Evaluate covariance over upper triangle of distance matrix

Evaluates the covariance over the upper triangle of a distance matrix rather than over the entire matrix to reduce computation time. Note that the chol function only requires the upper triangle of the covariance matrix to perform the Cholesky decomposition.

ExponentialUpper(distMat, range = 1, alpha = 1/range, theta = NULL)

Arguments

distMat

The distance matrix to evaluate the covariance over.

range

Range parameter default is one. Note that the scale can also be specified through the "aRange" scaling argument used in fields covariance functions)

alpha

1/range

theta

Also the range parameter.

Value

The covariance matrix, where only the upper triangle is calculated.

Author

John Paige

See also

Exponential

Examples

set.seed(123)

#a  distance matrix 
coords = matrix(runif(10), ncol=2)
distMat = rdist(coords)

#compute covariance matrix, but only over the upper triangle
upperCov = ExponentialUpper(distMat, range=.1)

print(distMat)
#>           [,1]       [,2]      [,3]       [,4]      [,5]
#> [1,] 0.0000000 0.69540037 0.8555197 0.78132050 0.7715140
#> [2,] 0.6954004 0.00000000 0.5259413 0.09754322 0.1681197
#> [3,] 0.8555197 0.52594131 0.0000000 0.58393877 0.6873190
#> [4,] 0.7813205 0.09754322 0.5839388 0.00000000 0.1108665
#> [5,] 0.7715140 0.16811974 0.6873190 0.11086647 0.0000000
print(upperCov)
#>      [,1]         [,2]         [,3]        [,4]         [,5]
#> [1,]    1 0.0009548048 0.0001925418 0.000404360 0.0004460228
#> [2,]    0 1.0000000000 0.0051983548 0.377029350 0.1861509438
#> [3,]    0 0.0000000000 1.0000000000 0.002910624 0.0010351697
#> [4,]    0 0.0000000000 0.0000000000 1.000000000 0.3299993164
#> [5,]    0 0.0000000000 0.0000000000 0.000000000 1.0000000000