# Generation of gaussian univariate functional data

### Description

`generate_gauss_fdata`

generates a dataset of univariate functional data
with a desired mean and covariance function.

### Usage

1 | ```
generate_gauss_fdata(N, centerline, Cov = NULL, CholCov = NULL)
``` |

### Arguments

`N` |
the number of distinct functional observations to generate. |

`centerline` |
the centerline of the distribution, represented as a one-
dimensional data structure of length |

`Cov` |
the covariance operator (provided in form of a |

`CholCov` |
the Cholesky factor of the covariance operator (provided in
form of a |

### Details

In particular, the following model is considered for the generation of data:

* X(t) =
m( t ) + ε(t), for all t in I = [a, b] *

where *m(t)* is the center and *ε(t)* is a centered gaussian
process with covariance function *C_i*.
That is to say:

*Cov( ε(s), ε(t) ) = C( s, t ), with s, t in I*

All the functions are supposed to be observed on an evenly-spaced, one-
dimensional grid of P points: *[a = t_0, t_1, …, t_{P-1} = b]
\subset I *.

### Value

The function returns a matrix containing the discretized
values of the generated observations (in form of an *N x P*
matrix).

### See Also

`exp_cov_function`

, `fData`

,
`generate_gauss_mfdata`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
N = 30
P = 1e2
t0 = 0
tP = 1
time_grid = seq( t0, tP, length.out = P )
C = exp_cov_function( time_grid, alpha = 0.1, beta = 0.2 )
CholC = chol( C )
centerline = sin( 2 * pi * time_grid )
generate_gauss_fdata( N, centerline, Cov = C )
generate_gauss_fdata( N, centerline, CholCov = CholC )
``` |