Inverse of a symmetric positive-definite matrix

The inverse of a symmetric positive-definite matrix and its log-determinant

pd.solve(x, silent = FALSE, log.det=FALSE)

Arguments

x: a symmetric positive-definite matrix.
silent: a logical value which indicates the action to take in case of an error. If silent==TRUE and an error occurs, the function silently returns a NULL value; if silent==FALSE (default), an error generates a stop with an error message.
log.det: a logical value to indicate whether the log-determinant of x is required (default is FALSE).

Value

the inverse matrix of x; if log.det=TRUE, this inverse has an attribute which contains the logarithm of the determinant of x.

Details

The function checks that x is a symmetric positive-definite matrix. If an error is detected, an action is taken which depends on the value of the argument silent.

Author

Adelchi Azzalini

Examples

  x <- toeplitz(rev(1:4))
  x.inv <- pd.solve(x)
  print(x.inv %*% x)
#>               [,1]          [,2]          [,3]         [,4]
#> [1,]  1.000000e+00  2.220446e-16 -8.326673e-17 5.551115e-17
#> [2,]  3.682912e-16  1.000000e+00  2.166951e-16 2.987480e-17
#> [3,]  1.110223e-16  4.440892e-16  1.000000e+00 0.000000e+00
#> [4,] -1.110223e-16 -2.220446e-16 -2.220446e-16 1.000000e+00
  x.inv <- pd.solve(x, log.det=TRUE)
  logDet <- attr(x.inv, "log.det")
  print(abs(logDet - determinant(x, logarithm=TRUE)$modulus))
#> [1] 4.440892e-16
#> attr(,"logarithm")
#> [1] TRUE