isIrreducible

0th

Percentile

Determine reducibility of a matrix

Determine whether a matrix is irreducible or reducible

Usage
isIrreducible(A)
Arguments
A

a square, non-negative numeric matrix of any dimension.

Details

isIrreducible works on the premise that a matrix A is irreducible if and only if (I+A)^(s-1) is positive, where I is the identity matrix of the same dimension as A and s is the dimension of A (Caswell 2001).

Value

TRUE (for an irreducible matrix) or FALSE (for a reducible matrix).

References

  • Caswell (2001) matrix Population Models, 2nd. ed. Sinauer.

See Also

Other PerronFrobeniusDiagnostics: isErgodic, isPrimitive

Aliases
  • isIrreducible
Examples
# NOT RUN {
  # Create a 3x3 irreducible PPM
  ( A <- matrix(c(0,1,2,0.5,0.1,0,0,0.6,0.6), byrow=TRUE, ncol=3) )

  # Diagnose reducibility
  isIrreducible(A)

  # Create a 3x3 reducible PPM
  B<-A; B[3,2] <- 0; B

  # Diagnose reducibility
  isIrreducible(B)

# }
Documentation reproduced from package popdemo, version 1.3-0, License: GPL (>= 2)

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