CHOLESKY - 3D Gaussian model¶
The CHOLESKY type prior utilizes Cholesky decomposition of the
covariance in order to generate realizations of a Gaussian random field.
The CHOLESKY type prior needs a full description of the covariance
model, which will be of size [nxyz*nxyz*nxyz], unlike using the
FFTMA type prior model that only needs a
specification of an isotropic covariance models of size [1,nxyz]
.
Hence, the CHOLESKY type prior is much more demanding on memory, and
CPU. However, the CHOLESKY type prior can be used to sample from any
covariance model, also non-stationary covariance model.
The CHOLESKY model is can be defined almost identically to the FFTMA type prior model. As an example:
im=1;
prior{im}.type='CHOLESKY';
prior{im}.x=[0:2:100];
prior{im}.y=[0:2:100];
prior{im}.m0=10;
prior{im}.Cm='1 Sph(10)';
the use of d_target
to specify target distributions is also
possible, using the same style as for the FFTMA type
prior.
Be warned that the ‘cholesky’ type prior model is much more memory demanding than the ‘fftma’ and ‘visim’ type prior models, as a full [nxyz*nxyz] covariance model needs to setup (and inverted). Thus, the ‘cholesky’ type prior is mostly applicable when the number of model parameters (nx*ny*nx) is small.