fdars.simulation¶

Simulation of functional data: Karhunen-Loeve expansion, Gaussian processes, and covariance matrices.

Functions¶

Function	Description
`simulate`	Simulate via Karhunen-Loeve expansion
`gaussian_process`	Generate Gaussian process samples
`covariance_matrix`	Compute covariance matrix from a kernel

fdars.simulate(n, argvals, n_basis=5, efun_type="fourier",
               eval_type="linear", seed=None)

Simulate functional data using a Karhunen-Loeve expansion with configurable eigenfunctions and eigenvalue decay.

Parameter	Type	Default	Description
`n`	`int`		Number of curves to generate
`argvals`	`ndarray (m,)`		Evaluation points
`n_basis`	`int`	`5`	Number of basis functions
`efun_type`	`str`	`"fourier"`	Eigenfunction type: `"fourier"`, `"poly"`, `"poly_high"`, `"wiener"`
`eval_type`	`str`	`"linear"`	Eigenvalue decay: `"linear"`, `"exponential"`, `"wiener"`
`seed`	`int` or `None`	`None`	Random seed for reproducibility

Returns	Type	Description
data	`ndarray (n, m)`	Simulated functional data

t = np.linspace(0, 1, 100)
data = fdars.simulate(50, t, n_basis=5, efun_type="fourier", seed=42)

fdars.gaussian_process(n, argvals, kernel="gaussian", length_scale=0.2,
                       variance=1.0, seed=None)

Generate samples from a Gaussian process with a specified kernel.

Parameter	Type	Default	Description
`n`	`int`		Number of curves
`argvals`	`ndarray (m,)`		Evaluation points
`kernel`	`str`	`"gaussian"`	Kernel: `"gaussian"`, `"exponential"`, `"matern"`, `"periodic"`
`length_scale`	`float`	`0.2`	Kernel length scale
`variance`	`float`	`1.0`	Kernel variance (signal variance)
`seed`	`int` or `None`	`None`	Random seed

Returns	Type	Description
samples	`ndarray (n, m)`	Gaussian process samples

t = np.linspace(0, 1, 200)
gp = fdars.gaussian_process(30, t, kernel="matern", length_scale=0.1, seed=42)

fdars.covariance_matrix(argvals, kernel="gaussian", length_scale=0.2, variance=1.0)

Compute a covariance matrix from a specified kernel function.

Parameter	Type	Default	Description
`argvals`	`ndarray (m,)`		Evaluation points
`kernel`	`str`	`"gaussian"`	Kernel: `"gaussian"` or `"exponential"`
`length_scale`	`float`	`0.2`	Kernel length scale
`variance`	`float`	`1.0`	Kernel variance

Returns	Type	Description
cov	`ndarray (m, m)`	Covariance matrix

t = np.linspace(0, 1, 100)
C = fdars.covariance_matrix(t, kernel="gaussian", length_scale=0.2)