# Creates the lattice information for a specific geometry.

### Description

Given a specific geometry and the initial information supplied in an LKinfo list create the information that is needed to define the lattice for a given model. This function is required for any new geometry added to LatticeKrig.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
LKrigSetupLattice(object, ...)
## Default S3 method:
LKrigSetupLattice(object, ...)
## S3 method for class 'LKBox'
LKrigSetupLattice(object,x, verbose, NC,
NC.buffer = 5, ...)
## S3 method for class 'LKRectangle'
LKrigSetupLattice(object,x, verbose, NC,
NC.buffer = 5, ...)
## S3 method for class 'LKInterval'
LKrigSetupLattice(object,x, verbose, NC,
NC.buffer = 5, ...)
## S3 method for class 'LKRing'
LKrigSetupLattice(object,x, verbose, NC,
NC.buffer = 5, ...)
## S3 method for class 'LKCylinder'
LKrigSetupLattice(object,x, verbose, NC,
NC.buffer = 5, ...)
``` |

### Arguments

`object` |
A list that is an LKinfo object. |

`NC` |
For cartesian geometries a parameter to specify to number of the
grid points in the largest dimension of the spatial domain and for the
coarsest lattice.
For |

`NC.buffer` |
The number of lattice points to add to the margins beyond the spatial domain. Thus in the largest spatial dimension there are a total of NC + NC.buffer*2 grid points. This is the number of lattice points for LKInterval. |

`verbose` |
If TRUE print out intermediate information for debugging. |

`x` |
Locations of the observations that define spatial domain. |

`...` |
Any additional arguments. |

### Details

This method takes the LKInfo object and the other arguments and computes the
lattice information needed for a specific geometry. The functions are
called from within LKrigSetup and the results are added as a component to`latticeInfo`

as part of the LKinfo object. The way
to design what should be in `latticeInfo`

is to keep in mind that
creating the spatial AR matrix (LKrigSAR) and determining the multi-resolution
lattice points (LKrigLatticeCenters) use the information in the LKinfo
object.

Because the lattice must depend on the geometry the default method just prints out an error message.

### Value

For the `LKInterval, LKRectangle, LKBox`

geometries.
A list with required components:

- m
The total number of lattice points. i.e. the total number of basis functions.

- mx
A matrix giving the number of lattice points in each coordinate (columns) and at each level (rows) of the multiresolution.

- offset
When the lattice points are unrolled as a single array, a vector of indexes giving the start of each lattice level in the coefficient vector.

- delta
A vector of the lattice point spacings for each level.

- rangeLocations
Limits of spatial domain.

- mLevel
A vector giving number of lattice points at each level.

In addition, the methods for cartesian and cartesian-like spatial domains ( LKInterval, LKRectangle, LKBox, LKRing, LKCylinder) include the additional components:

- mx
A matrix giving number of grid points at each level and for each dimension.

- mLevelDomain
Same as mLevel but restricted to lattice points within the spatial domain.

- mxDomain
Same as mx but restricted to the points within the spatial domain.

- NC
Passed value.

- NC.buffer
Passed value.

- grid
A list where each component is also list giving the grid points of the lattice in each coordinate.

### Author(s)

Doug Nychka

### See Also

`LKGeometry`

`LKrigSetup`

,
`LKrigSAR`

,
`LKrigLatticeCenters`