Based on moving-average model.

Base classes

• public vtb::core::ARMA_wavy_surface_generator_base< T, N >

Types

• using grid_type = Grid< T, N >
• using array_type = Array< T, N >
• using default_coefficient_solver = Fixed_point_iteration_yule_walker_solver< T, N >
• using solver_ptr = std::unique_ptr< solver_type >
• using solver_type = Yule_walker_solver< T, N >

Methods

• generate(const grid_type & grid, array_type & result) -> voidvirtual
• operator=(const MA_wavy_surface_generator &) -> MA_wavy_surface_generator &
• MA_wavy_surface_generator(const MA_wavy_surface_generator &)
• MA_wavy_surface_generator()

Based on autoregerssive model.

Base classes

• public vtb::core::ARMA_wavy_surface_generator_base< T, N >

Types

• using solver_ptr = std::unique_ptr< solver_type >
• using grid_type = Grid< T, N >
• using array_type = Array< T, N >

Methods

• generate(const grid_type & grid, array_type & result) -> voidvirtual
• ~AR_wavy_surface_generator()virtual
• AR_wavy_surface_generator()

Derived classes

• vtb::core::AR_wavy_surface_generator< T, N >
• vtb::core::MA_wavy_surface_generator< T, N >

Types

• using rect3 = blitz::RectDomain< N >
• using vec3 = blitz::TinyVector< T, N >
• using generator_ptr = std::unique_ptr< generator_type >
• using generator_type = Wavy_surface_generator< T >
• using solver_ptr = std::unique_ptr< solver_type >
• using solver_type = Yule_walker_solver< T, N >
• using prng_type = std::mt19937
• using array_type = Array< T, N >
• using grid_type = Grid< T, N >

Methods

• generate_white_noise(array_type result) -> voidprotected
• calculate_coefficients() -> void
• decay() const -> const vec3 &
• decay(const vec3 & rhs) -> void
• coefficient_solver() -> solver_type *
• coefficient_solver() const -> const solver_type *
• coefficient_solver(solver_ptr && ptr) -> void
• template <class SeedSequence>
seed(SeedSequence & seq) -> void
• seed() -> void
• variance() const -> T
• white_noise_variance() const -> T
• coefficients() const -> const array_type &
• acf() const -> const array_type &
• acf(array_type acf_in) -> void
• acf_generator() const -> const generator_ptr &
• acf_generator(generator_ptr ptr) -> void
• has_acf_generator() const -> bool
• has_acf() const -> bool
• has_coefficients() const -> bool
• generate(const grid_type & grid, array_type & result) -> voidvirtual
• ARMA_wavy_surface_generator_base(array_type acf_in)explicit
• ~ARMA_wavy_surface_generator_base()virtual
• ARMA_wavy_surface_generator_base()

Base classes

• public exception

Methods

• what() const -> const char *
• num_bad_roots() const -> int
• Invalid_ARMA_process(int nbadroots)explicit

Computes autocovariance function of three-dimensional field.

rhs

symmetric three-dimensional field

• Does not subtract mean value.
• Does not divide by the variance.
• Uses the following formula. $$\gamma_{i,j,k} = \frac{1}{n_1 n_2 n_3} \sum\limits_{i_1=0}^{n_1-1} \sum\limits_{i_1=0}^{n_2-1} \sum\limits_{k_1=0}^{n_3-1} \zeta_{i_1,j_1,k_1} \zeta_{(i_1+i) \bmod n_1,(j_1+i) \bmod n_2,(k_1+k) \bmod n_3}$$ Assumes, that the field is symmetric and periodic in each dimension. Uses fast Fourier transforms to speed up the computation: $$\gamma = \mathcal{F}^{-1}\left\{ \left| \mathcal{F}\left\{\zeta\right\} \right|^2 \right\}.$$

Check AR (MA) process stationarity (invertibility).

1. Find roots of the polynomial $P_n(\Phi)=1-\Phi_1 x-\Phi_2 x^2 - ... -\Phi_n x^n$.
2. Check if some roots do not lie outside the unit disk.