handle slightly negative eigenvalue when simulating

[kylebaron]

Summary

• MASS::mvrnorm will accept covariance matrices with small negative eigenvalues, setting them to zero
• this PR implements the same behavior
• note: mrgsolve has historically checked for positive determinant for incoming model matrices and is working toward changing the check to be based on eigen values instead

Example

Showing both MASS and mrgsolve simulating from a matrix with negative eigenvalue

mat <- mrgsolve::bmat(
1.53394, 
1.22232, 0.974014,
2.78342 , 2.211570, 9.86881
)

mat
#>         [,1]     [,2]    [,3]
#> [1,] 1.53394 1.222320 2.78342
#> [2,] 1.22232 0.974014 2.21157
#> [3,] 2.78342 2.211570 9.86881

eigen(mat)$values
#> [1]  1.130541e+01  1.071351e+00 -7.148461e-08
det(mat)
#> [1] -8.658264e-07

set.seed(1010)
a <- MASS::mvrnorm(1000000, c(0,0,0), mat)
b <- mrgsolve::mvgauss(mat,  1000000)

cov(a)
#>          [,1]      [,2]     [,3]
#> [1,] 1.533910 1.2223026 2.778312
#> [2,] 1.222303 0.9740056 2.207535
#> [3,] 2.778312 2.2075348 9.832882
cov(b)
#>          [,1]      [,2]     [,3]
#> [1,] 1.532405 1.2211011 2.777505
#> [2,] 1.221101 0.9730461 2.206862
#> [3,] 2.777505 2.2068619 9.854215

^{Created on 2022-03-28 by the reprex package (v2.0.1)}