Upper triangular factor of a symmetric positive definite matrix

This function is an analog to the Cholesky decomposition.

UpperTriFactor(Sigma)

Arguments

Sigma	A symmetric positive definite k x k matrix that can be passed as argument to chol.

Value

an upper triangular matrix Sigma_x, such that Sigma = Sigma_x %*% t(Sigma_x)

See also

chol;

the option PCMBase.Transpose.Sigma_x in PCMOptions.

Examples

# S is a symmetric positive definite matrix
M<-matrix(rexp(9),3,3); S <- M %*% t(M)

# This should return a zero matrix:
UpperTriFactor(S) %*% t(UpperTriFactor(S)) - S
#>      [,1] [,2] [,3]
#> [1,]    0    0    0
#> [2,]    0    0    0
#> [3,]    0    0    0

# This should return a zero matrix too:
t(chol(S)) %*% chol(S) - S
#>               [,1] [,2] [,3]
#> [1,] -4.440892e-16    0    0
#> [2,]  0.000000e+00    0    0
#> [3,]  0.000000e+00    0    0

# Unless S is diagonal, in the general case, this will return a
# non-zero matrix:
chol(S) %*% t(chol(S)) - S
#>           [,1]      [,2]      [,3]
#> [1,] 10.202674 -3.055276 -1.745188
#> [2,] -3.055276 -7.784033 -4.275878
#> [3,] -1.745188 -4.275878 -2.418641