> [1] 0.25 0.50 0.75
#> 
#> $dropind
#> NULL
#> 
#> $quadvals
#> NULL
#> 
#> $values
#> list()
#> 
#> $basisvalues
#> list()
#> 
#> $names
#> [1] "bspl4.1" "bspl4.2" "bspl4.3" "bspl4.4" "bspl4.5" "bspl4.6" "bspl4.7"
#> 
#> attr(,"class")
#> [1] "basisfd"
#> 
mdbs2$dimSupp
#> [1] 2
mdbs2$nbasis
#> [1] 5 7
mdbs2$supp
#>          [,1] [,2]
#> [1,] 0.000000    0
#> [2,] 6.283185    1
dim(mdbs2$gram)
#> [1] 35 35
arg_mdbs <- list(1:10, 1:9 / 10)
mdbs2$eval(arg_mdbs)
#> [[1]]
#>           const        sin1       cos1       sin2        cos2
#>  [1,] 0.3989423  0.47474916  0.3048329  0.5130161 -0.23478571
#>  [2,] 0.3989423  0.51301614 -0.2347857 -0.4269801 -0.36877892
#>  [3,] 0.3989423  0.07961844 -0.5585435 -0.1576433  0.54171807
#>  [4,] 0.3989423 -0.42698008 -0.3687789  0.5581856 -0.08208960
#>  [5,] 0.3989423 -0.54101509  0.1600393 -0.3069310 -0.47339542
#>  [6,] 0.3989423 -0.15764331  0.5417181 -0.3027289  0.47609361
#>  [7,] 0.3989423  0.37066500  0.4253438  0.5588904  0.07714571
#>  [8,] 0.3989423  0.55818562 -0.0820896 -0.1624321 -0.54030150
#>  [9,] 0.3989423  0.23251296 -0.5140502 -0.4236992  0.37254381
#> [10,] 0.3989423 -0.30693104 -0.4733954  0.5150742  0.23023565
#> 
#> [[2]]
#>       bspl4.1 bspl4.2     bspl4.3    bspl4.4     bspl4.5 bspl4.6 bspl4.7
#>  [1,]   0.216   0.592 0.181333333 0.01066667 0.000000000   0.000   0.000
#>  [2,]   0.008   0.416 0.490666667 0.08533333 0.000000000   0.000   0.000
#>  [3,]   0.000   0.128 0.588000000 0.28266667 0.001333333   0.000   0.000
#>  [4,]   0.000   0.016 0.409333333 0.53866667 0.036000000   0.000   0.000
#>  [5,]   0.000   0.000 0.166666667 0.66666667 0.166666667   0.000   0.000
#>  [6,]   0.000   0.000 0.036000000 0.53866667 0.409333333   0.016   0.000
#>  [7,]   0.000   0.000 0.001333333 0.28266667 0.588000000   0.128   0.000
#>  [8,]   0.000   0.000 0.000000000 0.08533333 0.490666667   0.416   0.008
#>  [9,]   0.000   0.000 0.000000000 0.01066667 0.181333333   0.592   0.216
#> 
image(as.matrix(mdbs2$gram))