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distr (version 2.3.1)

solve-methods: Methods for Function solve in Package `distr'

Description

solve-methods using generalized inverses for various types of matrices

Usage

solve(a,b, ...)
## S3 method for class 'ANY,ANY':
solve(a, b, generalized = 
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S3 method for class 'PosSemDefSymmMatrix,ANY':
solve(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S3 method for class 'PosDefSymmMatrix,ANY':
solve(a, b, tol = 1e-10)

Arguments

a
matrix to be inverted / to be solved for RHS.
b
a numeric or complex vector or matrix giving the right-hand side(s) of the linear system. If missing, b is taken to be an identity matrix and solve will return the inverse of a.
...
further arguments to be passed to specific methods (see solve).
generalized
logical: should generalized / Moore-Penrose inverses be used? By default uses the corresponding global option to be set by distroptions.
tol
the tolerance for detecting linear dependencies in the columns of a. Default is .Machine$double.eps.

concept

  • pseudo inverse
  • inverse
  • svd
  • eigenvalue decomposition

Details

The method for the Moore-Penrose inverse for signature(a = "PosSemDefSymmMatrix", b = "ANY") uses eigen to find the eigenvalue decomposition of a and then simply "pseudo-inverts" the corresponding diagonal matrix built from eigen(a)$values, while for signature(a = "ANY", b = "ANY") it uses the svd decomposition of a and then simply "pseudo-inverts" the corresponding diagonal matrix built from svd(a)$d.

See Also

solve for the default method, eigen and svd for the pseudo inversion