# constrained_adjacency_covariance_function: Construct a constrained covariance matrix from the adjacency... In BSBT: The Bayesian Spatial Bradley--Terry Model

## Description

This function constructs a covariance function from the graph's adjacency matrix. The covariance function may be squared exponential, rational quadratic, Matern or the matrix exponential. It includes a constraint, where a linear combination of the parameters can be fixed.

## Usage

 ```1 2 3 4 5 6 7``` ```constrained_adjacency_covariance_function( adj.matrix, type, hyperparameters, linear.combination, linear.constraint = 0 ) ```

## Arguments

 `adj.matrix` The graph adjacency matrix `type` The type of covariance function used. One of "sqexp", "ratquad", "matern" or "matrix". Note: only matern with nu = 5/2 is supported. `hyperparameters` A vector containing the covariance function hyperparameters. For the squared exponential and matern, the vector should contain the variance and length scale, for the rational quadratic, the vector should contain the variance, length scale and scaling parameters `linear.combination` A matrix which defines the linear combination of the parameter vector lambda = (lambda_1, ..., lambda_N)^T. The linear combination is a vector of coefficients such that linear.combination %*% lambda = linear.constraint. `linear.constraint` The value the linear constraint takes. Defaults to 0.

## Value

The mean vector and covariance matrix

 ```1 2 3 4 5``` ```#Construct covariance matrix of Dar es Salaam, Tanzania, using network metric data(dar.adj.matrix, package = "BSBT") #load dar es salaam adjacency matrix k <- constrained_adjacency_covariance_function(dar.adj.matrix, type = "sqexp", hyperparameters = c(1, 1), rep(1, dim(dar.adj.matrix)), 0) #Covariance registetred by sum of subwards is 0 using rational quadratic function ```